Use Of Mathematical Expressions Research Articles

Parameters of the Planting Machine for Sugar Beet Sets

Abstract For seed production of sugar and fodder beet, the creation of machines and working bodies for planting root crops on testes and pollinators is of current importance. It was found out that the seed-and-water production was spreading with the use of “schteklings” [sugar beet roots]. In the countries with minus temperatures between the vegetation seasons it is necessary to dig out beets and plant them again at the beginning of the vegetation season. Advantages and disadvantages of machines and apparatus for disembarking the schteklings were determined. Under the conditions of applicability, we chose a design scheme and a type of landing gear. With the use of mathematical expressions and standards for the labor intensity of the operator of the above machine, the optimal parameters of its planting apparatus were determined. It was determined that the work of the operator of the schteklings planting machine’s stem will meet the safety standards for the intensity of labor if the planting unit of this machine is a rotor-type. It should be equipped with planting cones and a charging device, a conveyor type. The number of holders of landing cones should be 6-8 pieces, and the radius of the rotor is within the range of 0.344 ... 0.382 m. Such a scheme, type and parameters of the landing gear will allow operators to work at the speed of the planter of up to 1.2 m·s−1.

Modeling discrete and continuous entities with fractions and decimals.

When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers.

Extracting Textual Descriptions of Mathematical Expressions in Scientific Papers

Mathematical concepts and formulations play a fundamental role in many scientific domains. As such, the use of mathematical expressions represents a promising method of interlinking scientific papers. The purpose of this study is to provide guidelines for annotating and detecting natural language descriptions of mathematical expressions, enabling the semantic enrichment of mathematical information in scientific papers. Under the proposed approach, we first manually annotate descriptions of mathematical expressions and assess the coverage of several types of textual span: fixed context window, apposition, minimal noun phrases, and noun phrases. We then developed a method for automatic description extraction, whereby the problem was formulated as a binary classification by pairing each mathematical expression with its description candidates and classifying the pairs as correct or incorrect. Support vector machines (SVMs) with several different features were developed and evaluated for the classification task. Experimental results showed that an SVM model that uses all noun phrases delivers the best performance, achieving an F1-score of 62.25% against the 41.47% of the baseline (nearest noun) method.

Simple object oriented designed computer algebra system

Computer Algebra System (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a typical CAS is manipulation of mathematical expressions in symbolic forms. The expressions manipulated by CAS normally include polynomials in multiple variables, standard trigonometric and exponential functions, various special functions for example gamma, zeta, Bessel, etc. and also arbitrary functions like derivatives, integrals, sums, and products of expressions. Our implementation of a CAS tool provides an object oriented design framework. The system is portable to other platforms and highly scalable. The other key features include a very simple and interactive user GUI support for a formula editor, making it a self contained system, additionally the formula editor provides a real-time syntax checking for expressions.

Using pharmacokinetic/pharmacodynamic modelling in safety pharmacology to better define safety margins: a regional workshop of the Safety Pharmacology Society

This meeting was convened to encourage the incorporation of empirical and mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) modelling into safety pharmacology to improve the predictability of nonclinical investigations for human outcomes. These technologies make use of mathematical expressions relating measured variables to derive essential parameters for describing responses and predicting the behaviour of biological systems to a drug. Hence, empirical PK/PD modelling is intended to define the in vivo interrelationship between three basic entities: time; drug concentrations; and drug effects. The most widely applied equation relating drug bioresponses to plasma concentrations is the Hill sigmoidal Emax model, which allows the calculation of drug potency (EC50) and intrinsic activity (Emax). However, since the latter parameters depend on attributes of the drug and on the biological system itself, this approach can fail to accurately foretell drug concentration–effect behaviour, particularly between species. A particular phenomenon of PK/PD analysis is hysteresis, which refers to the delay of the bioresponse time–course with respect to exposure time–course, as this provides valuable information on the direct or indirect nature of the drug mechanism of action. The application of these concepts to the examination of the QT interval prolongation produced by dofetilide was discussed. A development surmounting the limitations of empirical PK/PD models is mechanism-based PK/PD modelling because its toolkits integrate specific mathematical expressions replicating the drug (e.g., affinity, intrinsic efficacy), and the physiological system (e.g., nonlinear, time-dependent, transduction processes), properties that play a crucial role in the cascade of biological events culminating in bioresponses. The usefulness of this approach was illustrated by a thorough analysis of nonclinical respiratory depressant and antinociceptive data on buprenorphine and fentanyl for successfully predicting the human safety and efficacy of these analgesic agents. Thus, PK/PD models can be viewed as in silico clones of drug and biological system activities that provide high-level knowledge that can avoid inappropriate attrition, and hasten the progress, of novel drugs, along the entire critical path of pharmaceutical development.

Lifetime total radiation risk of cosmonauts for orbital and interplanetary flights

This paper presents results of calculations of total radiation risk for cosmonauts over their lifetimes and assessments of possible shortening of life expectancy on the basis of generalized doses calculated for cosmonauts after a long term interplanetary and orbital space missions on “MIR” station and International space station with the use of mathematical expressions coming from a model of change mortality rate of mammals after irradiation. Tumor risk assessments for cosmonauts over lifetime after flights are also given. Dependences of the delayed radiation consequences mentioned above on flight duration, spacecraft shielding thicknesses, solar activity and cosmonauts' age are analyzed.

Rationales in the Development of Dissolution Testing for Solid Oral Dosage Forms - An Industrial, Biopharmaceutical and Regulatory Perspective

AbstractThis article encompasses various concepts, methods and procedures used in the dissolution testing of solid oral dosage forms. Regulatory considerations during the dissolution method development, including the application of new Biopharmaceutics Classification System have been discussed. The use of mathematical expressions in comparing dissolution profiles and setting Q value specifications form an imperative part of the discussion. The importance of these during developmental stages has been highlighted. Dissolution testing parameters that include choice of medium, apparatus and agitation speed have been recommended based on the recent FDA guidance. A biopharmaceutical perspective to the selection of media has also been presented.

The When, the How and the Why of Mathematical Expression in the History of Economic Analysis

In writings about the history of the use of mathematical expression in economics, there seems to be a conviction that the movement towards its current flowering was cumulative, inevitable, and indeed, natural. While, such notions are widely held among practicing economists, I want to argue that they are not historically valid. The deployment of mathematical expression in economic discourse enjoyed neither an inexorable nor unhindered progress, but rather was characterized by two primary ruptures in the history of economic thought, episodes marking the inflection points in the rise of mathematical discourse. The main reason for such a disjointed narrative is that, in the evolution of economic thought, most of the participants were not convinced that the subject matter intrinsically demanded mathematical expression, while those so enamored experienced great difficulty in creating a community which could agree upon a formalism which was thought to be well-suited to economic issues.

Mode of action and the assessment of chemical hazards in the presence of limited data: use of structure-activity relationships (SAR) under TSCA, Section 5.

Section 5 of the Toxic Substances Control Act (TSCA) requires that manufacturers and importers of new chemicals must submit a Premanufacture Notification (PMN) to the U.S. Environmental Protection Agency 90 days before they intend to commence manufacture or import. Certain information such as chemical identity, uses, etc., must be included in the notification. The submission of test data on the new substance, however, is not required, although any available health and environmental information must be provided. Nonetheless, over half of all PMNs submitted to the agency do not contain any test data; because PMN chemicals are new, no test data is generally available in the scientific literature. Given this situation, EPA has had to develop techniques for hazard assessment that can be used in the presence of limited test data. EPA's approach has been termed "structure-activity relationships" (SAR) and involves three major components: the first is critical evaluation and interpretation of available toxicity data on the chemical; the second component involves evaluation of test data available on analogous substances and/or potential metabolites; and the third component involves the use of mathematical expressions for biological activity known as "quantitative structure-activity relationships" (QSARs). At present, the use of QSARs is limited to estimating physical chemical properties, environmental toxicity, and bioconcentration factors. An important overarching element in EPA's approach is the experience and judgment of scientific assessors in interpreting and integrating the available data and information. Examples are provided that illustrate EPA's approach to hazard assessment for PMN chemicals.

The growth and structure of gold and silver deposits formed by evaporation inside an electron microscope

Abstract Single crystal films of gold and silver have been prepared by evaporation onto molybdenum disulphide inside an electron microscope, in order to allow direct observation of the mode of growth. These experiments provide detailed information on the remarkable liquid-like behaviour of the coalescence of the initial metal nuclei, and the mode of formation of a continuous film. In addition, re-orientation and re-crystallization phenomena are observed, and these effects are shown to be predominant during the growth of a polycrystal-line deposit on an amorphous substrate. The various possible mechanisms for the liquid-like behaviour are considered, by making use of mathematical expressions initially derived to describe the sintering of spherical particles. A semi-quantitative explanation of the liquid-like behaviour is given in terms of the surface diffusion of the metal atoms over the metal islands, the driving force for the mass transfer being the associated reduction in surface energy.

Sociology and obligations of interpretation

This short paper submits generalizations about the interpretative use in certain contexts of referential verbal language. I am not concerned here with mathematical uses of expressions, nor with discussions on the use of mathematics as a model for logic as against the traditional terminol ogy of logic. It may or may not be practicable to develop the use of mathematical expressions in the qualitative and quantitative formulation of social phenomena. I do not know enough of the experiments which I believe are taking place. The emphasis is on the verbal responsibilities of social scientists in writing to one another, and on their obligations (which they share with others) to influence within their communities (a) a more realistic dissem ination of information by people entrusted with a public communication function, and (b) a universally more intelligent handling of words through recognition that (1) ambiguity is an inevitable and basic aspect of language, (2) meaning is not the quality of a word but its function, (3) in the structure of our languages 'we preserve delusional, psycho pathological factors'. It is submitted that the interpretation of words, and of complexes of words, is only possible by a studied reference to elements in the conjoint individual experience of writer and reader, or of speaker and listener. By the 'experience' of each of us I mean both the universe as apprehended by us and the subjective fact of apprehending it. The three levels of experience that must be related are sense experience, perceptual experience, and conceptual experience (involving interests, attitudes and motives). The pragmatic approach to problems of interpretation, with equal stress on the psychological and logical factors involved, is therefore necessary and ineradicable. The purely logical approach to verbal interpretation is unrealistic, and is of little practical use. Because they are akin to the absolute logical approach, I would also sound a note of caution about a too narrow application of some of the theories of cybernetics. There is surely danger here of what has been called 'the thermometer' view of man

Magnetic Recording with AC Bias

The function of alternating-current (ac) bias in magnetic recording is analyzed in a manner similar to that used to explain amplitude modulation. Certain simplifying assumptions are made to facilitate manipulation of mathematical expressions. The analytical results are compared with experimental observations of harmonic distortion, amplitude of fundamental, spurious recorded frequencies, frequency response, difficulty of erasure, and the like.