Arabian Journal of Mathematics最新文献

The main objective of this paper is to investigate the equivalence problem for fifth-order differential operators on the line. We specifically focus on the case where the differential operators are subjected to general fiber-preserving transformations. To tackle this problem, we employ the Cartan method of equivalence via direct equivalence problem. This method allows us to determine whether two given differential operators are equivalent or not under a certain transformation. By applying this method, we are able to establish the conditions under which two fifth-order differential operators are equivalent under general fiber-preserving transformations. This provides us with a comprehensive understanding of the equivalence problem for these operators on the line. Overall, this paper contributes to the field of differential equations by shedding light on the equivalence problem for fifth-order operators and providing a systematic approach to analyze their equivalence under general fiber-preserving transformations.

Let (mathcal {R}(R)) denote the commutative semiring of radical ideals of a commutative ring with identity, and (mathcal {R}(M)) denote the (mathcal {R}(R))-semimodule consisting of all radical submodules of an R-module M. Moreover, (mathcal {R}(-)) will be the covariant functor from the category of R-modules ({{R}{-}Mod}) to the category of (mathcal {R}(R))-semimodules ({mathcal {R}(R){-}Semod}) mapping any R-module M to the (mathcal {R}(R))-semimodule (mathcal {R}(M)) and any R-module homomorphism ( f:Mrightarrow M') to the (mathcal {R}(R))-semimodule homomorphism (mathcal {R}(f): mathcal {R}(M)rightarrow mathcal {R}(M')) defined by (mathcal {R}(f)(N)=operatorname {rad}(f(N))). In this article, we investigate the conditions under which the natural tensor functor (mathcal {R}(-)otimes _{mathcal {R}(R)} mathcal {R}(T)) (for an R-module T) preserves module exact sequences, by considering a tensor product for semimodules over commutative semirings and an exactness for semimodule sequences similar to those of modules over commutative rings. Among others, it is proved that for any ideal I of an absolutely flat ring R, (mathcal {R}(-)otimes _{mathcal {R}(R)} mathcal {R}(R/I)) preserves any short exact sequence of finitely generated faithful multiplication R-modules. Also, it is shown that for any F-vector space W, (mathcal {R}(-)otimes _{mathcal {R}(F)} mathcal {R}(W)) preserves any short exact sequence of vector spaces.

Our work shows that, for any given ideal (mathcal {I}) on a non empty set X, we can find a topology (tau ) in which the set of all closed and discrete sets in X coincides with (mathcal {I}). We prove that if (mathcal {I}) is any proper ideal on X, then we can find a topology (tau ^{prime }) in which (tau ^{prime }) makes (mathcal {I}) closed and discrete and (tau ^{prime }) is (T_{0}). Furthermore, we derive some properties of this topology. Finally, we find a compact extension of the newly constructed space.

The purpose of this study is to introduce new (p, q)-Hermite–Hadamard and (p, q)-Hermite–Hadamard–Fej(acute{e})r inequalities for LR-((h_{1},h_{2}))-convex interval-valued functions by means of pseudo-order relation ((le _{p})). The results of this paper generalize previously known results and lay a preliminary foundation for the further study on interval post-quantum integral inequalities. Useful examples are provided to verify the validity of the theory established in this research.

In this paper, we extended the applicability of the convergence analysis of the sixth-order iterative methods for solving nonlinear equations studied by Yaseen and Zafar (Arab J Math 11:585-599, 2022), whose analysis uses derivatives up to order seven. Also, we have done convergence analysis for the fourth-order method which can be obtained from their method by considering first two steps. Our analysis is applicable in more general Banach space settings and uses only the first three Frechet derivatives of the involved operator with Lipschitz-type conditions. Also, our analysis gives the computable radius of the convergence ball and the number of iterations to obtain the solution with a given accuracy.

The spectral decomposability of a closed linear relation T on a complex Banach space is demonstrated through three new characterisations: The first two are expressed in terms of the extended Bishop and decomposition properties while the third one is given by means of the coinduced operator of T and its local spectral subspaces. This has been achieved through the intensive study of the properties of the last mentioned subspaces as well as the ER-SVEP.

In this paper, we investigate the unique solvability of a generalized Tricomi problem with an integral condition for a loaded equation involving a fractional operator. By analyzing the problem for a third-order equation with a telegraph operator, we extend the results to a generalized operator with small parameters. Furthermore, the integral condition in the parabolic region enables the generalization of local problems associated with second- and third-order equations.

For the modified Newton-type (MN) iteration method for solving the GAVE, the convergence conditions and the quasi-optimal parameter matrix are discussed. The sufficient conditions are supplied to ensure that the GAVE has a unique solution. Besides, the numerical experiments are illustrated to show some of the presented results.

Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The present paper aims at studying some properties of ({textrm{Hom}_{textrm{R}}}(C, M)) and (C otimes _{R} M) where M is a non-zero finitely generated R-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to C. Finally, we establish relative versions of Ischebeck and Chouinard formulas for R-modules of finite relative homological dimensions with respect to C.