Let R be a noncommutative prime ring of char (R) =6 2, Q(r) be its right Martindale quotient ring and C be its extended centroid. Suppose that f (r(1), ... , r(n)) is a noncentral multilinear polynomial over C and F : R -> R is an X-generalized skew derivations of R. We describe all possible forms of the maps F when R satisfies the condition a[F(f (r)), f (r)] - [F(f (r)), f (r)]a is an element of C for all r = (r(1), ... , r(n))is an element of R-n. As an application of this result, we also describe the possible forms of the maps F and G satisfying the conditions (i) [F(f (r)), f (r)] is an element of C for all r = (r(1), ... , r(n)) is an element of R-n; (ii) [[F(u), u], [G(v), v]] = 0 for all u, v is an element of f (R), where F and G are both X-generalized skew derivations of R.
This paper is concerned with the so-called Bouchut-Boyaval relaxation model, which is a fully linearly degenerate 4 & times; 4 hyperbolic system of conservation laws. The well-known Suliciu relaxation model is its particular situation. The Riemann problem is completely solved with four different structures. The first is composed of the contact discontinuities, the second contains a single overcompressible (delta-shock wave, and the last two involve a contact discontinuity and a non-overcompressible (delta-shock wave. As the main feature, the Bouchut-Boyaval relaxation model as well as the Suliciu relaxation model admits not only the overcompressible (delta-shock waves but also non-overcompressible (delta-shock waves.
This study concerns the existence of positive solutions for the following non-linear boundary value problem {-Delta u = am(x)u-bu(2)-c u(P) /uP+1-K in Omega, n.Vu+ g (u) = 0, x E partial derivative Q. where Delta u = div(del(u)) is the Laplacian of u, while a, b, c, p, K are positive constants with p > 2, Q is a bounded smooth domain of R-N with partial derivative Q in C(2)and g is an element of C-1 ([0,infinity), [0, infinity)) is decreasing for some theta > 0. The weight function m satisfies m is an element of C(Omega) and m(x) > m(0) > 0 for x is an element of Q, also ||m||infinity = l < infinity. This model describes the dynamics of the fish populations. Our existence results are established via the well-known sub-super solution method.
In this paper, we introduced bivariate Chlodowsky variant of BernsteinSchurer operators based on (p,q)-integers. We also studied the estimates of moments of these operators, the weighted approximation theorem, and Korovkin-type approximation theorems. Besides these, the error of approximation using full modulus of continuity and partial modulus of continuity, the rate of convergence, and a convergence theorem for Lipschitz continuous functions were also presented. Furthermore, we generalised the Chlodowsky variant of Bernstein-Schurer operators based on (p,q)integers. Lastly, the numerical results for the defined operators are comparatively illustrated to show the minimised error of approximation to some functions.
In this paper, we investigate the symmetric matrix H = [H-max(i,H-j)](n) (i,)j=1 and its Hadamard exponential e(degrees H) = [ e(H)max(i,j) ], where H-k denotes the kth harmonic number. We derive explicit formula for the determinants and inverses of these matrices, and we establish expressions for their Euclidean norms as well as bounds for their spectral norms. Illustrative examples and tables are provided to highlight and verify these properties.
Domination parameters are defined by combining domination with another graph-theoretical property. This paper considers some of the five fundamental domination parameters in domination theory like total domination and paired domination. Initially, we determine the domination number gamma for bishop's and rook's graph, then find the total domination number gamma(t) and paired domination gamma(pr )for queen's graph, bishop's graph, and rook's graph on a hexagonal board of order N (H-N).
This paper investigates the initial value problems for a class of magnetohydrodynamics Euler equations. First, the elementary wave interactions including the overtaking and collisions of shock waves and central rarefaction waves are studied. Then, one special Riemann problem of the magnetohydrodynamics Euler equations with three constant initial values is considered, and the global solution structure is obtained. Finally, a class of Cauchy problems with general initial values for the magnetohydrodynamics Euler equations is studied, and the global existence of weak entropy solution is established.
We prove global well-posedness of the 3D fractional porous medium equation with critical dissipative for small initial data in the Triebel-Lizorkin spaces F-p,q(s), s > p , p, q is an element of (1, infinity). In particular, our result implies the global existence for small initial 3 data in the Sobolev spaces H-p(s), s > 3/p, p is an element of (1, infinity) since H-p(s)(R-3) = F-p,2(s)(R-3). The key ingredients of our proof are the pointwise exponential decay estimate of the semigroup e-t alpha(-Delta)( 1 /2 )and maximum principle.
A sequential closure relative to a given topology tau provides a method for constructing a new topology tau S, the associated sequential topology, which is the finest topology possessing the same convergent sequences. In this paper, we give the elementary properties of this topology in relation with many topological concepts such as convergence, continuity, capacity and density. We will also be concerned with the problem of the stability of the associated sequential topologies. We shall explore the relationship between the intrinsic associated sequential topology and the induced associated sequential topology relative to inductive topology, projective topology and disjoint union topology.
In this paper, a characterization of normed barrelled spaces is given, as well as a similar characterization of rings of sets with the Nikodym Property. Finally, a condition that is equivalent to a Banach space having a separable quotient is discussed.
The authors have introduced the concept of Cayley conjugate digraph C(G, S), associated with a finite group G and a subset S of G and obtained its basic properties, as well as the structure of its components. In this paper the concepts of component preserving bijection of a digraph and the component preserving inner bijection of the Cayley conjugate digraphC(G, S), are introduced and establish that the set CP(C) of all component preserving bijections of the digraphC(G, S), forms a group under the composition of mappings. Further it is shown that the set CPI ( ') of all component preserving inner bijections of the digraphC(G, S), is a subgroup of CP(C) and CPI (C) congruent to G/Z, where Z is the center of the group G.
In this paper, we modify the notion of a A-structure on a set X provided by Magill Jr. and Subbiah in 1974, to suit the setting of the semigroup T(sic)(X, Y ) of full transformations on X mapping Y into itself, where Y is a fixed nonempty subset of X. With this modification, we obtain a class of subsemigroups of T(sic)(X, Y ). Regularity and Green's relations for regular elements of semigroups in this class are also studied. We end this paper by extending the 2022 work of Konieczny to the setting of the semigroup of full transformations belonging to a given subsemigroup of T(sic)(X, Y ) whose restrictions belong to a given subsemigroup of the semigroup T (Y ) of full transformations on Y. This is done by using the modified notion of a A-structure.
We study rings having the property that every cyclic right module is pseudoinjective or automorphism-invariant. Such rings are called right cpsi-rings. We show that a ring R is right nonsingular right cpsi-ring if and only if R = S x T, where S is a semisimple ring and T is a strongly regular ring such that for any ideal A of T, T/A is such that it contains all the invertible elements of its maximal right ring of quotients; moreover the ring R is a right a-ring (i.e., every right ideal is automorphism-invariant). However, an explicit example shows that not every a-ring is right nonsingular right cpsi-ring.
In this paper we give a characterization of a regular multiplicative ternary hyperring using semiprime hyperideals. We introduce the notion of semiprime hyperideal in a multiplicative ternary hyperring and study it. We obtain some characterizations of semiprime hyperideals. We also introduce the notions of weak-n-system and strong nsystem in a multiplicative ternary hyperring and using these we characterize semiprime hyperideal. We prove that in a regular multiplicative ternary hyperring, every hyperideal is semiprime. Lastly we obtain some conditions under which the converse of the above result holds.
In this paper, we investigated the characteristics of P0-almost distributive lattices by leveraging foundational concepts from Traczyk and Rao et al. The central focus lies in the structural intricacies of P-0-ADLs, marked by specific ascending sequences and established correlations among prime ideals, chain bases, and specific ideals. A key revelation emerges, indicating that prime ideals align with disjoint maximal chains containing at most n-1 members. In conclusion, the paper provides concise overviews of equivalent conditions for properties pertaining to prime ideals and chain bases in P-0-ADLs.
In this paper, we study the uniqueness of an entire function when it shares a small function with its various order differences. In particular, our result is an improvement of a results of J.P. Wang and H.X. Yi [13].
In this paper, we establish unitarily invariant norm inequalities of matrices, which generalize some recent results.
Let p be a prime greater than 5. In this paper, we show that the composite homtotopy element involving Pi(n), gamma(p-1)Pi(n), is nontrivial for n >= 4, and is trivial for n = 3 in the stable homotopy groups of spheres.
In this paper, we propose to solve a problem where we have two linear fractional utility functions to optimize over the efficient set of a multiobjective integer linear fractional problem. The problem can also arise when one wants to find the intersection between two efficient sets of two multiobjective problems. This type of problem arises to model real-life situations where two decision makers are working on the same problem and each of them has their own objectives that they want to optimize, and the goal is to find the best compromise solutions. The proposed method is an exact method based on the branch-and-cut technique, which uses efficient cuts to eliminate the dominated solutions for both problems from the search space. We also demonstrate how to extend the proposed method to the general case of multiple utility functions. We present a computational study to show the performance of the method and presented a didactic example.
In this paper, we study the concept of statistical order convergence and some generalized statistical convergence in (l)-group by using weighted density [3] and modulus function. We study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequences under which the subsequence is also generalized statistically convergent. Also we consider similar type of results for the case of generalized statistically bounded sequences. The entire investigation is performed in the setting of (l)-group extending the recent results in [8].
