List of papers

We adopt the modelization of Blunier and all (2009) based on a geometrical description of the scroll wraps in order to study scroll compressor. A precise geometry is necessary because this is the main factors which affects the efficiency of the compressor and this is the basis to establish an accurate thermodynamic model. With Mathematica, this paper uses this novel description of the geometry based on the parametric equations for the circle involutes in a novel reference system, in order to exploit the symmetry of the compressor: we obtain exact analytical expressions of the compression and discharge chamber volumes, together with all the geometrical parameters. Such formal calculus allowes the compressor to be optimized geometrically and to investigates a lot of others geometries. We can also analytically observe the conjugacy points, describe the compression process in detail and estimate the chamber volumes . The gap between scroll due to manufacturing and wear is analyzed because this determines the leakage between neighboring chambers in the compressor. Description of the chambers and of the leakage give us a set of ordinary coupled differential equations for the temperature and pressure which represent the kinematic of the scroll associated with the thermodynamic evolutions of air or refrigerant.

Here we will examine rotations and spherical harmonics in both 4D and 6D, present a simple derivation of the associated addition theorems and related generalised Green's functions, with application to exact solution of the Fock (1954, 1958) expansion for Helium.

Integer geometric relation of the strength of gravitation to the speed of light c.

This paper proposes a theoretical equation for the Newtonian constant of gravitation G derived from the fine structure constant α, electron charge e, Rydberg-Infinity constant R∞ and the strength of a quantum of the gravitational force Fg defined by a stunningly simple integer geometric relation to the forth power of the speed of light c:

G_proposed = α^10 · (e·R∞)^-4 · (4·π·μ0])^-2 · Fg [m^3·kg^-1·s^-2]

This article describes how Mathematica can be used to analyze texts. Here an application is shown which analyses various papers mostly written by students of an University of Cooperative Education. The work of the students is analyzed in different ways using the abilities of Mathematica 10, especially the Dataset functionality. The effects of giving early feedback to the students in their work is shown an visualized.

Word Clouds are a popular visualization tools for keywords. Creating word clouds is a combination of text analysis, and geometric computations that could be as simple as in [www.wolfram.com/...cloud.html] or in [demonstrations.wolfram.com/CreatingWordClouds/] but produces poor results. In this talk, we explore - using Mathematica - how the use of complex bin-packing algorithms, of precise intersection checking and of advanced strategies of placement, coloring and weight representation can produces really aesthetically nice results.

We present in this paper a computational method for the design of 3-dimensional spatial lattices made of ultra-high performance fibre-reinforced concrete (UHPC). It consists in a GA-based topological optimization, including multi-objective evaluation of the trusses to deal with mechanical performances, architectural constraints and construction issues simultaneously. The whole algorithm, from the direct stiffness method for mechanical analysis to the implementation of geometrical constraints, is written in Mathematica®. The optimized geometry is to be cast in 3D-printed sand and cement moulds according to a validated fabrication process that we first introduced in Archilab 2013 in Orléans (France).

This integrated method of conducting the architectural project takes advantage of the efficiency and adaptability of coding in Mathematica® that allows us to control many constructive issues by actually including them in the form-finding process. It also gives us the ability to freely handle communication between each software and machine involved in the project: from design to manufacturing.

In a polar coordinate system we consider fifteen classes of forces resulting in countless undiscovered orbitals. The classic Keplerian forces and its accompanied conic section orbitals are one of the special subclasses. Aside from the common theoretical foundation, the characteristics of the individual orbitals are given by the solution of corresponding equations of motion. These are nonlinear coupled differential equations. Solving these equations numerically and utilizing a Computer Algebra System such as Mathematica is conducive to the trajectories. Simulation of the trajectories provides a visual understanding about the motion under the influence of the generalized non-central forces. Our current investigation is a continuation of our keen interest in nonlinear physics phenomena. This report would be stimulating to individuals interested in physics in general and to those involved in classical mechanics in particular. In this report we include ample examples and their accompanied Mathematica codes. Utilizing these codes an interested reader may produce our findings and launch his/her own investigation.

The Mathematica package “QuantumCircuit” for simulation of quantum computation based on the circuit model is described. The package provides a user-friendly interface to specify a quantum circuit, to draw it, and to construct the corresponding unitary matrix for quantum computation defined by the circuit. This matrix enables to compute the final state of the quantum memory register by its given initial state and to check the operation of the algorithm determined by quantum circuit. Simulation of quantum circuits implementing the best known quantum algorithms such as the quantum Fourier transform, and the Shor algorithm for order finding and integer factorization is presented.

The implementation of the Method of Inverse Differential Operators (MIDO) which is an extension to DSolve in Mathematica is applied to Initial Value Problems (IVP) and Boundary Conditions (BC) of homogeneous and non-homogeneous, linear PDEs of 2nd order such as the Laplace equation, the wave equation and the heat/ diffusion equation with respect to different types of boundary conditions. For selected examples of 2nd order PDEs explicit analytical solutions will be given in order to demonstrate the potential of MIDO.

As to the homogeneous Laplace equation (with 3 or 4 spatial dimensions) the solutions will be obtained by quaternion factorization of the differential polynomial (e.g. in 3 variables x,y,z): X₃ = α² D²_x + β ² D²_y + γ² D²_z

hence the homogenous PDE

(D_x α - D_y i_q β - D_z j_q γ)(D_x α + D_y i_q β + D_z j_q γ)u(x,y,z) = 0

will be factorized and solved.

In order to obtain the analytical soution of the Wave function (in 1 spatial dimension) with a inhomogeneity such as (D_t² - c₂D_x²)u(x,t) = e^-|x|sin(t) it is required to resort to distributions (for example replacing the built-in Mathematica function Abs[x] by an equivalent distribution abs(x) = x (Θ(x) - Θ(-x)) where Θ is the built-in HeavisideTheta function).

With regards to the Heat/Diffusion equation (τ D_t - D²_x - D²_y)u(t,x,y) = 0 analytical solutions are given for six different types of (non-)homogeneous boundary conditions and initial values for 1 spatial dimension. In the case of 2 spatial dimensions boundary conditions of Dirichlet and v. Neumann type are investigated.

The present work identifies and generalizes two different classes of self-contacting binary trees that are separately mapped along the piecewise smooth boundary of the symmetric binary trees Mandelbrot set. The only common tree of these two classes of fractals is the Sierpinski 2-gon gasket tree, commonly known as H-tree, and it is mapped in a topological critical point of the trees Mset boundary. The critical points for other Sierpinski gasket trees (symmetric trees with b equally- spaced branches per node) play an analogous role. Using these critical points as references, we develop a notation to parameterize and classify all the families of generalized symmetric fractal trees. We deduce their boundary equations where the tip-to-tip self-contact takes place, and we provide several diagrams, their fractal dimension and examples of self-contacting fractal trees with N-fold rotational symmetry.

Pattern matching is a widely spread mechanism to search for relevant data by specifying a pattern which specifies the features we are interested in. We usually specify the features of the objects we want to match, but there are many situations when we want to of exclude objects with certain characteristics.

Antipatterns are an extension of the notion of pattern that allows to express negative information in a via a complement symbol, and offer a compact and expressive representation for sets of terms. This concept was proposed by Claude Kirchner and his coworkers in 2007, and it turns to be useful in programming languages (especially rule-based programming) and for symbolic computation.

We developed a small package, called Antipatterns`, that enables the direct use of anti- patterns in Mathematica programs. We describe the capabilities of our package and illustrate its usage on a simple example.

Feed mechanisms are the main source of inertia forces in the sagittal direction of a sewing machine. These forces cause undesirable vibrations which are necessary to suppress. Balancing by using of counterweights can significantly reduce the inertia forces and thus vibrations. The parameters of balancing are optimized in sw Mathematica. The input data for the optimization are obtained from the dynamic analysis of the mechanisms model which is created in sw SystemModeler. The optimized balancing is used in a real industrial sewing machine. The purpose of the paper is to show how these sw can help with solving real problems in industry.

Mathematica has been used in our company for R/D evaluation of measurements, analysis and calculations since version 2. During that time many experiences have been gathered, summarized in our internal packages. Also large progress was made in Mathematica, especially in versions 9 and 10. This presentation aims to share these experiences and give tips both for ordinary users and maybe also for Mathematica developers for further development.

One of the most important engineering paradigms in programming is probably CoC - Convenience over Configuration. Mathematica was always able to perform all the tasks engineers need in praxis, however their configuration has been too complicated. Engineers do not care only on “what is possible”, but how easily and without user mistakes (which often comes) it can be used. For this reason internal package Signals has been developed some time ago in our company. In many areas it is similar to new TimeSeries datatype, but suggests many other future implementation enhancements based on our experiences especially in mechanical engineering and modelling. Contribution will show examples and ideas in area of evaluation and processing of measured signals and their visualization.

For couple of years Mathematica provides wonderful data sources from many different areas (from AdministrativeDivisionData to ZIPCodeData, taken by alphabet). Cloud integration now provides the way to share custom know-how and data. However in our company we missed the opportunity to create our own data source based on our input. Such data can arise as the result of some large set of experiments and their evaluation. In our case typically some measurements are performed with different parameter settings and environment conditions. Such measurements should be stored in some general structure with a symbolic way of extraction of data. Then some analysis are performed and again their results are stored to be symbolically retrieved later.

We present computer-assisted methods for constructing polygonal knots with verification. We start from the most basic crossing of a paper tape. The construction and the subsequent verification are performed through the interaction with the software tool called e-origami system (abbreviated to Eos), which we have been developing. We tackle the problems of construction and verification of polygonal knots with a simulated tape, i.e. a sheet of origami paper long enough to make a desired knot. Eos has its own simple programming language with which the users of Eos communicate to perform step-wise construction, as if a piecework of an origami is made by hand. The challenge is to construct regular polygonal knots with rigor and rigidity. This required a method beyond classical Huzita’s method. We extended the Eos language of the first-order logic specialized to geometry. This enables a line of development from a regular triangle pre-knot to 2n+1 polygonal knot and arbitrary n-gon knot-like objects.

At the University of Zurich we are using Mathematica for the required course on Empirical Methods with 150 business administration students at master's level. We ask the students to learn coding with Mathematica and to solve real problems using real data. All course materials such as slides, tutorials, group assignments and performance reports were deployed as Mathematica notebooks. The final exams, which are personalized, randomized, and contain various types of questions, were written in Mathematica and graded fully automatically.

This interactive presentation aims to show our recent developments of teaching materials, to share our vision and experience, and to critically discuss the opportunities of using Wolfram Technologies for teaching.

In French engineering curriculums, teachers are requested to initiate students into research. The author has developed such an activity in the context of a course in acoustic modeling. Although doing genuine research with students is unrealistic, the paper shows that it remains possible to mimic a research activity at the borderline of mathematical modeling and scientific computing, by resorting to symbolic manipulations, which enable innovating aspects.

The paper presents application of OpenCLLink in Wolfram Mathematica to accelerate fully recurrent neural networks using GPU. We also show the idea of automatically generated parts of source code using SymbolicC.

One of the most difficult problems in undestanding mechanics of large deformation of the continuum are ability of students and engineers (also those with professor titles) to deal with continuum as a curved space due to large deformations. There are many misunderstanding in many books on Continuum Mechanics connected with disability with dealing with curvilinear systems of coordinates. The most useful educational method of explaining problems for engineers is 3D animated graphics. Mathematica with its tools of dealing with vectors, tensors and interactive visualization makes it possible to override this perception problem. Application of Manipulate function and graphical facilities of Mathematica makes it possible to understand many aspects of deformation description like differences between Gausian and Lagrangian coordinates, reference and actual configuration.

In the Summer of 2014, Touch Press and Profile Books brought out "Incredible Numbers", an e-book/app for iOS. The app's text was written by Professor Ian Stewart of the University of Warwick, author of dozens of highly popular math books for a general readership.

The app is as fascinating and accessible as Professor Stewart's books. What's different is that it's filled with interactive resources, most of which were developed and prototyped by the current author using Mathematica's dynamic functionality.

This talk will tell the story of the project's genesis and development, illustrated by demonstrations of the Mathematica prototypes and the final app.

Deductive or experimental reasoning, most benefit with less effort, deep theories needed but no time for deep study. These are some problems of teaching mathematics in applied sciences, and they hardly can be resolved.

Based on the long teaching science, engineering and math students, we give a summary of the experiences, and deal with professional, didactic as well as psychological aspects. We present our way of teaching, in which the computer-aided experiments and complex modeling approach are of central role. We show many applications, dynamic demonstrations in different topics, used regularly in our courses. Finally, we consider how deep mathematical fields, such as impulses, nonlinear and delay systems as well as their qualitative properties can be introduced at elementary level by simple examples with the help of Mathematica demonstrations.

Research is supported by the Hungarian National Foundation for Scientific Research Grant No. K109782, and by the European Union in the frame of the projects IPA HU-SRB/1203/221/024 and TÁMOP-4.2.2.A-11/1/KONV-2012-0073.

The use of copulas in the study of Value-at-Risk in competitive markets is a research method which offers rich possibilities of computer modelling. Application of the theory of statistical distributions as skewnormal or Laplace distribution is one of the strongest mathematical tools used to study financial risk. In this paper we compare VaR based on selected copula with different marginals. We illustrate how to compute Value-at-Risk using Monte Carlo simulations using Wolfram Mathematica.

Interest in the capture and analysis of personal fitness and health data has been growing rapidly in recent years thanks to the ease with which this can be accomplished using the ubiquitous smart phone or if needed, an appropriate specialized wearable electronic device. This paper will describe how Mathematica was used to analyze daily bicycle commutes to and from work over a span of five recent month. Data was captured using an iPhone 4S and the Cyclemeter app from Abvio. Several newly released version 10 features including time series and geographic data computations will be demonstrated.

An epidemiological model describing a dengue disease transmission is formulated together with the associated basic reproduction number. The model is based on monitoring the dynamics of the humans and mosquitoes populations. The human population is classified into three epidemiological states, the susceptible, infected, and recovered humans. The mosquito’s populations is subdivided into three classes of the aquatic stage or larva mosquitoes, uninfected female mosquitoes, and infected female mosquitoes. A sensitivity analysis is carried out to study how sensitive is the model to a particular parameter. Using Mathematica as a computational tool, a parameter is varied over a wide range to determine the relative importance of the model parameters to the disease propagation and control.Numerical results of sensitivity indices shown that the reproduction number is most sensitive to the average daily biting, the natural death rate of mosquitoes and the human natural death rate. The recruitment rate of mosquitoes and natural death rate of larva mosquitoes were found to be less sensitive.

Conservative nonlinear dynamical system is studied numerically. The condition for stability of simple solution is found in the parameter space. The bifurcaton gives rise to a new kind of solutin. This solution is computed using the continuation technique.

In this paper we present CaffeLink an open-source library for Mathematica which is a binding of a well-established Caffe deep learning framework. Caffe is a highly-optimized CUDA accelerated library with focus on convolutional neural networks written in C++ with Python and Matlab bindings. CaffeLink is based upon Mathematica's LibraryLink. It makes accessible most functionalities of Caffe directly from Mathematica environment which includes work with datasets, building networks, training them as well as evaluating them. Here we present an overview of the CaffeLink library with examples on MNIST and ImageNet datasets.

Image Processing is not limited to what a human eye can see. A computer can process image features that are virtually invisible, either because the features are too subtle or too irregular to attract our attention. Be amazed, when we tackle the following questions:

• Why bother about face recognition if you can identify someone by looking into his or her eye?
• Why bother measuring someones pulse if you can see him or her blush?
• Why listen to this talk if you can see the sound?