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The encouragement of presented writing is to acquire various theorems for α-(Ƒ, ℏ)-Geraghty contraction type mappings having a mixed monotone property in partial order on metric spaces. An instance is preferred to display the straightness of the obtained findings. Further, we propel the applicability of our conclusion in finding the solution for a two-point boundary value problem. Our results not only extend and generalize several results in the fixed point theory literature but also unify most of them. [ABSTRACT FROM AUTHOR]

A prime ring S with the centre Z and generalised derivations that meet certain algebraic identities is considered. Let's assume that Ψ and Φ are two generalised derivations associated with ψ and φ on S, respectively. In this article, we examine the following identities: (i) Ψ(a)b-aΦ(b) ∈ Z, (ii) Ψ(a)b-bΦ(a) ∈ Z, (iii) Ψ(a)a-bΦ(b) ∈ Z, (iv) Ψ(a)a-aΦ(b) ∈ Z, (v) Ψ(a)a - bΦ(a) ∈ Z, for every a, b ∈ J, where J is a non-zero two sided ideal of S. We also provide an example to show that the condition of primeness imposed in the hypotheses of our results is essential. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new coincidence and common fixed point theorem of hybrid mappings using the C-class function and T-weak commutativity. Finally, we give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

We prove a Brooks type coincidence minimization result for boundary preserving maps on compact surfaces with boundary. As an application we obtain non-boundary Wecken results for pairs of maps f, g : (X, ∂X) → (X, ∂X) for most surfaces X. [ABSTRACT FROM AUTHOR]

In this paper, we define the i j-almost-set Menger (i j-ASM) property in bitopological spaces. We put up some equivalences of i j-almost-set Menger bitopological spaces and investigate the behaviours of such spaces under some different types of mappings. We later take the preservation of these properties under union, subspaces, products into consideration and give some related examples. We finally introduce the concept of i j-almost Pγ-set in bitopological spaces. [ABSTRACT FROM AUTHOR]

Let M be a topological space that admits a free involution τ, and let N be a topological space. A homotopy class β ∈ [M, N] is said to have the Borsuk–Ulam property with respect to τ if for every representative map f : M → N of β, there exists a point x ∈ M such that f(τ(x)) = f(x). In this paper, we determine the homotopy class of maps from the 2-torus T² to the Klein bottle K² that possess the Borsuk–Ulam property with respect to any free involution of T² for which the orbit space is K² . Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of T² and K² . This completes the analysis of the Borsuk–Ulam problem for the case M = T² and N = K², and for any free involution τ of T². [ABSTRACT FROM AUTHOR]

In this paper, we aim to obtain some new common attractors with the assistance of finite families of generalized contractive mappings, that belong to the special class of mappings defined on a partial metric space. Consequently, a variety of results for iterated function systems satisfying a different set of generalized contractive conditions are acquired. We present some examples to reinforce the results proved herein. These results generalize, unify and extend a variety of results that exist in current literature. [ABSTRACT FROM AUTHOR]

Given a domain of some Riemannian surface, we consider questions related to the possibility of a continuous extension to the boundary of one class of Sobolev mappings. It is proved that such maps have a continuous boundary extension in terms of prime ends, and under some additional restrictions their families are equicontinuous at inner and boundary points of the domain. We have separately considered the cases of homeomorphisms and mappings with branching. [ABSTRACT FROM AUTHOR]

Correlation functions in a dynamic quartic matrix model are obtained from the twopoint function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These "nested Catalan tables" have a description as diagrams of non-crossing chords and threads. [ABSTRACT FROM AUTHOR]

As applications on infra − β − open set for new classes of mappings and new concepts topological spaces are introduced, namely, infra- β−continuous, infra−β−irresolute, infra−β−open(closed) mapping, infra − β − τi (i = 0, 1, 2, 3, 4), infra − β − compact and infra − β − connected space. Some of special results and properties which belong to these various applications are established and studied. Moreover, the relations and opposite relations between these new concepts and others are discussed and counter examples are given in order to investigate opposite relations. [ABSTRACT FROM AUTHOR]

In this paper we deal with the Banach space Cmb[0,+∞) of all m-times continuously derivable, bounded with all derivatives up to the order m, real functions defined on [0,+∞). We prove, for any ϵ>0, the existence of a new proper k-ball-contractive retraction with k<1+ϵ of the closed unit ball of the space onto its boundary, so that the Wośko constant Wγ(Cmb[0,+∞)) is equal to 1. [ABSTRACT FROM AUTHOR]

It is natural to ask whether the weak fixed point property for nonexpansive mappings in Banach spaces is inherited by other generalized nonexpansive mappings without using weak normal structure or close-to normal structure (also called quasi-normal structure) (see C.S. Wong, Close-to-normal structure and its applications, J. Func. Anal. 16 (1974), no. 4, 353-358). In this paper, we give an affirmative answer to this question for Suzuki mappings and other generalized nonexpansive mappings in the setting of various Banach spaces. In addition, we prove the existence of common fixed points for commuting affine (c)-mappings and Suzuki mappings acting on convex bounded L0-closed subsets in the Banach space L¹(Ω,Σ,μ). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effect of mappings and some decompositions of pairwise continuity on (i, j)-almost Lindelöf spaces and (i, j)-weakly Lindelöf spaces. The main results are that an (i, j)-θ-continuous image of an (i, j)-almost Lindelöf space is (i, j)- almost Lindelöf and a pairwise almost continuous image of an (i, j)- weakly Lindelöf space is (i, j)-weakly Lindelöf. We also show that (i, j)-almost Lindelöf, pairwise almost Lindelöf, (i, j)-weakly Lindelöf and pairwise weakly Lindelöf properties are bitopological properties. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative scheme with the help of the gradientprojection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem. [ABSTRACT FROM AUTHOR]

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on SJS- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results. [ABSTRACT FROM AUTHOR]

In the present paper, we define an analogue of Hardy-Rogers type contraction in A-metric spaces and prove a fixed point theorem for such mappings under appropriate conditions in such spaces. Also, we give some results for Kannan, Chatterjea, Reich, Ciric type contraction mappings in A-metric spaces. Our results generalize many known results in the fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(2x + y) + f(2x - y) - 6f(x) - 2f(-x) - f(y) - f(-y); t) ≥ N(f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y); kt) for some fixed real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

This paper develops an effective semi-discrete method based on the 2D Chelyshkov polynomials (CPs) to provide an approximate solution of the fractal–fractional nonlinear Emden–Fowler equation. In this model, the fractal–fractional derivative in the concept of Atangana–Riemann–Liouville is considered. The proposed algorithm first discretizes the fractal–fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using the 𝜃 -weighted finite difference scheme. The differentiation operational matrices and the collocation method play an important role to obtaining a linear system of algebraic equations. Last, solving the obtained system provides an approximate solution in each time step. The validity of the formulated method is investigated through a sufficient number of test problems. [ABSTRACT FROM AUTHOR]

This article concerns recurrent motion in the fractional complex Ginzburg–Landau equation with a small recurrent force. By using Galerkin’s method and energy estimate method, we obtain the existence of the bounded solutions, periodic solutions, quasiperiodic solutions, almost periodic solutions, and almost automorphic solutions under suitable assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive con- ditions of integral type. Our results generalize a host of previously the- orems. We also present some illustrative examples which support our main results and show the applicability and validity of these results. [ABSTRACT FROM AUTHOR]

Let Y be an n-Banach space, M be a nonempty closed convex subset of , and S:M→M be a mapping that belongs to the class D(L,q) mapping. The purpose of this paper is to study the stability and data dependence results of a Mann iteration scheme on n-Banach space . [ABSTRACT FROM AUTHOR]

Introduction. By method of induction using three independent parameters (numbers of panels) formulas for deflection under different types of loading are derived. Curves based on the derived formulas are analyzed, and the asymptotic of solutions for the number of panels are sought. The frame is statically definable, symmetrical, with descending braces. The problem of deflection under the action of a load evenly distributed over the nodes of the upper chord, a concentrated load in the middle of the span, and the problem of shifting the mobile support is considered. Materials and methods. The calculation of forces in the truss bars is performed in symbolic form using the method of cutting nodes and operators of the Maple computer mathematics system. The deflection is determined by the Maxwell – Mohr formula. Operators of the Maple computer mathematics system are used for composing and solving homogeneous linear recurrent equations that satisfy sequences of coefficients of the required dependencies. The stiffness of all truss bars is assumed to be the same. Results. All the obtained dependencies have a polynomial form for the number of panels. To illustrate the obtained solutions and their qualitative analysis, curves of the deflection dependence on the number of panels are constructed. Conclusions. A scheme of a statically definable three-parameter truss is proposed that allows an analytical solution of the problem of deflection and displacement of the support. The obtained dependences can be used in engineering practice in problems of structural rigidity optimization and for evaluating the accuracy of numerical solutions. [ABSTRACT FROM AUTHOR]

A new class of contraction pairs in uniformly convex metric spaces is introduced. The coincidence and best proximity points of this class of mappings is studied, and finally, illustrative examples are given to support the new results. [ABSTRACT FROM AUTHOR]

In this paper, motivated by [F. Vetro, Filomat, 29:9 (2015), 2011-2020] we present some fixed point results for a class of nonexpansive self-mappings and multi-valued mappings in the framework of b-metric spaces. Our results generalize and improve the consequences of [ Khojasteh et al. Abstract and Applied Analysis, vol. 2014, Article ID 325840, 5 pages, 2014.] and [F. Vetro, Filomat, 29:9 (2015), 2011-2020]. Some examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems for non-self mappings, which solve the problem 1 in [1], satisfying special contractive conditions in complete metric spaces. [ABSTRACT FROM AUTHOR]

We present an extended class of complete and strong complete monomials over a finite field. These monomials can also be viewed as generalized complete and strong complete mappings. In the second part of the article we give basic properties of polynomials induced by complete mappings, orthomorpisms and strong complete mappings over a multiplicative group of the finite field. [ABSTRACT FROM AUTHOR]

Two novel nonlinearly activated recurrent neural networks (RNNs) with finite-time convergence [called finite-time RNNs (FTRNNs)] are proposed and analyzed to solve efficiently time-varying systems of nonlinear equations (SoNEs). Compared with previously presented neural networks for solving such a SoNE, the FTRNNs are activated by new nonlinear activation functions and thus possess a better finite-time convergence property. In addition, theoretical analyses about FTRNNs are presented to determine the upper bounds of convergence time under the context of using such two novel nonlinear activation functions. Computer simulations based on a numerical example validate the preponderance of the proposed FTRNNs for time-varying SoNE, as compared to the recently proposed Zhang neural network and its improved version. Finally, an engineering practical example to motion tracking of a robot manipulator demonstrates the feasibility and applicability of the FTRNNs. [ABSTRACT FROM AUTHOR]

Standard correspondence analysis plots are readily misinterpreted by research users. This paper presents a new plot, called the moon plot, which is less susceptible to misinterpretation. Row points are plotted in the traditional way. Column points are plotted equidistant from the origin, with their directions from the origin as in traditional correspondence analysis plots, and the information traditionally communicated by the distance of the points to the origin instead communicated by the size of the fonts of the labels. [ABSTRACT FROM AUTHOR]

In this paper, we propose new types of non-convex functions called strongly Eh-b-vex functions and semi strongly Eh-b-vex functions. We study some properties of these proposed functions. As an application of these functions in optimization problems, we discuss some optimality properties of the generalized nonlinear optimization problem for which we use, as an objective function, strongly Eh-b-vex function and semi strongly Eh-b-vex function. [ABSTRACT FROM AUTHOR]

Abstract Let L / F be a field extension, φ , ψ even-dimensional quadratic forms over F. Assume that the forms φ L and ψ L are similar over L. In the first section we investigate whether it is possible to choose a similarity coefficient from F ⁎. The answer turns out to be positive if the degree of L / F is odd, and negative in general if L / F is a quadratic extension. In the second and third sections we apply the main theorem of the paper to the following problem: Let L (e) / L be a quadratic extension, e ∈ L ⁎ , Φ a form over L. Suppose that dim Φ is even and ind (Φ L (e)) = 1 2 ind (Φ). Does there exist a form Ψ over L such that Ψ L (e) is similar to Φ L (e) , disc (Ψ) = disc (Φ) , and ind (Ψ) = 1 2 ind (Φ) ? We show that the answer is negative in general almost for all conceivable pairs (dim Φ , ind (Φ)). On the other hand, the answer is positive if ind (Φ) = 2 , 4 ≤ dim Φ ≤ 8 , and if ind (Φ) = 4 , dim Φ = 6. In the fourth section we describe the set of similarity coefficients for pairs of 4-dimensional forms. Applying this description, we investigate the CV property with respect to quadratic extensions and pairs of forms (φ , ψ) , where φ and ψ are similar to 2-fold and 1-fold Pfister forms respectively. In the final section we establish general nontriviality of the quotient groups N F (e) / F F (e) ⁎ ∩ F ⁎ 2 Nrd (D F ⁎) F ⁎ 2 N F (e) / F (Nrd (D F (e) ⁎)) and N F (d) / F F (d) ⁎ ∩ N F (e) / F F (e) ⁎ ∩ D (π) F ⁎ 2 N F (d , e) / F (D (π F (d , e))) , where D ∈ Br 2 (F) , and π is a Pfister form over F. [ABSTRACT FROM AUTHOR]

Abstract Zassenhaus conjectured that any unit of finite order in the integral group ring Z G of a finite group G is conjugate in the rational group algebra of G to an element in ± G. We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in Z G , which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions. We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of G. Moreover, we show that if the condition holds then the HeLP Method adopts a more friendly form and use this to prove the Zassenhaus Conjecture for a special class of groups. [ABSTRACT FROM AUTHOR]

Abstract Szlachányi showed that bialgebroids can be characterised using skew monoidal categories. The characterisation reduces the amount of data, structure, and properties required to define them. Lack and Street provide a bicategorical account of that same fact; they characterise quantum categories in terms of skew monoidal structures internal to a monoidal bicategory. A quantum category is an opmonoidal monad on an enveloping monoidale R ∘ ⊗ R in a monoidal bicategory. In a previous paper, we characterised opmonoidal arrows on enveloping monoidales as a simpler structure called oplax action. This is the second paper based on the author's PhD thesis. Here, motivated by the fact that opmonoidal monads are monads in the bicategory of monoidales, opmonoidal arrows, and opmonoidal cells; we prove that right skew monoidales are "monads of oplax actions". To do so, we arrange oplax actions as the 1-simplices of a simplicial object in Cat. In nice cases this simplicial object is ought to be thought as a bicategory whose arrows are oplax actions, that is to say, it is weakly equivalent to a nerve of a bicategory. We define monads of oplax actions as simplicial maps out of the Catalan simplicial set and prove that these are in bijective correspondence with right skew monoidales whose unit has a right adjoint, no assumptions required on the ambient monoidal bicategory. [ABSTRACT FROM AUTHOR]

Let D n = 〈 σ , τ : σ n = τ 2 = 1 , τ σ τ − 1 = σ − 1 〉 be the dihedral group of order 2 n where n ≥ 2. Let 1 → R → F → ε D n → 1 be the free presentation of D n where F = 〈 s 1 , s 2 〉 is the free group of rank two and ε (s 1) = σ , ε (s 2) = τ. The conjugation maps of F provide an action of F on R. Thus R a b : = R / [ R , R ] becomes a Z [ D n ] -lattice. R a b is called the relation module of D n by Gruenberg. For any Galois extension K / k with Gal (K / k) = D n , K (R a b) D n is stably rational over k if and only if n is an odd integer. Moreover, (i) if K (R a b) D n is stably rational over k , it is rational over k , and (ii) if K (R a b) D n is not stably rational over k and k is an infinite field, then K (R a b) D n is not retract rational over k. We will also discuss the rationality of the purely monomial action where D n acts trivially on the field k. It will be shown that, if n is odd, then k (R a b) D n ≃ k (D n) (t) for any field k where t is an element transcendental over the field k (D n). [ABSTRACT FROM AUTHOR]

In this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposable objects in a basis of their Hom-space. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

The parameter plane investigation for a family of two-dimensional, nonlinear, and area contracting map is made. Several dynamical features in the system such as tangent, period-doubling, pitchfork, and cusp bifurcations were found and discussed together with cascades of period-adding, period-doubling, and the Feigeinbaum scenario. The presence of spring and saddle-area structures allow us to conclude that cubic homoclinic tangencies are present in the system. A set of complex sets such as streets with the same periodicity and the period-adding of spring-areas are observed in the parameter space of the mapping. [ABSTRACT FROM AUTHOR]

The motion of and interaction between phase singularities that lie at the centers of spiral waves capture many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their position is thus quite important, even if the data are noisy and sparse, as in electrophysiology studies of cardiac arrhythmias, for instance. A recently proposed global topological approach [Marcotte and Grigoriev, Chaos 27, 093936 (2017)] promises to meaningfully improve the quality of the reconstruction compared with traditional, local approaches. Indeed, we found that this approach is capable of handling noise levels exceeding the range of the signal with minimal loss of accuracy. Moreover, it also works successfully with data sampled on sparse grids with spacing comparable to the mean separation between the phase singularities for complex patterns featuring multiple interacting spiral waves. 1 --> a --> [ABSTRACT FROM AUTHOR]

Abstract For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A , is a 1-to-1, onto mapping to Σ ⁎ ? For which sets A does there exist such a mapping that respects the lexicographical ordering within A ? Both cases are types of perfect, minimal hash functions. The complexity-theoretic versions of these notions are known as compression functions and ranking functions. This paper defines and studies the recursion-theoretic versions of compression and ranking functions, and in particular studies which sets have, or lack, such functions. Thus this is a case where, in contrast to the usual direction of notion transferal, notions from complexity theory are inspiring notions, and an investigation, in computability theory. We show that the rankable and compressible sets broadly populate the 1-truth-table degrees, and we prove that every nonempty coRE cylinder is recursively compressible. [ABSTRACT FROM AUTHOR]

Abstract In contrast to the composition uniformity of homogeneous materials, heterogeneous materials are normally composed of two or more distinctive constituents. It is usually recognized that the effective material property of a heterogeneous material is related to the mechanical property and the distribution pattern of each forming constituent. However, to establish an explicit relationship between the macroscale mechanical property and the microstructure appears to be complicated. On the other hand, machine learning methods are broadly employed to excavate inherent rules and correlations based on a significant amount of data samples. Specifically, deep neural networks are established to deal with situations where input–output mappings are extensively complex. In this paper, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of other heterogeneous materials. Highlights • Predict the mechanical properties of heterogeneous materials by deep learning. • Generate numerous training samples based on stochastic reconstruction. • Transform sample images to finite element models by image processing. • An artificial neural network to predict mechanical properties by material structure. • The novel method is accurate and efficient in predicting mechanical properties. [ABSTRACT FROM AUTHOR]

Sliding-mode control is known as a popular approach of robust control methods. Fuzzy sliding-mode control method has been commonly used to prevent chattering phenomenon, drastic change of control factor, around sliding surface in sliding-mode control. In Hedge-algebras theory, inherent order relationships among linguistic values of each linguistic variable are always guaranteed and these values are determined by isomorphism mapping called semantically quantifying one based on a few fuzziness parameters of each linguistic variable instead of using fuzzy sets. In this paper, sliding-mode hedge-algebras-based controller is designed and applied in active control of a structure subjected to earthquake in order to show advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract Crowd counting is a challenging vision task which aims to accurately estimate the crowd count from a single image. To this end, we propose a novel architecture called De-background Detail Convolutional Network (DDCN) to learn a mapping from the input image to the corresponding crowd density map. DDCN focuses on removing the interference of background from crowds and reducing the mapping range from input to output. Such design optimizes the learning process to a large extent. The proposed DDCN is composed of three components: a decomposer, a feature extraction CNN and a regression CNN. Specifically, the decomposer produces a detail layer by subtracting the background interference from the crowd image. Feature extraction CNN works for extracting high level features and regression CNN is used to estimate the density map. In addition, a weighted Euclidean loss is designed to calculate the Euclidean distances of the crowd and the background separately with different loss weights, which further improves the counting performance. Extensive experiments were conducted on three crowd counting datasets to validate the performance of DCNN. And experimental results demonstrate that DDCN achieves performance improvements compared with the state-of-the-art. [ABSTRACT FROM AUTHOR]

This paper studies the spectrum of the Hénon map and the spectrum of the baker's map. The character of fixed points of the Hénon map and randomness of the baker's map are analyzed. Attractors of the modified Hénon map and the modified baker's map are considered; cases where attractors are fractal sets are selected. [ABSTRACT FROM AUTHOR]

In this article, the authors establish the recurrence relations and q-difference equations for the 2-iterated q-Appell polynomials. The recurrence relations and the q-difference equations for the 2-iterated q-Bernoulli polynomials, the q-Euler polynomials and the q-Genocchi polynomials are also derived. An analogous study of certain mixed type q-special polynomials is also presented. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we deal with complete generalized linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form, which means that there exists a linear relation involving some of the higher order mean curvatures. In this setting, we show that such a spacelike hypersurface must be totally umbilical, provided that its Gauss mapping has some appropriate behavior and that the tangential component of a fixed nonzero vector has integrable norm along it. Our approach is based on a suitable divergence formula jointly with an appropriate maximum principle at the infinity. [ABSTRACT FROM AUTHOR]

The author proves that there are at most two meromorphic mappings of ℂm into ℙn(ℂ) (n ≥ 2) sharing 2n+2 hyperplanes in general position regardless of multiplicity, where all zeros with multiplicities more than certain values do not need to be counted. He also shows that if three meromorphic mappings f1, f2, f3 of ℂm into ℙn(ℂ) (n ≥ 5) share 2n+1 hyperplanes in general position with truncated multiplicity, then the map f1×f2×f3 is linearly degenerate. [ABSTRACT FROM AUTHOR]

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature. [ABSTRACT FROM AUTHOR]

Reaction-diffusion equations on time-variable domains are instrinsically nonautonomous even if the coefficients in the equation do not depend explicitly on time. Thus the appropriate asymptotic concepts, such as attractors, are nonautonomous. Forward attracting sets based on omega-limit sets are considered in this paper. These are related to the Vishik uniform attractor but are not as restrictive since they depend only on the dynamics in the distant future. They are usually not invariant. Here it is shown that they are asymptotically positively invariant, in general, and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant as well as upper semi continuous dependence in a parameter will be established. These results also apply to reaction-diffusion equations on a fixed domain. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence of solutions for space-fractional parabolic hemivariational inequalities by means of the well-known surjectivity result for multivalued (S+) type mappings. [ABSTRACT FROM AUTHOR]