Afrika Matematika最新文献

We consider the inviscid Burgers equation with force (partial _t u+partial _x(u^2/2)=nu ), where the discontinuities of initial datum (u_0) are interpreted as force sources. Thence, (nu ) is the force of shocks in a sticky dynamics of (paradoxically) non accelerated particles, whose the mass distribution field is (partial _xu). The force has its own dynamics of density field (eta =u-w) (the experienced impulsion), where w denotes the sticky particle velocity field. Along the sticky particle trajectory (tmapsto X_t), the processes (tmapsto eta (X_t,t),u(X_t,t),w(X_t,t)) are backward martingales.

This work deals with the existence and uniqueness of (mu )-pseudo almost periodic solutions to some transport processes along the edges of a finite network with inhomogeneous conditions in the vertices. For that, the strategy consists of seeing these systems as a particular case of the semilinear boundary evolution equations

where (A:= A_m|ker L) generates a C(_0)-semigroup admitting an exponential dichotomy on a Banach space. Assuming that the forcing terms taking values in a state space and in a boundary space respectively are only (mu )-pseudo almost periodic in the sense of Stepanov, we show that (SHBE) has a unique (mu )-pseudo almost periodic solution which satisfies a variation of constant formula. Then we apply the previous result to obtain the existence and uniqueness of (mu )-pseudo almost periodic solution to our model of network.

In this paper we investigate a family of bivariate orthogonal functions arising as a generalization of Koornwinder polynomials in two variables. General properties like recurrence relations and partial differential equations are introduced. Some special cases are considered and a limit relation of these functions is studied. As a consequence, a new class of bivariate orthogonal polynomials is presented.

In this paper, the problem of an annular fin of hyperbolic profile with temperature dependent thermal conductivity is discussed. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Furthermore, a more accurate discussion of the effect of fin dimensions, surface convection characteristics and the thermal conductivity parameter on the thermal performance of the fin is graphically presented.

It is given a characterization of being a matrix (Q_{g({a_3},{b_3})}^{(k)}) of linear combination of a matrix (Q_{g({a_1},{b_1})}^{(n)}) and a matrix (Q_{g({a_2},{b_2})}^{(m)}), where (a_{i}, b_{i} in mathbb {R}^{*}), (i=1, 2, 3), (m, n, k in mathbb {Z}), and (Q_{g({a},{b})}^{(l)}) denotes an (a, b)-generalized Fibonacci Q-matrix with (lin mathbb {Z}). In addition, some examples are presented illustrating the main result. Finally, some applications of the main result obtained are given.

This paper deals with a class of second-order linear differential equations with periodic coefficients. By viable transformation, we put the second-order linear differential equation into Riccati’s equation. By means of two periodic solutions of Riccati’s equation and variable transformation, we obtain the existence and uniqueness of the periodic solution of the nonhomogeneous second-order linear differential equation, some new results are obtained.

In this work, we use the finiteness of the Mordell–Weil group of the Jacobian variety of the curve (mathcal {C}:y^2 =x(x-3)(x-4)(x-6)(x-7)) and the Riemann Roch spaces to determine explicitly the set of algebraic points of given degree l over (mathbb {Q}) on the curve (mathcal {C}). The results obtained extend the work of Gordon and Grant, who determined the Mordell–Weil group (J(mathbb {Q})) and the set of rational points on the same curve.

In this study, we obtain the necessary and sufficient conditions for the boundedness of the fractional maximal operator (M_{alpha }) in the local Morrey–Lorentz spaces (M_{p,q;lambda }^{loc}({mathbb {R}}^n)). We use sharp rearrangement inequalities while proving our result. We apply this result to the Schrödinger operator (-Delta + V) on ({mathbb {R}}^n), where the nonnegative potential V belongs to the reverse Hölder class (B_{infty }({mathbb {R}}^n)). The local Morrey–Lorentz (M_{p,r;lambda }^{loc}({mathbb {R}}^n) rightarrow M_{q,s;lambda }^{loc}({mathbb {R}}^n)) estimates for the Schrödinger type operators (V^{gamma } (-Delta +V)^{-beta }) and (V^{gamma } nabla (-Delta +V)^{-beta }) are obtained.

In this paper, we prove some generalizations of Darbo’s fixed point theorem for multivalued mappings by considering a measure of noncompactness which does not necessarily have the maximum property. Moreover, we prove some coupled fixed point theorems for multivalued mappings. Our results generalize, prove and extend well-known results in the subject. An application to solve a nonlinear system of integral inclusions is given.

Information warfare requires more attention as competing interests get escalated by the spread of information on various Internet-based social media platforms in recent times. In this work, we construct and analyze a mathematical model with a system of ordinary differential equations to consider how two interacting pieces of information, where the first one is incomplete and misleading while the second one is corrective of the first, evolve with time in an online population. The counter and correctional information is the rejoinder. Human psychological and sociological attributes like disbelief in the rejoinder and increased tendency to keep spreading the misleading information even after knowing the correct one are factored into our model. We find that in correcting a misleading piece of information that is already spreading within a population, the rejoinder has to be released early enough within a certain time range. The findings can help us appreciate the impact of misinformation on the society and promote information literacy at optimal cost.