In this paper, we study the geometric behavior of a class of normalized Ramanujan entire-type functions and their Alexander transforms in the open unit disc. We establish new criteria ensuring that these functions are lemniscate starlike or lemniscate convex with respect to the right half of the Bernoulli lemniscate. Several illustrative examples are provided to demonstrate the behavior of the functions under the obtained conditions. These results contribute to a deeper understanding of the geometric properties of Ramanujan-type special functions.
Let f : V (G) -> {0, 1, 2} be a function defined on a graph G with vertex set V (G). For each i is an element of {0, 1, 2}, let Vi = {v is an element of V (G) : f (v) = i}. The function f is called an independent Roman dominating function on G if V1 boolean OR V2 is an independent set of G and every vertex in V0 is adjacent to at least one vertex in V2. The weight of f is defined as . The independent Roman domination number of G, denoted by iR (G), is the minimum weight among all independent Roman dominating functions on G. In this paper, we study this parameter in the edge corona product graph G & diam; H of two graphs G and H . Specifically, we establish tight bounds for iR (G & diam; H ) in terms of invariants of the factor graphs G and H. Furthermore, we derive closed formulas for iR (G & diam; H ) for some well-known families of graphs G.
A topological space X is called connected modulo an ideal of its subsets if there exists no continuous function f : X -> [0, 1] such that and yet . This paper establishes that X is connected modulo precisely when is Coz-prime (i.e., for cozero-sets A, B subset of X satisfying implies , or equivalently, the ring ideal is pseudo-irreducible in C (X ). This result provides a complete characterization of connectedness modulo ideals in terms of topological and algebraic properties. As applications, we unify and simplify several known results while also addressing two unresolved questions in existing research.
In this paper, we first prove that there exists a weakly Lindel & ouml;f non-CCC space X which is the union of a countable family of closed discrete subsets of X , which gives a positive answer to Question 3.14 of [11]. By using the same example, we show that a weakly Lindel & ouml;f Tychonoff space in which every Lindel & ouml;f subspace is CCC may not be CCC, which answers Question 3.13 of [11] negatively. Finally, we prove that |X | <= 2 Delta 2 (X )hLc(X ) for any star Lindel & ouml;f space X , where Delta 2 (X ) is the minimal cardinal kappa such that X has a rank 2 G kappa-diagonal and hLc(X ) is the supremum of the cellularities of Lindel & ouml;f subspaces of X .
In this paper, we investigate the conditions under which global solutions do not exist for the following inhomogeneous parabolic equation with two nonlocal nonlinear terms:We focus on how the memory effects introduced by the nonlinear terms |u|p and |del u|q, through the Riemann-Liouville fractional integrals and , influence the existence or blow-up of solutions. Using the test function method, we analyze various cases depending on the values of alpha and beta.
This paper examines the behavior of Ricci solitons within the framework of hyperbolic geometric flow on twisted warped product manifolds. By studying the influence of conformal and concurrent vector fields, we establish conditions under which these solitons reduce to Einstein manifolds, particularly when the warping function is constant or satisfies specific criteria. The analysis reveals that concurrent vector fields lead to Ricci-flat structures in both the base and fiber components, while Ricci bi-conformal vector fields introduce new geometric constraints. These results deepen the understanding of how curvature and flow dynamics interact in product manifolds, with potential implications for theoretical physics and differential geometry. The study provides foundational insights for future explorations of geometric evolution equations and their applications in mathematical cosmology.
The Euler-Sombor index is a vertex-degree-based topological index defined for a graph G = (V,E) as where du and dv denote the degrees of adjacent vertices u and v. In prior work [6], the chemical trees and unicyclic graphs with the minimum Euler-Sombor indices were characterized, prompting the search for extremal values over all chemical graphs. This paper extends that work by determining the first three minimum Euler-Sombor indices among chemical bicyclic graphs and the first seven among chemical tricyclic graphs. Furthermore, we prove that the minimum Euler-Sombor index for both unicyclic and bicyclic chemical graphs is attained when the maximum degree is at most 4, thereby conclusively establishing the minimum values for these graph classes.
Let H be an infinite-dimensional Hilbert space over the real or complex number field the algebra of all bounded linear operators on H . Assume that is an additive map. In this paper, we prove that delta is a local Jordan derivation if and only if delta(P ) = delta(P )P + P delta(P ) holds for all idempotent operators , if and only if delta is an inner derivation, that is, there exsits some such that delta(A) = AR - RA for all . As applications, we show that delta satisfies delta(A)B + A delta(B) + delta(B)A + B delta(A) = D for all with AB + BA = C , where are any two fixed operators if and only if there exsits some and some such that D = delta(C ) + & micro;C and delta(A) = AR - RA + & micro;A for all ; and give complete characterizations of delta satisfying delta(A)A + A delta(A) = delta(P ) for all with A2 = P , where P = 0, I or a nontrivial idempotent operator with infinite-dimensional range and infinite- dimensional kernel. These generalize several known results.
This paper investigates a fourth-order parabolic equation with double logarithm nonlinearities. Using the Galerkin method, we establish the global existence and uniqueness of weak solutions. By classifying the initial energy, we derive blow-up criteria of solutions and obtain explicit upper bounds for the blow-up time of solutions. Moreover, we present new threshold criteria for the extinction and non-extinction behavior of solutions. Specifically, we give the upper bound and lower bound for the extinction rate of solutions. These results generalize and improve some earlier related results in the literature.
Sharp upper bounds for the Hankel, generalized Zalcman and Krushkal coefficient functionals are investigated for the class of normalized analytic functions f defined in an open unit disk with the quantity zf ' / f lying in the evolute of a nephroid curve in the right-half plane. The similar analysis is also carried out when the expression zf '/f is replaced with . Moreover, the sharp radii constants concerning the class are also computed.
The paper is devoted to those subsets in the dual of a Banach lattice E for which every almost Dunford-Pettis weakly p-summable sequence (x(n) ) in E converges uniformly on them (the almost Right sets of order p). As an application, Banach lattices with the strong relatively compact Dunford-Pettis property of order p and weak Dunford-Pettis property of order p are characterized, with respect to almost Dunford-Pettis p-convergent operators. After that, the classes of disjoint Dunford-Pettis p-convergent operators and positively unconditionally p-converging operators are studied. It is established that positively unconditionally p-converging operators are exactly the disjoint p-convergent operators for all p >= 2.
We introduce the two-Arens-Eells space and the bi-Lipschitz tensor product for two pointed metric spaces, extending the classical Lipschitz tensor product. We show that the space of two-Lipschitz operators admits a canonical linearization through these constructions. We obtain isometric identifications between bi-Lipschitz tensor products and tensor products of Lipschitz-free Banach spaces. As an application, we characterize integral Lip-linear operators in terms of injective bi-Lipschitz tensor norms.
The question regarding the location of Banach spaces inside their biduals has been investigated and answered reasonably satisfactorily in the linear theory of Banach spaces. Thus, for instance, whereas it is known that a dual Banach space is complemented inside its bidual, the space c0 is not! However, it turns out that c0 is a Lipschitz retract of & ell;infinity , the bidual of c0 . In his famous paper of 1964, Lindenstrauss asked if each Banach space is a Lipschitz retract of its bidual. In this short note, we show how to relate the Lindenstrauss Problem (LP) to certain other important and well-known questions that remain open in the Lipschitz theory of Banach spaces and how these latter questions may be settled in the affirmative under the assumption of (LP) having a positive solution.
Based on the mixed cone-volume measure, we introduce in this paper a new ellipsoid, called the mixed-sine Lutwak-Yang-Zhang (LYZ) ellipsoid, which serves as a sine counterpart to the mixed LYZ ellipsoid. Several related volume inequalities for this ellipsoid are also established.
This paper studies multiplicative fractional Simpson-like inequalities, which are commonly employed in the error analysis of quadrature formulas within the multiplicative Riemann-Liouville (RL) fractional framework. First, we develop a multiplicative fractional identity for multiplicatively twice-differentiable functions. Utilizing the introduced identity, we formulate Simpson-like inequalities under the following two conditions: (i)J** satisfies multiplicative s-convexity, or (ii)(In J**)(q) is s-convex for q > 1. To validate and illustrate the presented inequalities, we finally provide numerical examples and graphical depictions, which clearly support the theoretical results.
