A method of implementing non-numerical spread sheets for the medical and legal domains using a computer-assisted iterative problem solving technique which starts from initial non-numerical data and develops possible solutions within a framework of an interrelation ship among pre-selected non-numerical data which are divided into a plurality of mutually exclusive categories differentiated according to readiness for decision making, including the steps of: displaying on a video display, a work sheet having a plurality of cells each corresponding to one of said mutually exclusive categories for displaying the non-numerical data; entering initial non-numerical data into respective cells in the work sheet; selecting a query designating at least a first cell in the work sheet with the initial non-numerical data as an input and requesting related non-numerical data for at least one cell of the plurality of cells in the work sheet; identifying non-numerical data for the at least one cell that is related to non

The definitions serve the purpose of communication and preservation of knowledge in scientific inquiry. However, it is quite often to perceive number sense concept without well-accepted definitions in the field of mathematics education research. Despite the mentioned issue, the current literature on childrens number sense provide a glean for introducing, implementing, and even measuring the number sense using the specific and contextualized indicators in early mathematics. Consequently, this phenomenon offers to bridge a gap in the literature concerning definitions of number sense and its indicators. This article systematically reviews on the indicators in measuring childrens number sense based on the past research guided by the PRISMA statements. The metadata were analysed using open-coding and were further re-coded through axial coding and selective coding to form a definition of number sense. This article discusses on limitations, implications, and the future research directions for studying

Number sense in animals is the ability of creatures to represent and discriminate quantities of relative sizes by number sense. It has been observed in various species, from fish to primates. Animals are believed to have an approximate number system, the same system for number representation demonstrated by humans, which is more precise for smaller quantities and less so for larger values. An exact representation of numbers higher than 3 has not been attested in wild animals, but can be demonstrated after a period of training in captive animals. In order to distinguish number sense in animals from the symbolic and verbal number system in humans researchers use the term numerosity, rather than number, to refer to the concept that supports approximate estimation but does not support an exact representation of number quality. Number sense in animals includes the recognition and comparison of number quantities. Some numerical operations, such as addition, have been demonstrated in many species, ...

The simplest conceivable example of evolving systems is RNA molecules that can replicate themselves. Since replication produces a new RNA strand complementary to a template, all templates would eventually become double-stranded and, hence, become unavailable for replication. Thus the problem of how to separate the two strands is considered a major issue for the early evolution of self-replicating RNA. One biologically plausible way to copy a double-stranded RNA is to displace a preexisting strand by a newly synthesized strand. Such copying can in principle be initiated from either the (+) or (-) strand of a double-stranded RNA. Assuming that only one of them, say (+), can act as replicase when single-stranded, strand displacement produces a new replicase if the (-) strand is the template. If, however, the (+) strand is the template, it produces a new template (but no replicase). Modern transcription exhibits extreme strand preference wherein anti-sense strands are always the template. Likewise,

When children are acquiring the symbolic system for representing numbers and learning about math in school, theyre tapping into this primitive number sense, said Elizabeth Brannon, Ph.D., a professor of psychology and neuroscience, who led the study. Its the conceptual building block upon which mathematical ability is built.. Brannon explained that babies come into the world with a rudimentary understanding referred to as a primitive number sense. When looking at two collections of objects, primitive number sense allows them to identify which set is numerically larger even without verbal counting or using Arabic numerals. For example, a person instinctively knows a group of 15 strawberries is more than six oranges, just by glancing. Understanding how infants and young children conceptualize and understand number can lead to the development of new mathematics education strategies, said Brannons colleague, Duke psychology and neuroscience graduate student Ariel Starr. In particular, this ...

View Notes - mathstudysec1 from MTH 141, 142, at SUNY Empire State. Number Sense Number Sense Statistics, Data Analysis, Probability Algebra Measurement Math and and Reasoning Functions Geometry

The effects of transcranial electrical stimulation (tES) have been documented for a variety of mental functions, including numerical cognition. This article first reviews 2 prominent forms of tES, transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS). This is followed by an assessment of the applications of this technology in the enhancement of aspects of numerical cognition, including numerosity, magnitude representation, and more complex arithmetic operations. The review concludes with discussions of directions for future research. These include the need to take individual differences into account in experimental designs, extending research to individuals with difficulties and deficits in working with numbers, the need to consider potential cognitive costs that may offset cognitive benefits of tES. A recurring theme in this article is the need to move toward greater ecological validity of experimental findings.

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Adults, infants and non-human primates are thought to possess similar non-verbal numerical systems, but there is considerable debate regarding whether all vertebrates share the same numerical abilities. Despite an abundance of studies, cross-species comparison remains difficult because the methodology employed and the context of species examination vary considerably across studies. To fill this gap, we used the same procedure, stimuli and numerical contrasts to compare quantity abilities of five teleost fish: redtail splitfin, guppies, zebrafish, Siamese fighting fish, and angelfish. Subjects were trained to discriminate between two sets of geometrical figures using a food reward. Fish initially were trained on an easy numerical ratio (5 vs. 10 and 6 vs. 12). Once they reached the learning criterion, they were subjected to non-reinforced probe trials in which the set size was constant but numerical ratios varied (8 vs. 12 and 9 vs. 12). They also were subjected to probe trials in which the ratio was

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Considering eye-fixation behavior is standard in reading research to investigate underlying cognitive processes. However, in numerical cognition research eye-tracking is used less often and less systematically. Nevertheless, we identified over 40 studies on this topic from the last 40 years with an increase of eye-tracking studies on numerical cognition during the last decade. Here, we review and discuss these empirical studies to evaluate the added value of eye-tracking for the investigation of number processing. Our literature review revealed that the way eye-fixation behavior is considered in numerical cognition research ranges from investigating basic perceptual aspects of processing non-symbolic and symbolic numbers, over assessing the common representational space of numbers and space, to evaluating the influence of characteristics of the base-10 place-value structure of Arabic numbers and executive control on number processing. Apart from basic results such as reading times of numbers ...

DescriptionThe concentration in mathematical concepts of engineering is designed for students who seek a strong foundation in mathematics to support their studies in engineering. Combining a core foundation in the quantitative and analytical skills found in the field of mathematics with related skills in engineering fields, the program provides students with a solid mathematical background well-suited for multiple career paths.RequirementsStudents must complete a minimum of 21 credit hours which includes 12 upper division hours for this concentration.All courses must be completed with a grade of

Division of numerical quantities is a great way to start exploring and understanding division of polynomials. In this activity students start with what they know about division of numerical quantities and then apply this to division of polynomials. This assists with some of the terminology and also developing a deeper understanding. Polynomials can be regenerated dynamically and rapidly including the resultant quotient and, where applicable, the remainder, this helps students identify and explain patterns. The visual representation of polynomial division also helps students understand the factor and remainder theorem, particularly expressing a polynomial as a product of its linear factors.

In the per construction, use a forward slash only when (1) the construction involves units of measure (including time) and (2) at least 1 element includes a specific numerical quantity and (3) the element immediately adjacent on each side is either a specific numerical quantity or a unit of measure. In such cases, the units of measure should be abbreviated in accordance with , Abbreviations, Units of Measure. (See also , Numbers and Percentages, Forms of Numbers, Reporting Proportions and Percentages.)The hemoglobin level was 14 g/dL. The CD4+ cell count was 200/μL. Blood volume was 80 mL/kg of body weight. Less ...

In the per construction, use a forward slash only when (1) the construction involves units of measure (including time) and (2) at least 1 element includes a specific numerical quantity and (3) the element immediately adjacent on each side is either a specific numerical quantity or a unit of measure. In such cases, the units of measure should be abbreviated in accordance with , Abbreviations, Units of Measure. (See also , Numbers and Percentages, Forms of Numbers, Reporting Proportions and Percentages.)The hemoglobin level was 14 g/dL. The CD4+ cell count was 200/μL. Blood volume was 80 mL/kg of body weight. Less ...

Adults, infants and some non-human animals share an approximate number system (ANS) to estimate numerical quantities, and are supposed to share a second, object-tracking, system (OTS) that supports the precise representation of a small number of items (up to 3 or 4). In relative numerosity judgments, accuracy depends on the ratio of the two numerosities (Webers Law), for numerosities | 4 (the typical ANS range), while for numerosities ≤ 4 (OTS range) there is usually no ratio effect. However, recent studies have found evidence for ratio effects for small numerosities, challenging the idea that the OTS might be involved for small number discrimination. Here we tested the hypothesis that the lack of ratio effect in the numbers 1-4 is largely dependent on the type of stimulus presentation.We investigated relative numerosity judgments in college students using three different procedures: a simultaneous presentation of intermingled and separate groups of dots in separate experiments, and a further

Innumeracy in the Wild explains how numeric ability supports the quality of the decisions we make and, ultimately, the life outcomes we experience. It dissects three ways that people can be good or ... More. Innumeracy in the Wild explains how numeric ability supports the quality of the decisions we make and, ultimately, the life outcomes we experience. It dissects three ways that people can be good or bad with numbers and how each of these numeric competencies matter to decision making. Furthermore, it delves into how we can use this knowledge to improve decision making. Understanding the roles of numeric ability (often called numeracy) is particularly important today due to widespread innumeracy. In addition, policies in health and financial domains have shifted toward giving consumers and patients more information (which is often numeric). These changes are intended to empower individuals to take charge of their own welfare. The evidence is clear, however, that not everybody is prepared to ...

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied (scaled) by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.[clarification needed] Euclidean vectors are an example of a vector space. They represent physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces. Vectors in vector spaces do not necessarily have to be arrow-like objects as they appear in the mentioned examples: ...

Based on previous investigations, positive and negative sign is an important factor of SNARC (Spatial-Numerical Association of Response Codes) effect. Magnitude judgments of different signed numbers are solved by an obvious sign shortcut mechanism. When both numbers are negative, there are arguments between ontogenetic hypothesis and phylogenetic hypothesis. The ontogenetic hypothesis supposes that negative numbers are mapped onto the mental number line according to their numerical value, but phylogenetic hypothesis inserts that the representation of negative numbers depends on their absolute numerical value. Whether the SNARC effect is processed in the stage of response selection or stimulus presentation is also under discussion. Although frontal lobe and parietal lobe are generally considered as the key brain regions of the SNARC effect, hemispheric dominance of this effect still needs exploration. Therefore, our research focused on four points: 1) how sign shortcut mechanism affected the ...

Käser, Tanja; Kucian, Karin; Ringwald, M; Baschera, G M; von Aster, Michael; Gross, M (2011). Therapy software for enhancing numerical cognition. In: In Özyurt, J; Anschütz, A; Bernholt, S; Lenk, J. Interdisciplinary perspectives on cognition, education and the brain-Hanse-Studies. Oldenburg: BIS Verlag, 207-216. ...

by Bambang Parmanto PhD, Matthew Scotch, and Sjarif Ahmad Abstract Many healthcare processes involve a series of patient visits or a series of outcomes. The modeling of outcomes associated with these types of healthcare processes is different from and not as well understood as the modeling of standard industry environments.

Today Katie focuses on delivering measurable improvement for the laboratory in three areas - productivity, quality, and service - by implementing Lean Six Sigma practices, identifying opportunities for improvement, and leading initiatives to deliver the improvements. This involves a lot of facilitating and coaching clients, sharing tools and methods, defining, and measuring new metrics, and analyzing data to improve and also sustain the improvements made. Theres a lot of communication involved as I serve as a change agent, influencing teams and driving results.. Katie manages projects over multiple years beginning with an extensive assessment of each lab department. Over the initial few months of an engagement, there is an intense review of all workflows, including observation of all three shifts. There are some pretty long, odd hours but its essential to identify what strengths and best practices are already in place. A dozen or more opportunities might also be noted in the assessment of a ...

A mobile environment to improve the process of an integrated treatment of obese people will be identified, developed, introduced and clinically evaluated. The study will include 150 patients aged between 25 to 65 for men and 25 to 70 for women, diagnosed with obesity (BMI≥30 or BMI,27,5 and 20% risk or more for developing a cardiovascular diseases). One group of patients will visit conventional live workshops for weight loss and the other group will use ICT. At the initial examination by the doctor all survey participants will have measured blood pressure, body mass, waist circumference, percentage of body fat, percentage of skeletal muscle, resting metabolic rate, estimated risk of developing cardiovascular disease and will be directed to laboratory examination (blood lipids and cholesterol, blood sugar). Both groups will go through 16 workshops for weight loss. Each week they will monitor their body mass, waist circumference, physical activity (type, duration, intensity) and food intake ...

How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding?Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards.

Much evidence suggests that humans and many animals possess an abstract sense of approximate quantity: a sense of number. Recently Arrighi et al. (2014) provided behavioral evidence for a generalized number sense by showing that numerosity adaptation occurs cross-modally (from vision to audition and viceversa) and across stimuli presentation format (sequential and simultaneous). Here we extend these findings to show that producing a sequence of motor actions (finger tapping) without tactile feedback (no finger/surface contact during the motor routine) also causes adaptation of numerosity estimation of visual stimuli. In the high adaptation condition, participants were asked to tap as quickly as possible (average 5-6 taps/s) whilst in a low adaptation condition they were required to tap more slowly (around 1 tap/s). After the adapting phase the test stimulus - either a sequence of flashes or a cloud of dots (tested on separate sessions) - was randomly displayed either to the same side of the ...

There are several points that people tend to misunderstand about the problem already on the beginners level, so let me mention some pitfalls. First, note that the problem is not that the information is inaccessible behind a horizon. There is no horizon in the endstate, look at the diagram. Its flat Minkowski space with infinitely thinly dispersed thermal radiation. Think of the black hole as a black box. You start with flat Minkowski space, something happens in between, you end with flat Minkowski space. Yet, this evolution cannot be described by quantum mechanics as we know it. Second, to lay out the problem I didnt have to refer to measurement at all. Its a fundamental incompatibility in the evolution, you dont solve that incompatibility by waving your hands and yelling measurement problem. Third, we are talking about the microscopic laws. Yes, on macroscopic scales we do have an arrow of time and entropy tends to increase anyway, but the problem is to accommodate the black hole ...

Throughout history there have been numerous technological advances in the medical field. Some so minute that we don t even know about them, others that have changed the entire medical field at the blink of an eye. The applications of higher dimensional vector spaces have helped doctors diagnose breast cancer and heart disease. Vector spaces help doctors figure out if a lump found in a woman s breast is benign or malignant. Diagnosing heart disease in someone has also started using the application of vector spaces. ...

Before I answer your question, I think an explanation on Hex and Decimal values are needed.. The 40 bit hexadecimal is a number representation of base 16. A decimal is of base 10. So you can convert a Hex Value to Decimal. As this is out of scope for the question, you can google on how to convert from one to another. There are some online converters:. Hex to Decimal Converter. You will see when you convert the Hex value to decimal, that its just a number representation. When you convert, you drop the ...

Molecular Cloning, also known as Maniatis, has served as the foundation of technical expertise in labs worldwide for 30 years. No other manual has been so popular, or so influential.

Molecular Cloning, also known as Maniatis, has served as the foundation of technical expertise in labs worldwide for 30 years. No other manual has been so popular, or so influential.

Survival Math for Marketers is a simple and fun solution to the age-old problem of a lack of mathematical knowledge among marketing professionals. Many are former English, psychology, or science graduates who have become responsible for advertising, promotion, and sales in their organizations. Without a solid grounding in accounting, finance, mathematics, or economics, they often find themselves frustrated and confused by this unfamiliar world.. This book provides an introduction to the underlying mathematical concepts in marketing and management in terms accessible to students of all levels. Weiglin also explains the relevant non-mathematical issues, such as price sensitivity, product distribution, and sales estimates, and provides the tools necessary to fully understand the basics of each.. Presented in an irreverent, conversational style, this book includes numerous real-world examples and illustrations that gently introduce the reader to the important mathematical concepts behind marketing ...

They were then shown cards with different numbers of items on them, and asked to give a gesture that represented the number of items. The homesigners were accurate only up to the number 3. In addition, they had difficulty making a second row of checkers match a target row when there were more than three checkers in the target, despite the fact that this task did not require any comprehension or production of number gestures. Their difficulty in understanding large numbers therefore did not stem from an inability to communicate about large numbers, but rather from an inability to think about them, the researchers concluded ...

The katal (symbol: kat) is the SI unit of catalytic activity. It is a derived SI unit for expressing quantity values of catalytic activity of enzymes and other catalysts. Its use is recommended by the General Conference on Weights and Measures and other international organizations. It replaces the non-SI enzyme unit. Enzyme units are, however, still more commonly used than the katal in practice at present, especially in biochemistry. The katal is not used to express the rate of a reaction; that is expressed in moles per second. Rather, it is used to express catalytic activity which is a property of the catalyst. The katal is invariant of the measurement procedure, but the numerical quantity value is not and depends on the experimental conditions. Therefore, in order to define the quantity of a catalyst, the rate of conversion of a defined chemical reaction has to be specified, preferably of the first order, under strictly controlled conditions. One katal of trypsin, for example, is that amount ...

By looking at infant brain activity, researchers have found that babies as young as 3 months old are sensitive to differences in numerical quantity. Additionally, the scientists were able to see that babies process information about objects and numbers in different, dissociated parts of the brain, which is also the case in older children and in adults.

begingroup$ Thanks you for the reply. I just finished reading the documentation. I found out that I can use Chimera to see the percentage of identity, so one problem is solved. The main problem is of a different nature: lets say that I have the MSA from residue 1 to 100 of the query. I would like to have a tool that automatically computes the number of insertions, deletions etc... Some numerical quantities that I can use to see if the alignment is good and how much. Thank you. $\endgroup$ - wrong_path Dec 21 16 at 16:59 ...

This strategy book for primary maths teachers benefits students who are struggling with whole number computation in addition, subtraction, multiplication, and division. By analyzing student work for error patterns-such as on a diagnostic test-and then providing timely, specific, and meaningful intervention, repetition of those errors can be decreased.. Strategies for Teaching Whole Number Computation: Using Error Analysis for Intervention and Assessment provides a model of what can be used as part of a mathematics intervention programme. The material may be used by teachers as a programme to support direct classroom work with whole-number computation at whatever grade level intervention is needed to support these skills. By focusing on specific student error patterns and then providing pinpoint instruction based on sound pedagogical practices, this resource helps prevent as well as correct errors while providing guidance for teachers to teach in a meaningful way that promotes student ...

In physics the critical locus of the action functional, hence the solution space to the partial differential equations of motion is often called the shell, or the physical shell (the diffiety corresponding to the PDE of motion).. This terminology derives from the case of the free relativistic particle propagating in Minkowski spacetime, for which the space of solutions is the hyperbola of vectors whose Minkowski norm square is the mass of the particle. This hyperbola is naturally called the mass shell.. It is common to use the adjective on-shell for statements that apply after restriction to the shell, and off-shell for statements that apply generally.. For instance Noethers theorem gives for each symmetry of a local Lagrangian an on-shell conserved current, namely a differential form on spacetime, depending on the field configurations, which is closed (only, in general) if the given field configuration satisfies its equations of motion. Such a differential form which is closed even if the ...

Correlated neuronal activity and the flow of neural information. Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering. Nonlinear information transmission of the cerebral cortex. Conventional measure: cross-correlation. Slideshow 6735842 by alana-fulton

By assuming that the ideas proposed in the previous sections (mainly in General analysis>General analysis) are right, the Lorentz transformation would be invalid and also most of the calculations in the Theory of relativity. Note that the main intention of Einstein was precisely trying to explain certain physical phenomena (e.g., gravity) by applying the Lorentz transformation, a system of equations assumed to measure (relative variations) of space and time more accurately than Classical Mechanics ...

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Friedrich Everhard Anton Joseph Julius Freiherr von Mering was a German physiologist, physician, pharmacologist and experimental pathologist, who jointly discovered that removal of the pancreas in a dog produces the symptoms of diabetes. He worked with Oskar Minkowski, who recognized the resulting polyuria and tested the animals blood for glucose, an indicator of diabetes. This led Minkowski to propose that the pancreas secreted some antidiabetic substance. Though they did not isolate it, they wrote a paper* reporting this finding. Thus diabetes, which had long been held to be a kidney disease, was recognized as pancreatic disorder. Edward Sharpey-Schafer coined the term insulin in 1915, some years in advance of its eventual isolation. Insulin is a hormone synthesized in the pancreas that is important for the body to make proper use of sugar.«[* Archiv f r experimentelle Pathologie und Pharmakologie (26, 371; 1890). Note: A few sources give Dec or Sep as the birth month, but the Feb birth date ...

The European Physical Journal C (EPJ C) presents new and original research results in theoretical physics and experimental physics

On Mon, Oct 22, 2012 at 11:39 AM, Karel ,akk64 at quick.cz, wrote: , Shriramana Sharma napsal(a): , , On Mon, Oct 22, 2012 at 9:25 AM, xiolyxioly ,xiolyxioly at yahoo.com,mailto: ,, xiolyxioly at yahoo.com,, wrote: ,, ,, ftp://ftp.cs.technion.ac.il/**pub/misc/gershon/papers/ff_** ,, minkowski_sum.pdf.gz,ftp://ftp.cs.technion.ac.il/pub/misc/gershon/papers/ff_minkowski_sum.pdf.gz, ,, ,, ,, The above PDF seems to be corrupted. Can anyone confirm this? ,, ,, its ok for me (slow donwload ,btw) -- luigi -------------- next part -------------- An HTML attachment was scrubbed... URL: ,http://tug.org/pipermail/metapost/attachments/20121022/4a57873d/attachment.html ...

糖尿病自古代就已被發現，糖尿病被最早記載於西元一千五百年前的古埃及[30][31][31]。在中世紀以後在世界各地出現了多種不同的治療方法，但是，直到1900年左右糖尿病的發病機理才被科學實驗所證實。1889年，德國科學家約瑟夫·馮·梅林（Joseph von Mering）和俄裔德國科學家奧斯卡·明科夫斯基（Oskar Minkowski）發現摘除了胰腺的狗出現了糖尿病所有的症狀並在不久後死亡。1910年，愛德華·阿爾伯特·沙比-謝弗爵士提出患有糖尿病的病人是因為缺少一種胰腺製造的物質，他建議稱這種物質為「insulin」（源自拉丁文「insula」，原意為小島，中文譯為「胰島素」）。. 直到1921年，胰臟在新陳代謝中的內分泌作用以及胰島素是否真的存在才被進一步的研究所證實。1921年，弗雷德里克·格蘭特·班廷爵士和查爾斯·赫伯特·貝斯特（Charles Herbert ...

Are humans endowed with abstract representations of the surrounding world? In the domain of number, animals and preverbal infants have been shown to react to the cardinal values of sets presented in a variety of different stimulus formats, and this core number sense is thought to guide learning of numeric symbols and arithmetic in human children and adults (1-5). For example, by the age of 4.5 to 6 months, infants are able to discriminate between numbers differing in a 1:2 ratio (e.g., 16 vs. 32, 8 vs. 16, 4 vs. 8), when presented with arrays of dots (6, 7), sequences of sounds (8), or sequences of actions (9). In each of these experiments, however, infants were tested with only 1 type of stimulus, raising the question of the level of abstraction of these numeric representations.. From the early 1980s to present, several investigations have tested for numeric cross-modal matching in infants with mixed results. Although infants initially were reported to look longer at a set of objects that ...

When the responses are not arranged in one continuous string in the record, instruct Winsteps to skip over or ignore the gaps.. Example: The 18 item string is in columns 40 to 49 and then 53 to 60 of your data file. The person-id is in columns 11-30. Data look like:. xxxxxxxxxxPocahontas Smith, Jrxxxxxxxxx1001001110xxx11001110. Method a: Delete unwanted items in columns 50, 51, 52 using an item delete file, IDFILE=.. NAME1 =11 in original record. NAMLEN=20 length in original record. ITEM1 =40 in original record. NI =21 include deleted items. IDFILE =DEL5052 file of deletions. The contents of DEL5052 are:. 11 - 13 Cols 50-52 are items 11-13. Method b: Rescore items in columns 50, 51, 52 as missing values with RESCORE=.. NAME1 =11 in original record. NAMLEN=20. ITEM1 =40. NI =21 include rescored items. RESCORE=000000000011100000000 rescore 50-52. CODES =01 (the standard). NEWSCORE=XX non-numerical characters specify missing. Method c: Make the items form one continuous string in a new record ...

If a numerical use option is given default value zero, Inform doesnt compile the appropriate I6 Constant definition. If the option is used with a positive value, an incorrect Problem message is issued instead. This seems to be because the use option is being treated as if it were a non-numerical one (see example below ...

Sobel, D. M. (in press). Causality. In Bornstein, M. (Ed.), Sage Encyclopedia of Lifespan Human Development. Thousand Oaks, CA: Sage Publication Inc.. Sobel, D. M., & Letourneau, S. M. (in press-a). Preschoolers understanding of learning through play and instruction. Child Development.. Sobel, D. M., & Letourneau, S. (in press-b). Curiosity, exploration, and childrens understanding of learning. In M. Saylor, & P. Ganea (Eds.), Language and concept development from infancy through childhood: Motivation, cognition, and linguistic mechanisms of learning.. Erb, C., Moher, J., Song, J., & Sobel, D. M. (in press-a). Numerical cognition in action: Reaching behavior reveals numerical distance effects in 5- to 6-year-olds. Journal of Numerical Cognition.. Erb, C., Moher, J., Song, J., & Sobel, D. M. (in press-b). Reach tracking reveals dissociable processes underlying inhibitory control in 5- to 10-year-olds. Developmental Science. Legare, C. H., Sobel, D. M., & Callanan, M. (in press). Causal learning ...

Explaining and Exploring Mathematics is designed to help you teach key mathematical concepts in a fun and engaging way by developing the confidence that is vita

The consideration of deliberate versus automatic processing of numeric representations is important to math education, memory for numbers, and decision-making. In this commentary, we address the possible roles for numeric representations ...

In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance, chronology, and so on (e.g., third, tertiary). They differ from cardinal numerals, which represent quantity (e.g., three) and other types of numerals. In traditional grammar, all numerals, including ordinal numerals, are grouped into a separate part of speech (Latin: nomen numerale, hence, noun numeral in older English grammar books); however, in modern interpretations of English grammar, ordinal numerals are usually conflated with adjectives. Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced. For example: 5 November 1605 (pronounced the fifth of November ... ); November 5, 1605, (November (the) Fifth ...). When ...

While there is evidence of associations between spatial skills and mathematics, relatively few studies explore these associations in children aged 5-10 years. I will present findings from longitudinal and cross-sectional studies to highlight the importance of spatial skills as both longitudinal and concurrent predictors of mathematics. First, secondary data analysis of the Millennium Cohort Study indicates that spatial performance at both 5 and 7 years is a significant predictor of mathematics at age 7 (N = 12099). Second, cross-sectional findings from children aged 5-10 years (N=156), suggest that spatial skills explain 10-12% of the variation in standardised maths performance and approximate number sense, even after accounting for vocabulary skills. That is, spatial scaling was a significant predictor of mathematics for all age groups, while the role of mental rotation and mental folding varied with age. These findings have implications for the design of mathematics interventions customised ...

0068] The present description uses specific numerical values to quantify certain parameters relating to the invention, where the specific numerical values are not expressly part of a numerical range. It should be understood that each specific numerical value provided herein is to be construed as providing literal support for a broad, intermediate, and narrow range. The broad range associated with each specific numerical value is the numerical value plus and minus 60 percent of the numerical value, rounded to two significant digits. The intermediate range associated with each specific numerical value is the numerical value plus and minus 30 percent of the numerical value, rounded to two significant digits. The narrow range associated with each specific numerical value is the numerical value plus and minus 15 percent of the numerical value, rounded to two significant digits. For example, if the specification describes a specific temperature of 62° F., such a description provides literal support ...

Cambridge IGCSE Mathematics (0580) Past Papers. Updates. 25 October 2019 : Cambridge IGCSE Mathematics (0580) other resources and other quick revision resources are now available. Cambridge Primary Cambridge IGCSE Mathematics Other Resources. Cambridge IGCSE Mathematics (0580). An essential subject for all learners, Cambridge IGCSE Mathematics encourages the development of mathematical knowledge as a key life skill, and as a strong basis for more advanced study. The syllabus aims to build learners confidence by helping them develop competence and fluency with mathematical concepts, methods and skills, as well as a feel for numbers, patterns and relationships. The syllabus also places a strong emphasis on solving problems and presenting and interpreting results. Learners also gain an understanding of how to communicate and reason using mathematical concepts.. Please note: From 2017 Cambridge IGCSE Mathematics (0580) is not regulated for use in state schools in England. Cambridge IGCSE (9-1) ...

0023] Based on the development process event information thus collected, the rule execution component 104 compares conditions established by one or more executable verification rules (stored in the rules storage component 108) against the development process event information. Each executable verification rule, stored in the rule storage component 108, is representative of a software code development process to the extent that the conditions established by the executable verification rule establish those actions or events needed to be identified within the development process event information in order to confirm that a developer has (or has not) properly adhered to the software code development process. For example, a software code development process may require that a given code quality tool is to be used on a given portion of code (e.g., a module, sub-routine, etc.) subsequent to the most recent edits to that portion of code but before such code is checked into the configuration management ...

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Each book in the Number Sense series illustrates a basic math skill with a step-by-step approach, followed with lots of practice. Lessons are carefully designed to simultaneously build students mastery and self-confidence.. 10 Student books each cover a particular a particular concept. The Teachers Resource Guide and Answer Key provides a placement test, additional activities, answer keys, and CASAS correlation.. ...

Comparing and classifying functions of gene products are important in todays biomedical research. The semantic similarity derived from the Gene Ontology (GO) annotation has been regarded as one of the most widely used indicators for protein interaction. Among the various approaches proposed, those based on the vector space model are relatively simple, but their effectiveness is far from satisfying. We propose a Hierarchical Vector Space Model (HVSM) for computing semantic similarity between different genes or their products, which enhances the basic vector space model by introducing the relation between GO terms. Besides the directly annotated terms, HVSM also takes their ancestors and descendants related by

Nanofluids have increasingly drawn interest in recent years with their various applications in a number of fields. The method for the preparation of stable nanofluids is a key concern for extending the application of nanofluids. This study focuses on the effect of pH, dosage of surfactant (TX-100), and nanofluid concentration on the stability of a silica nanofluid. Particle size and zeta potential are two important factors to consider in evaluating the stability of the silica nanofluid. Results indicate that the stability of the silica nanofluid highly depends on pH, dosage of surfactant (TX-100), and nanofluid concentration. On the basis of these experiments, the best conditions for the preparation of a silica nanofluid are 0.1 wt. % for the concentration of silica nanoparticles and TX-100 and 10 for pH. A transparent and stable silica nanofluid can thus be obtained.

By Elder Lawrence Nelson. There are many questions concerning the 144,000. Some can be answered others cannot. For instance, is the 144,000 a literal or a symbolic number? Are the 144,000 sealed before or after the latter rain. Will the 144,00 convert a great multitude to Gods truth? Why will the 144,000 be translated without dying? What are the character developments that are necessary to become a part of the 144,000?. In this presentation we will not dabble into speculation nor will we claim any new light. But we will search for what has been revealed in the Bible and the Spirit of Prophecy. First let us seek for divine guidance. Oh loving Father, we believe the end to be very near. Through Thy Holy Spirit Thou hast revealed knowledge of a very special group of saints, described as the 144,000, who are to reveal to the universe that Thy eternal law can be kept, when a person joins his humanity with the power of divinity. Therefore, these 144,000 individuals have fully experienced ...

Mathematics Awareness Month is held each year in April. Its goal is to increase public understanding of and appreciation for mathematics. Mathematics Awareness Month began in 1986 as Mathematics Awareness Week with a proclamation by President Ronald Reagan, who said in part:. Despite the increasing importance of mathematics to the progress of our economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system. Yet the application of mathematics is indispensable in such diverse fields as medicine, computer sciences, space exploration, the skilled trades, business, defense, and government. To help encourage the study and utilization of mathematics, it is appropriate that all Americans be reminded of the importance of this basic branch of science to our daily lives.. In 1986 activities concentrated on national-level events, such as opening an exhibit at the Smithsonian Institution on mathematics and hosting a Capitol Hill reception. Since ...

Abstract: We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of dimensions. The key is the gauging of the Sp(2) duality symmetry that treats position and momentum (x,p) as a doublet in phase space. As a consequence of the gauging, the Minkowski space-time vectors (x^\mu, p^\mu) get enlarged by one additional space-like and one additional time-like dimensions to (x^M,p^M). A manifest global symmetry SO(d,2) rotates (x^M,p^M) like d+2 dimensional vectors. The SO(d,2) symmetry of the parent theory may be interpreted as the familiar conformal symmetry of quantum field theory in Minkowski spacetime in one gauge, or as the dynamical symmetry of a totally different physical system in another gauge. Thanks to the gauge symmetry, the theory permits various choices of ``time which correspond to different looking Hamiltonians, ...

APC 199 / MAT 199 (QR) Graded A-F, P/D/F, Audit. Math Alive. Ian M. Griffiths. Adam W. Marcus. Mathematics has profoundly changed our world, from the way we communicate with each other and listen to music, to banking and computers. This course is designed for those without college mathematics who want to understand the mathematical concepts behind important modern applications. The course consists of individual modules, each focusing on a particular application (e.g., digital music, sending secure emails, and using statistics to explain, or hide, facts). The emphasis is on ideas, not on sophisticated mathematical techniques, but there will be substantial problem-set requirements. Students will learn by doing simple examples.. APC 350 / CEE 350 / MAT 322 (QR) Graded A-F, P/D/F, Audit. Introduction to Differential Equations. Staff. This course will introduce the basic theory, models and techniques for ordinary and partial differential equations. Emphasis will be placed on the connection with other ...

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time - so-called axiomatic approaches -, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to indicate the passage of time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time.. ...

In mathematics we can easily get the complete study of the various important topics like quality, structure, space as well as change. This is one of the interesting topics for the students that provides the complete information about the addition, subtraction, multiplications as well as division. Mathematics is the pillar of the students education because we need the mathematics in our daily life to solve various problems. Students get various tasks in mathematics to score the best marks. They received the various kinds of mathematics assignments, worksheets, homework sheets etc. They need the best assistance and guidance to complete the mathematics tasks. We have best team of mathematics experts and each and every expert has good command in the mathematics theories. They know the best way to write the solutions in the Math subject. They provide the each and every solution for online math assessment writing service according to the students subject requirements. ...

Some activities will be delivered face-to-face and others online, following a blended learning approach. Our mathematics degrees offer both in-depth analysis of mathematical concepts and methods as well as applications to many diverse areas such as the motion of fluids, modelling of financial products or modelling epidemics, mostly using differential equations and data analysis. The first year of the programme consists of compulsory course units which provide the background needed for later courses. During the second year you begin to choose which aspects of mathematics you wish to pursue, and includes a group project on a choice of topics. In Year 3 you have an option of taking an individual project in an area that suits your interests in addition to choosing from a wide range of options. Each year builds on your mathematical skills and understanding, giving you the knowledge and confidence towards becoming a graduate mathematician. A typical week in your first year of study will comprise about ...

The program is ideally suited for: a) adults who want to work with and help children learn the language of mathematics; b) current teachers who wish to add mathematics as a new subject area; c) those wishing to become National Board Certified mathematics teachers, mathematics coaches, mathematics specialists, and mathematics coordinators/directors; d) non-mathematics majors who wish to earn a highly qualified title to their academic experience to enhance and broaden their teaching careers; and e) career changers who wish to pursue a more meaningful career in working with children. Teachers of mathematics at all school levels remain in high demand nationally; and individuals coming from careers in business, engineering, finance and the military are often very successful in relating the importance of the mathematics they teach to the real world they have worked in for many years.. ...

The former Mathematics 1150 and Mathematics 1151 were courses designed specifically for students who intended to graduate with a degree in Primary or Elementary Education. No other students can receive credit for these courses. These courses are not acceptable as alternatives to any other First Year Mathematics course listed in this calendar. Students who have received credit for Education 125 or Mathematics 115/125 cannot receive additional credit for the former Mathematics 1150 or Mathematics 1151 or the current Mathematics 1050 or Mathematics 1051. ...

Is a Mathematics Degree Right for You? An online bachelors degree in mathematics teaches students advanced mathematical concepts, as well as how to think analytically and solve problems at increasing levels of complexity. Math students apply mathematical principles to find solutions to problems in a variety of applied fields, such as computer science, engineering, or ...

By Reta McDermott. Georgios Petridis, University of Rochester, will present, Two Questions in Arithmetic Combinatorics as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Tuesday, Feb. 2, in 122 Cardwell Hall.. The abstract for the lecture is: Petridis will present two theorems of number-theoretic nature where combinatorial arguments have been particularly effective. Both theorems are related to so-called inverse results of the following kind: Suppose an arithmetic progression satisfies a property P and A is a set of integers which nearly satisfies P, then A must nearly be an arithmetic progression.. The first concerns cardinality questions on sumsets - or Minkowski sums of sets - in a commutative group. It asserts that if the number of pairwise sums formed by the elements of a set is small, then so is the set of h-fold sums.. The second concerns exponential sums of finite sets of integers. It says, roughly speaking, that the L^1-norm of the exponential sum of a ...

Details fundamental concepts and techniques of non-numerical analysis in computer programming, and discusses mathematical linguistics, language translation programming and basic, seminumerical, combinatorial, and syntactical algorithms.

Discrete mathematics and probability theory provide the foundation for many algorithms, concepts, and techniques in the field of Electrical Engineering and Computer Sciences. For example, computer hardware is based on Boolean logic. Induction is closely tied to recursion and is widely used, along with other proof techniques, in theoretical arguments that are critical to understanding the foundations of many things, ranging from algorithms to control, learning, signal processing, communication, and artificial intelligence. Similarly for modular arithmetic and probability theory. CS70 will introduce you to these and other mathematical concepts. By the end of the semester, you should have a firm grasp of the theoretical basis of these concepts and their applications to general mathematical problems. In addition, you will learn how they apply to specific, important problems in the field of EECS. This course is divided into two main units, each of which will introduce you to a particular mathematical ...

InfoMC is a fast-paced, growing company which provides collaborative healthcare process management technology to improve the quality, cost and value of care. At InfoMC, we believe that it is possible to directly improve care through technology, and provide state of the art capabilities that improve care coordination of chronic illness and wellness. Our solution provides process management software to the commercial and public sector markets, for use in managed behavioral healthcare, disease management, and EAP/Work-Life. Our member centric approach offers integrated technology solutions that enhance interaction between payers, providers and consumers.. The SQL Performance Engineer is responsible for the performance and reliability of ETL processes across InfoMC products and loud-based implementations. You will increase the performance of ETL processes through understanding the architecture, evaluating the design approach, making recommendations and gaining approval for design, data, process, and ...

Implementation science involves controlled research, in this case a cluster randomized delayed intervention trial, but that is pragmatic and thus more directly relevant to real-world settings [9, 61, 62]. By engaging all of the stakeholders on the front-end about the importance of healthcare process and outcome metrics for documenting healthcare quality, the results should be more directly usable by both primary care and potential funding and reimbursement agencies. This is especially so when including practical measures that can be embedded into clinical systems [63], applying a feasible and flexible intervention that provides direct feedback based on these practical measures, and assessing outcomes of importance to patient, provider, and policy maker stakeholders, including costs.. This type of science is needed because evidence alone is not enough [64, 65]. In addition to the best evidence, as in this case recommendations for primary care-based health behavior and psychosocial counseling, ...

How Does Number Sense Work? Numbers derive meaning from their positions relative to one another. It is for this reason that number sense is best measured by indexing a persons accuracy in comparing sets. The Approximate Number System (ANS) evolved to do just that, but in an approximate fashion. For example, Neider and Miller (2003)…

Page contains details about carbon nanotube/water nanofluid . It has composition images, properties, Characterization methods, synthesis, applications and reference articles : nano.nature.com

Outpatient services, like CT and MRI scans, X-rays, and lab tests such as blood work and urine tests, can be a time-consuming process for most people.. There you are, at your doctors office, being told you have to go somewhere else for a test. Time is precious. So, we dont want to waste yours. We understand that life is busy, so we aim to make this part of your healthcare process as easy as possible for you and your family.. Theres no calling for hours for an appointment only to be told you cant be seen for a week. Or, getting to your testing site and being told you have to wait…even more waiting.. If your test is covered under your insurance (most private insurance carriers require pre-authorization before testing), we can see you the same day.. ...

Major: Mathematics and Applied Mathematics. Duration of Study: 4 Years. Core Courses:. Mathematical Analysis. Advanced Algebra. Analytic Geometry. Complex Variable Function. Ordinary Differential Equations. Modern Algebra. Real Variable Function. Probability and Mathematical Statistics. Mathematics Education. Visual C++ Programming. University Physics. Elementary Mathematics. Higher Geometry. Elementary Number Theory. Combinatorial Mathematics. Mathematical Modeling. Mathematics Experiment. Topology. Functional Analysis. Degree Awarded: Bachelor of Science. ...

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Adults who do believe that zero is even can nevertheless be unfamiliar with thinking of it as even, enough so to measurably slow them down in a reaction time experiment. Stanislas Dehaene, a pioneer in the field of numerical cognition, led a series of such experiments in the early 1990s. A numeral or a number word is flashed to the subject on a monitor, and a computer records the time it takes the subject to push one of two buttons to identify the number as odd or even. The results showed that 0 was slower to process than other even numbers. Some variations of the experiment found delays as long as 60 milliseconds or about 10% of the average reaction time-a small difference but a significant one.[55]. Dehaenes experiments were not designed specifically to investigate 0 but to compare competing models of how parity information is processed and extracted. The most specific model, the mental calculation hypothesis, suggests that reactions to 0 should be fast; 0 is a small number, and it is easy to ...

Indexing and Representation: The Vector Space Model. Document represented by a vector of terms Words (or word stems) Phrases (e.g. computer science) Removes words on

Pre-K - 3rd Grade. PRIDEs one-on-one multisensory math program is for students who are struggling with basic math skills. At PRIDE, we build an understanding of mathematical concepts by using visual learning tools, game-playing and exercises that engage all the senses. Our students gain a deep understanding of numbers and learn to master computation and problem solving. We teach mathematics through a structured, systematic, cumulative, repetitive and step-by-step math program that targets students with learning differences, short- term memory deficits and dyscalculia.. Features of PRIDEs Math Skills Program:. ...

Business Technology colleges educate the science of Information Technology as applied to business. Enterprise Technology college students are taught find out how to develop, restore and maintain communications pathways for companies, together with computers, software program, networking, Internet purposes, and telecommunications. CSE 351: The Hardware/software Interface Examines key computational abstraction ranges below modern high-level languages; number representation, assembly language, introduction to C, memory management, the operating-system process mannequin, excessive-stage machine structure including the reminiscence hierarchy, and the way excessive-level languages are applied. Prerequisite: CSE 143.. This superior and intelligent contains some instrumentation mounted on the helicopter and some on the bottom. These instrumentations monitor the place, course, orientation, velocity, acceleration and spin of the helicopter in a number of dimensions. A floor-based computer crunches the ...

Ms. Hedrington is in her 16th year of teaching secondary school mathematics and her 10th year of teaching in Malden. She works hard to develop lessons that promote higher order thinking skills and that encourage her students to explore mathematical concepts, and she also teaches her students whole selves. She takes time for commercial breaks during her math lessons to discuss issues that are affecting the school or larger community. She supported students when they spoke to the School Committee to address racist incidents, and she has delivered professional development presentations about trauma-informed classrooms. One year, she created the League of Distinguished Gentleman to promote participants engagement and growth in their community and school ...

In the latest episode in this series I talked about hypothetical compile-time rewriting facilities that would be used to turn our intermediate representation of control-flow driven code using our Control Library into efficient IL code. In a somewhat hand-waving way I communicated the fairly trivial nature of such a translation but as I dont want to hold any information back, lets have a look at it today.. But first, refresh your mind on what were doing here. Starting from C# code, were in the midst of proving we can compile away control flow concepts as a first class citizen in the language and replace them by library calls. Using method calls for such concepts allows for extensibility, e.g. overloading the meaning of if when applied to a certain operand (instead of requiring a more generally applicable implicit conversion to Boolean for example). After all, this is more of an academic exercise at this point, but definitely worth the brain cycles.. Once we end up with (control flow ...

On Tuesday, March 15, there will be no tutoring at Learning Centers because of a scheduled early release day. Instead of tutoring, join us for our second Upper School Math Workshop this school year. Once again, this interactive workshop that will teach new and experienced tutors the style and methods of the Math in Focus curriculum. Participants will learn to engage Upper School students in mathematical concepts, build confidence, and develop problem solving skills. This session will cover what Math in Focus implementation looks like in Upper School classrooms, review strategies and student work from the curriculum, and engage tutors in problems from the Math in Focus 6th, 7th, and 8th grade books. This session will cover new concepts that were not covered in the fall session and will be relevant for both new and experienced Upper School tutors.. Sign up online or email Kasey to RSVP.. Lead by ...

This course builds upon IPTMs Event Data Recorder (EDR) Use in Traffic Crash Reconstruction - Level I by teaching you how to apply mathematical concepts to your EDR-based reconstructions. We will begin by reviewing the math and physics concepts necessary to analyze EDR data in more complex non-central collisions. Topics such as the Law of Cosines; the Law of Sines; the concept of area under the curve; vector arithmetic; momentum; closing velocity; change in velocity relationships; and the First Law of Thermodynamics (aka the Conservation of Energy) will be discussed in detail. You will learn how each of these can be used in your reconstruction. Actual EDR reports from a variety of collisions will be utilized to show you how to determine all the values necessary for a complete reconstruction. Projects and problem sets have been designed to reinforce the materials presented during lectures and will provide you with the tools you will need to complete actual reconstructions. Topics include:

Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its mother tongue, and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Math · Pre-algebra · Exponents, radicals, and scientific notation. It always helps me to see a lot of examples of something so I figured it wouldnt hurt to do more scientific notation examples. So Im just going to write a bunch of numbers and then write them in scientific notation. And hopefully thisll cover almost every case youll.. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to.. Scootle provides Australian teachers with access to more than 20,000 quality-assured digital learning resources aligned to the Australian Curriculum.. Addition and Subtraction with Scientific Notation (like exponents) Addition and Subtraction with Scientific Notation Worksheet - like exponents.docx 48.1 KB.. math. We make the study of numbers easy as 1,2,3. From basic equations to advanced calculus, we explain mathematical concepts and help you ace your next ...

Each poster from this set of 10 features a different mathematical concept and asks a question to kick-start students thinking. The posters provide an engaging and thought-provoking visual reference for your students and will support you and your colleagues in your delivery of GCSEs ...

3 - 7 years. These bilingual books focus on counting and will help children rapidly expand their ability to understand mathematical concepts. Set of 4 ...

Performance expectations in this DCI help high-school students answer the questions: How do organisms obtain and use energy they need to live and grow? How do matter and energy move through ecosystems? Students can construct explanations for the role of energy in the cycling of matter in organisms and ecosystems. They can apply mathematical concepts to develop evidence to support explanations of the interactions of photosynthesis and cellular respiration, and develop models to communicate these explanations. They can relate the nature of science to how explanations may change in light of new evidence and implications for our understanding of the tentative nature of science. Students understand organisms interactions with each other and with their physical environment, how organisms obtain resources, change the environment, and how these changes affect both organisms and ecosystems. ...

Picking up a polished sample of ulexite, one of us thought that the parallel fibrous microstructure of this mineral was not unlike the matchstick morphology of columnar thin films shown to him by the other some years earlier. A telephone conversation led to a brainstorming session from which the mathematical concept of sculptured thin films--STFs for short--began to emerge. That was in 1992. A 1966 paper of J.M. Niuewenhuizen and H.B. Haanstra provided the initial morphological bedrock, which was brought into optical focus by a 1989 paper of T. Motohiro and Y. Taga. Four years after our initial presentation in 1994 at a conference in France, and three years after our definitive presentation of the STF concept at Penn State, we stumbled upon a 1959 paper of N.O. Young and J. Kowal that provided an antecedent confirming the STF concept, which ties morphology and optics together. Imagine a mass of isolated parallel matchsticks, all stuck on their lower ends to a glassy substrate. This arrangement ...

Picking up a polished sample of ulexite, one of us thought that the parallel fibrous microstructure of this mineral was not unlike the matchstick morphology of columnar thin films shown to him by the other some years earlier. A telephone conversation led to a brainstorming session from which the mathematical concept of sculptured thin films--STFs for short--began to emerge. That was in 1992. A 1966 paper of J.M. Niuewenhuizen and H.B. Haanstra provided the initial morphological bedrock, which was brought into optical focus by a 1989 paper of T. Motohiro and Y. Taga. Four years after our initial presentation in 1994 at a conference in France, and three years after our definitive presentation of the STF concept at Penn State, we stumbled upon a 1959 paper of N.O. Young and J. Kowal that provided an antecedent confirming the STF concept, which ties morphology and optics together. Imagine a mass of isolated parallel matchsticks, all stuck on their lower ends to a glassy substrate. This arrangement ...