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In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.

In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. Current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator., We deleted a proposition and a corollary from section 4, and simplified the proof of the main theorem. **The article has been published in Archiv der Mathematik**

In this paper, the authors first construct a dynamical system which is strongly mixing but has no weak specification property. Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper, respectively, and the authors prove the equivalence of quasi-weak specification property, semi-weak specification property and strongly mixing.

In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.

We study etale extensions of rings that have FIP., Comment: The paper entitled FIP and FCP products of ring morphisms (arXiv: 1312.1250 [math.AC]) is now split into three papers. The present paper contains the last section of the original paper and many other results on etale FIP extensions

In this paper, we study some uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial. The results of the paper improve the concerning results due to Xu et al. (Mat Vesnik 64:1–16, 2012).

In the paper, using the concept of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain type of difference polynomials that share a small function. The results of the paper improve and extend some recent results due to C. Meng [Math. Bohem., 139(2014), 89–97] and the present first author [Commun. Math. Stat., 3(2015), 227–238].

Some version of the statement of the Fundamental Theorem of Algebra first appeared early in the 17th century in the writings of several mathematicians, including Peter Roth, Albert Girard, and Rene Descartes. The first proof of the Fundamental Theorem was published by Jean Le Rond d’Alembert in 1746 [2], but his proof was not very rigorous. Carl Friedrich Gauss is often credited with producing the first correct proof in his doctoral dissertation of 1799 [15], although this proof also had gaps. (For a comparison of these two proofs, see [26, pp. 195–200].) Today there are many known proofs of the Fundamental Theorem of Algebra, including proofs using methods of algebra, analysis, and topology. (The references include many papers and books containing proofs of the Fundamental Theorem; [14] alone contains 11 proofs.) Our focus in this paper will be on the use of pictures to see why the theorem is true. Of course, if we want to use pictures to display the behavior of polynomials defined on the complex numbers, we are immediately faced with a difficulty: the complex numbers are two-dimensional, so it appears that a graph of a complex-valued function on the complex numbers will require four dimensions. Our solution to this problem will be to use color to represent some dimensions. We begin by assigning a color to every number in the complex plane. Figure 1 is a picture of the complex plane in which every point has been assigned a different color. The origin is colored black. Traveling counterclockwise around a circle centered at the origin, we go through the colors of a standard color wheel: red, yellow, green, cyan, blue, magenta, and back to red. Points near the origin have dark colors, with the color assigned to a complex number z approaching black as z approaches 0. Points far from the origin are light, with the color of z approaching white as |z| approaches infinity. Every complex number has a different color in this picture, so a complex number can be uniquely specified by giving its color. We can now use this color scheme to draw a picture of a function f : C → C as follows: we simply color each point z in the complex plane with the color corresponding to the value of f(z). From such a picture, we can read off the value of f(z), for any complex number z, by determining the color of the point z in the picture, and then consulting Figure 1 to see what complex number is represented by that color.

The present paper gives several subordination results involving a generalized Srivastava–Attiya operator (defined below). Among the results presented in this paper include also a sufficiency condition for the convexity of the convolution of certain functions and a sharp result relating to the convolution structure. We also mention various useful special cases of the main results including those which are related to the Zeta function.

Let \(\Gamma \) be a closed co-compact subgroup of a second countable locally compact abelian (LCA) group \(G\). In this paper we study translation-invariant (TI) subspaces of \(L^2(G)\) by elements of \(\Gamma \). We characterize such spaces in terms of range functions extending the results from the Euclidean and LCA setting. The main innovation of this paper, which contrasts with earlier works, is that we do not require that \(\Gamma \) be discrete. As a consequence, our characterization of TI-spaces is new even in the classical setting of \(G=\mathbb {R}^n\). We also extend the notion of the spectral function in \(\mathbb {R}^n\) to the LCA setting. It is shown that spectral functions, initially defined in terms of \(\Gamma \), do not depend on \(\Gamma \). Several properties equivalent to the definition of spectral functions are given. In particular, we show that the spectral function scales nicely under the action of epimorphisms of \(G\) with compact kernel. Finally, we show that for a large class of LCA groups, the spectral function is given as a pointwise limit.

Let $R$ be a commutative (Noetherian) local ring of prime characteristic $p$ that is $F$-pure. This paper is concerned with comparison of three finite sets of radical ideals of $R$, one of which is only defined in the case when $R$ is $F$-finite (that is, is finitely generated when viewed as a module over itself via the Frobenius homomorphism). Two of the afore-mentioned three sets have links to tight closure, via test ideals. Among the aims of the paper are a proof that two of the sets are equal, and a proposal for a generalization of I. M. Aberbach's and F. Enescu's splitting prime., 17 pages. This paper has been accepted for publication in Acta Mathematica Vietnamica

In this paper, we consider the split common null point problem in Banach spaces. Then using the metric resolvents of maximal monotone operators and the metric projections, we prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces. The result of this paper seems to be the first one to study it outside Hilbert spaces.

This paper is Appendix of the paper of T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli [8].

In this paper, we give some properties of the generalized derivation algebra \(\mathrm{GDer}(T)\) of a Hom–Lie triple systems T. In particular, we prove that \(\mathrm{GDer}(T) = \mathrm{QDer}(T) + \mathrm{QC}(T)\), the sum of the quasiderivation algebra and the quasicentroid. We also prove that \(\mathrm{QDer}(T)\) can be embedded as derivations in a larger Hom–Lie triple system. General results on centroids of Hom–Lie triple systems are also developed in this paper.

A Lie algebra L over a field $$\mathbb {F}$$ is said to be zero product determined (zpd) if every bilinear map with the property that $$f(x,y)=0$$ , whenever x and y commute, is a coboundary. The main goal of the paper is to determine whether or not some important Lie algebras are zpd. We show that the Galilei Lie algebra , where V is a simple $$\mathfrak {sl}_2$$ -module, is zpd if and only if $$\dim V =2$$ or $$\dim V$$ is odd. The class of zpd Lie algebras also includes the quantum torus Lie algebras $$\mathscr {L}_q$$ and $$\mathscr {L}^+_q$$ , the untwisted affine Lie algebras, the Heisenberg Lie algebras, and all Lie algebras of dimension at most 3, while the class of non-zpd Lie algebras includes the (4-dimensional) aging Lie algebra and all Lie algebras of dimension more than 3 in which only linearly dependent elements commute. We also give some evidence of the usefulness of the concept of zpd Lie algebra by using it in the study of commutativity preserving linear maps.

Let R be a noncommutative ring. Two epimorphisms $$\alpha_{i}:R\to (D_{i},\leqslant_{i}),\quad i = 1,2 $$ from R to totally ordered division rings are called equivalent if there exists an order-preserving isomorphism ϕ : (D 1, ⩽ 1) → (D 2, ⩽ 2) satisfying ϕ ∘ α 1 = α 2. In this paper we study the real epi-spectrum of R, defined to be the set of all equivalence classes (with respect to this relation) of epimorphisms from R to ordered division rings. We show that it is a spectral space when endowed with a natural topology and prove a variant of the Artin-Lang homomorphism theorem for finitely generated tensor algebras over real closed division rings.

We extend the result of Downarowicz (Israel J Math 165:189–210, 2008) to the case of amenable group actions, by showing that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group G can be modeled as the entire simplex of invariant measures on some other zero-dimensional dynamical system with free action of G. This is a continuation of our investigations from Frej and Huczek (Groups Geom Dyn 11:567–583, 2017), inspired by an earlier paper (Downarowicz in Israel J Math 156:93–110, 2006).

The purpose of this paper is to give some fixed point results for mappings involving generalized $$(\psi ,\varphi )$$ -contractions via rational expressions in the setup of partially ordered b-metric spaces. Our main results extend, generalize and enrich several well known comparable results in the recent literature. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.

In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szego inequalities for this class.

This paper is the first attempt to systematically study properties of the effective Hamiltonian $$\overline{H}$$ arising in the periodic homogenization of some coercive but nonconvex Hamilton–Jacobi equations. Firstly, we introduce a new and robust decomposition method to obtain min–max formulas for a class of nonconvex $$\overline{H}$$ . Secondly, we analytically and numerically investigate other related interesting phenomena, such as “quasi-convexification” and breakdown of symmetry, of $$\overline{H}$$ from other typical nonconvex Hamiltonians. Finally, in the appendix, we show that our new method and those a priori formulas from the periodic setting can be used to obtain stochastic homogenization for the same class of nonconvex Hamilton–Jacobi equations. Some conjectures and problems are also proposed.

In this paper, we study a category whose objects are Hilbert $$C^*$$ -modules and whose morphisms are completely semi- $$\phi $$ -maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi- $$\phi $$ -maps on Hilbert $$C^*$$ -modules, leading to an analog of the Arveson’s extension theorem for completely semi- $$\phi $$ -maps (in contrast with $$\phi $$ -maps). This theorem together with previous results suggest that the completely semi- $$\phi $$ -maps are proper generalizations of the completely positive maps.

The first aim of this paper is to show a second main theorem for algebraic curves into the n-dimensional projective space sharing hypersurfaces in subgeneral position. We then use it to study the value distribution of the generalized Gauss map of the complete (regular) minimal surfaces in \(\mathbb {R}^{m}\) with finite total curvature, as well as the unicity problem, sharing hypersurfaces in subgeneral position. Our results generalize and complete previous results in this area, especially the works of Chern and Osserman (J. Anal. Math. 19, 15–34, 1967), Jin and Ru (Differ. Geom. Appl. 25: 701–712, 2007).

Let X be a non-singular, projective surface and $$f: X\rightarrow \mathbb {P}^1$$ a non-isotrivial, semistable fibration defined over $$\mathbb {C}$$ . It is known that the number s of singular fibers must be at least 5, provided that the genus of the fibration is greater than or equal to 2 and is at least 6 if the surface is not birationally ruled. In this paper, we deduce necessary conditions for the number s of singular fibers being 5. Concretely, we prove that if $$s=5$$ , then the condition $$(K_X+F)^2=0$$ holds unless S is rational and $$g\le 17$$ . The proof is based on a “vertical”version of Miyaoka’s inequality and positivity properties of the relative canonical divisor.

In this paper we give a generalization of the Conze–Guivarc’h limit set. With this definition the limit set has very similar properties to those of the limit set in hyperbolic spaces. Moreover, we prove a relation between this new limit set and the Kulkarni limit set. Additionally we show that some closed subsets can be approximated by the Conze–Guivarc’h limit set. This is a result in the theory of classic Kleinian groups.

In this paper, we introduces the property (a B w), a variant of generalized a-Weyl’s theorem for a bounded linear operator T on an infinite-dimensional Banach space $\mathbb {X}$ . We establish several sufficient and necessary conditions for which property (a B w) holds. Also, we prove that if $T\in \mathbf {L(\mathbb {X})}$ satisfies property (a B w) then T satisfies property (B w). Certain conditions are explored on Hilbert space operators T and S so that T ⊕ S obeys property (a B w).

In this paper, we investigate some analytic properties for a class of holomorphic matrixvalued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on ℂ2×2 and Julia set of one dimensional complex dynamic system.

Let C be a bounded closed convex subset of a uniformly convex multi-Banach space X and let $${\mathfrak {I}}_{j} = \{T_j(t) : t\in G\}$$ be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we prove the strong mean ergodic convergence theorem for the almost-orbit of $$\mathfrak {I}$$ . Our results extend and unify many previously known results especially (Dong et al. On the strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in Banach space, preprint).

Some generalized contractions using altering distances in partially ordered metric spaces are investigated and their applications to fuzzy partial differential equations are considered. Starting from the Banach contraction principle, our theorems presented here generalize, extend, and improve different results existing in the literature on the existence of coincidence points for a pair of mappings. In terms of their applicability, this might constitute the first paper dealing with the solvability of fuzzy partial differential equations from the point of view of considering the structure of the fuzzy number space as a partially ordered space. Under the generalized contractive-like property over comparable items, which is weaker than the Lipschitz condition, we show that the existence of just a lower or an upper solution is enough to prove the existence and uniqueness of two types of fuzzy solutions in the sense of gH-differentiability.

The main purpose of this paper is to give a complete description of isometry groups on the 4-dimensional simply connected nilpotent Lie groups. We distinguish between two geometrically distinct cases of degenerate and nondegenerate center of the group. Since Walker metrics appear as the underlying structure of neutral signature metrics on the nilpotent Lie groups with degenerate center, we find necessary and sufficient condition for them to locally admit the nilpotent group of isometries.

Classification problems of subcategories have been deeply considered so far. In this paper, we discuss classifying dense resolving and dense coresolving subcategories of exact categories via their Grothendieck groups. This study is motivated by the classification of dense triangulated subcategories of triangulated categories due to Thomason.

In this paper we study invariant means on and amenability of double coset spaces. We prove the amenability of Gelfand pairs. As an application we prove a stability theorem for a functional equation related to spherical functions.

WOS: 000425301900011 In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz-Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators. Ahi Evran UniversityAhi Evran University [FEF.A3.16.024]; Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [02.a03.21.0008] The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008).

Ergodic homeomorphisms T and S of Polish probability spaces X and Y are evenly Kakutani equivalent if there is an orbit equivalence ϕ: X 0 → Y 0 between full measure subsets of X and Y such that, for some A ⊂ X 0 of positive measure, ϕ restricts to a measurable isomorphism of the induced systems T A and S ϕ(A). The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two zero-entropy loosely Bernoulli systems are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, while systems such as the Morse minimal system are both measurable and topological. Recently del Junco, Rudolph and Weiss studied a new relation, called nearly continuous Kakutani equivalence. A nearly continuous Kakutani equivalence is an even Kakutani equivalence where also X 0 and Y 0 are invariant G δ sets, A is within measure zero of both open and closed, and ϕ is a homeomorphism from X 0 to Y 0. It is known that nearly continuous Kakutani equivalence is strictly stronger than even Kakutani equivalence, and nearly continuous Kakutani equivalence is the natural strengthening of even Kakutani equivalence to the nearly continuous category—the category of maps that are continuous after sets of measure zero are removed. In this paper, we show that the Morse minimal substitution system is nearly continuously Kakutani equivalent to the binary odometer.

In this paper we pose some questions about superderivations on $${\mathbb {Z}}_{2}$$ -graded rings. Then we consider the quaternion rings and upper triangular matrix rings with special $${\mathbb {Z}}_{2}$$ -gradings and we check the answer to these questions about them.

In this paper, we define and study strong Kato chaos for a group action on a compact metric space. Let X be a compact metric space without isolated points, and let G be a topologically commutative group on X. If the dynamical system (X, G) is weakly mixing, then it is chaotic in the strong sense of Kato.

The present paper is devoted to the study of some subclasses of H-rings, i.e., rings in which all subrings are ideals. In the description of H-rings an important role is played by almost null rings. We classify, up to isomorphism, torsion almost null rings of bounded exponent.

In this paper, the functorial property of the inverse image for transitive Lie algebroids is proved and also there is proved the functorial property for all objects that are necessary for building transitive Lie algebroids due to K. Mackenzie—bundles L of finite-dimensional Lie algebras, covariant connections of derivations ▽, associated differential 2-dimensional forms Ω with values in the bundle L, couplings, and the Mackenzie obstructions. On the base of the functorial properties, a final object for the structure of transitive Lie prealgebroid and for the universal cohomology class inducing the Mackenzie obstruction can be constructed.

In the representation theory of finite groups, the stable equivalence of Morita type plays a prominent role. However, except for self-injective algebras, one does not know much on existence of such equivalences between arbitrary algebras. Moreover, this notion seems to be not general enough, to be preserved by classical algebraic constructions. In the paper there is introduced a notion of relative stable equivalence of Morita type. Such an equivalence appears in the context of stable equivalence of Morita type, as is showed in Theorem 0.1.

We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is λ-saturated iff it has cofinality ≥ λ and the underlying order has no (κ, κ)-gaps for regular κ < λ. We also answer a question about balanced pairs of models of PA. Second, assuming instances of GCH, we prove that SOP 2 characterizes maximality in the interpretability order ∇*, settling a prior conjecture and proving that SOP 2 is a real dividing line. Third, we establish the beginnings of a structure theory for NSOP 2, proving that NSOP 2 can be characterized by the existence of few so-called higher formulas. In the course of the paper, we show that ps = ts in any weak cofinality spectrum problem closed under exponentiation (naturally defined). We also prove that the local versions of these cardinals need not coincide, even in cofinality spectrum problems arising from Peano arithmetic.

In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.

In this paper, we give some new essential norm estimates of weighted composition operators \(uC_{\varphi }\) from analytic Besov spaces into the Bloch space, where u is a function analytic on the unit disk \(\mathbb {D}\) and \(\varphi \) is an analytic self-map of \(\mathbb {D}\). Moreover, new characterizations for the boundedness, compactness and essential norm of weighted composition operators \(uC_{\varphi }\) are obtained by the nth power of the symbol \(\varphi \) and the Volterra operators \(I_u\) and \(J_u\).

In this paper, we will consider subfractals, defined as a subset of the attractor of hyperbolic iterated function systems, which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a sofic subshift on the symbolic space. We find that the zeros of the lower and upper topological pressure functions are lower and upper bounds, respectively, for the Hausdorff, packing, lower and upper box dimensions of the subfractal.

An N-partite state is considered lazy, if the entropy rate of one subsystem with respect to time is zero under any coupling to the other subsystems. In this paper, we show that all biaxial or purely second rank tensor polarized systems are lazy. Such a system can be produced in the laboratory by the interaction of a spin-1 nuclei with non-zero quadrupole moment like H2, N14 with an external quadrupole field found in suitable crystal lattice. We then investigate the ’laziness’(property of the system to be lazy) of N-qubit mixed symmetric separable states and enumerate the conditions for them to be lazy. Further, we study the laziness of direct product states on application of a global and local noisy channels.

We define a class of inverse semigroup amalgams and derive normal forms for the amalgamated free products in the variety of semigroups. The class includes all amalgams of finite inverse semigroups, recently studied by Cherubini, Jajcayova, Meakin, Nuccio, Piochi and Rodaro (2005–2014), and lower bounded amalgams, that were introduced by the author (1997). We provide sufficient conditions for decidable word problem. We show that the word problem is decidable for an amalgamated free product of finite inverse semigroups. The normal forms can be used to study amalgams in subvarieties of inverse semigroups. In a forthcoming paper by the author, the results are used for varieties of semilattices of groups.

In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. With respect to concepts, we give some related results. In particular, we prove that an ideal is an n-fold integral ideal if and only if is an n-fold Boolean and (prime)maximal ideal. Also, we prove that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal $$\{0\}$$ is an n-fold integral ideal. Moreover, we study relation between n-fold integral ideals and n-fold obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between n-fold Boolean ideals and n-fold positive implicative filters in BL-algebras.

The aim of this paper to establish the existence and uniqueness of coincidence and common fixed points of Nadler type set-valued mappings under various generalized contractive conditions in the context of ultrametric spaces. Illustrative examples are provided to support our results. As an application, we have obtained well-posedness of the common fixed point problems. The presented results generalize several existing results in the literature in ultrametric space setting.

In this paper, we investigate the properties of right orthogonal modules of $${{\mathscr {C}}}$$ , where $${{\mathscr {C}}}$$ is a class of left R-modules. As an application, we investigate the properties of right orthogonal modules of Ding injective left R-modules, and present various characterizations of semisimple and von Neumann regular rings and so on. Moreover, we also consider another cohomology, strong Tate cohomology, which connects the usual cohomology with the Ding cohomology.

In this paper, we generalize the notion of soft connectedness (Chen, Some Local Properties of Soft Semi-Open Sets, 2013; Kandil et al., J New Results Sci 4:90–108, 2014; Lin, Int J Math Sci Eng 7(2):1–7, 2013) by using the notion of $$\beta $$ -open soft sets. Also, the concept of $$\beta $$ -irresolute soft functions is introduced, as a generalization of $$\beta $$ -continuous soft functions and several properties of it is investigated. Further, we introduce and study the notion of $$\beta $$ -connectedness and gave the basic definitions and theorems about it. Finally, we show that, the surjective $$\beta $$ -irresolute soft image of soft $$\beta $$ -connected space is also soft $$\beta $$ -connected. This study is a standard generalization of some notions in classical topological spaces to soft topological spaces.

The aim of this paper is to propose some equivalent conditions of uniform integrability for a sequence of measurable operators. Based on this result, we introduce some kinds of Cesaro uniform integrability in noncommutative probability. In addition, several results on the laws of large numbers related to these notions are established. Our results not only generalize related previously reported results but also improve them.

This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation $$\begin{aligned} u^{\prime \prime }+cu^{\prime }-a(t)u+f(t,u)=0, \end{aligned}$$ where \(c\ge 0\) is a constant and the functions a and f are continuous and not necessarily periodic in t. Under other suitable assumptions on a and f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.