1. Introduction: The Issue. The use of single letters in displaying patterns, functions, generalizations, and unknowns, dominates mathematical expression, and for that reason, appears in every domain of theoretical and technical discourse employing even the slightest bit of mathematical language. These variables, as they have come to be called, are the very mark of abstract power and precision,...

The paper presents mathematical and implementation challenges associated with testing of embedded software systems with dynamic behavior. These challenges are related to notation of tests, calculation of test coverage, implementation of a test comparator, and automatic generation of test cases. Some author’s ideas and solutions are presented with the help of abstract models that describe behavi...

We perform a mathematical analysis of the classical computational complexity of two genuine quantum-mechanical problems, which are inspired in the calculation of the expected magnetizations and the entanglement between subsystems for a quantum spin system. These problems, which we respectively call SES and SESSP, are specified in terms of pure slightly-entangled quantum states of n qubits, and ...

We present here a detailed, self–contained treatment of the mathematical formalism for describing the theory of polarized anisotropy in the cosmic microwave background. This didactic review is aimed at researchers who are new to the field. We first develop the mathematical tools for describing polarized scattering of CMB photons. Then we take the reader through a detailed derivation of the line...

We apply analytical methods of determination of workspaces of mechanical systems on Stewart Platforms. Four main tools are needed. The modelling gives the relationships between the parameters of the system. Mathematical analysis helps to get universal-that is not personal-approach and results. Mathematical optimization is used for we are quickly led when using analytical approach to the minimiz...

The principle of mathematical morphology and morphological operation filter are briefly introduced.A new signal processing method based on mathematical filter is presented.In order to remove non-linear noise in vibration signal, a kind of filter with structuring element adaptive,morphological opening and closing operators combination is designed.With moving structuring element,the signal can be...

Abstract. This paper presents a one-dimensional-in-space mathematical model of an amperometric biosensor. The model is based on the reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The stated problem is solved numerically by applying the finite difference method. Several types of finite difference schemes are used. The nu...

Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of ...

Although clinical practitioners often express concerns about the mathematical functioning of children with autism spectrum disorder (ASD), the field of mathematics remains a relatively unexplored topic in individuals with ASD. Moreover, research findings are fragmentary and hold inconclusive results. The present study aimed to examine whether grade 1 (aged 6-7 years) to 4 (aged 9-10 years) elem...

Individuals who do well in mathematics and science also often have good spatial skills. However, the predictive direction of links between spatial abilities and mathematical learning has not been firmly established, especially for young children. In the present research, we addressed this issue using a sample from a longitudinal data set that spanned 4 years and which includes measures of mathe...