Aequationes Mathematicae最新文献

We study the zero–Hopf bifurcations of all quadratic polynomial differential jerk systems in ({mathbb {R}^3})

where the dot denotes derivative with respect to the independent variable t and the coefficients (a_{k}), for (k=0,1,...,9), are real.

Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such sets to convex and isometric subgraphs are studied. Dual mutual-visibility sets are shown to be intrinsically different from other types of mutual-visibility sets. It is proved that for every finite subset Z of positive integers there exists a graph G that has a dual mutual-visibility set of size i if and only if (iin Zcup {0}), while for the other types of mutual-visibility such a set consists of consecutive integers. Visibility polynomials are introduced and their properties derived. As a surprise, every polynomial with nonnegative integer coefficients and with a constant term 1 is a dual visibility polynomial of some graph. Characterizations are given for total mutual-visibility sets, for graphs with total mutual-visibility number 1, and for sets which are not total mutual-visibility sets, yet every proper subset is such. Along the way an earlier result from the literature is corrected.

In this paper, we introduce a new class of contractive definitions known as convex Meir-Keeler-Ćirić-Matkowski contractive mappings. We establish several fixed point theorems under this new condition, allowing for both continuity and discontinuity at the fixed points. Our results not only encompass all previously known findings in this domain but also offer new insights into the continuity of contractive mappings at their fixed points. As an application of our theorem, we demonstrate the existence and uniqueness of solutions to a functional equation in the Lipschitz space. The functional equation we consider broadly encompasses various functional equations, including those recently studied for analyzing the two-choice behavior of the paradise fish and for solving models involving two prey species and one predator.

In this work, we want to prove global stability of one time-continuous model and two time-discrete variants for a non-linear, extended three-compartmental model of ethanol metabolism in the human body, which has been recently proposed in one current article (https://dx.doi.org/10.1002/mma.10858). This means that we show that all trajectories, independent of our non-negative chosen initial values, converge to the ethanol-free equilibrium state. Hence, we extend local stability results of the aforementioned work such that the time-continuous and both proposed time-discrete models possess one unique ethanol-free equilibrium state which is globally asymptotically stable. Here, we mainly apply results of Sundarapandian (https://dx.doi.org/10.1016/S0893-9659(01)00130-6) on non-linear cascade systems. Finally, we strengthen our theoretical findings by numerical examples.

Let (kge 1) be an integer, and let G be a finite and simple graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is defined in [Signed double Roman k-domination in graphs, Australas. J. Combin. 72 (2018), 82–105] as a function (f :V(G) rightarrow {-1,1,2,3}) satisfying the conditions that (sum _{xin N[v]}f(x)ge k) for each vertex (vin V(G)), where N[v] is the closed neighborhood of v, every vertex u for which (f(u)=-1) is adjacent to at least one vertex v for which (f(v)=3) or adjacent to two vertices x and y with (f(x)=f(y)=2), and every vertex u with (f(u)=1) is adjacent to vertex v with (f(v)ge 2). The weight of an SDRkDF f is (textrm{w}(f) = sum _{vin V(G)}f(v)). The signed double Roman k-domination number (gamma _{textrm{sdR}}^k(G)) of G is the minimum weight among all SDRkDF on G. In this paper we continue the study of the signed double Roman k-domination number of graphs, and we present new bounds on (gamma _{textrm{sdR}}^k(G)). In addition, we determine the signed double Roman k-domination number of some classes of graphs. Some of our results are extensions of well-known properties of the signed double Roman domination number, (gamma _{textrm{sdR}}(G)=gamma _{textrm{sdR}}^1(G)), introduced and investigated in [1, 2].

We prove that certain classical groups (Gsubseteq {{,textrm{GL},}}(d,mathbb {R}^d)) serve to characterize ordinary polynomials in d real variables as elements of finite-dimensional subspaces of (C(mathbb {R}^d)) that are invariant by changes of variables induced by translations and elements of G. We also show that, if the field (mathbb {K}) has characteristic 0, the elements of (mathbb {K}[x_1,dots ,x_d]) admit a similar characterization for (G={{,textrm{GL},}}(d,mathbb {K})).

An example of some iteration group in a ring of formal power series over a field of characteristic 0 is given in [2]. It is proved under the hypothesis that some system of combinatorial identities is valid. Here we discuss a proof that the mentioned system of identities is indeed satisfied. It is based on the Chu–Vandermonde identity. From this result we obtain an explicit formula for some one-parameter group of (truncated) formal power series. Moreover we describe some non-commutative groups of solutions of the third Aczél–Jabotinsky differential equation in the ring of truncated formal power series.

We present a construction of graph-directed invariant sets of weak contractions in the sense of Matkowski-Rus on semi-metric spaces. We follow the approach by Bessenyei and Pénzes, which applies the Kuratowski noncompactness measure without relying on Blascke’s completeness theorem. We also establish a relationship between this approach and a generalized de Rham’s functional equation indexed by a finite directed graph.

We complete the section method with new simple and versatile techniques to solve some equations that have composite functions as solutions and to study Ulam stability and their hyperstability. We exemplify the malleability of the results obtained by solving equations of the form

on relevant real domains, then giving Ulam stability couples and control functions that induce hyperstability for these equations.

Assume that ((Omega ,mathcal A,mathbb {P})) is a probability space, ((X,rho )) is a compact metric space and Y is a separable Banach space. Under relevant assumptions about the given function ( f :X times Omega rightarrow X ) we show that the set of all continuous functions (F :X rightarrow Y) such that the equation

has a continuous solution (varphi :X rightarrow Y) is small from the points of view of both category and measure theory.