Arabian Journal of Mathematics最新文献

Given a nonempty convex subset X of a topological vector space and a real bifunction f defined on (X times X), the associated equilibrium problem consists in finding a point (x_0 in X) such that (f(x_0, y) ge 0), for all (y in X). A standard condition in equilibrium problems is that the values of f to be nonnegative on the diagonal of (X times X). In this paper, we deal with equilibrium problems in which this condition is missing. For this purpose, we will need to consider, besides the function f, another one (g: X times X rightarrow mathbb {R}), the two bifunctions being linked by a certain compatibility condition. Applications to variational inequality problems, quasiequilibrium problems and vector equilibrium problems are given.

Fourth order problems with the differential equation (y^{(4)}-(gy')'=lambda ^2y), where (gin C^1[0,a]) and (a>0), occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation (y^{(4)}-(gy')'=lambda ^2y) and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non-self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

Let N be a (mathbb {Z})-nearalgebra; that is, a left nearring with identity satisfying ( k(nn^{prime })=(kn)n^{prime }=n(kn^{prime })) for all (kin mathbb {Z}), (n,n^{prime }in N) and G be a finite group acting on N. Then the skew group nearring (N*G) of the group G over N is formed. If N is 3-prime ((aNb=0) implies (a=0) or (b=0)), then a nearring of quotients ( Q_{0}(N)) is constructed using semigroup ideals (A_{i}) (a multiplicative closed set (A_{i}subseteq N) such that (A_{i}Nsubseteq A_{i}supseteq NA_{i})) of N and the maps (f_{i}:A_{i}rightarrow N) satisfying ( (na)f_{i}=n(af_{i})), (nin N) and (ain A_{i}). Through (Q_{0}(N)), we discuss the relationships between invariant prime subnearrings (I-primes) of (N*G) and G-invariant prime subnearrings (GI-primes) of N. Particularly we describe all the I-primes (P_{i}) of (N*G) such that each ( P_{i}cap N={0}), a GI-prime of N. As an application, we settle Incomparability and Going Down Problem for N and (N*G) in this situation.

Given a group G and a G-category ({textbf{C}}), we give a condition on a diagram of simplicial sets indexed by ({textbf{C}}) that allows us to define a natural action of G on its homotopy colimit, and some other simplicial sets defined in terms of the diagram. Well-known theorems on homeomorphisms and homotopy equivalences are generalized to equivariant versions.

We mainly give a numerical condition to ensure the finite generation of the effective monoids of some smooth projective rational surfaces. These surfaces are constructed from the blow-up of any fixed Hirzebruch surface at some special configurations of ordinary points. Under this numerical condition, we determine explicitly the list of all ((-1)) and ((-2))-curves. In particular, we complete a result obtained by Harbourne (Duke Math J 52(1):129–148, 1985) and another result obtained by the third author (C R Math 338(11):873–878, 2004). Moreover, the Cox rings of these surfaces are finitely generated. Our ground field is assumed to be algebraically closed of any characteristic.

Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for nonlinear equations called the reaction–diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction–diffusion model is designed, and its convergence is established. Numerical experiments using the HMM method are presented to facilitate the study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium.

We identify a norm-dense subspace of the dual of the sequence space (l^{(p,infty )}), thus closing the existing gap in the literature. We based our approach on the notion of James orthogonality, absolutely continuous norms and on the uniform convexity and the uniform smoothness of the underlying subspaces.

In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit the same one-parameter point transformations which leave the equations invariant. Reductions with these invariant functions lead to highly nonlinear third-order ordinary differential equations. We use a power series to establish interesting solutions to the reduced equations, whereby recurrence relations occur and convergence of the series may be tested. Finally, the conserved vectors of the class are constructed.

In the present study, we are interested in solving the nonhomogeneous second-order linear difference equation with periodic coefficients of period ( pge 2), by bringing two new approaches enabling us to provide both analytic and combinatorial solutions to this family of equations. First, we get around the problem by converting this kind of equations to an equivalent family of nonhomogeneous linear difference equations of order p with constant coefficients. Second, we propose new expressions of the solutions of this family of equations, using our techniques of calculating the powers of product of companion matrices and some properties of generalized Fibonacci sequences. The study of the special case ( p=2 ) is provided. And to enhance the effectiveness of our approaches, some numerical examples are discussed.

The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 2.1 in [Berinde, Vasile. Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators, Annals of West University of Timisoara-Mathematics and Computer Science, vol. 56, no. 2, 2018, pp. 13–27], as well as, several related results. Further results, in Hilbert spaces without a partial order, are stated too.