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15 results on '"Simsek, Buket"'

2. The Formulae and Symmetry Property of Bernstein Type Polynomials Related to Special Numbers and Functions.

Author

Yilmaz Ceylan, Ayse and Simsek, Buket

Subjects
*BERNSTEIN polynomials, *GENERATING functions, *SPECIAL functions, *FUNCTIONAL equations, *POLYNOMIALS
Abstract

The aim of this paper is to derive formulae for the generating functions of the Bernstein type polynomials. We give a PDE equation for this generating function. By using this equation, we give recurrence relations for the Bernstein polynomials. Using generating functions, we also derive some identities including a symmetry property for the Bernstein type polynomials. We give some relations among the Bernstein type polynomials, Bernoulli numbers, Stirling numbers, Dahee numbers, the Legendre polynomials, and the coefficients of the classical superoscillatory function associated with the weak measurements. We introduce some integral formulae for these polynomials. By using these integral formulae, we derive some new combinatorial sums involving the Bernoulli numbers and the combinatorial numbers. Moreover, we define Bezier type curves in terms of these polynomials. [ABSTRACT FROM AUTHOR]

Published
2024
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3. New moment formulas for moments and characteristic function of the geometric distribution in terms of Apostol–Bernoulli polynomials and numbers.

Author

Simsek, Buket

Subjects
*GEOMETRIC distribution, *CHARACTERISTIC functions, *POLYNOMIALS, *GEOMETRIC series, *GENERATING functions, *BERNOULLI numbers, *COSINE function
Abstract

Although it is very easy to calculate the 1st moment and 2nd moment values of the geometric distribution with the methods available in existing books and other articles, it is quite difficult to calculate moment values larger than the 3rd order. Because in order to find these moment values, many higher order derivatives of the geometric series and convergence properties of the series are needed. The aim of this article is to find new formulas for characteristic function of the geometric random variable (with parameter p) in terms of the Apostol–Bernoulli polynomials and numbers, and the Stirling numbers. This characteristic function characterizes the geometric distribution. Using the Euler's identity, we give relations among this characteristic function, the Apostol–Bernoulli polynomials and numbers, and also trigonometric functions including cosine and sine. A relations between the characteristic function and the moment generating function is also given. By using these relations, we derive new moments formulas in terms of the Apostol–Bernoulli polynomials and numbers. Moreover, we give some applications of our new formulas. [ABSTRACT FROM AUTHOR]

Published
2024
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12. Remarks on Statistical Evaluations for Facial Expression Recognition.

Author

Simsek, Buket

Subjects
*FACIAL expression, *BERNSTEIN polynomials, *MACHINE learning, *CURVATURE, *MATHEMATICS
Abstract

In “Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial ex- ´ pression recognition based on curvature, Appl. Math. Comput. 344–345 (2019) 150–162”, some statistical evaluations on feature vectors were given in order to analyse their meaningfulness while classifying human facial expressions. In this paper, by using some results arising from SPSS program, we provide some further statistical evaluations and observations which are related to features based on the calculated Hausdorff distances between Bezier curves belonging to the regions that shape human facial expressions. [ABSTRACT FROM AUTHOR]

Published
2020
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15. Investigation of the Blood Behaviour and Vascular Diseases by using Mathematical Physic Principles.

Author

Yardimci, Ahmet and Simsek, Buket

Subjects
*BLOOD flow, *HEMODYNAMICS, *BLOOD circulation, *VASCULAR diseases, *ATHEROSCLEROSIS, *THROMBOSIS
Abstract

In this paper we prepare a short survey for using of mathematical physic principles in blood flow and vascular diseases researches. The study of the behavior of blood flow in the blood vessels provides understanding on connection between flow and the development of dieseases such as atherosclerosis, thrombosis, aneurysms etc. and how the flow dynamics is changed under these conditions. Blood flow phenomena are often too complex that it would be possible to describe them entirely analytically, although simple models, such as Poiseuille model, can still provide some insight into blood flow. Blood is not an "ideal fluid" and energy is lost as flowing blood overcomes resistance. Resistance to blood flow is a function of viscosity, vessel radius, and vessel length. So, mathematical Physic principles are useful tools for blood flow research studies. Blood flow is a function of pressure gradient and resistance and resistance to flow can be estimates using Poiseuille's law. Reynold's number can be used to determine whether flow is laminar or turbulent. [ABSTRACT FROM AUTHOR]

Published
2017
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