A study of the power-cosine copula
OMA-Vol. 5 (2021), Issue 1, pp. 85 – 97 Open Access Full-Text PDF
Christophe Chesneau
Abstract: Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.
Modelling and simulation of a dynamic contact problem in thermo-piezoelectricity
EASL-Vol. 4 (2021), Issue 2, pp. 43 – 52 Open Access Full-Text PDF
Youssef Ouafik
Abstract: In this work, we numerically study a dynamic frictional contact problem between a thermo-piezoelectric body and a conductive foundation. The linear thermo-electro-elastic constitutive law is employed to model the thermo-piezoelectric material. The contact is modelled by the Signorini condition and the friction by the Coulomb law. A frictional heat generation and heat transfer across the contact surface are assumed. The heat exchange coefficient is assumed to depend on contact pressure. Hybrid formulation is introduced, it is a coupled system for the displacement field, the electric potential, the temperature and two Lagrange multipliers. The discrete scheme of the coupled system is introduced based on a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivate. The thermo-mechanical contact is treated by using an augmented Lagrangian approach. A solution algorithm is discussed and implemented. Numerical simulation results are reported, illustrating the mechanical behavior related to the contact condition.
The incubation periods, the critical immunisation threshold and some other predictors of SARS-CoV-2 disease for different location and different climate countries
EASL-Vol. 4 (2021), Issue 2, pp. 36 – 42 Open Access Full-Text PDF
Marwan Al-Raeei
Abstract: We estimate the incubation period values and other forecasting predictors of SARS-CoV-2 for different countries located in different geographical locations of the earth and each one has a certain climate. The considered countries are the United States, Russia, the United Kingdom, Brazil, Spain, Bahrain, Egypt, Iran, Cyprus, India, France, and the Syrian Arab Republic. For estimating of the forecasting predictors values, we use the SEIR epidemic model and Runge-Kutta simulation method. The estimations are done up to the beginning of 2021 in aforementioned countries based on the collected data in these countries. We find that the incubation period values of SARS-CoV-2 are located between 2.5 days which returns to Bahrain and 10 days which returns to some countries in middle east. Also, we find that the average value of this period is about 6.5 days for the different location countries. Besides, we find that the average values of SARS-CoV-2 critical immunisation threshold, SARS-CoV-2 basic reproduction number and SARS-CoV-2 steady state population are 0.5, 2.3 and 0.5 respectively.
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.
