###### Mathematics

###### Models, Biological

###### Models, Theoretical

###### Mathematical Concepts

###### Computer Simulation

###### Glomerular Filtration Rate

###### Algorithms

###### Regression Analysis

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.

###### Models, Statistical

###### Reproducibility of Results

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.

###### Models, Chemical

###### Diffusion

###### Technetium Tc 99m Pentetate

###### Cystatin C

###### Body Composition

###### Nonlinear Dynamics

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.

###### Linear Models

###### Anthropometry

###### Predictive Value of Tests

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.

###### Calorimetry, Indirect

###### Stochastic Processes

###### Enzymes

###### Skinfold Thickness

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)

###### Reference Values

###### Iothalamic Acid

###### Kidney Function Tests

###### Numerical Analysis, Computer-Assisted

###### Basal Metabolism

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.

###### Renal Insufficiency, Chronic

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)

###### Models, Cardiovascular

###### Body Weight

###### Energy Metabolism

###### Physical Phenomena

###### Longitudinal Studies

###### Models, Psychological

###### Thermodynamics

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)

###### Mathematical Computing

###### Physics

###### Water

###### Viscosity

###### Indicator Dilution Techniques

###### Body Height

###### Cross-Sectional Studies

###### Iohexol

###### Engineering

###### Age Factors

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.

###### Sensitivity and Specificity

###### Cohort Studies

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.

###### Least-Squares Analysis

###### Membrane Potentials

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).

###### Sex Factors

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.

###### Biometry

###### Monte Carlo Method

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)

###### Data Interpretation, Statistical

###### Temperature

###### Prospective Studies

###### Risk Factors

###### Calibration

###### Adipose Tissue

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.

###### Solutions

###### Models, Neurological

###### Pressure

###### Body Mass Index

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)

###### Models, Genetic

###### Statistics as Topic

###### Ions

###### Hydrogen-Ion Concentration

###### Rheology

###### Potassium

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.

###### Cattle

###### Inulin

###### Kidney Failure, Chronic

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.

###### Vital Capacity

###### Software

###### Sodium

###### Questionnaires

###### Systems Biology

###### Chemistry, Physical

###### Absorptiometry, Photon

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.

###### Drug Dosage Calculations

###### Respiratory Function Tests

###### Biomechanical Phenomena

###### Bias (Epidemiology)

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.

###### Biological Markers

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.

###### Chronic Disease

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)

###### Potassium Radioisotopes

###### Kidney

###### Severity of Illness Index

###### Risk Assessment

###### Models, Anatomic

###### Analysis of Variance

###### Finite Element Analysis

###### Hydrodynamics

###### Factor Analysis, Statistical

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.

###### Nephelometry and Turbidimetry

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.

###### Meat

###### European Continental Ancestry Group

###### Body Fluid Compartments

###### Forecasting

###### Deuterium Oxide

###### Lung Volume Measurements

###### Cell Membrane Permeability

###### Decapodiformes

###### Oxygen Consumption

###### Physicochemical Phenomena

###### Energy Transfer

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.

###### Normal Distribution

###### Pharmacokinetics

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.

###### Nutritional Requirements

###### Cystatins

###### Retrospective Studies

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.

###### Prevalence

###### Solvents

###### African Continental Ancestry Group

###### Membranes

###### Electrochemistry

###### Likelihood Functions

###### Porosity

###### Multivariate Analysis

###### Biochemistry

###### Poisson Distribution

###### Ventilation

###### Oxygen

###### Vapor Pressure

###### Metabolic Clearance Rate

###### Logistic Models

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, Pharmaceutical

###### Aging

###### Follow-Up Studies

###### Osmolar Concentration

###### Reference Standards

###### Forced Expiratory Volume

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.

###### Twins, Dizygotic

###### Proteins

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.

###### Stress, Mechanical

###### Photons

###### Ion Exchange

###### Biochemical Phenomena

###### Phantoms, Imaging

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)

###### Convection

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)

###### Action Potentials

###### Signal Processing, Computer-Assisted

###### Image Interpretation, Computer-Assisted

###### Pregnancy

###### Systems Theory

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.

###### Body Weights and Measures

###### Obesity

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).

###### Radioisotope Dilution Technique

###### Fractals

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.

###### Carbon Dioxide

###### Pharmaceutical Preparations

###### Tablets

###### Asian Continental Ancestry Group

###### Blood Flow Velocity

###### Respiratory Dead Space

###### Motion

###### Thermal Conductivity

###### Electrophysiology

###### Nitrogen

###### Densitometry

###### Swine

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).

###### Ion Channels

###### Urea

###### Lung

###### Scattering, Radiation

###### Twins, Monozygotic

###### Breeding

###### Permeability

###### Surface Properties

###### Sex Characteristics

###### Ultrasonics

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.

###### ROC Curve

###### Mollusca

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, Analog

###### Group of Monuments at Mahabalipuram

**Equations**. p. 29. R. Nagaswamy (2010). Mahabalipuram: Monumental Legacy. Oxford University Press. pp. 81-82. ISBN 978-0-19- ...

###### The Nine Chapters on the Mathematical Art

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 ...###### Rape during the Kashmir conflict

**EQUATIONS**. pp. 131-. Khan, Waheeda; Deb, Sibnath (5 August 2015). Child Safety, Welfare and Well-being: Issues and Challenges. ...

###### Kashmir

**EQUATIONS**. "Jammu and Kashmir bird checklist - Avibase - Bird Checklists of the World". avibase.bsc-eoc.org. Retrieved 20 ...

###### Jaipal Singh Munda

"This is Our Homeland: A Collection of Essays on the Betrayal of Adivasi Rights in India".

**EQUATIONS**. 27 January 2018 - via ...###### Muthanga incident

**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. ...

###### Viscous vortex domains method

**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 ...

###### Mangalore Today

Equitable Tourism Options (

**EQUATIONS**). Tourism and Displacement: Pilikula - Karnataka's model Tourism Project?.**EQUATIONS**. p. ...###### Poomala Dam

"Poomala dam to be made tourist centre".

**Equations**. Retrieved 26 June 2013. "Poomala dam makeover nearing completion". The Hindu ...###### Swaminarayan Akshardham (New Delhi)

**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 ...

###### List of physical constants

CS1 maint: discouraged parameter (link) Huray, Paul G., 1941- (2010). Maxwell's

**equations**. Hoboken, N.J.: Wiley. pp. 8, 57. ...###### Jacobi coordinates

Differential

**Equations**. Springer. p. 58; Figure 2.15. ISBN 0-387-95140-7. Patrick Cornille (2003). "Partition of forces using ...###### Electric field

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 ...###### Conserved quantity

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). ...###### Impulse response

"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 ...###### Autonomous system (mathematics)

...

**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). ...###### Bifurcation theory

"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, ...###### Kenneth M. Golden

Mackenzie, Dana (27 March 2009). "Cold

**Equations**". Science. 324 (5923): 32-3. doi:10.1126/science.324.5923.32. ISSN 0036-8075. ...###### Institute of Mathematics of National Academy of Sciences of Armenia

... 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, ...###### A Treatise on Electricity and Magnetism

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) ...###### Timeline of thermodynamics

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 ...###### 1946 in science

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. ...###### Charles Gaines (artist)

Holte, Michael Ned (October 2011). "Differential

**Equations**". Artforum International. 50 (2). "In the Shadow of Numbers". Pomona ...###### Poloidal-toroidal decomposition

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 ...###### Optical telescope

"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. ...###### Magic hypercube

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:// ...###### Coulomb's law

Maxwell's

**equations**. Hoboken, N.J.: Wiley. pp. 8, 57. ISBN 978-0-470-54991-9. OCLC 739118459.CS1 maint: multiple names: authors ...###### Arithmetic geometry

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 ...###### EDSAC

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 ...###### Computational photography

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 ...###### Fresnel **equations** - Wikipedia

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 ...###### Competitive Lotka-Volterra **equations** - Wikipedia

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**...###### The 11 Most Beautiful Mathematical **Equations**

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 ...###### Oseen **equations** - Wikipedia

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 ...###### Faddeev **equations** - Wikipedia

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. ...###### Diffusion **Equations** | Waterstones

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**. ...###### Partial Differential **Equations**

Math 597J: Partial Differential

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###### Dynamical Systems4

- Differential Equations and Dynamical Systems, Vol. 26, Issue. (cambridge.org)
- 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. (ecampus.com)
- 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. (ecampus.com)
- 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. (ecampus.com)

###### Mathematical16

- Mathematical equations aren't just useful - many are quite beautiful. (yahoo.com)
- 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. (yahoo.com)
- 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. (uni-ulm.de)
- If you have the desktop version of Word, that's where you can add or edit mathematical equations. (microsoft.com)
- The real-world applications of mathematical equations. (weforum.org)
- Mathematical Methods in the Physical Sciences , by Mary Boas, is a classic text covering many topics, including ODEs and PDEs (partial differential equations). (answers.com)
- G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert Spaces,", London Mathematical Society Lecture Notes , 293 (2002). (aimsciences.org)
- 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. (routledge.com)
- This is an introduction to the geometry of non-linear partial differential equations that arise in many models of mathematical physics. (rug.nl)
- The Analysis & Partial Differential Equations (APDE) research group is part of the Department of Mathematics in the School of Mathematical & Physical Sciences. (sussex.ac.uk)
- The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations. (claymath.org)
- In order to better present mathematical equations, Flashcard Machine provides a tool that allows the user to write LaTeX code. (flashcardmachine.com)
- Partial differential equations form an adequate and powerful instrument to provide a mathematical model for nature. (wias-berlin.de)
- 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. (wias-berlin.de)
- The mathematical description of many scientific and technological problems leads to systems of partial differential equations (PDEs). (wias-berlin.de)
- 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. (newswise.com)

###### Exact Solutions1

- 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. (maplesoft.com)

###### Calculus8

- 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. (waterstones.com)
- In this video I show you how to derive the equations of motion using simple Calculus (integration) techniques and some simple algebra (factorisation/expansion). (youtube.com)
- However, you will find it very hard to excel in physics if you are a poor in algebra, calculus, vector calculus and differential equations. (answers.com)
- 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. (answers.com)
- Eventually, if you stick in long enough, everything boils down to differential equations and must be solved using calculus. (answers.com)
- 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. (worldcat.org)
- Extends the concepts developed in Calculus to functions of several variables and differential equations. (edu.au)
- 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. (cambridge.org)

###### Solve18

- This course covers the foundational concepts in algebra that students need to solve equations. (lynda.com)
- Mr. Artist needs to solve a set of subtraction problems, but he has trouble understanding these equations as they are written. (education.com)
- 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. (britannica.com)
- How Do You Solve Quadratic Equations by Factoring? (reference.com)
- 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. (mathworks.com)
- You simply cannot go from 'an ODE is like an equation with functions and derivatives' to 'let's solve one' in 5 sentences. (ycombinator.com)
- 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. (nature.com)
- 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. (physicsforums.com)
- You can solve the 3 equations for a, b, and c. (physicsforums.com)
- Everything is explained using equations and then interpreting those equations based on the problem you are trying to solve. (answers.com)
- In this unit, we extend these processes to solve a greater variety of equations, like rational and radical equations. (khanacademy.org)
- We also solve systems that include quadratic equations, and learn how we can use graphs to estimate a solution for any kind of equation! (khanacademy.org)
- In Exercises 4756, solve the given equation for the indicated variable. (bartleby.com)
- Solve linear and quadratic equations 2. (coursera.org)
- Solve some classes of rational and radical equations 3. (coursera.org)
- Solve exponential and logarithm equations 6. (coursera.org)
- examples of how quadratic equations can help us solve word problems. (coursera.org)
- 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. (newswise.com)

###### Evolution Equations3

- Evolution Equations & Control Theory , 2012, 1 (1) : 43-56. (aimsciences.org)
- 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. (wias-berlin.de)
- 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. (wias-berlin.de)

###### Difference Equations6

- This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. (springer.com)
- The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. (springer.com)
- 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. (springer.com)
- A study of difference equations and inequalities. (routledge.com)
- It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations. (routledge.com)
- We deal with $m$-periodic, $n$-th order difference equations and study whether they can be globally linearized. (aimsciences.org)

###### Coefficients8

- 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 . (wikipedia.org)
- 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). (wikipedia.org)
- 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 . (wikipedia.org)
- It treats diffusion equations with variable coefficients associated with boundary conditions and the corresponding elliptic differential equations. (waterstones.com)
- 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. (cdc.gov)
- 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. (britannica.com)
- Enter the coefficients for your Quadratic Equation and this simple app will output the solutions. (apple.com)
- 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. (routledge.com)

###### Exponential5

- In the equations for predation, the base population model is exponential . (wikipedia.org)
- Alex Proekt's data fit a power law, a simple exponential equation denoting scale-free dynamics. (rockefeller.edu)
- 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. (slashdot.org)
- Understand the inverse relations between exponential and logarithm equations 7. (coursera.org)
- 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. (wsu.edu)

###### Ordinary13

- 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. (easychair.org)
- Chebfun has powerful capabilities for solving ordinary differential equations as well as partial differential equations involving one space and one time variable. (mathworks.com)
- 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. (nature.com)
- 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 . (nature.com)
- 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. (answers.com)
- 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. (coursera.org)
- However, if necessary, you may consult any introductory level text on ordinary differential equations. (coursera.org)
- 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. (coursera.org)
- 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. (routledge.com)
- 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). (google.com)
- The book's practical approach assumes only prior understanding of ordinary differential equations. (cambridge.org)
- books.google.com - 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. (google.com)
- 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. (google.com)

###### PDEs7

- Then, a detailed study on some important PDEs, namely Laplace's equation, the heat equation and the wave equation are given. (uni-ulm.de)
- Partial Differential Equation Toolbox™ provides functions for solving partial differential equations (PDEs) in 2-D, 3-D, and time using finite element analysis. (mathworks.com)
- 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. (answers.com)
- 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. (psu.edu)
- Research in this group spans a broad spectrum underpinned by the rigorous treatment and analysis of linear and nonlinear partial differential equations (PDEs). (sussex.ac.uk)
- 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). (google.com)
- 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. (google.com)

###### Partial Differential Equations and Evolution1

- After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. (routledge.com)

###### Systems of equati1

- In this lesson students will reason about solutions to systems of equations while modeling the systems on mobiles. (ti.com)

###### Stochastic Equations1

- G. Da Prato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions,", Encyclopedia of Mathematics and its Applications , 44 (1992). (aimsciences.org)

###### Radical equations3

- CAn someone help me with my radical equations? (answers.com)
- There are several good websites to find help with radical equations. (answers.com)
- You tube has several good videos on radical equations that are free of charge. (answers.com)

###### Elliptic1

- Complex Variables and Elliptic Equations, Vol. 63, Issue. (cambridge.org)

###### Chemical equation9

- To write the chemical equation of alkali metal with oxides and predict the nature of oxide in the compound. (bartleby.com)
- What is the chemical equation or magnesium and hydrochloric acid? (answers.com)
- What is a balanced chemical equation for magnesium hydroxide and hydrochloric acid? (answers.com)
- What is the balanced chemical equation of hydrochloric acid and magnessium ribbon? (answers.com)
- We express the stoichiometry as a balanced chemical equation. (wsu.edu)
- What is a chemical equation? (reference.com)
- When speaking of a specific reaction, a chemical equation must be balanced. (reference.com)
- What is any substance to the right of the arrow in a chemical equation? (reference.com)
- 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. (reference.com)

###### Course in Differential Equations2

- The book I used in college, and still use when needed, is A First Course in Differential Equations, by Dennis Zill. (answers.com)
- 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. (routledge.com)

###### Differential equations with applications1

- A class of singular first order differential equations with applications in reaction-diffusion. (aimsciences.org)

###### Boundary6

- This book presents a self-contained exposition of the theory of initial-boundary value problems for diffusion equations. (waterstones.com)
- Boundary conditions are needed for solving differential equations, but they have no effect when a chebop is simply applied to a chebfun. (mathworks.com)
- The periodic boundary value problems of a class of nonlinear differential equations are investigated. (hindawi.com)
- It lets you specify and mesh 2-D and 3-D geometries and formulate boundary conditions and equations. (mathworks.com)
- 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. (coursera.org)
- 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. (ecampus.com)

###### Fundamental4

- The Clapeyron equation (also called the Clausius-Clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties. (carleton.edu)
- The present chapter is devoted to chebops, the fundamental Chebfun tools for solving differential (or integral) equations. (mathworks.com)
- 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. (caltech.edu)
- A fundamental property of Oseen's equation is that the general solution can be split into longitudinal and transversal waves. (wikipedia.org)

###### Delay differential equations1

- Invariance and monotonicity for stochastic delay differential equations. (aimsciences.org)

###### Order differential equations1

- We handle first order differential equations and then second order linear differential equations. (coursera.org)

###### Describe5

- While the first two equations describe particular aspects of our universe, another favorite equation can be applied to all manner of situations. (yahoo.com)
- He came up with a system of equations that describe how two chemicals react together, resulting in surprisingly lifelike arrangements. (newscientist.com)
- 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. (caltech.edu)
- 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. (wikipedia.org)
- 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. (wikipedia.org)

###### Quadratic3

- In Mathematics I and II, students solves linear and quadratic equations, and learned how the two processes are based on the same logical principles. (khanacademy.org)
- Quadratic Equations. (coursera.org)
- In this module, we explore a variety of methods for solving quadratic equations. (coursera.org)

###### 20181

- 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. (easychair.org)

###### Volterra Equations4

- For the predator-prey equations, see Lotka-Volterra equations . (wikipedia.org)
- The competitive Lotka-Volterra equations are a simple model of the population dynamics of species competing for some common resource. (wikipedia.org)
- 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. (wikipedia.org)
- 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. (nature.com)

###### Approaches to the equation of st1

- 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. (britannica.com)

###### Methods6

- in the context of differential equations such techniques are called spectral collocation methods. (mathworks.com)
- This is the basic reason for the use of simultaneous equation methods of estimation in econometrics. (encyclopedia.com)
- 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. (usda.gov)
- books.google.com - 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. (google.com)
- This site provides tutorials, examples, and exercises for those wishing to learn basic or specialized structural equation modeling methods. (usgs.gov)
- Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. (cambridge.org)

###### Approximation3

- 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. (britannica.com)
- Abstract Solvability of forward-backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. (psu.edu)
- This approximation, often used by astronomers, is based upon equations developed by the 18th-century mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace. (caltech.edu)

###### Solutions10

- Seidl H. (1994) Least solutions of equations over N . In: Abiteboul S., Shamir E. (eds) Automata, Languages and Programming. (springer.com)
- New Action button: you can send your equation solutions with WhatsApp and email (for example) or save it with Note app. (apple.com)
- Some of them don't even really have solutions (non-linear differential equations). (ycombinator.com)
- There certainly are differential equations without solutions, but I'm almost positive that's not what's meant here. (ycombinator.com)
- In this case, the solutions of these equations are encoded into the time evolution of the voltage waveform produced by the analog computer. (nature.com)
- Extraneous solutions of equations Get 3 of 4 questions to level up! (khanacademy.org)
- 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. (claymath.org)
- Learn how to find and represent solutions of basic differential equations. (khanacademy.org)
- FIRST ORDER chemical kinetics equations and solutions. (wsu.edu)
- Stochastic differential equations are differential equations whose solutions are stochastic processes. (cambridge.org)

###### Favorite equations1

- What are some of your favorite equations? (slashdot.org)

###### Behavior3

- 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. (rockefeller.edu)
- Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains. (aimsciences.org)
- The Schrödinger Equation is the foundation of quantum mechanics: It describes the non-intuitive behavior of systems at atomic and subatomic scales. (caltech.edu)

###### Theoretical1

- 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. (yahoo.com)

###### Linear8

- 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. (easychair.org)
- 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. (ycombinator.com)
- 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. (nature.com)
- In this talk we survey recent progress on the design of provably fast algorithms for solving linear equations in the Laplacian matrices of graphs. (psu.edu)
- The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. (ecampus.com)
- Aram Harrow and colleagues have just published on the arXiv a quantum algorithm for solving systems of linear equations ( paper , PDF). (slashdot.org)
- 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. (slashdot.org)
- 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). (slashdot.org)

###### Einstein's3

- 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. (yahoo.com)
- All of Einstein's true genius is embodied in this equation. (yahoo.com)
- 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. (rug.nl)

###### Reaction12

- The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. (springer.com)
- 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. (carleton.edu)
- Using the Clapeyron equation, only the slope of the equilibrium is determined, not the actual position of the reaction in pressure-temperature space. (carleton.edu)
- Use Boettcher's results as a starting point and apply the Clausius-Clapeyron Equation to determine the temperature of reaction at 10 Kbar. (carleton.edu)
- 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. (aimsciences.org)
- A remark on reaction-diffusion equations in unbounded domains. (aimsciences.org)
- Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. (aimsciences.org)
- Write balanced equations for the reaction of lithium, sodium, and potassium with O 2 . (bartleby.com)
- What is the Word equation for reaction of magnesium with dilute hydrochloric acid? (answers.com)
- Whats the word equation for the reaction between magnisium and hydrochloric acid? (answers.com)
- What is the word equation for the reaction between magnesium hydroxide and hydrochloric acid? (answers.com)
- Chemical equations are illustrations of the reactants and products in a chemical reaction. (reference.com)

###### Https2

- https://en.wikibooks.org/w/index.php?title=Physics_Exercises&oldid=2236789 Lots of exercises! (wikiversity.org)
- https://en.wikiversity.org/w/index.php?title=Tables_of_Physics_Formulae&oldid=767433 OR USE WIKIPEDIA? (wikiversity.org)

###### Geometry3

- An "oldie but goodie" equation is the famous Pythagorean theorem, which every beginning geometry student learns. (yahoo.com)
- The equation is at the core of much of geometry, links it with algebra, and is the foundation of trigonometry. (businessinsider.com)
- The twelve lectures in the (non)commutative geometry of differential equations' (Part I, 2012), on-line IHES/M-12-13, 140 pages. (rug.nl)

###### Diffusion1

- This study proposes a semi-Lagrangian scheme for numerical simulation of advection-diffusion equation. (easychair.org)

###### Theory4

- The equation above was formulated by Einstein as part of his groundbreaking general theory of relativity in 1915. (yahoo.com)
- Claude Shannon's equation expressing information theory - - the quantity of information without any reference to its exact content or meaning. (rockefeller.edu)
- Fundamentals of Differential Equationspresents the basic theory of differential equations and offers a variety of modern applications in science and engineering. (ecampus.com)
- 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. (cambridge.org)

###### Physics1

- 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. (wikipedia.org)

###### Subtraction5

- Karin Hutchinson starts with one-step addition, subtraction, multiplication, and division equations, then progresses to multistep equations and equations featuring fractions and decimals. (lynda.com)
- This printable math worksheet asks your second grader to rewrite each subtraction equation, stacking the larger number on top, and write down each answer. (education.com)
- This printable page of subtraction problems will give your second grader invaluable two-digit subtraction practice and a familiarity with writing equations. (education.com)
- Your child will rewrite the subtraction equation, then find the difference. (education.com)
- Your kid will get subtraction practice and learn to express equations in different ways. (education.com)

###### Practice2

- Your child will practice solving problems and writing equations too! (education.com)
- 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 . (britannica.com)