In this paper, we study Rota–Baxter operators and super \(\mathcal {O}\)-operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and L-dendriform superalgebras. Then we give some properties of pre-Lie superalgebras constructed from associative superalgebras, Lie superalgebras and L-dendriform superalgebras. Moreover, we provide all Rota–Baxter operators of...

We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is...

We study the problem of topological conjugacy of Brouwer flows. We give a sufficient and necessary condition for Brouwer flows to be topologically conjugate. To obtain this result we use a cover of the plane by maximal parallelizable regions and relations between parallelizing homeomorphisms of these regions. We show that for topologically equivalent Brouwer flows there exists a...

It is known that all Moufang loops of order \(p^4\) are associative if p is a prime greater than 3. Also, nonassociative Moufang loops of order \(p^5\) (for all primes p) and \(pq^3\) (for distinct odd primes p and q, with the necessary and sufficient condition \(q\equiv 1({\text{ mod }}\ p)\)) have been proved to exist. Consider a Moufang loop L of order \(p^{\alpha }q^{\beta...

We write expressions connected with numerical differentiation formulas of order 2 in the form of Stieltjes integral, then we use Ohlin lemma and Levin–Stechkin theorem to study inequalities connected with these expressions. In particular, we present a new proof of the inequality $$\begin{aligned} f\left( \frac{x+y}{2}\right) \le \frac{1}{(y-x)^2} \int _x^y\int _x^yf\left( \frac{s...

In this paper, for a graph G and a family of partitions \(\mathcal {P}\) of vertex neighborhoods of G, we define the general corona \(G \circ \mathcal {P}\) of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.

We show that if \(k\ge 2\) is an integer and \(\big (F_n^{(k)}\big )_{n\ge 0}\) is the sequence of k-generalized Fibonacci numbers, then there are only finitely many triples of positive integers \(1<a<b<c\) such that \(ab+1,~ac+1,~bc+1\) are all members of \(\big \{F_n^{(k)}: n\ge 1\big \}\). This generalizes a previous result where the statement for \(k=3\) was proved. The...

In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of...

Following Clunie and Sheil-Small, the class of normalized univalent harmonic mappings in the unit disk is denoted by \({\mathcal {S}}_{{\mathcal {H}}}\). The aim of the paper is to study the properties of a subclass of \({\mathcal {S}}_{{\mathcal {H}}}\), such that the analytic part is a convex function. We establish estimates of some functionals and bounds of the Bloch’s...

Let \(D\subset \mathbb {C}\) and \(0\in D\). A set D is circularly symmetric if, for each \(\varrho \in \mathbb {R}^+\), a set \(D\cap \{\zeta \in \mathbb {C}:|\zeta |=\varrho \}\) is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing \(\varrho \). A function f analytic in the unit disk \(\Delta \equiv \{\zeta \in \mathbb...

A dominating set of a graph \(G = (V,E)\) is a set D of vertices of G such that every vertex of \(V(G){\setminus }D\) has a neighbor in D. The domination number of a graph G, denoted by \(\gamma (G)\), is the minimum cardinality of a dominating set of G. The non-isolating bondage number of G, denoted by \(b'(G)\), is the minimum cardinality among all sets of edges \(E' \subseteq...

The distant graph \(G=G({\mathbb {P}}(Z), \vartriangle )\) of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein’s geometric interpretation of Euclidean continued fractions. In case the minimal path is non-unique, all the possible splitting are described which allows us to give necessary and sufficient...

Let \({\mathcal {F}}\) denote the class of all functions univalent in the unit disk \(\Delta \equiv \{\zeta \in {\mathbb {C}}\,:\,\left| \zeta \right| <1\}\) and convex in the direction of the real axis. The paper deals with the subclass \({\mathcal {F}}^{(n)}\) of these functions \(f\) which satisfy the property \(f(\varepsilon z)=\varepsilon f(z)\) for all \(z\in \Delta...

The aim of this paper is to study the process of contact with adhesion between a piezoelectric body and an obstacle, the so-called foundation. The material’s behavior is assumed to be electro-viscoelastic; the process is quasistatic, the contact is modeled by the Signorini condition. The adhesion process is modeled by a bonding field on the contact surface. We derive a...

We consider a generalized logistic equation driven by the Neumann p-Laplacian and with a reaction that exhibits a superdiffusive kind of behavior. Using variational methods based on the critical point theory, together with truncation and comparison techniques, we show that there exists a critical value \(\lambda _*>0\) of the parameter, such that if \(\lambda >\lambda _*\), the...

In this paper, we study the existence of the free and cofree objects in the categories Dcpo-\(S\) (and Cpo-\(S\)) of all directed complete posets (with bottom element) equipped with a compatible right action of a dcpo-monoid (cpo-monoid) \(S\), with (strict) continuous action-preserving maps between them. More precisely, we consider all forgetful functors between these categories...

The aim of a study of the presented paper is the differential subordination involving harmonic means of the expressions \(p(z)\), \(p(z) + zp'(z)\), and \(p(z) + \frac{zp'(z)}{p(z)}\) when \(p\) is an analytic function in the unit disk, such that \(p(0)=1, p(z)\not \equiv 1\). Several applications in the geometric functions theory are given.