Afrika Matematika最新文献

We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ (Anco and Bluman in Eur J Appl Math 13:545–566, 2002; Eur J Appl Math 13:567–585, 2002). It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. The equations admit five first integrals of which two are independent but the significance of the five are that they correspond to a five-dimensional algebra of Noether symmetries obtained without the need to construct a Lagrangian.

In this paper, a new concept of L-fuzzy cover spaces regarding fuzzy topological spaces is added. Secondly, the ideas of L-fuzzy compact open topology is established and the number of their interesting properties are studied.

Locally Rotationally Symmetric(LRS) Bianchi type I cosmological model interacting with scalar field and exponential potential is presented and phase plane analysis is done in the framework of dynamical systems. Evolution equations are analyzed and reduced to a system of ordinary differential equations which are autonomous by suitable variable transformations. All critical points both hyperbolic and non hyperbolic of the system are listed and their stability properties are analyzed and examined from the cosmological point of view. For non hyperbolic points perturbation theory is applied. Some representations of phase diagrams are shown explicitly.

In the paper, the authors establish several identities and relations involving q-analogues of the Pochhammer k-symbol. Moreover, the authors generalize several identities and relations for q-analogues of the Catalan numbers and the Catalan–Qi numbers.

In this paper, an expansion of the classical hyperbolic functions is presented and studied. Also, many features of the (k-) Pell hyperbolic functions are given. Finally, some graph and curved surfaces related to the k − Pell hyperbolic functions are introduced.

In the current study, we look at the majorization characteristics of the subclass (U_{m}(alpha ,eta ,delta )) of analytical functions described by the fractional Ruscheweyh–Goyal derivative. There are additional linkages made between the major findings of this study and those of prior researchers that are pertinent. Furthermore, we highlight a few novel or established implications of our primary finding.

The purpose of the present paper is to introduce subclasses of (p-)valent functions defined by linear operator. Inclusion relationships for functions in these subclasses are discussed.

In this work, we present methods for constructing representations of polynomial covariance type commutation relations (AB=BF(A)) by linear integral operators in Banach spaces (L_p). We derive necessary and sufficient conditions on the kernel functions for the integral operators to satisfy the covariance type commutation relation for general polynomials F, as well as for important cases, when F is arbitrary affine or quadratic polynomial, or arbitrary monomial of any degree. Using the obtained general conditions on the kernels, we construct concrete examples of representations of the covariance type commutation relations by integral operators on (L_p). Also, we derive useful general reordering formulas for the integral operators representing the covariance type commutation relations, in terms of the kernel functions.

In this paper we introduce a new class of (vartheta )-bi-pseudo-starlike functions with respect to symmetric points associated with telephone numbers and determine the bounds of the initial Taylor–Maclaurin coefficients and the Fekete–Szegö problem for functions belonging to this class. Some special cases of main results presented here are stated which are new and give better improvement to the initial Taylor-Maclaurin coefficients.

A mechanistic model that incorporates public health enlightenment, treatment, and snake developmental stages is developed and rigorously analyzed. The model is used to gain more insights into the dynamics and control of snakebite envenoming (SBE). Some interesting equilibrium points that demonstrate the presence and absence of snakes in a given population were computed. It has been shown that the existence or extinction of snakes in a given community depends on snake existence threshold (R_S). Whenever the threshold is greater than one, snakes exist in the community, while if the threshold is exactly equal to one, then snakes seize to exist. Furthermore, a rigorous qualitative study of the model revealed that each of the snake-free, SBE-free, and SBE-endemic equilibrium points is globally asymptotically stable. In addition, a sensitivity analysis of the model parameters was conducted in order to identify the most influential parameters on SBE transmission dynamics. It is shown that an effective contact rate is the most important parameter. Therefore, preventive strategies that focus on reducing contact between humans and snakes, such as the use of snakebite repellent and protective gloves, are very important in controlling SBE. Finally, simulations have indicated that public health education on the use of snakebite preventive measures in combination with treatment of SBE victims is critical in reducing the number of new cases and deaths, respectively.