Possibility Pythagorean bipolar fuzzy soft sets and its application
ODAM-Vol. 4 (2021), Issue 2, pp. 17 – 29 Open Access Full-Text PDF
M. Palanikumar, K. Arulmozhi
Abstract: We interact the theory of possibility Pythagorean bipolar fuzzy soft sets, possibility bipolar fuzzy soft sets and define complementation, union, intersection, AND and OR. The possibility Pythagorean bipolar fuzzy soft sets are presented as a generalization of soft sets. Notably, we tend to showed De Morgan’s laws, associate laws and distributive laws that are holds in possibility Pythagorean bipolar fuzzy soft set theory. Also, we advocate an algorithm to solve the decision making problem primarily based on soft set model.
Nirmala energy
ODAM-Vol. 4 (2021), Issue 2, pp. 11 – 16 Open Access Full-Text PDF
Ivan Gutman, Veerabhadrappa R. Kulli
Abstract: A novel vertex-degree-based topological invariant, called Nirmala index, was recently put forward, defined as the sum of the terms \(\sqrt{d(u)+d(v)}\) over all edges \(uv\) of the underlying graph, where \(d(u)\) is the degree of the vertex \(u\). Based on this index, we now introduce the respective “Nirmala matrix”, and consider its spectrum and energy. An interesting finding is that some spectral properties of the Nirmala matrix, including its energy, are related to the first Zagreb index.
On generalization of extended Gegenbauer polynomials of two variables
OMA-Vol. 5 (2021), Issue 1, pp. 76 – 84 Open Access Full-Text PDF
Ahmed Ali Al-Gonah, Ahmed Ali Atash
Abstract: Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.
New-type Hoeffding’s inequalities and application in tail bounds
OMS-Vol. 5 (2021), Issue 1, pp. 248 – 261 Open Access Full-Text PDF
Pingyi Fan
Abstract: It is well known that Hoeffding’s inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding’s inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz [1]. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding’s inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding’s inequality and its refined version by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding’s inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding’s inequalities could get more interesting applications in some related fields that use Hoeffding’s results.
Qualitative analysis of solutions for a parabolic type Kirchhoff equation with logarithmic nonlinearity
ODAM-Vol. 4 (2021), Issue 2, pp. 1 – 10 Open Access Full-Text PDF
Erhan Pişkin, Tuğrul Cömert
Abstract: In this work, we investigate the initial boundary-value problem for a parabolic type Kirchhoff equation with logarithmic nonlinearity. We get the existence of global weak solution, by the potential wells method and energy method. Also, we get results of the decay and finite time blow up of the weak solutions.
A hybrid method for solution of linear Volterra integro-differential equations (LVIDES) via finite difference and Simpson’s numerical methods (FDSM)
OMA-Vol. 5 (2021), Issue 1, pp. 69 – 75 Open Access Full-Text PDF
Bashir Danladi Garba, Sirajo Lawan Bichi
Abstract: In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.
