We introduce a local version of the Kreiss resolvent condition for Banach space operators and we relate it to the local growth of powers. Also, we introduce a local Yosida approximation and we establish some local results.

We generalize work of Stacy (Open Book Ser. 4 (2020), 387–401). to obtain upper bounds independent of $p$ for the minimal height of a totally $p$-adic algebraic number of degree 4. We also compute actual values of this minimal height for small primes $p$.

The power graph $\mathcal{𝒫}(G)$ of a finite group $G$ is defined to be the graph whose vertex set is $G$ and in which two distinct vertices $u,v\in \mathcal{𝒫}(G)$ are adjacent if and only if $u=v^m$ or $v=u^n$ for some positive integers $m,n$. The distance signless Laplacian matrix of a graph $\mathcal{𝒢}$, denoted by $D^Q(\mathcal{𝒢})$, is defined as $D^Q(\mathcal{𝒢})=\text{Tr}(\mathcal{𝒢})+D(\mathcal{𝒢})$, where $D(\mathcal{𝒢})$ is the distance matrix of $\mathcal{𝒢}$ and $\text{Tr}(\mathcal{𝒢})$ is the transmission matrix of $\mathcal{𝒢}$. We determine the distance signless Laplacian eigenvalues of the power graphs of the finite cyclic group ${\mathbb{Z}}_n$ and the dihedral group ${\text{D}}_n$. We provide upper and lower bounds on the largest eigenvalue of the distance signless Laplacian matrix of $\mathcal{𝒫}({\mathbb{Z}}_n)$ and $\mathcal{𝒫}({\text{D}}_n)$. We also give a short proof of the lower bound on the algebraic connectivity of $\mathcal{𝒫}({\mathbb{Z}}_n)$ obtained by Chattopadhyay and Panigrahi (Linear and Multilinear Algebra 63:7 (2015), 1345–1355).

For integers $N\ge 2$ and $g\ge 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.

We introduce new generalized fractional integrals for interval-valued functions. Then we prove generalized Hermite–Hadamard type inclusions for interval-valued convex functions using these newly defined generalized fractional integrals. We also show that these results generalize several results obtained in earlier works.

We introduce a family of commuting generalised symmetries of the Dunkl–Dirac operator inspired by the Maxwell construction in harmonic analysis. As an application, we use these generalised symmetries to construct bases of the polynomial null-solutions of the Dunkl–Dirac operator. These polynomial spaces form representation spaces of the Dunkl–Dirac symmetry algebra. For the ${\mathbb{Z}}_2^d$ case, the results are compared with previous investigations.

Here elastic transformation and its inverse transformation are used to solve two kinds of first- and third-order nonlinear ordinary differential equations (ODEs) with variable coefficients. First, elastic transformations are used to upgrade and reduce the first- and third-order nonlinear ODEs to a class of second-order linear homogeneous ODEs. Then the general solutions of the first- and third-order ODEs are obtained separately by using the general solution of the obtained second-order linear homogeneous ODEs, elastic transformation, inverse transformation of elastic transformation and related operation rules. Second, the steps for solving these two kinds of ODEs are summarized. Finally, examples and parametric analysis are given to prove that it is effective, simple and feasible to solve two kinds of first- and third-order nonlinear ODEs by elastic transformation and its inverse transformation. Elastic transformation and its inverse transformation provide a new method for solving ODEs. The research in this paper expands the solvable classes of ODEs.

Let $X$ be a Hausdorff continuum (a nondegenerate, compact, connected Hausdorff space). Let $C(X)$ denote the hyperspace of its subcontinua, endowed with the Vietoris topology. We extend some results of the metric case about unicoherence and the existence of selections for $C(X)$. We also introduce two definitions of contractibility of $C(X)$ and discuss their relation with some properties of $X$. In particular, we show that both definitions are equivalent in the metrizable case, but one of them is more general in the Hausdorff continuum case.

The variable exponent differential inclusion systems with a multivalued reaction term depending on the gradient are considered in this paper. Under general assumptions on the multivalued reaction term, we prove the existence of a nontrivial weak solution by using the surjectivity theorem.

Given a continuum $X$ and $n\in \mathbb{N}$, let $C_n(X)$ (resp. $F_n(X)$) be the hyperspace of nonempty closed sets with at most $n$ components (resp. $n$ points). Given $1\le m\le n$, we consider the quotient space $C_n(X)∕F_m(X)$. The homogeneity degree of $X$, $\text{Hd}(X)$, is the number of orbits of the group of homeomorphisms of $X$. We discuss lower bounds for the homogeneity degree of the hyperspaces $C_n(X)$, $C_n(X)∕F_m(X)$ when $X$ is a finite graph. In particular, we prove that for a finite graph $X$:

We show that for each $n=3,4,\dots$ there is a space-filling curve $f:[0,1]\to {[0,1]}^n$ such that $f$ is at most $(n+1)$-to-$1$ at every point of ${[0,1]}^n$. The fact that any such dimension raising continuous function is at least $(n+1)$-to-$1$ has been known since the 1930s, so the examples we provide here are, in that sense, the best possible. The classic space-filling curves due to first Peano and a year later, Hilbert, that map $[0,1]$ onto ${[0,1]}^2$ are both $4$-to-$1$ at a dense set of points and their generalizations to ${[0,1]}^n$ are known to be $2^n$-to-$1$ at a dense set of points. Flaten, Humke, Olson and Vo (J. Math. Anal. Appl. 500:2 (2021), art. id. 125113) gave an example, $f:[0,1]\to {[0,1]}^2$ based on the Hilbert linear ordering of somewhat altered Hilbert partitions which is at most $3$-to-$1$ at every point of ${[0,1]}^2$, but there are technical difficulties with generalizing that example to higher dimensions. In a sense, this paper represents an overcoming of those difficulties.

We propose a hybrid Leslie–Gower predator-prey system with feedback control and hunting cooperation among predators on nonuniform time domain. Our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system. Using comparison theorems and some dynamic inequality on the time scale, we study the permanence results for the proposed system. Also, with the help of a suitable Lyapunov function, we establish some sufficient conditions that will ensure the global attractivity of the proposed model. Furthermore, simulation studies are provided to verify the theoretical results, as well as to further investigate the effects of feedback control strategy and hunting cooperation on the predator-prey system. These findings suggest that hunting cooperation and feedback control strategy have a substantial influence on controlling the population of a predator-prey dynamical system.

We give sufficient conditions for any linear combination over $\mathbb{Q}$ of numbers ${\sum }_{n=1}^{\infty }{b}_{1,n}∕{\alpha }_{1,n},\dots ,{\sum }_{n=1}^{\infty }{b}_{K,n}∕{\alpha }_{K,n}$ to have algebraic degree greater than an arbitrary fixed integer $D$ when the numbers ${\alpha }_{i,n}$ are algebraic integers of sufficiently rapidly increasing modulus and the $b_{i,n}$ are positive integers that are not too large.

We demonstrate some properties of Hadamard fractional operators such as boundedness, monotonicity, continuity, and acting conditions in Orlicz spaces $L_{\phi }$. We apply these properties with a proper measure of noncompactness (MNC) to inspect the existence of monotonic solutions of some general, but abstract, form of quadratic Hadamard-type fractional integral equations in $L_{\phi }$. We also discuss the uniqueness of the solution.

In the first part of the paper, we give some criteria of continuity of the spectral radius functions on strongly sequential $\mathrm{\Sigma }$-fundamental $F$-algebras. Several examples of spectral continuity are discussed as well. The second part uses the results of the first part to investigate the automatic continuity of linear mappings and homomorphisms on a class of $F$-algebras.

For , and $\frac{1}{q}=\frac{1}{p}-\frac{\alpha }{n}$, we obtain the boundedness from $H_w^p({ℝ}^n)$ into $L_{w^{q∕p}}^q({ℝ}^n)$ of certain generalized Riesz potentials for certain weights $w$. This result is achieved via the infinite atomic decomposition we previously developed (Rev. Un. Mat. Argentina 61:2 (2020), 229–247).

Let $G$ be a finite group. In this expository paper, we provide a detailed proof of the polynomiality property of the structure coefficients of the center of the wreath product $G\wr {\mathcal{𝒮}}_n$ algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group $G\wr {\mathcal{𝒮}}_n$ algebra for every $n$. We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on $\left|G^{\star }\right|$ alphabets.

Let $F(x)$ be any analytic function. Suppose that $w$ is a fixed point of $F(x)$, that is, $F(w)=w$. We previously (Rocky Mountain J. Math. 52:6 (2022)) gave solutions of the recurrence equation $x_{n+1}=F(x_n)$ for $n=0,1,2,\dots$. In this note, we give more general solutions of the form

$$x_n=w+\sum _{i=1}^{\infty }{A}_i{(u_n{r}^n)}^i$$

for any $u_n$ such that $u_n∕u_{n+1}\to 1$ as $n\to \infty$.

We introduce the notion of cyclic Ricci semisymmetric real hypersurfaces in the complex quadric $Q^m={SO}_{m+2}∕{SO}_m{SO}_2$. We also give a classification of real hypersurfaces in the complex quadric $Q^m={SO}_{m+2}∕{SO}_m{SO}_2$ with cyclic semisymmetric Ricci tensor.

We consider the convexity with respect to a pair of functions and establish a Hermite–Hadamard type inequality for Riemann–Liouville fractional integrals. Moreover, we derive some new Simpson’s and Ostrowski’s type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.

In “Experiments and discoveries in $q$-trigonometry”, W. Gosper defined the $q$-analogues ${\text{sin}}_q(z)$ and ${\text{cos}}_q(z)$ of $\text{sin }z$ and $\text{cos }z$ respectively. He also conjectured identities for ${\text{sin}}_q(2z),{\text{sin}}_q(3z)$ and ${\text{sin}}_q(5z)$. Here, we give a brief account of Gosper’s $q$-trigonometric functions and build some generalized Gosper’s kind of $q$-trigonometric identities. As a consequence of which, we build four generalized finite $q$-trigonometric sums, three of which seem to be new. We also give simple proofs to one of Gosper’s Lambert series identities and two of Ramanujan’s Eisenstein series identities. We make use of the technique of this article to show how some new unusual Eisenstein series identities can be deduced.

Let $\mathcal{𝒜}$ be a unital $\ast$-algebra. Under some mild conditions on $\mathcal{𝒜}$, we show that $\varphi$ is a nonlinear bi-skew Lie-type derivation on $\mathcal{𝒜}$ if and only if $\varphi$ is an additive $\ast$-derivation. As applications, nonlinear bi-skew Lie-type derivations on prime $\ast$-algebras, von Neumann algebras with no central summands of type $I_1$, factor von Neumann algebras and standard operator algebras are characterized.

We study the Hyers–Ulam–Rassias stability of $p$-order linear recurrence over the quaternion skew yield by considering the related first-order linear recurrence system in complex Banach space.