In this paper, we investigate the curvature properties of a family of four-dimensional Walker manifolds. We establish the existence of non-trivial Ricci solitons on this family of manifolds and provide explicit examples to illustrate the results.
The object of the present article is to characterize Yamabe solitons admitting torse-forming vector fields with supporting non-trivial examples. Quotient Yamabe almost solitons with potential vector fields as infinitesimal harmonic transformations are studied. In addition, a triviality result of quotient almost Yamabe soliton is established using an integral inequality.
The set CS(L) of all convex sublattices of a lattice L, excluding & empty;, was studied by S. Lavanya and S. P. Bhatta using the partial order <=, defined as follows: for A, B is an element of CS(L), A <= B if and only if 'for each a is an element of A, there is b is an element of B such that a <= b' and 'for each b is an element of B, there is a is an element of A such that a <= b'. They showed that (CS(L), <=) is a lattice such that both L and CS(L) lie in the same equational class. Also, they obtained many significant results concerning CS(L). The present paper generalizes many of these results along with some related results of others, from lattices to trellises, by introducing the notion of 'strongly-convex subtrellises' in trellises in place of 'convex sublattices' in lattices.
In this paper, we show that if (A, ||.||(p)), 0 < p <= 1, is a unital semi-simple p-Banach algebra such that, for every non-zero idempotent element u of A, Sp(Au) (x) is finite for each x is an element of partial derivative(G(A(u)), where A(u) = uAu, then A is finite-dimensional. As a consequence, we obtain that a spectrally finite p-Banach algebra is finite-dimensional modulo its Jacobson radical. Similar results are also obtained with the spectrally convex property.
In this paper, we investigate the geometric aspects of the action of SL(3, R) subgroups in the real projective plane from an Erlangen perspective. Specifically, the study investigates the projective action of the subgroups of SL(3, R) on the non-degenerate conics in RP2, which is obtained as the two-dimensional homogeneous space of SL(3, R). By investigating the subgroup of SL(3, R) that preserves the projective unit circle, a connection is established between this subgroup and the Lie group SL(2, R). Expanding upon V. Kisil's research on the EPH classification of geometries related to the Mobius action of SL(2, R), this paper extends the analysis to the projective action of SL(3, R), with the adjoint representation of SL(2, R) playing a significant role. Mappings from the elliptic, parabolic, and hyperbolic (abbreviated as EPH) upper half plane to the interior, boundary, and exterior of the projective unit circle are investigated. A unified expression for isomorphisms facilitates a cohesive framework for analyzing these mappings. Furthermore, the study investigates Mobius -invariant cycle images, demonstrating that elliptic and hyperbolic cycles correspond to ellipses and hyperbolas, respectively, while parabolic cycles map to the projective unit circle.
This paper addresses the nonlo cal controllability of fractional systems, specifically focusing on systems where derivatives are interpreted in the generalized Caputo fractional sense, governed by a function phi. We establish sufficient conditions for the controllability of such systems, taking into account the lack of compactness in the characteristic operators that typically appear in the solutions. To overcome this challenge, we employ weak compactness conditions, which allow us to derive a fundamental result supporting the validity of the controllability outcomes. The theoretical framework developed in this study is demonstrated through a nontrivial example, illustrating its practical relevance and robustness in real-world applications. Our results contribute to advancing the understanding of fractional systems in control theory, particularly in contexts where traditional assumptions about compactness do not hold.
Every positive integer can be written as a sum of distinct nonadjacent terms of the Fibonacci sequence; it is known as Zeckendorf's Theorem. It is less well known that there exists a similar theorem for the real numbers in the open interval (0, 1). The converse of the theorem for generalized expansions, called periodic Zeckendorf expansions for the real numbers, is proved in the author's earlier paper. In this paper, we introduce a new approach to this converse problem.
We derive asymptotic estimates for some average values of the Jordan function evaluated over shifted smooth numbers in arithmetic progressions whose sum of digits as well as that of their successors are in arithmetic progression.
In this paper, we establish the boundedness of the multiple Erdelyi-Kober fractional integral operators involving Fox's H-function on the Hardy space H-1. Our results generalize recent results of Kwok-Pun Ho [Proyecciones 39 (3) (2020), 663-677]. Some useful connections related to the Hausdorff operators are also mentioned.
In this paper, we consider the classes of h-convex and m-convex functions and prove some continuous versions of Petrovic-type inequalities. Then, as an application of these results, we provide some new properties for the generalized Caputo-type fractional integrals.
In this paper, we provide the generating functions for partial generalized mock theta functions of the second order, as well as for some new partial generalized mock theta functions.
The aim of this paper is to obtain the sufficient conditions for oscillation and nonoscillation of vector solutions of a class of first-order two-dimensional nonautonomous neutral delay difference systems of the form triangle[alpha(nu) +q(nu)alpha(nu-p)beta(nu) +q(nu)beta(nu-p)]=[a1(nu)a2(nu)a3(nu)a4(nu)][phi(alpha(nu-l))psi(beta(nu-m))]+[omega 1(nu)omega 2(nu)], where p >0,m >= 0,l >= 0 are integers, aj(nu),j= 1,2,3,4,q(nu),omega 1(nu),omega 2(nu) are real valued sequences for nu is an element of N(nu 0), and phi,psi is an element of C(R,R) are bounded functions with the propertiesu phi(u)>0,v psi(v)>0 foru6= 0,v6= 0.We verify some of our results with illustrative examples
In this research article, we undertake a detailed study of f(lambda)-convergence and fa-Cauchy sequences in the setting of neutrosophic 2-normed linear spaces. We further introduce and rigorously examine the notions of f(lambda)-limit points and fa-cluster points of a sequence, elucidating the intricate relationships between these two concepts within this mathematical framework.
In this paper, the notions of equal convergence (ec), uniform equal convergence (u.ec), discrete convergence (dc), and uniform discrete convergence (u.dc), which were defined for the sequences of real-valued functions, are generalized with regard to any regular matrix A = (a(n,k)), and their generalized form are studied. The classical and generalized versions of these convergence concepts are compared, and some inclusions are given. Through constructed examples, it is shown that inclusions between them are strict. Finally, as an application, a more general form of the famous Korovkin's theorem is presented.
This article proposes new general inequalities based on the integral of two adaptive functions. The main originality of these results lies in two key aspects: (i) the assumptions considered, which combine monotonicity and primitive-like inequalities, and (ii) the expression of the bounds, in which the power and logarithmic transformations play a significant role. Several complementary integral inequalities are established under additional assumptions, including convexity assumptions. Applications and future directions are also discussed.
This study develops a new general partial summation formula for harmonic series, utilizing finite calculus techniques. The formula provides highly accurate upper and lower bounds without a correction term within which the exact partial sum lies. Additionally, an improved approximation formula for the summation of the harmonic series is introduced. The proposed general formula offers a straightforward and precise method for summing harmonic series, but has an unsolved term. The derived bounds are the closest to the exact partial sum, marking a significant advancement in the field. Comparisons with Euler's formula, based on general and RMS errors, demonstrate that the proposed approximation formula achieves superior accuracy. These findings bring a novel approach to harmonic series analysis, with potential applications in numerical analysis and theoretical research.
We derive a complete asymptotic expansion for an approximation operator based on Hermite polynomials. All coefficients are presented in an explicit form.
A triple Roman dominating function (TRDF) on a graph $G$ is a function $f :V(G)\to \{0, 1, 2, 3, 4\}$ satisfying the condition that for every vertex $v\in V(G)$ with $f(v)< 3$, $f(N_G[v])\geq |AN(v)|+3$, where $AN(v)$ is the set of vertices $w\in N_G(v)$ such that $h(w)\geq 1$. The weight of a TRDF $f$ is $\sum_{v\in V(G)}f(v).$ The triple Roman domination number $\gamma_{[3R]}(G)$ is the minimum weight of an TRDF on $G$. The $gamma_{[3R]}$-stability ($\gamma<^>-_{[3R]}$-stability, $\gamma<^>+_{[3R]}$-stability) of $G$, denoted by ${\rm st}_{\gamma_{[3R]}}(G) $ (${\rm st}<^>-_{\gamma_{[3R]}}(G)$, ${\rm st}<^>+_{\gamma_{[3R]}}(G)$), is defined as the minimum size of a set of vertices whose removal changes (decreases, increases) the triple Roman domination number. In this paper, we determine the exact values of the $\gamma_{[3R]}$-stability of some special classes of graphs, and present some bounds on ${\rm st}_{\gamma_{[3R]}}(G)$. Furthermore, for a tree $T$ with maximum degree $\Delta$, we show that ${\rm st}_{\gamma_{[3R]}}(T)=1 $ and ${\rm st}<^>-_{\gamma_{[3R]}}(T)\le \Delta $, and we characterize the trees that achieve the upper bound.
McKay, Miller, and Siran (1998) introduced a family of graphs, denoted H-q for prime powers q > 2, of order 2q(2), diameter 2, and degree (3q - delta )/2, where q equivalent to delta (mod 4) with delta is an element of {-1, 0, 1}. The McKay-Miller-Siran (MMS) graphs are vertex-transitive for q is an element of {3,4} and for every q equivalent to 1 (mod 4), with H-3 and H-4 being the only two Cayley graphs in the family. For other prime powers, the automorphism group of H(q )exhibits two vertex orbits. Originally, the MMS graphs were constructed as lifts of complete bipartite graphs K-q,K-q with attached loops or semi-edges. Later, Siagiova (2001) showed that for q equivalent to 1 (mod 4), these graphs are bi-Cayley; that is, they are lifts of two-vertex graphs. Using Hafner's (2004) results on the automorphism groups of MMS graphs, we show that MMS graphs H-q are bi-Cayley for every prime power q > 2.
In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Riemann-Liouvile type fractional Langevin equations equipped with nonlo cal multi-point and multi-strip coupled boundary conditions. We make use of Leray-Schauder's alternative and Banach's fixed point theorem to derive the desired results, which are well-illustrated with examples. Our results are useful in the given configuration and enrich the literature on boundary value problems for fractional Langevin equations.
