On the $${{\varvec{}}}$$-length of the mutually ermutable roduct of two $${{\varvec{}}}$$-soluble grous

Let a finite group \(G=AB\) be the mutually permutable product of two p-soluble subgroups A and B for some prime p. We give a bound of the p-length of G from the p-lengths of A and B.     

Type $${{\varvec{D}}}_{{\varvec{n}}}^\mathbf{(1)}$$ rigged configuration bijection

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type \(D^{(1)}_n\) in full generality. We prove the invariance of rigged configurations under the action of the combinatorial R-matrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type \(D_n^{(1)}\). In addition, we establish that the bijection is a classical crystal isomorphism.     

A note on fractional $${\varvec{}}$$-Lalacian roblems with singular weights

We study a class of fractional p-Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well as characterizations of critical groups and related applications.     

Density of translates in weighted $${{\varvec{L}}}^{{\varvec{p}}}$$ spaces on locally compact groups

Let G be a locally compact group, and let \(1\leqslant p < \infty \). Consider the weighted \(L^p\)-space \(L^p(G,\omega )=\{f:\int |f\omega |^p<\infty \}\), where \(\omega :G\rightarrow \mathbb {R}\) is a positive measurable function. Under appropriate conditions on \(\omega \), G acts on \(L^p(G,\omega )\) by translations. When is this action hypercyclic, that is, there is a function in this space such that the set of all its translations is dense in \(L^p(G,\omega )\)? Salas (Trans Am Math Soc 347:993–1004, 1995) gave a criterion of hypercyclicity in the case \(G=\mathbb {Z}\). Under mild assumptions, we present a corresponding characterization for a general locally compact group G. Our results are obtained in a more general setting when the translations only by a subset \(S\subset G\) are considered.     

Existence results to positive solutions of fractional BVP with $${\varvec{}}$$-derivatives

This paper investigates the existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem with fractional q-derivative

$$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$

where \(D_{q}^{\alpha }\) denotes the Riemann–Liouville q-derivative of order \(\alpha \), \(0<\eta <1\) and \(1-\beta \eta ^{\alpha -3}>0\). Our analysis relies a fixed point theorem in partially ordered sets. An example to illustrate our results is given.

     

Alternating groups as a quotient of $${{\varvec{PSL}}}\left( \mathbf{2}, \pmb {\mathbb {Z}} \left[ {{\varvec{i}}}\right] \right) $$

In this study, we developed an algorithm to find the homomorphisms of the Picard group \(\textit{PSL}(2,Z[i])\) into a finite group G. This algorithm is helpful to find a homomorphism (if it is possible) of the Picard group to any finite group of order less than 15! because of the limitations of the GAP and computer memory. Therefore, we obtain only five alternating groups \( A_{n}\), where \(n=5,6,9,13\) and 14 are quotients of the Picard group. In order to extend the degree of the alternating groups, we use coset diagrams as a tool. In the end, we prove our main result with the help of three diagrams which are used as building blocks and prove that, for \(n\equiv 1,5,6(\mathrm { mod}\, 8)\), all but finitely many alternating groups \(A_{n}\) can be obtained as quotients of the Picard group \(\textit{PSL}(2,Z[i])\). A code in Groups Algorithms Programming (GAP) is developed to perform the calculation.     

$$\varvec{\varphi }$$-admissibility results via extended simulation functions

We introduce the class of extended simulation functions, which is more large than the class of simulation functions, recently introduced in (Khojasteh et al. Filomat 29(6):1189–1194, 2015). We obtain a \(\varphi \)-admissibility result involving extended simulation functions, for a new class of mappings \(T: X\rightarrow X\), with respect to a lower semi-continuous function \(\varphi : X\rightarrow [0,\infty )\), where X is a set equipped with a certain metric d. The main theorem in this paper generalizes a recent \(\varphi \)-admissibility result obtained in (Karap?nar et al. Fixed Point Theory Appl 2015:152, 2015), and many other related results.     

Existence results for quasilinear elliptic equations with multivalued nonlinear terms

In this paper we study the existence of solutions u ∈ \({{W}^{1,p}_{0}}\) (Ω) with △ _p u ∈ L ²(Ω) for the Dirichlet problem 1 $$ \left\{ \begin{array} [c]{l}-\triangle_{p}u\left( x\right) \in-\partial{\Phi}\left( u\left( x\right) \right) +G\left( x,u\left( x\right) \right) ,x\in{\Omega},\\ u\mid_{\partial{\Omega}}=0, \end{array} \right. $$ where Ω ? R ^N is a bounded open set with boundary ?Ω, △ _p stands for the p?Laplace differential operator, ?Φ denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function Φ and G : Ω × R → 2^R is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map u ? G(x, u) is upper semicontinuous with closed convex values and the second one deals with the case when u ? G(x, u) is lower semicontinuous with closed (not necessarily convex) values.     

Recognition of PSL($$\mathbf {2, 2}^{{\varvec{a}}}$$) by the orders of vanishing elements

Here, we show that the simple groups PSL\((2, 2^a)\), \(a\ge 2\), are characterized by the orders of vanishing elements.     

$$\varvec{}$$-Polar Fuzzy Labeling Graphs with Application

In this article, we apply the concept of m-polar fuzzy sets in labeling graphs and introduce the concept of m-polar fuzzy labeling graphs. We present properties of m-polar fuzzy labeling cycle and m-polar fuzzy labeling with bridge and cut nodes. We introduce several different types of distances, including w-distance, strongest strong distance, strong geodesic distance, \(\delta \)-distance in m-polar fuzzy labeling graph and investigate some of their properties. We also present an application of m-polar fuzzy labeling graphs in image processing.     

Large $${\varvec{p}}^{\prime }$$-orbits for $${\varvec{p}}$$p-nilpotent linear groups

Let G be a p-nilpotent linear group on a finite vector space V of characteristic p. Suppose that |G||V| is odd. Let P be a Sylow p-subgroup of G. We show that there exist vectors \(v_1\) and \(v_2\) in V such that \(C_G(v_1) \cap C_G(v_2)=P\). A striking conjecture of Malle and Navarro offers a simple global criterion for the nilpotence (in the sense of Broué and Puig) of a p-block of a finite group. Our result implies that this conjecture holds for groups of odd order.     

Positive steady states for a prey-predator model with some nonlinear diffusion terms

This paper discusses a prey-predator system with strongly coupled nonlinear diffusion terms. We give a sufficient condition for the existence of positive steady state solutions. Our proof is based on the bifurcation theory. Some a priori estimates for steady state solutions will play an important role in the proof.     

Comparison results for nonlinear elliptic equations with lower–order terms

We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) + g(x, u) = f, where the principal term is a Leray–Lions operator defined on and g(x, u) is a term having the same sign as u and satisfying suitable growth assumptions. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.     

Regularity results for non-autonomous functionals with $$\varvec{{L}\log {L}}$$-growth and Orlicz Sobolev coefficients

We study the regularity properties of local minimizers of non-autonomous convex integral functionals of the type

$$\begin{aligned} \mathcal {F}( u, \Omega )= \int _{\Omega } \! f(x,Du) \, \,dx, \end{aligned}$$

when the integrand f has almost linear growth with respect to the gradient variable and the dependence on the x-variable is controlled by a function which belongs to a suitable Orlicz Sobolev space.

     

A gradient estimate on graphs with the $$\varvec{}$$-condition

Let \(\omega \) be an unbounded radial weight on \(\mathbb {C}^d\), \(d\ge 1\). Using results related to approximation of \(\omega \) by entire maps, we investigate Volterra type and weighted composition operators defined on the growth space \(\mathcal {A}^\omega (\mathbb {C}^d)\). Special attention is given to the operators defined on the growth Fock spaces.     

Extremal Problems for Mappings with Generalized Parametric Representation in $${{\mathbb {C}}}^{n}$$

In this paper we are concerned with the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) (\(t\ge 0\)) of normalized biholomorphic mappings on the Euclidean unit ball \(\mathbb {B}^n\) in \({\mathbb {C}}^n\) that can be embedded in normal Loewner chains whose normalizations are given by time-dependent operators \(A\in \widetilde{\mathcal {A}}\), where \(\widetilde{\mathcal {A}}\) is a family of measurable mappings from \([0,\infty )\) into \(L({\mathbb {C}}^n)\) which satisfy certain natural assumptions. In particular, we consider extreme points and support points associated with the compact family \(\widetilde{S}^t_A(\mathbb {B}^n)\), where \(A\in \widetilde{\mathcal {A}}\). We prove that if \(f(z,t)=V(t)^{-1}z+\cdots \) is a normal Loewner chain such that \(V(s)f(\cdot ,s)\in \mathrm{ex}\,\widetilde{S}^s_A(\mathbb {B}^n)\) (resp. \(V(s)f(\cdot ,s)\in \mathrm{supp}\,\widetilde{S}^s_A(\mathbb {B}^n)\)), then \(V(t)f(\cdot ,t)\in \mathrm{ex}\, \widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\) (resp. \(V(t)f(\cdot ,t)\in \mathrm{supp}\,\widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\)), where V(t) is the unique solution on \([0,\infty )\) of the initial value problem: \(\frac{d V}{d t}(t)=-A(t)V(t)\), a.e. \(t\ge 0\), \(V(0)=I_n\). Also, we obtain an example of a bounded support point for the family \(\widetilde{S}_A^t(\mathbb {B}^2)\), where \(A\in \widetilde{\mathcal {A}}\) is a certain time-dependent operator. We also consider the notion of a reachable family with respect to time-dependent linear operators \(A\in \widetilde{\mathcal {A}}\), and obtain characterizations of extreme/support points associated with these families of bounded biholomorphic mappings on \(\mathbb {B}^n\). Useful examples and applications yield that the study of the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) for time-dependent operators \(A\in \widetilde{\mathcal {A}}\) is basically different from that in the case of constant time-dependent linear operators.     

$${\varvec{teaspoon}}$$ : solving the curriculum-based course timetabling problems with answer set programming

Annals of Operations Research - Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities....