scholarly journals Preserving Log-Convexity for Generalized Pascal Triangles

10.37236/2255 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Moussa Ahmia ◽  
Hacène Belbachir
Keyword(s):  
Power Series ◽  
Convexity Property ◽  
Binomial Convolution

We establish the preserving log-convexity property for the generalized Pascal triangles. It is an extension of a result of H. Davenport and G. Pólya "On the product of two power series", who proved that the binomial convolution of two log-convex sequences is log-convex.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

Sign in / Sign up

Export Citation Format

Share Document