scholarly journals ON APPROXIMATION OF PERIODIC ATEB-FUNCTIONS

2021 ◽  
pp. 76-83
Author(s):  
Vasiliy Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Good Accuracy ◽  
Special Functions ◽  
Trigonometric Functions ◽  
Comparison Analysis ◽  
Approximation Accuracy ◽  
Type Approximation ◽  
Collocation Points ◽  
Separate Table ◽  
In The Beginning ◽  
Hybrid Approximation

Two versions of approximation formulae for periodic Ateb-sine and Ateb-cosine in the first quarter of their common period are proposed. The first version is a Pade type approximation derived when constructing analytical solution of corresponding integral equation by iteration method with transforming the power series into a closed sum by Shanks’ formula. Two iteration approximations are considered. The first one is more concise but of worse approximation accuracy which deteriorates with increasing the argument value. To improve the approximation accuracy a hybrid approximation is proposed when the values of the Ateb-functions in the beginning (for the cosine) and in the end (for the sine) of the quarter period are computed by a separate formula obtained a priory by the asymptotic method. The comparison analysis of the approximate and exact values of the special functions indicates the error of the approximation proposed to be less than one per cent. The second variant of approximation is by replacing the periodic Ateb-functions by trigonometric functions of specific argument. The arguments are chosen so that the values of the special functions are exact at specific points of the quarter period. Five such collocation points are introduced in the paper. To implement this version of approximation a separate table of the values of the periodic Ateb-functions at the collocation points is compiled. The computational examples presented in the paper show the approximate values of the special functions obtained by the second version of approximation to have a good accuracy.

scholarly journals On solutions of the combined KdV-nKdV equation

2019 ◽  
Vol 30 (2) ◽  
pp. 33
Author(s):  
Mohammed Allami ◽  
A. K. Mutashar ◽  
A. S. Rashid
Keyword(s):  
Vries Equation ◽  
Special Functions ◽  
Elliptic Functions ◽  
Rational Functions ◽  
Trigonometric Functions ◽  
Exponential Functions ◽  
Jacobian Elliptic Functions ◽  
Negative Order ◽  
De Vries ◽  
Wave Reduction

The aim of this work is to deal with a new integrable nonlinear equation of wave propagation, the combined of the Korteweg-de vries equation and the negative order Korteweg-de vries equation (combined KdV-nKdV) equation, which was more recently proposed by Wazwaz. Upon using wave reduction variable, it turns out that the reduced combined KdV-nKdV equation is alike the reduced (3+1)-dimensional Jimbo Miwa (JM) equation, the reduced (3+1)-dimensional Potential Yu-Toda-Sasa-Fukuyama (PYTSF) equation and the reduced (3 + 1)¬dimensional generalized shallow water (GSW) equation in the trav¬elling wave. In fact, the four transformed equations belong to the same class of ordinary differential equation. With the benefit of a well known general solutions for the reduced equation, we show that sub¬jects to some scaling and change of parameters, a variety of families of solutions are constructed for the combined KdV-nKdV equation which can be expressed in terms of rational functions, exponential functions and periodic solutions of trigonometric functions and hyperbolic func¬tions. In addition to that the equation admits solitary waves, and double periodic waves in terms of special functions such as Jacobian elliptic functions and Weierstrass elliptic functions.

scholarly journals ON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS

2016 ◽  
Vol 56 (4) ◽  
pp. 283-290 ◽  
Author(s):  
Jiri Hrivnak ◽  
Lenka Motlochova
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Jacobi Polynomials ◽  
Special Functions ◽  
The Other ◽  
Trigonometric Functions ◽  
The One ◽  
Sine Functions

<p>The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the connection that is made between the one-variable orbit functions of <em>A<sub>1</sub></em> and the four kinds of Chebyshev polynomials. It is shown that there exists a similar connection for the two-variable orbit functions of <em>A<sub>2</sub></em> and a specific version of two variable Jacobi polynomials. The connection with recently studied <em>G<sub>2</sub></em>-polynomials is established. Formulas for connection between the four types of orbit functions of <em>B<sub>n</sub></em> or <em>C<sub>n</sub></em> and the (anti)symmetric multivariate cosine and sine functions are explicitly derived.</p>

scholarly journals Methods of Preschoolers’ Preparation for School by the Means of the Latest Technologies and Software

2020 ◽  
Author(s):  
Gulshoda Nozihhonovna Yunusova
Keyword(s):  
Russian Language ◽  
Logical Thinking ◽  
Comparison Analysis ◽  
New Approach ◽  
Warm Up ◽  
Logical Memory ◽  
Full Development ◽  
Analysis And Synthesis ◽  
Memory Control ◽  
In The Beginning

The following article describes new aspects of computer and software utilization in the forms of games for preschoolers with the use of the latest technologies and methods for the purpose of effective preparation for school. The creation and the appliance of programs in the forms of games aimed at focusing, memory improvement, logical thinking, teachings of alphabets of three languages, teaching of robotics, constructing and assembling parts of a robot helps in preschoolers’ preparation for school. The present work shows the method of teachings of parts of a machine or a robot by the means of completing other exercises such as learning English words or math tasks, it also promotes usage of the newest STEAM technologies and appliance of mnemonic in memory control for more efficient memorizing of new knowledge. In the beginning of studies as a warm-up it is possible to use programs for child’s focusing, concentrating, memory improving and logical thinking. It allows to begin other exercises aimed at acquisition of knowledge in different fields. The article describes the methods of teachings of foreign words associating them with the words of first or Russian language based on the methods of mnemonic, comparison, analysis and synthesis of data. The result of teachings with such methods offered the children knowledge of alphabets of three languages, it also allowed the children to concentrate, develop and improve their visual and logical memory, the children independently noted the similarities and differences of letters and pronunciation. Education in STEAM technologies and mnemonic offers the new approach to full development with child’s entrance in the world of knowledge of alphabets of three languages, the thesaurus of English words, based on effective methods of mnemonic.

scholarly journals ON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS

2016 ◽  
Vol 56 (4) ◽  
pp. 283 ◽  
Author(s):  
Jiri Hrivnak ◽  
Lenka Motlochova
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Jacobi Polynomials ◽  
Special Functions ◽  
The Other ◽  
Trigonometric Functions ◽  
The One ◽  
Sine Functions

<p>The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the connection that is made between the one-variable orbit functions of <em>A<sub>1</sub></em> and the four kinds of Chebyshev polynomials. It is shown that there exists a similar connection for the two-variable orbit functions of <em>A<sub>2</sub></em> and a specific version of two variable Jacobi polynomials. The connection with recently studied <em>G<sub>2</sub></em>-polynomials is established. Formulas for connection between the four types of orbit functions of <em>B<sub>n</sub></em> or <em>C<sub>n</sub></em> and the (anti)symmetric multivariate cosine and sine functions are explicitly derived.</p>

scholarly journals THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS

2016 ◽  
Vol 56 (3) ◽  
pp. 156
Author(s):  
Agata Bezubik ◽  
Severin Pošta
Keyword(s):  
Fourier Transforms ◽  
Special Functions ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Trigonometric Functions ◽  
New Class ◽  
The Common

The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3<em>D</em> lattice is shown in an example.

Drug Induced Changes in Cell Organelles

1968 ◽  
Vol 26 ◽  
pp. 110-111
Author(s):  
Sarah A. Luse
Keyword(s):  
Clinical Medicine ◽  
Cell Organelles ◽  
Riboflavin Deficiency ◽  
Drug Induced ◽  
New Era ◽  
Health And Disease ◽  
In The Beginning ◽  
Cellular Pathology ◽  
Induced Changes ◽  
The Impact

In the mid-nineteenth century Virchow revolutionized pathology by introduction of the concept of “cellular pathology”. Today, a century later, this term has increasing significance in health and disease. We now are in the beginning of a new era in pathology, one which might well be termed “organelle pathology” or “subcellular pathology”. The impact of lysosomal diseases on clinical medicine exemplifies this role of pathology of organelles in elucidation of disease today.Another aspect of cell organelles of prime importance is their pathologic alteration by drugs, toxins, hormones and malnutrition. The sensitivity of cell organelles to minute alterations in their environment offers an accurate evaluation of the site of action of drugs in the study of both function and toxicity. Examples of mitochondrial lesions include the effect of DDD on the adrenal cortex, riboflavin deficiency on liver cells, elevated blood ammonia on the neuron and some 8-aminoquinolines on myocardium.

A View of the Lexical–Grammatical Link in Young Latinos With Specific Language Impairment Using Language-Specific and Conceptual Measures

2019 ◽  
Vol 62 (6) ◽  
pp. 1775-1786 ◽  
Author(s):  
Lucía I. Méndez ◽  
Gabriela Simon-Cereijido
Keyword(s):  
Low Income ◽  
Language Impairment ◽  
Specific Language Impairment ◽  
L2 Acquisition ◽  
Cross Sectional ◽  
Specific Language ◽  
Vocabulary Skills ◽  
In The Beginning ◽  
Study Participants ◽  
L1 And L2

Purpose This study investigated the nature of the association of lexical–grammatical abilities within and across languages in Latino dual language learners (DLLs) with specific language impairment (SLI) using language-specific and bilingual measures. Method Seventy-four Spanish/English–speaking preschoolers with SLI from preschools serving low-income households participated in the study. Participants had stronger skills in Spanish (first language [L1]) and were in the initial stages of learning English (second language [L2]). The children's lexical, semantic, and grammar abilities were assessed using normative and researcher-developed tools in English and Spanish. Hierarchical linear regressions of cross-sectional data were conducted using measures of sentence repetition tasks, language-specific vocabulary, and conceptual bilingual lexical and semantic abilities in Spanish and English. Results Results indicate that language-specific vocabulary abilities support the development of grammar in L1 and L2 in this population. L1 vocabulary also contributes to L2 grammar above and beyond the contribution of L2 vocabulary skills. However, the cross-linguistic association between vocabulary in L2 and grammar skills in the stronger or more proficient language (L1) is not observed. In addition, conceptual vocabulary significantly supported grammar in L2, whereas bilingual semantic skills supported L1 grammar. Conclusions Our findings reveal that the same language-specific vocabulary abilities drive grammar development in L1 and L2 in DLLs with SLI. In the early stages of L2 acquisition, vocabulary skills in L1 also seem to contribute to grammar skills in L2 in this population. Thus, it is critical to support vocabulary development in both L1 and L2 in DLLs with SLI, particularly in the beginning stages of L2 acquisition. Clinical and educational implications are discussed.

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