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The cur­rent pan­demic sit­u­a­tion caused by COVID-19 has affected human life globally at the economic, social and men­tal health levels. Specifically, ten­sion has led an in­creas­ing number of people to the consumption of various types of to­bacco.. In this work, an existing tobacco smoking model with a specific class of tobacco snuffing is converted into a fractional order as many applications of fractional derivatives to recall the past history of smokers in the present model. For this purpose, we use fractional derivative in Caputo sense to study the model in the form of fractional order. Then Positivity, boundness and dynamics of the proposed model are investigated. For numerical results, the generalized “Adams–Bashforth–Moulton Method (GABMM) and fourth-order Runge–Kutta (RK4) method” are used to solve the proposed model and Matlab numerical computing environment is the current software used.

Recent advances in execution environments for JavaScript and WebAssembly that run on a broad range of devices, from workstations and mobile phones to IoT devices, provide new opportunities for portable and web-based numerical computing. Indeed, numerous numerical libraries and applications are emerging on the web, including Tensorflow.js, JSMapReduce, and the NLG Protein Viewer. This paper evaluates the current performance of numerical computing on the web, including both JavaScript and WebAssembly, over a wide range of devices from workstations to IoT devices. We developed a new benchmarking approach, which allowed us to perform centralized benchmarking, including benchmarking on mobile and IoT devices. Using this approach we performed four performance studies using the Ostrich benchmark suite, a collection of numerical programs representing the numerical dwarf categories identified by Colella. We studied the performance evolution of JavaScript, the relative performance of WebAssembly, the performance of server-side Node.js, and a comprehensive performance showdown for a wide range of devices.

It is a commonly held view that Java's lack of support for true rectangular arrays is one of the main impediments to its widespread applicability in numerical computing. In a recent work, we have proposed efficient implementation of linear algebra kernels such as matrix-vector and matrix-matrix multiplications by formulating arithmetic calculations in terms of diagonals, and thereby giving an orientation-neutral (column-/row-major layout) computational scheme. Diagonally-structured computation is especially suitable for banded matrices. In this paper we show that, using our diagonal framework, Java native arrays can yield superior computational performance. We present two alternative implementations for matrix-matrix multiplication operation in Java. The results from numerical testing demonstrate the advantage of our proposed methods.

We present an easy-to-use, Python-based framework that allows a researcher to automate their computational simulations. In particular the framework facilitates assembling several long-running computations and producing various plots from the data produced by these computations. The framework makes it possible to reproduce every figure made for a publication with a single command. It also allows one to distribute the computations across a network of computers. The framework has been used to write research papers in numerical computing. This paper discusses the design of the framework, and the benefits of using it. The ideas presented are general and should help researchers organize their computations for better reproducibility.

The Python programming language, combined with the numerical computing library NumPy and the scientific computing library SciPy, has become the de facto standard for scientific computing in a variety of fields. This popularity is mainly due to the ease with which a Python program can be written and executed (easy syntax, dynamical typing, no compilation etc.), coupled with the existence of a large number of specialized third-party libraries that aim to lift all the limitations of the raw Python language. NumPy introduces vector programming, improving execution speeds, whereas SciPy brings a wealth of highly optimized and reliable scientific functions. There are cases, however, where vector programming alone is not sufficient to reach optimal performance. This issue is addressed with dedicated compilers that aim to translate Python code into native and statically typed code with support for the multi-core architectures of modern processors. In the present article it is shown how these approaches can be efficiently used to tackle different problems, with increasing complexity, that are relevant to crystallography: the 2D Laue function, scattering from a strained 2D crystal, scattering from 3D nanocrystals and, finally, diffraction from films and multilayers. For each case, detailed implementations and explanations of the functioning of the algorithms are provided. Different Python compilers (namely NumExpr, Numba, Pythran and Cython) are used to improve performance and are benchmarked against state-of-the-art NumPy implementations. All examples are also provided as commented and didactic Python (Jupyter) notebooks that can be used as starting points for crystallographers curious to enter the Python ecosystem or wishing to accelerate their existing codes.

Despite their widespread use, implementations of numerical computing algorithms are generally tested manually with fuzzily defined thresholds determining success or failure. Modern software testing methods, such as automated regression testing, are difficult to apply because both test oracles and algorithm output are approximate. Based on the observation that high accuracy numerical algorithms appear to be fragile by design to errors in their parameters, we propose to compare the error of target implementations to mutated versions of themselves with the expectation that the mutants will suffer degraded accuracy. We test the idea on Matlab implementations of some basic numerical algorithms, and find that most mutants are worse while the few which are better show a distinctive pattern of mutation.

This paper reports on the results of a developing Python-MATLAB interface program to implement optical wireless communication system simulation. We implement Python interface for entering input values and simulation environment variables for MATLAB. We operate MATLAB to numerical computing process about communication system simulation to generate a signal, to approximate channel characteristics and to recover the signal. Python passes input data and environment variables to MATLAB and displays output data and graphs from the simulation after MATLAB numerical computing.

Vectors, matrices, and arrays of higher dimensions are essential tools in numerical computing. When a computation must be repeated for a set of input values, it is natural and advantageous to represent the data as arrays and the computation in terms of array operations. Computations that are formulated this way are said to be vectorized. Many modern processors provide instructions that operate on arrays. These are also known as vectorized operations, but here vectorized refers to high-level array-based operations, regardless of how they are implemented at the processor level. Vectorized computing eliminates the need for many explicit loops over the array elements by applying batch operations on the array data. The result is concise and more maintainable code, and it enables delegating the implementation of (for example, elementwise) array operations to more efficient low-level libraries. Vectorized computations can therefore be significantly faster than sequential element-by-element computations. This is particularly important in an interpreted language such as Python, where looping over arrays element-by-element entails a significant performance overhead.

Open Beagle is a well-known framework for evolutionary computation. A miniature version of it is Beagle Puppy. Puppy allows running genetic programming (GP). Moreover, given its small code, it is amenable for learning about the implementation of a typical GP system. Both Open Beagle and Beagle Puppy are written in C++. In the past, we implemented Puppy in Java. In this paper, we reporat our work about wrapping Beagle puppy for Octave. Octave is a high-level numerical computing environment that is particularly suitable for scientific research. In wrapping Puppy for Octave, our hope was to retain the computational efficiency of Java, while making the aforementioned GP system more user-friendly.

Recent advances in execution environments for JavaScript and WebAssembly that run on a broad range of devices, from workstations and mobile phones to IoT devices, provide new opportunities for portable and web-based numerical computing. Indeed, numerous numerical libraries and applications are emerging on the web, including Tensorflow.js, JSMapReduce, and the NLG Protein Viewer. This paper evaluates the current performance of numerical computing on the web, including both JavaScript and WebAssembly, over a wide range of devices from workstations to IoT devices. We developed a new benchmarking approach, which allowed us to perform centralized benchmarking, including benchmarking on mobile and IoT devices. Using this approach we performed four performance studies using the Ostrich benchmark suite, a collection of numerical programs representing the numerical dwarf categories identified by Colella. We studied the performance evolution of JavaScript, the relative performance of WebAssembly, the performance of server-side Node.js, and a comprehensive performance showdown for a wide range of devices.

MATLAB (MATrix LABoratory) is a multi-paradigm numerical computing environment and fourth-generationprogramming language. MATLAB allows matrix manipulations, plotting of functions and data, implementationof algorithms, creation of user interfaces and interfacing with programs written in other languages,including C, C++, Java, Fortran and Python. Electrochemistry is a branch of chemistry that studies the relationshipbetween electricity, as a measurable and quantitative phenomenon, and identifiable chemical change, with eitherelectricity considered an outcome of a particular chemical change or vice versa. MATLAB has obtained a widerange of applications in different fields of science and electrochemists are also using it for solving their problemswhich can help them to obtain more quantitative and qualitative information about systems under their studies. Inthis review, we are going to cast a look on different applications of MATLAB in electrochemistry and for eachsection, a number of selected articles published in the literature will be discussed and finally, the results will besummarized and concluded Fil: Jalalvand, Ali R.. Kermanshah University Of Medical Sciences; Irán Fil: Roushani, Mahmoud. Kermanshah University Of Medical Sciences; Irán Fil: Goicoechea, Hector Casimiro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral; Argentina Fil: Rutledge, Douglas N.. Agro Paristech; Francia Fil: Gu, Hui-Wen. Yangtze University; China

Numerical computing is a field of mathematics where problems are made to be solved on a computing device. A variety of software tools exists for this purpose. In fact, MATLAB, Mathematica, Octave, and Scilab are specialized softwares for this purpose. A developer can also use general-purpose programming languages such as C, C++, Python, and Julia to define mathematical problems, but specialized softwares present predefined libraries that have been either optimized for stability or speed or, in same cases, for both. They can also be produced on targeted hardware for a chosen hardware platform. Thus, using specialized software is a good way to learn the numerical recipes for physical problems in an easy fashion. But, the primary question is why we should go for a numerical solution at all.

This paper presents deep reification, which is a language mechanism for reflective computing. It reifies a self-contained partial snapshot of the current execution environment. The snapshot contains not only data but also code and type definitions. This mechanism can be used as a common component of execution systems of embedded domain-specific languages (DSLs). Unlike typical implementations of embedded DSLs, the mechanism enables a DSL to borrow the host-language's syntax yet execute under a different semantics on different platforms from the host language's. DSL implementation can allow programmers to first construct a function closure as DSL code, reify a snapshot necessary for executing the function closure, transform the code in the snapshot into a program for a target platform, and finally execute the program. As a prototype system of deep reification, we have implemented Bytespresso for Java. This paper shows Bytespresso and also Bytespresso-C, our DSL built on top of Bytespresso. The target of this DSL is numerical computing on cluster computers and GPUs.

In this paper we evaluate the performance of a Java library in the context of designing numerical solutions for linear algebra problems. Nowadays there are a number of libraries like LAPACK or ATLAS available in C or FORTRAN for solving such problems. Java is a relatively new object-oriented language and is almost universally recognized as a very good programming language for writing portable programs. Despite these advantages, it is a common believe that Java still lags behind C/C++ or Fortran performance especially for computational intensive numerical applications. We developed a Java library for matrix computations and show that using a set of optimization techniques Java can achieve performance comparable with other libraries developed in C or Fortran.

Konrad Zuse verallgemeinerte das 1934 mit seiner Studienarbeit am Beispiel der statisch unbestimmten Analyse entwickelte programmformige Rechenschemata 1936 zum “Verfahren des Rechenplanes oder Programms” (Konrad Zuse). Von 1936 bis 1941 entfaltete er dieses Verfahren in erster Linie fur die Bau- und Flugzeugstatik. Diese numerischen Rechenplane bildeten eine wesentliche Seite der historisch-logischen Entwicklung von Zuses programmgesteuerten Rechenautomaten Z1 (1938) und Z3 (1941). Mit den numerischen Rechenplanen ist auch die erste Stufe der Initialphase der Computerstatik benannt. Ihre zweite Stufe hebt mit Zuses Plankalkul an (1942—1949) — der ersten “Plattform fur Softwareentwicklung” (Peter Jan Pahl ) — in dessen Zentrum sein allgemeines Konzept des Rechnens steht, das Zuse aus dem Kalkul-Begriff der Mathematik entwickelt und das Zahlenrechnen als Sonderfall enthalt. Die beiden Stufen werden im Folgenden eingehend dargestellt und durch eine exemplarische Skizze der um 1950 einsetzenden Konstituierungsphase der Computerstatik abgerundet. Konrad Zuse and the theory of structures — on the formation of computational mechanics (part 2). It was in 1936 that Konrad Zuse generalised the program-type calculation scheme, which he had developed in his student project of 1934 using the example of the statically indeterminate analysis, to form the ”computing plan or program method” (Konrad Zuse). Between 1936 and 1941 he continued to develop this method, in the first place for structural and aviation engineering. These numerical computing plans formed one fundamental element in the historico-logical evolution of Zuse’s program-controlled automatic computers Z1 (1938) and Z3 (1941). The numerical computing plans also mark the first step in the initial phase of computational mechanics. The second step (1942—1949) began with Zuse’s ”Plankalkul” (Calculus of Programs) — the first ”software development platform” (Peter Jan Pahl) —, the heart of which is his general calculation concept, which Zuse developed from the formal system concept of mathematics and which contains numerical computation as a special case. Both of these steps are presented in detail below and rounded off with an illustrative outline of the constitution phase of computational mechanics which began around 1950.

The use of open-source Python as opposed to traditional computing platforms such MATLAB, Mathematica, and C/C++, is becoming more and more noticeable as all forms of opensource software develop. The Python user community itself is very vibrant, but what really stands out for those of us in signals and systems, is what is happening in the numerical computing side of Python. This paper will describe how in particular, the IPython notebook can be used as an analysis and simulation tool for teaching signals and systems courses. Specific code modules have been developed to augment existing Python code contained in the scipy.signal module. Case studies will be used to demonstrate the capabilities of the IPython notebook to augment lecture material with live calculations and simulations. Additionally, examples of how the IPython notebook has been successfully used by students for homework problems, computer projects and lab reports will be illustrated. Both student and industry team members in subcontract work, have responded favorably to the use of Python as an engineering problem solving platform.

First of all, based on the structure of vacuum breaker, the closing bounce model of vacuum circuit breaker is established. Several factors are analyzed with the help of the numerical computing software MATLAB to determine how these factors influence bounce time of moving-contact. Reducing closing speed is a good way to reduce bounce time of moving-contact. Secondly, according to SolidWorks and ADAMS software, a method is found to not only reduce bounce time of moving-contact but also ensure closing successfully. Thirdly, the result of experiment is proved that author's view is correct and helpful.

This book is about using Python for numerical computing. Python is a high-level, general-purpose interpreted programming language that is widely used in scientific computing and engineering. As a general-purpose language, Python was not specifically designed for numerical computing, but many of its characteristics make it well suited for this task. First and foremost, Python is well known for its clean and easy-to-read code syntax. Good code readability improves maintainability, which in general results in less bugs and better applications overall, but it also encourages rapid code development. This readability and expressiveness is essential in exploratory and interactive computing, which requires fast turnaround for testing various ideas and models.

This article propose a model of teaching quality evaluation, by combining the theory of fuzzy mathematics with classroom teaching quality evaluation system. Quantified by the 1st and 2nd approaches, the mode is calculated qualitatively and quantitatively, then gain the levels of teaching quality evaluation. Matlab (a numerical computing environment and fourth generation programming language) is also used for experiments, in order to form a scientific and objective appraise, apply and spread the model.

For many years, computing in physics and chemistry was mainly numerical computing. The availability of high-level symbolic languages, such as Prolog, on largely widespread microcomputers opens new horizons for the application of computers to physics and chemistry. In this tutorial introduction we focus on the use of Prolog's fundamental structures.

To enable effective human-agent collaboration, new human-centric computing paradigms are needed. This paper presents a soft constraint representation scheme based on generalized intervals. With logically quantified intervals, semantics and intent can be integrated in numerical computing. The interpretable numerical results allow for better human-agent communication.

Numerical computing with MATLAB is a new textbook for an introductory course in numerical methods, MATLAB, and technical computing.

The author reviews a book dealing with the intricacies associated with Matlab (a popular platform for numerical computing) and its Java interface.

It is pointed out that the Ada language has many built-in reliability mechanisms for supporting sophisticated real-time applications. These include: features provided by the language that can be used to make programming more reliable; predefined features that allow the user to built in reliabilities; and a numerical computing environment that increases accuracy and system reliability. Examples and performance constraints are given and discussed. >

Numerical and non-numerical computing have a real role to play in the process of catalyst design and invention. Numerical computing for the deterministic aspects of catalyst design, such as simulations of coupled reaction and diffusion phenomena, are of obvious importance to the process of improving via modification existing heterogeneous catalysts. However, industrial catalyst design and especially the invention of new catalysts, is not a process that is captured fully by deterministic, mathematical descriptions. Instead, human catalyst experts rely on a wide range of softer information that is semiquantitative, and descriptive in nature. This provisional knowledge, although non-mathematical, is logical, and is captured in the form of heuristics. The heuristics of catalysis design can be captured in a logical program code written in a language like PROLOG, thus providing the means to organize and save this very useful knowledge.

The Liverpool Single-transputer library [10] was ported to the i860 as part of the Esprit Genesis project, P2702. There are approximately 250 routines in this library, including the BLAS (which are a well-known set of subroutines providing functions commonly used in numerical computing, see [8],[3], [2],[1]) and a set of vector routines, known as the FLO routines

The predominant programming language for numerical and scientific applications is Fortran, and super-computers are primarily used to run large-scale numerical and scientific applications. C is not widely used for numerical and scientific programming, yet C provides many desirable linguistic features not present in Fortran-77. Furthermore, the existence of a standard library and preprocessor eliminates the worst portability problems. A comparison of C and Fortran-77 shows several key deficiencies in C that reduce its desirability for some numerical problems. Some of these problems have already been addressed by the new ANSI standard for C, but others remain. C with a few extensions and modifications could be suitable for all numerical applications and could become more popular in supercomputing environments.

The numerical capabilities of 8-bit, CP M -based , microcomputers are surveyed. The factors affecting the use of these packaged microsystems for applications which are predominantly numerical are discussed. A suite of test programs developed to test the floating-point arithmetic system in FORTRAN and BASIC are described and the results obtained from these using the Microsoft software are tabulated.

Publisher Summary This chapter discusses list structures in computing. Computing is the business of operating on data. In numerical work, the items of data are numbers, individually having large selective information content but also standing in some structural relation to one another. The quantity of information contained in the structure is usually quite small; if one considers the three components of an ordinary vector, each to six decimals, one has 1018 or so possibilities for the values, but only 6 possible assignments representing structural information. In non-numerical work, it seems likely that structure will play a relatively larger part and give rise to novel programming techniques. For example the list structure, which has not figured prominently in numerical computing, is likely to become a basic tool in non numerical work. List structures of various types have been occasionally employed by programmers for many years, but no mathematically appealing formalization appeared until the work of McCarthy was first published. LISP, as McCarthy's system is called, was a milestone in the programming art, because it used list processing as a medium for exploiting the technique of recursion, and succeeded in doing so without tiresome references to the code or language of a particular computer. By itself, the published account of LISP does not constitute a programming language in the general sense, but there can be no better introduction to nonnumerical techniques than a study of it. The chapter also discusses a short course of instruction in the use of LISP.