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Abstract: Abstract This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In particular, we extend the classical Massera’s theorem, dealing with periodic systems of the type $$\begin{aligned} x'=A(t)x+f(t) , \end{aligned}$$ and clarify that this theorem deals with a case of resonance. Then we provide instability results for the corresponding semilinear systems, with the linear part at resonance. We also use the solution curves developed previously by the author to establish the instability results for pendulum-like equations, and for first-order periodic equations. PubDate: 2024-05-16

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Abstract: Abstract The main result of this paper is to establish a weighted second-order Adams-type inequality on the whole set of \(\mathbb {R}^{4}\) . As an application of this result, we prove the existence of a solution for a Kirchhoff-type equation involving non-linearity with subcritical or critical exponential growth. In the critical case, the associated energy loses its compactness. To avoid this problem, we add an asymptotic condition to the nonlinearity PubDate: 2024-05-15

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Abstract: Abstract The t-path ideal \(I_t(G)\) of a graph G is the square-free monomial ideal generated by the monomials which correspond to the paths of length t in G. In this paper, we prove that the Stanley–Reisner complex of the 2-path ideal \(I_2(G)\) of an (undirected) tree G is vertex decomposable. As a consequence, we show that the Alexander dual \(I_2(G)^{\vee }\) of \(I_2(G)\) has linear quotients. For each \(t \ge 3\) , we provide a counterexample of a tree for which the Stanley–Reisner complex of \(I_t(G)\) is not vertex decomposable. PubDate: 2024-05-14

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Abstract: Abstract In this article, we investigate a class of nonsmooth multiobjective mathematical optimization problems with switching constraints (abbreviated as, (NMMPSC)) in the framework of Hadamard manifolds. Corresponding to (NMMPSC), the generalized Guignard constraint qualification (abbreviated as, (GGCQ)) is introduced in the Hadamard manifold setting. Karush–Kuhn–Tucker (abbreviated as, KKT) type necessary conditions of Pareto efficiency are derived for (NMMPSC). Subsequently, we introduce several other constraint qualifications for (NMMPSC), which turn out to be sufficient conditions for (GGCQ). We have furnished non-trivial illustrative examples to justify the significance of our results. To the best of our knowledge, constraint qualifications for (NMMPSC) have not yet been studied in the Hadamard manifold framework. PubDate: 2024-05-13

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Abstract: Abstract In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented. PubDate: 2024-05-13

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Abstract: Abstract We study the long-time dynamics of a wave equation with nonlocal weak damping, nonlocal weak anti-damping and sup-cubic nonlinearity. Based on the Strichartz estimates in a bounded domain, we obtain the global well-posedness of the Shatah–Struwe solutions. To overcome the difficulties brought by the nonlinear weak damping term, we present a new-type Gronwall’s lemma to obtain the dissipative for the Shatah–Struwe solutions semigroup of this equation. Finally, we establish the existence of a time-dependent exponential attractor with the help of a more general criteria constructed by the quasi-stable technique. PubDate: 2024-05-13

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Abstract: Abstract The aim of this paper is to introduce Clairaut conformal submersions between Riemannian manifolds. First, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. In particular, we obtain Clairaut relation for geodesics on the total manifolds of conformal submersions, and prove that Clairaut conformal submersions have constant dilation along their fibers, which are totally umbilical, with mean curvature being gradient of a function. Further, we calculate the scalar and Ricci curvatures of the vertical distributions of the total manifolds. Moreover, we find a necessary and sufficient condition for Clairaut conformal submersions to be harmonic. For a Clairaut conformal submersion we find conformal changes of the metric on its domain or image, that give a Clairaut Riemannian submersion, a Clairaut conformal submersion with totally geodesic fibers, or a harmonic Clairaut submersion. Finally, we give two non-trivial examples of Clairaut conformal submersions to illustrate the theory and present a local model of every Clairaut conformal submersion with integrable horizontal distribution. PubDate: 2024-05-08

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Abstract: Abstract In this article, a SIRS epidemic model with a general incidence rate is proposed and investigated. We briefly verify the global existence of a unique positive solution for the proposed system. Moreover, and unlike other works, we were able to find the stochastic threshold \(\mathcal {R}_s\) of the proposed model which was used for the discussion of the persistence in mean and extinction of the disease. Moreover, we utilize stochastic Lyapunov functions to show under sufficient conditions the existence and uniqueness of stationary distributions of the solution. Lastly, numerical simulation is executed to conform our analytical results. PubDate: 2024-05-07

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Abstract: Abstract This paper is devoted to deriving the multiplicity result of solutions to the nonlinear elliptic equations of Kirchhoff–Schrödinger type on a class of a nonlocal Kirchhoff coefficient which slightly differs from the previous related works. More precisely, the main purpose of this paper, under the various conditions for a nonlinear term, is to show that our problem has a sequence of infinitely many small energy solutions. In order to obtain such a multiplicity result, the dual fountain theorem is used as the primary tool. PubDate: 2024-04-30

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Abstract: Abstract Consider a bipartite distance-regularized graph \(\Gamma \) with color partitions Y and \(Y'\) . Notably, all vertices in partition Y (and similarly in \(Y'\) ) exhibit a shared eccentricity denoted as D (and \(D'\) , respectively). The characterization of bipartite distance-regularized graphs, specifically those with \(D \le 3\) , in relation to the incidence structures they represent is well established. However, when \(D=4\) , there are only two possible scenarios: either \(D'=3\) or \(D'=4\) . The instance where \(D=4\) and \(D'=3\) has been previously investigated. In this paper, we establish a one-to-one correspondence between the incidence graphs of quasi-symmetric SPBIBDs with parameters \((v, b, r, k, \lambda _1, 0)\) of type \((k-1, t)\) , featuring intersection numbers \(x=0\) and \(y>0\) (where \(y \le t < k\) ), and bipartite distance-regularized graphs with \(D=D'=4\) . Moreover, our investigations result in the systematic classification of 2-Y-homogeneous bipartite distance-regularized graphs, which are incidence graphs of quasi-symmetric SPBIBDs with parameters \((v,b,r,k, \lambda _1,0)\) of type \((k-1,t)\) with intersection numbers \(x=0\) and \(y=1\) . PubDate: 2024-04-29

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Abstract: Abstract For a Tychonoff space X, let \(C_{B}(X)\) be the \(C^{*}\) -algebra of all bounded complex-valued continuous functions on X. In this paper, we mainly discuss Tychonoff one-point extensions of X arising from closed ideals of \(C_{B}(X)\) . We show that every closed ideal H of \(C_{B}(X)\) produces a Tychonoff one-point extension \(X(\infty _{H})\) of X. Moreover, every Tychonoff one-point extension of X can be obtained in this way. As an application, we study the partially ordered set of all Tychonoff one-point extensions of X. It is shown that the minimal unitization of a non-vanishing closed ideal H of \(C_{B}(X)\) is isometrically \(*\) -isomorphic with the \(C^{*}\) -algebra \(C_{B}\left( X(\infty _{H})\right) \) . We provide a description for the Čech–Stone compactification of an arbitrary Tychonoff one-point extension of X as a quotient space of \(\beta X\) via a closed ideal of \(C_{B}(X)\) . Then, we establish a characterization of closed ideals of \(C_{B}(X)\) that have countable topological generators. Finally, an intrinsic characterization of the multiplier algebra of an arbitrary closed ideal of \(C_{B}(X)\) is given. PubDate: 2024-04-29

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Abstract: Abstract In this paper, we study the following critical \( p \& q\) -Laplacian problem with shifting subcritical perturbation nonlinearity: where \(\Omega \subset {\mathbb {R}}^{N}\) is open bounded, \(k>0\) , \(1<q<p<N\) , \(p^{*}=\frac{Np}{N-p}\) is the critical Sobolev exponent and \(h(x)\in C(\Omega )\) is nonnegative. Under suitable assumptions on exponents q and r, we show the existence of mountain pass solutions \(u_{k}\) to ( \(P_{k}\) ) for all \(k\in (0,+\infty )\) . Moreover, we also investigate the behavior of the solutions \(u_{k}\) for varying k and show the concentration phenomena as \(k\rightarrow +\infty \) . PubDate: 2024-04-24

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Abstract: Abstract We study properties of Wilder, strongly Wilder, continuumwise Wilder, D, \(D^*\) , and \(D^{**}\) Hausdorff continua. We present an example of a colocally connected continuum that is not a \(D^*\) -continuum, answering a question by Espinoza and Matsuhashi. We give several positive answers to this question for unicoherent continua. We also present some equivalences for the class of homogeneous Hausdorff continua with the property of Kelley. PubDate: 2024-04-23

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Abstract: Abstract By applying the “coefficient extraction method” to hypergeometric series, we establish several remarkable identities for infinite series of convergence rate \(\frac{1}{64}\) about harmonic numbers and central binomial coefficients, including three conjectured ones made recently by Sun Z-W. PubDate: 2024-04-16

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Abstract: Abstract We consider the following singular quasilinear Schrödinger equations involving critical exponent $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\Delta u-\frac{\alpha }{2}\Delta ( u ^{\alpha }) u ^{\alpha -2}u=\theta u ^{k-2}u+ u ^{2^{*}-2}u+\lambda f(u), x\in \Omega ,\\ \hspace{1.65in}u=\,0, x\in \partial \Omega , \end{array} \right. \end{aligned}$$ where \(0<\alpha <1\) . By using the variational methods, we first prove that for small values of \(\lambda \) and \(\theta \) , the above problem has infinitely many distinct solutions with negative energy. Besides, we point out that odd assumption on f is required; the problem has at least one nontrivial solution. Finally, a new modified technique is used to consider the existence of infinitely many solutions for far more general equations. PubDate: 2024-04-10

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Abstract: Abstract The eccentricity matrix of a simple connected graph G is obtained from the distance matrix of G by retaining the largest nonzero distance in each row and column, and the remaining entries are defined to be zero. A bi-block graph is a simple connected graph whose blocks are all complete bipartite graphs with possibly different orders. In this paper, we study the eccentricity matrices of a subclass \({\mathscr {B}}\) (which includes trees) of bi-block graphs. We first find the inertia of the eccentricity matrices of graphs in \({\mathscr {B}}\) , and thereby, we characterize graphs in \({\mathscr {B}}\) with odd diameters. Precisely, if the diameter of \(G\in {\mathscr {B}}\) is more than three, then we show that the eigenvalues of the eccentricity matrix of G are symmetric with respect to the origin if and only if the diameter of G is odd. Further, we prove that the eccentricity matrices of graphs in \({\mathscr {B}}\) are irreducible. PubDate: 2024-04-10

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Abstract: Abstract We investigate the following two types of nonlinear differential-difference equations $$ L(z,f)+H(z,f)=\sum _{k=1}^r\alpha _k(z)e^{\beta _k z}; \ \ \ \ $$ $$L(z,f)+H(z,f)=\sum _{k=1}^rF_k(z), \ \ \ \ \ \ \ \ \ $$ where \(\alpha _1, \ldots , \alpha _r\) are meromorphic functions of order \(<1,\) and \(F_1,\ldots , F_r\) are periodic transcendental entire functions, and L, H are defined by \(L(z,f)=\sum _{k=1}^pa_k(z)f^{(m_k)}(z+\tau _k)\not \equiv 0,\) \(H(z,f)=\sum _{k=1}^qb_k(z)\big [f^{(n_k)}(z+\zeta _k)\big ]^{s_k} \ \ \) with small meromorphic coefficients \(a_i, b_j.\) By introducing a new method, we obtain the exact forms of the solutions of these two equations under certain growth conditions. PubDate: 2024-04-09

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Abstract: Abstract G-character tables of a finite group G were defined in Felipe et al. (Quaest Math, 2022. https://doi.org/10.2989/16073606/16073606.2022.2040633). These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal subgroups which can be determined using their G-character tables. For instance, we prove an extension of the Thompson’s theorem from minimal G-invariant characters of a normal subgroup. We also obtain a variation of Taketa’s theorem for hypercentral normal subgroups considering their minimal G-invariant characters. This generalization allows us to introduce a new class of nilpotent groups, the class of nMI-groups, whose members verify that its nilpotency class is bounded by the number of irreducible character degrees of the group. PubDate: 2024-04-09

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Abstract: Abstract An interval in which a given graph has no eigenvalues is called a gap interval. We show that for any real number R greater than \(\frac{1}{2}(-1+\sqrt{2})\) , there exist infinitely many threshold graphs with gap interval (0, R). We provide a new recurrence relation for computing the characteristic polynomial of the threshold graphs and based on it, we conclude that the sequence of the least positive (resp. largest negative) eigenvalues of a certain sequence of threshold graphs is convergent. In some particular cases, we compute the limit points. PubDate: 2024-04-08

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Abstract: Abstract In this paper, we explore some properties of the dual Wills functional, which are part of the dual Brunn–Minkowski theory. We give the upper and lower bounds for the dual Wills functional in terms of the 1-th dual volume of star bodies. Moreover, an inequality that is associated with the section of convex bodies for isotropic measures is presented. PubDate: 2024-04-08