The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
Numeric or quantitative entities, descriptions, properties, relationships, operations, and events.
Computer-based representation of physical systems and phenomena such as chemical processes.
The volume of water filtered out of plasma through glomerular capillary walls into Bowman's capsules per unit of time. It is considered to be equivalent to INULIN clearance.
A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.
Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.
The rate dynamics in chemical or physical systems.
Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT.
A technetium imaging agent used in renal scintigraphy, computed tomography, lung ventilation imaging, gastrointestinal scintigraphy, and many other procedures which employ radionuclide imaging agents.
An extracellular cystatin subtype that is abundantly expressed in bodily fluids. It may play a role in the inhibition of interstitial CYSTEINE PROTEASES.
The relative amounts of various components in the body, such as percentage of body fat.
The resistance to the flow of either alternating or direct electrical current.
The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.
Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.
The technique that deals with the measurement of the size, weight, and proportions of the human or other primate body.
In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test.
Calculation of the energy expenditure in the form of heat production of the whole body or individual organs based on respiratory gas exchange.
Fluids composed mainly of water found within the body.
Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.
Biological molecules that possess catalytic activity. They may occur naturally or be synthetically created. Enzymes are usually proteins, however CATALYTIC RNA and CATALYTIC DNA molecules have also been identified.
The measurement of subcutaneous fat located directly beneath the skin by grasping a fold of skin and subcutaneous fat between the thumb and forefinger and pulling it away from the underlying muscle tissue. The thickness of the double layer of skin and subcutaneous tissue is then read with a caliper. The five most frequently measured sites are the upper arm, below the scapula, above the hip bone, the abdomen, and the thigh. Its application is the determination of relative fatness, of changes in physical conditioning programs, and of the percentage of body fat in desirable body weight. (From McArdle, et al., Exercise Physiology, 2d ed, p496-8)
The range or frequency distribution of a measurement in a population (of organisms, organs or things) that has not been selected for the presence of disease or abnormality.
A contrast medium in diagnostic radiology with properties similar to those of diatrizoic acid. It is used primarily as its sodium and meglumine (IOTHALAMATE MEGLUMINE) salts.
Elements of limited time intervals, contributing to particular results or situations.
Laboratory tests used to evaluate how well the kidneys are working through examination of blood and urine.
Computer-assisted study of methods for obtaining useful quantitative solutions to problems that have been expressed mathematically.
Heat production, or its measurement, of an organism at the lowest level of cell chemistry in an inactive, awake, fasting state. It may be determined directly by means of a calorimeter or indirectly by calculating the heat production from an analysis of the end products of oxidation within the organism or from the amount of oxygen utilized.
Pathological processes of the KIDNEY or its component tissues.
Conditions in which the KIDNEYS perform below the normal level for more than three months. Chronic kidney insufficiency is classified by five stages according to the decline in GLOMERULAR FILTRATION RATE and the degree of kidney damage (as measured by the level of PROTEINURIA). The most severe form is the end-stage renal disease (CHRONIC KIDNEY FAILURE). (Kidney Foundation: Kidney Disease Outcome Quality Initiative, 2002)
Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment.
The mass or quantity of heaviness of an individual. It is expressed by units of pounds or kilograms.
The chemical reactions involved in the production and utilization of various forms of energy in cells.
The entities of matter and energy, and the processes, principles, properties, and relationships describing their nature and interactions.
Studies in which variables relating to an individual or group of individuals are assessed over a period of time.
Theoretical representations that simulate psychological processes and/or social processes. These include the use of mathematical equations, computers, and other electronic equipment.
A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed)
Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.
The study of those aspects of energy and matter in terms of elementary principles and laws. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
A clear, odorless, tasteless liquid that is essential for most animal and plant life and is an excellent solvent for many substances. The chemical formula is hydrogen oxide (H2O). (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
The study of PHYSICAL PHENOMENA and PHYSICAL PROCESSES as applied to living things.
The resistance that a gaseous or liquid system offers to flow when it is subjected to shear stress. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
Methods for assessing flow through a system by injection of a known quantity of an indicator, such as a dye, radionuclide, or chilled liquid, into the system and monitoring its concentration over time at a specific point in the system. (From Dorland, 28th ed)
The distance from the sole to the crown of the head with body standing on a flat surface and fully extended.
The physical characteristics and processes of biological systems.
Studies in which the presence or absence of disease or other health-related variables are determined in each member of the study population or in a representative sample at one particular time. This contrasts with LONGITUDINAL STUDIES which are followed over a period of time.
An effective non-ionic, water-soluble contrast agent which is used in myelography, arthrography, nephroangiography, arteriography, and other radiographic procedures. Its low systemic toxicity is the combined result of low chemotoxicity and low osmolality.
The practical application of physical, mechanical, and mathematical principles. (Stedman, 25th ed)
Age as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or the effect of a circumstance. It is used with human or animal concepts but should be differentiated from AGING, a physiological process, and TIME FACTORS which refers only to the passage of time.
Binary classification measures to assess test results. Sensitivity or recall rate is the proportion of true positives. Specificity is the probability of correctly determining the absence of a condition. (From Last, Dictionary of Epidemiology, 2d ed)
Studies in which subsets of a defined population are identified. These groups may or may not be exposed to factors hypothesized to influence the probability of the occurrence of a particular disease or other outcome. Cohorts are defined populations which, as a whole, are followed in an attempt to determine distinguishing subgroup characteristics.
A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model.
The voltage differences across a membrane. For cellular membranes they are computed by subtracting the voltage measured outside the membrane from the voltage measured inside the membrane. They result from differences of inside versus outside concentration of potassium, sodium, chloride, and other ions across cells' or ORGANELLES membranes. For excitable cells, the resting membrane potentials range between -30 and -100 millivolts. Physical, chemical, or electrical stimuli can make a membrane potential more negative (hyperpolarization), or less negative (depolarization).
Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.
The use of statistical and mathematical methods to analyze biological observations and phenomena.
In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)
Measurement of volume of air inhaled or exhaled by the lung.
Application of statistical procedures to analyze specific observed or assumed facts from a particular study.
The property of objects that determines the direction of heat flow when they are placed in direct thermal contact. The temperature is the energy of microscopic motions (vibrational and translational) of the particles of atoms.
Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.
An aspect of personal behavior or lifestyle, environmental exposure, or inborn or inherited characteristic, which, on the basis of epidemiologic evidence, is known to be associated with a health-related condition considered important to prevent.
Determination, by measurement or comparison with a standard, of the correct value of each scale reading on a meter or other measuring instrument; or determination of the settings of a control device that correspond to particular values of voltage, current, frequency or other output.
The two dimensional measure of the outer layer of the body.
Specialized connective tissue composed of fat cells (ADIPOCYTES). It is the site of stored FATS, usually in the form of TRIGLYCERIDES. In mammals, there are two types of adipose tissue, the WHITE FAT and the BROWN FAT. Their relative distributions vary in different species with most adipose tissue being white.
The homogeneous mixtures formed by the mixing of a solid, liquid, or gaseous substance (solute) with a liquid (the solvent), from which the dissolved substances can be recovered by physical processes. (From Grant & Hackh's Chemical Dictionary, 5th ed)
Theoretical representations that simulate the behavior or activity of the neurological system, processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
A type of stress exerted uniformly in all directions. Its measure is the force exerted per unit area. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
The ability of a substrate to allow the passage of ELECTRONS.
The study of chance processes or the relative frequency characterizing a chance process.
An indicator of body density as determined by the relationship of BODY WEIGHT to BODY HEIGHT. BMI=weight (kg)/height squared (m2). BMI correlates with body fat (ADIPOSE TISSUE). Their relationship varies with age and gender. For adults, BMI falls into these categories: below 18.5 (underweight); 18.5-24.9 (normal); 25.0-29.9 (overweight); 30.0 and above (obese). (National Center for Health Statistics, Centers for Disease Control and Prevention)
Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
The science and art of collecting, summarizing, and analyzing data that are subject to random variation. The term is also applied to the data themselves and to the summarization of the data.
An atom or group of atoms that have a positive or negative electric charge due to a gain (negative charge) or loss (positive charge) of one or more electrons. Atoms with a positive charge are known as CATIONS; those with a negative charge are ANIONS.
The normality of a solution with respect to HYDROGEN ions; H+. It is related to acidity measurements in most cases by pH = log 1/2[1/(H+)], where (H+) is the hydrogen ion concentration in gram equivalents per liter of solution. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
The study of the deformation and flow of matter, usually liquids or fluids, and of the plastic flow of solids. The concept covers consistency, dilatancy, liquefaction, resistance to flow, shearing, thixotrophy, and VISCOSITY.
The accumulation of an electric charge on a object
An element in the alkali group of metals with an atomic symbol K, atomic number 19, and atomic weight 39.10. It is the chief cation in the intracellular fluid of muscle and other cells. Potassium ion is a strong electrolyte that plays a significant role in the regulation of fluid volume and maintenance of the WATER-ELECTROLYTE BALANCE.
Cellular processes, properties, and characteristics.
Domesticated bovine animals of the genus Bos, usually kept on a farm or ranch and used for the production of meat or dairy products or for heavy labor.
A starch found in the tubers and roots of many plants. Since it is hydrolyzable to FRUCTOSE, it is classified as a fructosan. It has been used in physiologic investigation for determination of the rate of glomerular function.
The end-stage of CHRONIC RENAL INSUFFICIENCY. It is characterized by the severe irreversible kidney damage (as measured by the level of PROTEINURIA) and the reduction in GLOMERULAR FILTRATION RATE to less than 15 ml per min (Kidney Foundation: Kidney Disease Outcome Quality Initiative, 2002). These patients generally require HEMODIALYSIS or KIDNEY TRANSPLANTATION.
The volume of air that is exhaled by a maximal expiration following a maximal inspiration.
Sequential operating programs and data which instruct the functioning of a digital computer.
Resistance and recovery from distortion of shape.
A member of the alkali group of metals. It has the atomic symbol Na, atomic number 11, and atomic weight 23.
Predetermined sets of questions used to collect data - clinical data, social status, occupational group, etc. The term is often applied to a self-completed survey instrument.
Comprehensive, methodical analysis of complex biological systems by monitoring responses to perturbations of biological processes. Large scale, computerized collection and analysis of the data are used to develop and test models of biological systems.
The study of CHEMICAL PHENOMENA and processes in terms of the underlying PHYSICAL PHENOMENA and processes.
A noninvasive method for assessing BODY COMPOSITION. It is based on the differential absorption of X-RAYS (or GAMMA RAYS) by different tissues such as bone, fat and other soft tissues. The source of (X-ray or gamma-ray) photon beam is generated either from radioisotopes such as GADOLINIUM 153, IODINE 125, or Americanium 241 which emit GAMMA RAYS in the appropriate range; or from an X-ray tube which produces X-RAYS in the desired range. It is primarily used for quantitating BONE MINERAL CONTENT, especially for the diagnosis of OSTEOPOROSIS, and also in measuring BONE MINERALIZATION.
Math calculations done for preparing appropriate doses of medicines, taking into account conversions of WEIGHTS AND MEASURES. Mistakes are one of the sources of MEDICATION ERRORS.
Measurement of the various processes involved in the act of respiration: inspiration, expiration, oxygen and carbon dioxide exchange, lung volume and compliance, etc.
The properties, processes, and behavior of biological systems under the action of mechanical forces.
Any deviation of results or inferences from the truth, or processes leading to such deviation. Bias can result from several sources: one-sided or systematic variations in measurement from the true value (systematic error); flaws in study design; deviation of inferences, interpretations, or analyses based on flawed data or data collection; etc. There is no sense of prejudice or subjectivity implied in the assessment of bias under these conditions.
Measurable and quantifiable biological parameters (e.g., specific enzyme concentration, specific hormone concentration, specific gene phenotype distribution in a population, presence of biological substances) which serve as indices for health- and physiology-related assessments, such as disease risk, psychiatric disorders, environmental exposure and its effects, disease diagnosis, metabolic processes, substance abuse, pregnancy, cell line development, epidemiologic studies, etc.
Diseases which have one or more of the following characteristics: they are permanent, leave residual disability, are caused by nonreversible pathological alteration, require special training of the patient for rehabilitation, or may be expected to require a long period of supervision, observation, or care. (Dictionary of Health Services Management, 2d ed)
Unstable isotopes of potassium that decay or disintegrate emitting radiation. K atoms with atomic weights 37, 38, 40, and 42-45 are radioactive potassium isotopes.
Body organ that filters blood for the secretion of URINE and that regulates ion concentrations.
Levels within a diagnostic group which are established by various measurement criteria applied to the seriousness of a patient's disorder.
The qualitative or quantitative estimation of the likelihood of adverse effects that may result from exposure to specified health hazards or from the absence of beneficial influences. (Last, Dictionary of Epidemiology, 1988)
Three-dimensional representation to show anatomic structures. Models may be used in place of intact animals or organisms for teaching, practice, and study.
A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.
A computer based method of simulating or analyzing the behavior of structures or components.
The motion of fluids, especially noncompressible liquids, under the influence of internal and external forces.
A set of statistical methods for analyzing the correlations among several variables in order to estimate the number of fundamental dimensions that underlie the observed data and to describe and measure those dimensions. It is used frequently in the development of scoring systems for rating scales and questionnaires.
Chemical analysis based on the phenomenon whereby light, passing through a medium with dispersed particles of a different refractive index from that of the medium, is attenuated in intensity by scattering. In turbidimetry, the intensity of light transmitted through the medium, the unscattered light, is measured. In nephelometry, the intensity of the scattered light is measured, usually, but not necessarily, at right angles to the incident light beam.
A series of steps taken in order to conduct research.
The edible portions of any animal used for food including domestic mammals (the major ones being cattle, swine, and sheep) along with poultry, fish, shellfish, and game.
Individuals whose ancestral origins are in the continent of Europe.
The two types of spaces between which water and other body fluids are distributed: extracellular and intracellular.
The prediction or projection of the nature of future problems or existing conditions based upon the extrapolation or interpretation of existing scientific data or by the application of scientific methodology.
The isotopic compound of hydrogen of mass 2 (deuterium) with oxygen. (From Grant & Hackh's Chemical Dictionary, 5th ed) It is used to study mechanisms and rates of chemical or nuclear reactions, as well as biological processes.
Measurement of the amount of air that the lungs may contain at various points in the respiratory cycle.
A quality of cell membranes which permits the passage of solvents and solutes into and out of cells.
A superorder of CEPHALOPODS comprised of squid, cuttlefish, and their relatives. Their distinguishing feature is the modification of their fourth pair of arms into tentacles, resulting in 10 limbs.
The rate at which oxygen is used by a tissue; microliters of oxygen STPD used per milligram of tissue per hour; the rate at which oxygen enters the blood from alveolar gas, equal in the steady state to the consumption of oxygen by tissue metabolism throughout the body. (Stedman, 25th ed, p346)
The physical phenomena describing the structure and properties of atoms and molecules, and their reaction and interaction processes.
The transfer of energy of a given form among different scales of motion. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed). It includes the transfer of kinetic energy and the transfer of chemical energy. The transfer of chemical energy from one molecule to another depends on proximity of molecules so it is often used as in techniques to measure distance such as the use of FORSTER RESONANCE ENERGY TRANSFER.
Continuous frequency distribution of infinite range. Its properties are as follows: 1, continuous, symmetrical distribution with both tails extending to infinity; 2, arithmetic mean, mode, and median identical; and 3, shape completely determined by the mean and standard deviation.
Dynamic and kinetic mechanisms of exogenous chemical and DRUG LIBERATION; ABSORPTION; BIOLOGICAL TRANSPORT; TISSUE DISTRIBUTION; BIOTRANSFORMATION; elimination; and DRUG TOXICITY as a function of dosage, and rate of METABOLISM. LADMER, ADME and ADMET are abbreviations for liberation, absorption, distribution, metabolism, elimination, and toxicology.
The amounts of various substances in food needed by an organism to sustain healthy life.
A homologous group of endogenous CYSTEINE PROTEINASE INHIBITORS. The cystatins inhibit most CYSTEINE ENDOPEPTIDASES such as PAPAIN, and other peptidases which have a sulfhydryl group at the active site.
Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.
Regular course of eating and drinking adopted by a person or animal.
The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.
Liquids that dissolve other substances (solutes), generally solids, without any change in chemical composition, as, water containing sugar. (Grant & Hackh's Chemical Dictionary, 5th ed)
Individuals whose ancestral origins are in the continent of Africa.
Thin layers of tissue which cover parts of the body, separate adjacent cavities, or connect adjacent structures.
The study of chemical changes resulting from electrical action and electrical activity resulting from chemical changes.
Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
Condition of having pores or open spaces. This often refers to bones, bone implants, or bone cements, but can refer to the porous state of any solid substance.
A set of techniques used when variation in several variables has to be studied simultaneously. In statistics, multivariate analysis is interpreted as any analytic method that allows simultaneous study of two or more dependent variables.
The study of the composition, chemical structures, and chemical reactions of living things.
The measurement of frequency or oscillation changes.
A distribution function used to describe the occurrence of rare events or to describe the sampling distribution of isolated counts in a continuum of time or space.
Inorganic compounds derived from hydrochloric acid that contain the Cl- ion.
Supplying a building or house, their rooms and corridors, with fresh air. The controlling of the environment thus may be in public or domestic sites and in medical or non-medical locales. (From Dorland, 28th ed)
An element with atomic symbol O, atomic number 8, and atomic weight [15.99903; 15.99977]. It is the most abundant element on earth and essential for respiration.
The contribution to barometric PRESSURE of gaseous substance in equilibrium with its solid or liquid phase.
Volume of biological fluid completely cleared of drug metabolites as measured in unit time. Elimination occurs as a result of metabolic processes in the kidney, liver, saliva, sweat, intestine, heart, brain, or other site.
Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.
Chemistry dealing with the composition and preparation of agents having PHARMACOLOGIC ACTIONS or diagnostic use.
The gradual irreversible changes in structure and function of an organism that occur as a result of the passage of time.
Studies in which individuals or populations are followed to assess the outcome of exposures, procedures, or effects of a characteristic, e.g., occurrence of disease.
The concentration of osmotically active particles in solution expressed in terms of osmoles of solute per liter of solution. Osmolality is expressed in terms of osmoles of solute per kilogram of solvent.
Total number of calories taken in daily whether ingested or by parenteral routes.
A country spanning from central Asia to the Pacific Ocean.
A basis of value established for the measure of quantity, weight, extent or quality, e.g. weight standards, standard solutions, methods, techniques, and procedures used in diagnosis and therapy.
Measure of the maximum amount of air that can be expelled in a given number of seconds during a FORCED VITAL CAPACITY determination . It is usually given as FEV followed by a subscript indicating the number of seconds over which the measurement is made, although it is sometimes given as a percentage of forced vital capacity.
Two offspring from the same PREGNANCY. They are from two OVA, fertilized at about the same time by two SPERMATOZOA. Such twins are genetically distinct and can be of different sexes.
Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.
A purely physical condition which exists within any material because of strain or deformation by external forces or by non-uniform thermal expansion; expressed quantitatively in units of force per unit area.
Discrete concentrations of energy, apparently massless elementary particles, that move at the speed of light. They are the unit or quantum of electromagnetic radiation. Photons are emitted when electrons move from one energy state to another. (From Hawley's Condensed Chemical Dictionary, 11th ed)
The physical measurements of a body.
Reversible chemical reaction between a solid, often one of the ION EXCHANGE RESINS, and a fluid whereby ions may be exchanged from one substance to another. This technique is used in water purification, in research, and in industry.
The chemical processes, enzymatic activities, and pathways of living things and related temporal, dimensional, qualitative, and quantitative concepts.
Devices or objects in various imaging techniques used to visualize or enhance visualization by simulating conditions encountered in the procedure. Phantoms are used very often in procedures employing or measuring x-irradiation or radioactive material to evaluate performance. Phantoms often have properties similar to human tissue. Water demonstrates absorbing properties similar to normal tissue, hence water-filled phantoms are used to map radiation levels. Phantoms are used also as teaching aids to simulate real conditions with x-ray or ultrasonic machines. (From Iturralde, Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990)
Transmission of energy or mass by a medium involving movement of the medium itself. The circulatory movement that occurs in a fluid at a nonuniform temperature owing to the variation of its density and the action of gravity. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed; Webster, 10th ed)
Abrupt changes in the membrane potential that sweep along the CELL MEMBRANE of excitable cells in response to excitation stimuli.
Computer-assisted processing of electric, ultrasonic, or electronic signals to interpret function and activity.
Methods developed to aid in the interpretation of ultrasound, radiographic images, etc., for diagnosis of disease.
The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.
Principles, models, and laws that apply to complex interrelationships and interdependencies of sets of linked components which form a functioning whole, a system. Any system may be composed of components which are systems in their own right (sub-systems), such as several organs within an individual organism.
Measurements of the height, weight, length, area, etc., of the human and animal body or its parts.
A status with BODY WEIGHT that is grossly above the acceptable or desirable weight, usually due to accumulation of excess FATS in the body. The standards may vary with age, sex, genetic or cultural background. In the BODY MASS INDEX, a BMI greater than 30.0 kg/m2 is considered obese, and a BMI greater than 40.0 kg/m2 is considered morbidly obese (MORBID OBESITY).
Method for assessing flow through a system by injection of a known quantity of radionuclide into the system and monitoring its concentration over time at a specific point in the system. (From Dorland, 28th ed)
Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time.
A colorless, odorless gas that can be formed by the body and is necessary for the respiration cycle of plants and animals.
Drugs intended for human or veterinary use, presented in their finished dosage form. Included here are materials used in the preparation and/or formulation of the finished dosage form.
Solid dosage forms, of varying weight, size, and shape, which may be molded or compressed, and which contain a medicinal substance in pure or diluted form. (Dorland, 28th ed)
Foodstuff used especially for domestic and laboratory animals, or livestock.
Individuals whose ancestral origins are in the southeastern and eastern areas of the Asian continent.
A value equal to the total volume flow divided by the cross-sectional area of the vascular bed.
That part of the RESPIRATORY TRACT or the air within the respiratory tract that does not exchange OXYGEN and CARBON DIOXIDE with pulmonary capillary blood.
Physical motion, i.e., a change in position of a body or subject as a result of an external force. It is distinguished from MOVEMENT, a process resulting from biological activity.
The heat flow across a surface per unit area per unit time, divided by the negative of the rate of change of temperature with distance in a direction perpendicular to the surface. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
The study of the generation and behavior of electrical charges in living organisms particularly the nervous system and the effects of electricity on living organisms.
An element with the atomic symbol N, atomic number 7, and atomic weight [14.00643; 14.00728]. Nitrogen exists as a diatomic gas and makes up about 78% of the earth's atmosphere by volume. It is a constituent of proteins and nucleic acids and found in all living cells.
The measurement of the density of a material by measuring the amount of light or radiation passing through (or absorbed by) the material.
Relating to the size of solids.
Any of various animals that constitute the family Suidae and comprise stout-bodied, short-legged omnivorous mammals with thick skin, usually covered with coarse bristles, a rather long mobile snout, and small tail. Included are the genera Babyrousa, Phacochoerus (wart hogs), and Sus, the latter containing the domestic pig (see SUS SCROFA).
Gated, ion-selective glycoproteins that traverse membranes. The stimulus for ION CHANNEL GATING can be due to a variety of stimuli such as LIGANDS, a TRANSMEMBRANE POTENTIAL DIFFERENCE, mechanical deformation or through INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS.
A compound formed in the liver from ammonia produced by the deamination of amino acids. It is the principal end product of protein catabolism and constitutes about one half of the total urinary solids.
Either of the pair of organs occupying the cavity of the thorax that effect the aeration of the blood.
The diversion of RADIATION (thermal, electromagnetic, or nuclear) from its original path as a result of interactions or collisions with atoms, molecules, or larger particles in the atmosphere or other media. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
Two off-spring from the same PREGNANCY. They are from a single fertilized OVUM that split into two EMBRYOS. Such twins are usually genetically identical and of the same sex.
The production of offspring by selective mating or HYBRIDIZATION, GENETIC in animals or plants.
Property of membranes and other structures to permit passage of light, heat, gases, liquids, metabolites, and mineral ions.
Characteristics or attributes of the outer boundaries of objects, including molecules.
Contractile tissue that produces movement in animals.
Those characteristics that distinguish one SEX from the other. The primary sex characteristics are the OVARIES and TESTES and their related hormones. Secondary sex characteristics are those which are masculine or feminine but not directly related to reproduction.
A subfield of acoustics dealing in the radio frequency range higher than acoustic SOUND waves (approximately above 20 kilohertz). Ultrasonic radiation is used therapeutically (DIATHERMY and ULTRASONIC THERAPY) to generate HEAT and to selectively destroy tissues. It is also used in diagnostics, for example, ULTRASONOGRAPHY; ECHOENCEPHALOGRAPHY; and ECHOCARDIOGRAPHY, to visually display echoes received from irradiated tissues.
A graphic means for assessing the ability of a screening test to discriminate between healthy and diseased persons; may also be used in other studies, e.g., distinguishing stimuli responses as to a faint stimuli or nonstimuli.
A phylum of the kingdom Metazoa. Mollusca have soft, unsegmented bodies with an anterior head, a dorsal visceral mass, and a ventral foot. Most are encased in a protective calcareous shell. It includes the classes GASTROPODA; BIVALVIA; CEPHALOPODA; Aplacophora; Scaphopoda; Polyplacophora; and Monoplacophora.
Computers in which quantities are represented by physical variables; problem parameters are translated into equivalent mechanical or electrical circuits as an analog for the physical phenomenon being investigated. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
The movement of materials across cell membranes and epithelial layers against an electrochemical gradient, requiring the expenditure of metabolic energy.
Equations. p. 29. R. Nagaswamy (2010). Mahabalipuram: Monumental Legacy. Oxford University Press. pp. 81-82. ISBN 978-0-19- ...
The "equations" discussed in the Fang Cheng chapter are equivalent to today's simultaneous linear equations. The solution ... but also general quadratic and cubic equations. It is the basis for solving higher-order equations in ancient China, and it ... 方程 Fangcheng - The two-sided reference (i.e. Equations). Problems of agricultural yields and the sale of animals that lead to ... The methods of completing the squares and cubes as well as solving simultaneous linear equations listed in The Nine Chapters on ...
EQUATIONS. pp. 131-. Khan, Waheeda; Deb, Sibnath (5 August 2015). Child Safety, Welfare and Well-being: Issues and Challenges. ...
EQUATIONS. "Jammu and Kashmir bird checklist - Avibase - Bird Checklists of the World". Retrieved 20 ...
"This is Our Homeland: A Collection of Essays on the Betrayal of Adivasi Rights in India". EQUATIONS. 27 January 2018 - via ...
EQUATIONS. pp. 75-. GGKEY:UXEKGL80Q7R. Retrieved 21 April 2012. CS1 maint: discouraged parameter (link) Oorukootams "132 ... CS1 maint: discouraged parameter (link) Equitable Tourism Options (EQUATIONS). Nilgiris Biosphere Reserve: fading glory. ...
equations". Doklady Physics. 49 (11): 648-652. Bibcode:2004DokPh..49..648D. doi:10.1134/1.1831530. Dynnikova, G.Ya. (16-21 May ... Such a motion results in vorticity evolution and satisfies Navier-Stokes equations. Fluid velocity V in point r can be ... method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in ... Direct solving Navier-Stokes equations (DNS) Calculation of the friction force at the body surfaces Proper description of the ...
Equitable Tourism Options (EQUATIONS). Tourism and Displacement: Pilikula - Karnataka's model Tourism Project?. EQUATIONS. p. ...
"Poomala dam to be made tourist centre". Equations. Retrieved 26 June 2013. "Poomala dam makeover nearing completion". The Hindu ...
EQUATIONS. Archived from the original on 3 March 2018. Malik, Rajiv (2006). "Pride of India: Swaminarayan Akshardham opens in ... Bengaluru, India: EQUATIONS. p. 71. Brosius, Christiane (2012). India's Middle Class: New Forms of Urban Leisure, Consumption ...
CS1 maint: discouraged parameter (link) Huray, Paul G., 1941- (2010). Maxwell's equations. Hoboken, N.J.: Wiley. pp. 8, 57. ...
Differential Equations. Springer. p. 58; Figure 2.15. ISBN 0-387-95140-7. Patrick Cornille (2003). "Partition of forces using ...
The equations represent a set of four coupled multi-dimensional partial differential equations which, when solved for a system ... the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of ... Since E and P are defined separately, this equation can be used to define D. The physical interpretation of D is not as clear ... The resulting two equations (Gauss's law ∇ ⋅ E = ρ ε 0 {\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0 ...
For a first order system of differential equations d r d t = f ( r , t ) {\displaystyle {\frac {d\mathbf {r} }{dt}}=\mathbf {f ... This may be derived by using the Euler-Lagrange equations. Conservative system Lyapunov function Hamiltonian system ... Differential Equations. Brooks/Cole Publishing Co. p. 486. ISBN 0-495-01265-3.CS1 maint: multiple names: authors list (link). ...
"Difference Equations". Time Series Analysis. Princeton University Press. p. 5. ISBN 0-691-04289-6. Hatemi-J, A. (2014). " ... or may be mathematical systems of equations describing such objects. Since the impulse function contains all frequencies, the ...
... equation, y(1) == 1); y2 = dsolve(equation, y(2) == 1); y3 = dsolve(equation, y(3) == 1); y4 = dsolve(equation, y(1) == 3); y5 ... Solving the equation symbolically in MATLAB, by running syms y(x); equation = (diff(y) == (2 - y) * y); % solve the equation ... Can we do something like this with higher order equations? The answer is yes for second order equations, but there's more work ... Third order autonomous equation at eqworld. Fourth order autonomous equation at eqworld. Blanchard; Devaney; Hall (2005). ...
"Journal of differential equations", Febrer 2011, vol. 250, núm. 4, pp. 1967-2023. DOI:10.1016/j.jde.2010.11.016 Wiggins, ... The dominant reason for the link between quantum systems and bifurcations in the classical equations of motion is that at ... Differential Equations. London: Thompson. pp. 96-111. ISBN 978-0-495-01265-8. Henri Poincaré. "L'Équilibre d'une masse fluide ... and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, ...
Mackenzie, Dana (27 March 2009). "Cold Equations". Science. 324 (5923): 32-3. doi:10.1126/science.324.5923.32. ISSN 0036-8075. ...
... differential equations; probability and statistics; integral equations; algebra. At present the Institute has about 30 main ... Gradually the sphere of investigations expanded and now includes Differential and Integral Equations, Functional Analysis, ...
General Equations of Dynamics. Application of Dynamics to Electromagnetism. Electrokinetics. Exploration of the Field by means ... General Equations. Dimensions of Electric Units. Energy and Stress. Current-Sheets. Parallel Currents. Circular Currents. ... J. J. Thomson) Volume 1, Volume 2 3rd edition 1892 (Dover reprint 1954) Volume 1, Volume 2 Original Maxwell Equations - ... Lagrange's equations appear in the Treatise as the culmination of a long series of rhetorical moves, including (among others) ...
1939 - Nikolay Krylov and Nikolay Bogolyubov give the first consistent microscopic derivation of the Fokker-Planck equation in ... doi:10.1070/RM1994v049n05ABEH002419 N. N. Bogoliubov and N. M. Krylov (1939). Fokker-Planck equations generated in perturbation ... N. N. Bogoliubov (1946). "Kinetic Equations". Journal of Experimental and Theoretical Physics (in Russian). 16 (8): 691-702. N ... giving the Arrhenius equation 1893 - Wilhelm Wien discovers the displacement law for a blackbody's maximum specific intensity ...
The BBGKY hierarchy of equations for s-particle distribution functions is applied to the derivation of kinetic equations by ... Bogoliubov, N. N. (1946). "Kinetic Equations". Journal of Physics USSR. 10 (3): 265-274. Kirkwood, John G. (March 1946). "The ... Bogoliubov, N. N. (1946). "Kinetic Equations". Journal of Experimental and Theoretical Physics. 16 (8): 691-702. ...
Holte, Michael Ned (October 2011). "Differential Equations". Artforum International. 50 (2). "In the Shadow of Numbers". Pomona ...
Applications to the boussinesq-equations, Schmitt, B. J. and von Wahl, W; in The Navier-Stokes Equations II - Theory and ... Anelastic Magnetohydrodynamic Equations for Modeling Solar and Stellar Convection Zones, Lantz, S. R. and Fan, Y.; The ... Stokes equations. G. D. McBain. ANZIAM J. 47 (2005) Backus, George (1986), "Poloidal and toroidal fields in geomagnetic field ...
"Telescope Equations". RocketMime. 17 November 2012. Ian S. McLean (2008). Electronic Imaging in Astronomy: Detectors and ... For visible light ( λ {\displaystyle \lambda } = 550 nm) in the small-angle approximation, this equation can be rewritten: α R ... The equation shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is ... The derivation of this equation is fairly straightforward and the result is the same for reflecting or refracting telescopes. ...
modular equations). This method is also specified by an n by n+1 matrix. However this time it multiplies the n+1 vector [x0,.., ... qualifiers are invariant under multiplication one can for example place any aspectial variant of nHm2 in the above equation, ... n-1 LPk mk J.R.Hendricks often uses modular equation, conditions to make hypercubes of various quality can be found on http:// ...
Maxwell's equations. Hoboken, N.J.: Wiley. pp. 8, 57. ISBN 978-0-470-54991-9. OCLC 739118459.CS1 maint: multiple names: authors ...
In the early 19th century, Carl Friedrich Gauss observed that non-zero integer solutions to homogeneous polynomial equations ... Weil, André (1949). "Numbers of solutions of equations in finite fields". Bulletin of the American Mathematical Society. 55 (5 ... Mordell, Louis J. (1969). Diophantine Equations. Academic Press. p. 1. ISBN 978-0125062503. Gowers, Timothy; Barrow-Green, June ... sets of solutions of a system of polynomial equations over number fields, finite fields, p-adic fields, or function fields, i.e ...
Wilkes and Wheeler had used EDSAC to solve a differential equation relating to gene frequencies for him. In 1951, Miller and ... differential equations; special functions; power series; logarithms; miscellaneous; print and layout; quadrature; read (input ...
Intelligent Image Processing (John Wiley and Sons book information). Comparametric Equations. GJB-1: Increasing the dynamic ... "The Lightspace Change Constraint Equation (LCCE) with practical application to estimation of the projectivity+gain ...
Making this substitution, we obtain equations using the refractive indices: R. s. =. ,. n. 1. cos. ⁡. θ. i. −. n. 2. cos. ⁡. θ ... When we make these substitutions in equations (13) to (16) and equations (21) to (26), the factor cμ0 cancels out, with the ... Using the material properties discussed above, we can eliminate B and D to obtain equations in only E and H: ω. μ. H. =. k. ×. ... so that the numerator in equation (33) becomes‍ n2‍sin θt − n1‍sin θi‍, which is zero (by Snells law). Hence rp = 0 and only ...
Then the equation for any species i becomes d. x. i. d. t. =. r. i. x. i. (. 1. −. ∑. j. =. 1. N. α. i. j. x. j. K. i. ). {\ ... Thus the competitive Lotka-Volterra equations are: d. x. 1. d. t. =. r. 1. x. 1. (. 1. −. (. x. 1. +. α. 12. x. 2. K. 1. ). ). ... For the predator-prey equations, see Lotka-Volterra equations.. The competitive Lotka-Volterra equations are a simple model of ... In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation ...
Mathematical equations arent just useful - many are quite beautiful. And many scientists admit they are often fond of ... The Callan-Symanzik equation. "The Callan-Symanzik equation is a vital first-principles equation from 1970, essential for ... This is in contrast with more familiar linear partial differential equations, such as the heat equation, the wave equation, and ... The minimal surface equation. "The minimal surface equation somehow encodes the beautiful soap films that form on wire ...
The equations of motion are the Navier-Stokes equations defined in the resting frame coordinates x → = x → m − U → ⋅ t {\ ... But Oseens equation was obtained applying the equation for the entire flow field. This question was answered by Proudman and ... The equations are u T t + U u T x = ν ∇ 2 u T , ∇ ⋅ u T = 0. {\displaystyle {\mathbf {u} _{\text{T}}}_{t}+U{\mathbf {u} _{\text ... The Oseen equations are, in case of an object moving with a steady flow velocity U through the fluid-which is at rest far from ...
The Faddeev equations, named after their inventor Ludvig Faddeev, are equations that describe, at once, all the possible ... In general, Faddeev equations need as input a potential that describes the interaction between two individual particles. It is ... The Faddeev equations are the most often used non-perturbative formulations of the quantum-mechanical three-body problem. ... using the Faddeev Equations. The nucleon-nucleon interaction is expanded (approximated) as a series of separable potentials. ...
Buy Diffusion Equations from Waterstones today! Click and Collect from your local Waterstones or get FREE UK delivery on orders ... and basic parts of the theory of integral equations. It treats diffusion equations with variable coefficients associated with ... Diffusion Equations - Translations of Mathematical Monographs (Hardback). Sign in to write a review ... This book presents a self-contained exposition of the theory of initial-boundary value problems for diffusion equations. ...
Math 597J: Partial Differential Equations III (Yuxi Zheng) Courses --Spring 2004 * Math 514: Partial Differential Equations II ... Partial Differential Equations at PSU Faculty (With a major interest in PDE ) Senior * Alberto Bressan, Eberly Chair Professor ... Math 513: Partial Differential Equations I * Math 597K: Intr. to Applied Math. I (Changed to official name M580) * MATH 505: ... Math 514: Partial Differential Equations II * Math 597F: Intr. to Applied Math. II: TR 9:45--11am (Changed to official name ...
In this video I show you how to derive the equations of motion using simple Calculus (integration) techniques and some simple ... This equation will change how you see the world - Duration: 18:39. Veritasium Recommended for you ... The Most Beautiful Equation in Math - Duration: 3:50. Carnegie Mellon University 5,831,962 views ... Equations of motion (Higher Physics) - Duration: 9:11. Mr Smiths Physics online 424,606 views ...
Balancing Chemical Equations. The law of conservation of mass states that mass can neither be created nor destroyed in a ... Balancing Chemical Equations.. The law of conservation of mass states that mass can neither be created nor destroyed in a ...
The X in the equation is age minus the value in the first column, here it is 18-9. This principle may be applied to each ... Each of the four other values refers to the constants for the polynomial equation ... to the coefficients needed to define the y-axis value on the growth curve using the third order polynomial spline equations ...
... 11 pages•Published: September 17, 2018. Patrick Musau, Diego ... Keyphrases: benchmark, differential-algebraic equations, reachability analysis. In: Goran Frehse (editor). ARCH18. 5th ... inproceedings{ARCH18:Linear_Differential_Algebraic_Equations_Benchmark, author = {Patrick Musau and Diego Manzanas Lopez and ... there is currently a lack of research methods for differential algebraic equations. Thus, the verification of DAE systems ...
... then progresses to multistep equations and equations featuring fractions and decimals. Next, she explores equations with ... So Im going to divide by negative 12…on both sides of the equation.…Its very important not to forget…the negative sign when ... Solving multistep equations using the distributive property and combining like terms 3m 23s ... Solving equations with variables on both sides using the distributive property 3m 33s ...
Some of the equations mentioned were the simplistic 1+1=2 and Eulers equation, ei + 1 = 0. What are some of your favori... ... What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New ... Some of the equations mentioned were the simplistic 1+1=2 and Eulers equation, e^in + 1 = 0. What are some of your favorite ... But are axioms equations ? Or some axioms are equations ? Well, strictly speaking the axioms are represented as well-formed ...
... Kenny Fister Kenny.Fister at Sat Apr 22 19:22:56 CEST 2006 ... Next message: [texhax] Question about aligning equations in LaTeX * Messages sorted by: [ date ] [ thread ] [ subject ] [ ... Next message: [texhax] Question about aligning equations in LaTeX * Messages sorted by: [ date ] [ thread ] [ subject ] [ ... Is there a way to align equations in LaTeX in inline text mode? I have looked everywhere and I can only find a way to do it in ...
The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically ... Geometric Partial Differential Equations. Editors: Chambolle, Antonin, Novaga, Matteo, Valdinoci, Enrico (Eds.) ... The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically ... On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force ...
... of a system of equations xi= fi, i=1,..., n, over N, i.e., the naturals (extended by ∞), where the right hand sides fiare... ... We consider the problem of computing the least solution X i , i=1,..., n, of a system of equations xi=fi, i=1,..., n, over N, i ... Seidl H. (1994) Least solutions of equations over N. In: Abiteboul S., Shamir E. (eds) Automata, Languages and Programming. ...
Then, a detailed study on some important PDEs, namely Laplaces equation, the heat equation and the wave equation are given. ... Partial differential equations Introduction Partial differential equations (PDEs) are fundamental to the modeling of natural ... 1] L. Evans, Partial Differential Equations, American Mathematical Society [2] M. Renardy, R. Rogers, An Introduction to ... Partial Differential Equations, Springer [3] F. Sauvigny, Partielle Differentialgleichungen der Geometrie und der Physik, ...
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Writing Subtraction Equations 5. Download Worksheet More info Your child will rewrite each equation according to the directions ... Writing Subtraction Equations 10. Download Worksheet More info Mr. Artist needs to solve a set of subtraction problems, but he ... Writing Subtraction Equations 9. Download Worksheet More info Give your kid a boost in math with this fun subtraction worksheet ... Writing Subtraction Equations 8. Download Worksheet More info Two-digit subtraction can be the bane of a second graders ...
Boltzmann equation: The simple mean free path description of gas transport coefficients accounts for the major observed ... Equation of state. To a first approximation, molecule-molecule collisions do not affect the ideal gas equation of state, pv = R ... This equation is difficult to solve in any general sense, but some progress can be made by assuming that the deviations from ... Boltzmann equation. The simple mean free path description of gas transport coefficients accounts for the major observed ...
As Matt (Built on Facts) did a while ago, it can be shown that you can get the equation of motion for a mass on a spring with ... If you could get an equation of motion, that would do it. ...
... also called the Clausius-Clapeyron equation) relates the slope of a reaction line on a phase diagram to ... ... Andrea Koziol (University of Dayton) and Dexter Perkins (University of North Dakota) The Clapeyron equation ( ... The Clapeyron equation (also called the Clausius-Clapeyron equation) relates the slope of a reaction line on a phase diagram to ... Now, we can use the Clapeyron equation to get: dP/dT = ΔS/ΔV = 10*102.68/40.155 = 25.57 bar/deg Using this value, we find that ...
... open your document in Word and add the equation there. Youll see it when you reopen the document in Word Online. ... Then follow the instructions in Write an equation or formula. When you save the document and reopen it in Word for the web, ... Not in Word for the web, though youll see equations that are already in your document. If you have the desktop version of Word ... thats where you can add or edit mathematical equations.. To open your document in the desktop version of Word, click Open in ...
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Edit equations right on the screen with your mouse, and never make a mistake. Guide the program through any complex algebraic ... Edit equations right on the screen with your mouse, and never make a mistake. Guide the program through any complex algebraic ... This is the PERFECT tool for manipulating equations while doing long derivations. ...
7.9 Nonlinear equations by Newton iteration As mentioned at the beginning of this chapter, nonlinear differential equations are ... Chebfun has powerful capabilities for solving ordinary differential equations as well as partial differential equations ... In Matlab, if A is a square matrix and b is a vector, then the command x=A\b solves the linear system of equations A*x=b. ... If L is a linear operator and E(t) = expm(t*L), then the partial differential equation u_t = Lu has solution u(t) = E(t)*u(0). ...
Systems of equations f1 = ··· = f n−1 = 0 in ℝ n = { x} having the solution x = 0 are considered under the assumption that the ... Systems of equations f 1 = ··· = f n−1 = 0 in ℝ n = {x} having the solution x = 0 are considered under the assumption that the ... A. D. Bruno, Power Geometry in Algebraic and Differential Equations, North-Holland, Amsterdam, 2000.Google Scholar ... V. V. Kozlov and S. D. Furta, Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations, Springer-Verlag, ...
... ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports ... Fractional and Time-Scales Differential Equations. Guest Editors: Dumitru Baleanu, Ali H. Bhrawy, Delfim F. M. Torres, and ... A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations, E. H. Doha, D. Baleanu, A. H. Bhrawy, and M. A. ... Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets, Ai-Min Yang, Xiao-Jun Yang, ...
... Xiaojing Yang Department of Mathematics, Tsinghua University, Beijing, ... The periodic boundary value problems of a class of nonlinear differential equations are investigated. ...
The initial classic assumption is changed in this article based on the available frequencies in the population growth equation ... "Analysis of economic growth differential equations," Social-Economic Debates, Association for Entreprenorial Spirit Promotion, ... The initial classic assumption is changed in this article based on the available frequencies in the population growth equation ...
  • Differential Equations and Dynamical Systems, Vol. 26, Issue. (
  • Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. (
  • Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. (
  • Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. (
  • Mathematical equations aren't just useful - many are quite beautiful. (
  • It is still amazing to me that one such mathematical equation can describe what space-time is all about," said Space Telescope Science Institute astrophysicist Mario Livio, who nominated the equation as his favorite. (
  • Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena arising in various fields of science such as heat conduction, elasticity, electrodynamics, fluid flow, chemical reaction, quantum mechanics or Black-Scholes option pricing model in mathematical finance. (
  • If you have the desktop version of Word, that's where you can add or edit mathematical equations. (
  • The real-world applications of mathematical equations. (
  • Mathematical Methods in the Physical Sciences , by Mary Boas, is a classic text covering many topics, including ODEs and PDEs (partial differential equations). (
  • G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert Spaces,", London Mathematical Society Lecture Notes , 293 (2002). (
  • Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. (
  • This is an introduction to the geometry of non-linear partial differential equations that arise in many models of mathematical physics. (
  • The Analysis & Partial Differential Equations (APDE) research group is part of the Department of Mathematics in the School of Mathematical & Physical Sciences. (
  • The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations. (
  • In order to better present mathematical equations, Flashcard Machine provides a tool that allows the user to write LaTeX code. (
  • Partial differential equations form an adequate and powerful instrument to provide a mathematical model for nature. (
  • At WIAS, functional analysis and operator theory are related, in particular, to problems of partial differential equations and evolutions equations, to analysis of multiscale, hybrid and rate-independent models and, finally, to mathematical problems of semiconductor models. (
  • The mathematical description of many scientific and technological problems leads to systems of partial differential equations (PDEs). (
  • This equation gives us a mathematical shortcut to describe a complex characteristic of turbulence called intermittency," said Meneveau, who also is director of the Center for Environmental and Applied Fluid Mechanics at Johns Hopkins. (
  • The Maple database of solutions to Einstein's equations, constructed digitizing the solutions found in the book "Exact Solutions of Einstein's Field Equations" by Stephani et al. (
  • Because it uses as little knowledge of functional analysis as possible, the book is accessible to those with a background in multivariable calculus, elementary Lebesgue integral theory, and basic parts of the theory of integral equations. (
  • In this video I show you how to derive the equations of motion using simple Calculus (integration) techniques and some simple algebra (factorisation/expansion). (
  • However, you will find it very hard to excel in physics if you are a poor in algebra, calculus, vector calculus and differential equations. (
  • The math should be okay for you to handle, as long as all the equations you will learn are in discrete form rather than differential form, which requires calculus. (
  • Eventually, if you stick in long enough, everything boils down to differential equations and must be solved using calculus. (
  • Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. (
  • Extends the concepts developed in Calculus to functions of several variables and differential equations. (
  • It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge-Kutta. (
  • This course covers the foundational concepts in algebra that students need to solve equations. (
  • Mr. Artist needs to solve a set of subtraction problems, but he has trouble understanding these equations as they are written. (
  • This equation is difficult to solve in any general sense, but some progress can be made by assuming that the deviations from the equilibrium distribution are small and are proportional to the external influences that cause the deviations, such as temperature , pressure , and composition differences. (
  • How Do You Solve Quadratic Equations by Factoring? (
  • You can use Partial Differential Equation Toolbox to solve PDEs from standard problems such as diffusion, heat transfer, structural mechanics, electrostatics, magnetostatics, and AC power electromagnetics, as well as custom, coupled systems of PDEs. (
  • You simply cannot go from 'an ODE is like an equation with functions and derivatives' to 'let's solve one' in 5 sentences. (
  • Regarding the solution of differential equations, memristor arrays have been employed as accelerators for digital solvers 31 , 32 and, recently, a digital approach based on memristor crossbar arrays have been employed to solve partial differential equations 33 with high precision. (
  • Just write out the equations after substituting the values of the points, along with the y' as you have written and solve them for a,b,c simultaneously. (
  • You can solve the 3 equations for a, b, and c. (
  • Everything is explained using equations and then interpreting those equations based on the problem you are trying to solve. (
  • In this unit, we extend these processes to solve a greater variety of equations, like rational and radical equations. (
  • We also solve systems that include quadratic equations, and learn how we can use graphs to estimate a solution for any kind of equation! (
  • In Exercises 4756, solve the given equation for the indicated variable. (
  • Solve linear and quadratic equations 2. (
  • Solve some classes of rational and radical equations 3. (
  • Solve exponential and logarithm equations 6. (
  • examples of how quadratic equations can help us solve word problems. (
  • The resulting equation gave them a tool to predict intermittency by merely solving this simple equation rather than having to solve complicated computer models of turbulence. (
  • Evolution Equations & Control Theory , 2012, 1 (1) : 43-56. (
  • H. Neidhardt , A. Stephan , V.A. Zagrebnov , Chapter 13: Trotter Product Formula and Linear Evolution Equations on Hilbert Spaces, in: Analysis and Operator Theory , Th .M. Rassias , V.A. Zagrebnov , eds. (
  • At the Weierstrass Institute this research has two essential focuses: (a) Regularity for the solutions of linear elliptic equations and (b) Existence, uniqueness and regularity for evolution equations. (
  • This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. (
  • The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. (
  • This monograph is a great source for graduate students in mathematics and science and for all researchers interested in the qualitative theory of Volterra difference equations and functional difference equations. (
  • A study of difference equations and inequalities. (
  • It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations. (
  • We deal with $m$-periodic, $n$-th order difference equations and study whether they can be globally linearized. (
  • The Fresnel equations (or Fresnel coefficients ) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media . (
  • The Fresnel equations describe the ratio of the reflected and transmitted electric fields to that of the incident beam (the waves' magnetic fields can also be related using similar coefficients). (
  • A complete classification of this dynamics, even for all sign patterns of above coefficients, is available, [1] which is based upon equivalence to the 3-type replicator equation . (
  • It treats diffusion equations with variable coefficients associated with boundary conditions and the corresponding elliptic differential equations. (
  • In the table, the first column is the x-axis value and the next four columns refer to the coefficients needed to define the y-axis value on the growth curve using the third order polynomial spline equations which define the curves. (
  • The virtue of this equation is that there is a rigorous connection between the virial coefficients and intermolecular forces, and experimental values of B ( T ) were an early source (and still a useful one) of quantitative information on intermolecular forces. (
  • Enter the coefficients for your Quadratic Equation and this simple app will output the solutions. (
  • The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. (
  • In the equations for predation, the base population model is exponential . (
  • Alex Proekt's data fit a power law, a simple exponential equation denoting scale-free dynamics. (
  • Here, we exhibit a quantum algorithm for solving linear sets of equations that runs in O(log n) time, an exponential improvement over the best classical algorithm. (
  • Understand the inverse relations between exponential and logarithm equations 7. (
  • The temperature dependence often follows Arrhenius' equation: k(T) = A exp(-Ea/RT) where T is the absolute temperature, R the universal gas constant, Ea is the activation energy (specific to each reaction), and A is the 'pre-exponential' or 'frequency' or 'entropy' factor. (
  • While in the last two decades numerous verification approaches and tools have been developed for systems described by ordinary differential equations, there is currently a lack of research methods for differential algebraic equations. (
  • Chebfun has powerful capabilities for solving ordinary differential equations as well as partial differential equations involving one space and one time variable. (
  • We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. (
  • An electrical analog computer is an active network composed of electrical elements, namely, resistors, capacitors and operational amplifiers which, connected together, are capable of simulating any set of linear ordinary differential equations 7 . (
  • The book Mathematics From the Birth of Numbers, by Jan Gullberg, is a cool book in general and also has a short and sweet introduction to ordinary differential equations (ODEs) at the end. (
  • In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. (
  • However, if necessary, you may consult any introductory level text on ordinary differential equations. (
  • This course is recommended for undergraduate students in mathematics, physics, engineering and the social sciences who want to learn basic concepts and ideas of ordinary differential equations. (
  • This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. (
  • Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). (
  • The book's practical approach assumes only prior understanding of ordinary differential equations. (
  • - The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB , Mathematica , and MapleTM, A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical. (
  • Although traditional in its coverage of basic topics of ODEs, A Course in Ordinary Differential Equations is one of the first texts to provide relevant computer code and instruction in MATLAB, Mathematica, and Maple that will prepare students for further study in their fields. (
  • Then, a detailed study on some important PDEs, namely Laplace's equation, the heat equation and the wave equation are given. (
  • Partial Differential Equation Toolbox™ provides functions for solving partial differential equations (PDEs) in 2-D, 3-D, and time using finite element analysis. (
  • Eventually, you'll need or want to learn about PDEs, and the most intuitive and comprehensible book I've seen regarding them is Partial Differential Equations for Scientists and Engineers , by Stanley Farlow. (
  • The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi- linear second order partial differential equations of parabolic and elliptic type, in short PDEs. (
  • Research in this group spans a broad spectrum underpinned by the rigorous treatment and analysis of linear and nonlinear partial differential equations (PDEs). (
  • Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). (
  • Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. (
  • After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. (
  • In this lesson students will reason about solutions to systems of equations while modeling the systems on mobiles. (
  • G. Da Prato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions,", Encyclopedia of Mathematics and its Applications , 44 (1992). (
  • CAn someone help me with my radical equations? (
  • There are several good websites to find help with radical equations. (
  • You tube has several good videos on radical equations that are free of charge. (
  • Complex Variables and Elliptic Equations, Vol. 63, Issue. (
  • To write the chemical equation of alkali metal with oxides and predict the nature of oxide in the compound. (
  • What is the chemical equation or magnesium and hydrochloric acid? (
  • What is a balanced chemical equation for magnesium hydroxide and hydrochloric acid? (
  • What is the balanced chemical equation of hydrochloric acid and magnessium ribbon? (
  • We express the stoichiometry as a balanced chemical equation. (
  • What is a chemical equation? (
  • When speaking of a specific reaction, a chemical equation must be balanced. (
  • What is any substance to the right of the arrow in a chemical equation? (
  • The substances to the right of the arrow in a chemical equation are called the products, while those on the left side of the arrow are the reactants. (
  • The book I used in college, and still use when needed, is A First Course in Differential Equations, by Dennis Zill. (
  • Overall, this book should convince math majors how demanding math modeling needs to be and biologists that taking another course in differential equations will be worthwhile. (
  • A class of singular first order differential equations with applications in reaction-diffusion. (
  • This book presents a self-contained exposition of the theory of initial-boundary value problems for diffusion equations. (
  • Boundary conditions are needed for solving differential equations, but they have no effect when a chebop is simply applied to a chebfun. (
  • The periodic boundary value problems of a class of nonlinear differential equations are investigated. (
  • It lets you specify and mesh 2-D and 3-D geometries and formulate boundary conditions and equations. (
  • For example, 'Elementary Differential Equations and Boundary Value Problems by W. E. Boyce and R. C. DiPrima from John Wiley & Sons' is a good source for further study on the subject. (
  • Fundamentals of Differential Equations with Boundary Value Problems, Fifth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. (
  • The Clapeyron equation (also called the Clausius-Clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties. (
  • The present chapter is devoted to chebops, the fundamental Chebfun tools for solving differential (or integral) equations. (
  • However, a surprising new discovery from a Caltech researcher suggests that the Schrödinger Equation-the fundamental equation of quantum mechanics-is remarkably useful in describing the long-term evolution of certain astronomical structures. (
  • A fundamental property of Oseen's equation is that the general solution can be split into longitudinal and transversal waves. (
  • Invariance and monotonicity for stochastic delay differential equations. (
  • We handle first order differential equations and then second order linear differential equations. (
  • While the first two equations describe particular aspects of our universe, another favorite equation can be applied to all manner of situations. (
  • He came up with a system of equations that describe how two chemicals react together, resulting in surprisingly lifelike arrangements. (
  • The Schrödinger Equation is well studied, and finding that such a quintessential equation is able to describe the long-term evolution of astrophysical disks should be useful for scientists who model such large-scale phenomena. (
  • In fluid dynamics, the Oseen equations (or Oseen flow) describe the flow of a viscous and incompressible fluid at small Reynolds numbers, as formulated by Carl Wilhelm Oseen in 1910. (
  • The Faddeev equations, named after their inventor Ludvig Faddeev, are equations that describe, at once, all the possible exchanges/interactions in a system of three particles in a fully quantum mechanical formulation. (
  • In Mathematics I and II, students solves linear and quadratic equations, and learned how the two processes are based on the same logical principles. (
  • Quadratic Equations. (
  • In this module, we explore a variety of methods for solving quadratic equations. (
  • inproceedings{HIC2018:Semi_Lagrangian_Scheme_for_Advection_Diffusion, author = {Ersin Bahar and Gurhan Gurarslan}, title = {A Semi-Lagrangian Scheme for Advection-Diffusion Equation}, booktitle = {HIC 2018. (
  • For the predator-prey equations, see Lotka-Volterra equations . (
  • The competitive Lotka-Volterra equations are a simple model of the population dynamics of species competing for some common resource. (
  • The form is similar to the Lotka-Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. (
  • We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. (
  • The most practical approaches to the equation of state for real fluids remain the versions of the principle of corresponding states first proposed by van der Waals. (
  • in the context of differential equations such techniques are called spectral collocation methods. (
  • This is the basic reason for the use of simultaneous equation methods of estimation in econometrics. (
  • 31:865-878, 2001) seminal article on the topic, it has become standard to develop nonlinear tree biomass equations to ensure compatibility among total and component predictions and to fit these equations using multistep generalized least-squares methods. (
  • - A systematic introduction to partial differentialequations and modern finite element methods for their efficient numerical solutionPartial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations. (
  • This site provides tutorials, examples, and exercises for those wishing to learn basic or specialized structural equation modeling methods. (
  • Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. (
  • To a first approximation, molecule-molecule collisions do not affect the ideal gas equation of state, p v = R T , but real gases at nonzero densities show deviations from this equation that are due to interactions among the molecules. (
  • Abstract Solvability of forward-backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. (
  • This approximation, often used by astronomers, is based upon equations developed by the 18th-century mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace. (
  • Seidl H. (1994) Least solutions of equations over N . In: Abiteboul S., Shamir E. (eds) Automata, Languages and Programming. (
  • New Action button: you can send your equation solutions with WhatsApp and email (for example) or save it with Note app. (
  • Some of them don't even really have solutions (non-linear differential equations). (
  • There certainly are differential equations without solutions, but I'm almost positive that's not what's meant here. (
  • In this case, the solutions of these equations are encoded into the time evolution of the voltage waveform produced by the analog computer. (
  • Extraneous solutions of equations Get 3 of 4 questions to level up! (
  • Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. (
  • Learn how to find and represent solutions of basic differential equations. (
  • FIRST ORDER chemical kinetics equations and solutions. (
  • Stochastic differential equations are differential equations whose solutions are stochastic processes. (
  • On a circadian time scale, the activity of individual animals all fit this equation when the lights went out (the transition from lowest arousal to highest), demonstrating a remarkable lawfulness of arousal-dependent behavior. (
  • Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains. (
  • The Schrödinger Equation is the foundation of quantum mechanics: It describes the non-intuitive behavior of systems at atomic and subatomic scales. (
  • The theory can be encapsulated in a main equation called the standard model Lagrangian (named after the 18th-century French mathematician and astronomer Joseph Louis Lagrange), which was chosen by theoretical physicist Lance Dixon of the SLAC National Accelerator Laboratory in California as his favorite formula. (
  • inproceedings{ARCH18:Linear_Differential_Algebraic_Equations_Benchmark, author = {Patrick Musau and Diego Manzanas Lopez and Hoang-Dung Tran and Taylor T. Johnson}, title = {Linear Differential-Algebraic Equations (Benchmark Proposal)}, booktitle = {ARCH18. (
  • For example, away from singularities, one can approximate the solution of a differential equation, even a non-linear one, numerically to an arbitrarily high degree of accuracy, almost exactly as the author does for linear equations. (
  • In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. (
  • In this talk we survey recent progress on the design of provably fast algorithms for solving linear equations in the Laplacian matrices of graphs. (
  • The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. (
  • Aram Harrow and colleagues have just published on the arXiv a quantum algorithm for solving systems of linear equations ( paper , PDF). (
  • Since solving linear equations is such a common task in computational science and engineering, this algorithm makes many more important problems that currently use thousands of hours of CPU time on supercomputers amenable to significant quantum speedup. (
  • The summary cleverly omits that solving a linear equation is neither NP complete nor NP hard, the speed up is from O(n) to O(log n). (
  • While certain famous equations, such as Albert Einstein's E = mc^2, hog most of the public glory, many less familiar formulas have their champions among scientists. (
  • All of Einstein's true genius is embodied in this equation. (
  • 5. ability to calculate the generations of Noether identities for the equations of motion (e.g., for the Yang-Mill models or Einstein's gravity equations) and construct the respective classes of gauge symmetries. (
  • The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. (
  • This equations states that the slope (rise/run) of an univariant equilibrium plotted on a P-T diagram is equal to the entropy change ( Δ S) of the reaction divided by the volume change ( Δ V) of the reaction. (
  • Using the Clapeyron equation, only the slope of the equilibrium is determined, not the actual position of the reaction in pressure-temperature space. (
  • Use Boettcher's results as a starting point and apply the Clausius-Clapeyron Equation to determine the temperature of reaction at 10 Kbar. (
  • Given a stochastic reaction-diffusion equation on a bounded open subset $\mathcal O$ of $\mathbb{R}^n$, we discuss conditions for the invariance of a nonempty closed convex subset $K$ of $L^2(\mathcal O)$ under the corresponding flow. (
  • A remark on reaction-diffusion equations in unbounded domains. (
  • Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. (
  • Write balanced equations for the reaction of lithium, sodium, and potassium with O 2 . (
  • What is the Word equation for reaction of magnesium with dilute hydrochloric acid? (
  • Whats the word equation for the reaction between magnisium and hydrochloric acid? (
  • What is the word equation for the reaction between magnesium hydroxide and hydrochloric acid? (
  • Chemical equations are illustrations of the reactants and products in a chemical reaction. (
  • Lots of exercises! (
  • An "oldie but goodie" equation is the famous Pythagorean theorem, which every beginning geometry student learns. (
  • The equation is at the core of much of geometry, links it with algebra, and is the foundation of trigonometry. (
  • The twelve lectures in the (non)commutative geometry of differential equations' (Part I, 2012), on-line IHES/M-12-13, 140 pages. (
  • This study proposes a semi-Lagrangian scheme for numerical simulation of advection-diffusion equation. (
  • The equation above was formulated by Einstein as part of his groundbreaking general theory of relativity in 1915. (
  • Claude Shannon's equation expressing information theory - - the quantity of information without any reference to its exact content or meaning. (
  • Fundamentals of Differential Equationspresents the basic theory of differential equations and offers a variety of modern applications in science and engineering. (
  • Advance praise: 'Stochastic differential equations have long been used by physicists and engineers, especially in filtering and prediction theory, and more recently have found increasing application in the life sciences, finance and an ever-increasing range of fields. (
  • In nuclear physics, the off the energy shell nucleon-nucleon interaction has been studied by analyzing (n,2n) and (p,2p) reactions on deuterium targets, using the Faddeev Equations. (
  • Karin Hutchinson starts with one-step addition, subtraction, multiplication, and division equations, then progresses to multistep equations and equations featuring fractions and decimals. (
  • This printable math worksheet asks your second grader to rewrite each subtraction equation, stacking the larger number on top, and write down each answer. (
  • This printable page of subtraction problems will give your second grader invaluable two-digit subtraction practice and a familiarity with writing equations. (
  • Your child will rewrite the subtraction equation, then find the difference. (
  • Your kid will get subtraction practice and learn to express equations in different ways. (
  • Your child will practice solving problems and writing equations too! (
  • The drawback of the virial equation of state is that it is an infinite series and becomes essentially useless at high densities, which in practice are those greater than about the critical density . (