Let \(\mathcal {I}\) be a meager ideal on \(\mathbf {N}\). We show that if x is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of x which preserve the set of \(\mathcal {I}\)-cluster points of x is topologically large if and only if every ordinary limit point of x is also an \(\mathcal {I}\)-cluster point of x. The analogue statement fails for all

The aim of this work is the construction of a new class of disconnected locally compact near-fields. They are all Dickson near-fields and derived from finite-dimensional division algebras over local fields by means of strong couplings with a finite Abelian Dickson group consisting of inner automorphisms.

In this article starting from some reductions of hyperelliptic integrals of genus 3 into elliptic integrals, due to Michael Roberts (A Tract on the addition of Elliptic and hyperelliptic integrals, Hodger, Foster and Co, 1871) we obtain several identities which, to the best of our knowledge, are all new. The strategy used at this purpose is to evaluate Roberts integrals, in two different ways, on one

In the paper, we study evolution equations of the scalar and Ricci curvatures under the Hamilton’s Ricci flow on a closed manifold and on a complete noncompact manifold. In particular, we study conditions when the Ricci flow is trivial and the Ricci soliton is Ricci flat or Einstein.

We study ruled real hypersurfaces whose shape operators have constant squared norm in nonflat complex space forms. In particular, we prove the nonexistence of such hypersurfaces in the projective case. We also show that biharmonic ruled real hypersurfaces in nonflat complex space forms are minimal, which provides their classification due to a known result of Lohnherr and Reckziegel.

A class of integral transforms, on the planar Gaussian Hilbert space with range in the weighted Bergman space on the bi-disk, is defined as the dual transforms of the 2d fractional Fourier transform associated with the Mehler function for Itô–Hermite polynomials. Some spectral properties of these transforms are investigated. Namely, we study their boundedness and identify their null spaces as well

The paper deals with some selection properties of set-valued functions and different types of set-valued integrals of a Young type. Such integrals are considered for classes of Hölder continuous or with bounded Young p-variation set-valued functions. Two different cases are considered, namely set-valued functions with convex values and without convexity assumptions. The integrals contain as a particular

In this paper, we study compact generalized \(\tau \)-quasi Ricci-harmonic metrics. In the first part, we explore conditions under which generalized \(\tau \)-quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for this case. In the second part, we obtain some rigidity results for compact \((\tau , \rho )\)-quasi Ricci-harmonic metrics which are a special case

Let \(\Gamma _n(\mathcal {\scriptstyle {O}}_{\mathbb {K}})\) denote the Hermitian modular group of degree n over an imaginary quadratic number field \(\mathbb {K}\) and \(\Delta _{n,\mathbb {K}}^*\) its maximal discrete extension in the special unitary group \(SU(n,n;\mathbb {C})\). In this paper we study the action of \(\Delta _{n,\mathbb {K}}^*\) on Hermitian theta series and Maaß spaces. For \(n=2\)

A counterpart of the Ohlin theorem for convex set-valued maps is proved. An application of this result to obtain some inclusions related to convex set-valued maps in an alternative unified way is presented. In particular counterparts of the Jensen integral and discrete inequalities, the converse Jensen inequality and the Hermite–Hadamard inequalities are obtained.

In this paper, we introduce the notion of (uniformly weakly) Banach-compact sets, (uniformly weakly) Banach-compact operators and (uniformly weakly) Banach-nuclear operators which generalize p-compact sets, p-compact operators and p-nuclear operators, respectively. Fundamental properties are investigated. Factorizations and duality theorems are given. Injective and surjective hulls are used to show

In our manuscript, we organize a group of sufficient conditions for the approximate controllability of second-order evolution hemivariational inequalities. By applying a suitable fixed-point theorem for multivalued maps, we prove our results. Lastly, we present an example to illustrate the obtained theory.

In this paper, we mainly prove a congruence conjecture of Z.-W. Sun involving Franel numbers: For any prime \(p>3\), we have $$\begin{aligned} \sum _{k=0}^{p-1}(-1)^kf_k\equiv \left( \frac{p}{3}\right) +\frac{2p^2}{3}B_{p-2}\left( \frac{1}{3}\right) \pmod {p^3}, \end{aligned}$$ where \(B_n(x)\) is the n-th Bernoulli polynomial.

We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley–Zehnder index for a periodic orbit of the flow of a specific

We establish direct estimates of the rate of weighted simultaneous approximation by the Baskakov operator for smooth functions in the supremum norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K-functionals.

Dual truncated Toeplitz operators and other restrictions of the multiplication by the independent variable \(M_z\) on the classical \(L^2\) space on the unit circle are investigated. Commutators are calculated and commutativity is characterized. A necessary and sufficient condition for any operator to be a dual truncated Toeplitz operator is established. A formula for recovering its symbol is stated

We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials.

The isoperimetric problem is one of the fundamental problems in differential geometry. By using the method of the calculus of variations we show that the circle centered at the origin in \({\mathbb {B}}^2(1)\) is a proper maximum of the isoperimetric problem in a 2-dimensional Finsler space of Funk type. We also obtain the formula of area enclosed by a simple closed curve in a spherically symmetric

In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed, finite dimension over a given finite field. We show how this method works in the case of 2-dimensional algebras over the field \({\mathbb {F}}_{2}\).

So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces. Here we discover various advantages of balanced unit norm tight frames in signal processing. They give an exact reconstruction in the presence of systematic errors

In this note, we study the Ulam stability of a functional equation both in Banach and m-Banach spaces. Particular cases of this equation are, among others, equations which characterize multi-additive and multi-Jensen functions. Moreover, it is satisfied by the so-called multi-linear mappings.

Let G be a topological Abelian semigroup with unit, and let E be a Banach space. We define, for functions mapping G into E, the classes of polynomials, generalized polynomials, local polynomials, exponential polynomials, and some other relevant classes. We establish their connections with each other and find their representations in terms of the corresponding complex valued classes. We also investigate

Let G be a locally compact group equipped with the left Haar measure \(m_G\), \(M_n\) be an \(n\times n\) matrix with entries in \({{\mathbb {C}}}\) and let \(L^1(G,M_n)\) be the Banach algebra respect to the convolution products \(*\) and \(*_\ell \) that consists all \(M_n\)-valued functions on G. We define the left and right positive type functions on \((L^1(G,M_n),*)\) and \((L^1(G,M_n),*_\ell

Steiner loops of affine type are associated to arbitrary Steiner triple systems. They behave to elementary abelian 3-groups as arbitrary Steiner Triple Systems behave to affine geometries over \({\mathrm {GF}}(3)\). We investigate algebraic and geometric properties of these loops often in connection to configurations. Steiner loops of affine type, as extensions of normal subloops by factor loops, are

The aim of this work is to provide a representation of the multifractal Hausdorff and packing dimensions of compact sets in the Euclidean space in terms of the lower and upper local \((q,\mu )\)-dimensions of a probability measure on \(\mathbb {R}^n\), respectively. In addition, a relationship is established allowing to determine the Olsen’s multifractal functions by means of the corresponding measures’

We introduce a kind of converse of Pompeiu’s theorem. Fix an equilateral triangle \(\triangle A_0B_0C_0\), then for any triangle \(\triangle ABC\) there is a unique point P inside the circumcircle \(\varGamma _0\) of \(\triangle A_0B_0C_0\) such that a triangle with edge lengths \(PA_0, PB_0\), and \(PC_0\) is similar to \(\triangle ABC\). It follows that an open disc inside \(\varGamma _0\) can be

This paper is concerned with the density estimation problem of negatively associated biased sample with the presence of multiple change-points. We use the peaks-over-threshold approach to estimate the number and locations of change-points and give an equispaced design estimation to evaluate the jump sizes for the underlying density function. Subsequently, we propose a nonlinear wavelet change-point

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.

We classify four-dimensional connected simply-connected Lorentzian symmetric spaces M with connected nontrivial isotropy group furnishing solutions of the Einstein–Yang–Mills equations. Those solutions are built with respect to some invariant metric connection \(\Lambda \) in the bundle of orthonormal frames of M and some diagonal metric on the holonomy algebra corresponding to \(\Lambda \).

A t-fold affine blocking set is a set of points in \({{\,\mathrm{AG}\,}}(n,q)\) intersecting each hyperplane in at least t points. In this paper we present a general construction of affine blocking sets in \({{\,\mathrm{AG}\,}}(n,q)\). The construction uses an arc in an r-dimensional subspace of \({{\,\mathrm{PG}\,}}(n,q)\) and a blocking set in the affine part \(\cong {{\,\mathrm{AG}\,}}(n-r-1,q)\)

Let \(\mu \) be a purely atomic finite measure. Without loss of generality we may assume that \(\mu \) is defined on \({\mathbb {N}}\), and the atoms with smaller indexes have larger masses, that is \(\mu (\{k\})\ge \mu (\{k+1\})\) for \(k\in {\mathbb {N}}\). By \(f_\mu :[0,\infty )\rightarrow \{0,1,2,\dots ,\omega ,{\mathfrak {c}}\}\) we denote its cardinal function \(f_{\mu }(t)=\vert \{A\subset

In this paper we first present the real homogeneous complex Finsler metrics (\(\mathbb {R}\)-complex Finsler metrics) and make use of them to generalize the Zermelo navigation on Hermitian manifolds. \(\mathbb {R}\)-complex Randers metrics are obtained by the Zermelo deformation of Hermitian metrics, with variable space-dependent ship’s relative speed under action of weak complex vector fields. Next

An explicit representation of the monodromy transformation of the space of solutions to the nonlinear ODE, utilized for the modeling of Josephson junctions, is given. In case of positive integer order, the transformation, interpreted as the square root of the noted monodromy transformation, is derived by making use of a symmetry possessed by the associated double confluent Heun equation.

Non-self-adjoint second-order differential operators on a finite interval with indefinite discontinuous weights are studied. Properties of spectral characteristics are established and inverse problems of recovering operators from their spectral characteristics are investigated. For these class of nonlinear inverse problems algorithms for constructing the global solutions are developed, and uniqueness

Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the considered Ricci-like soliton has a

Let G be an abelian group, let \(M_{2}(\mathbb {C})\) be the algebra of complex \(2\times 2\) matrices, and let \(\varphi :G\rightarrow G\) be an endomorphism that need not be involutive. We determine the solutions \(\Phi :G\rightarrow M_{2}(\mathbb {C})\) of the matrix functional equation $$\begin{aligned} \frac{\Phi (x+y)+\Phi (x+\varphi (y))}{2}=\Phi (x)\Phi (y),\quad x,y\in G. \end{aligned}$$ This

We confirm a few recent conjectures of Lassak on the perimeter and area of reduced spherical polygons of thickness \(\pi /2\). This paper is based on the study of the sufficient and necessary conditions whether a spherical polygon of thickness \(\pi /2\) is reduced. The perimeter (resp. area) of every reduced spherical k-gon of thickness \(\pi /2\) is not greater than that of the regular spherical

In this paper, we get a one-parameter family of local isometric immersions from a compact Riemann surface with a singular non-CSC extremal Kähler metric to \({\mathbb {R}}^3\), each of whom is a Weingarten surface. In fact, we can get explicit expressions of the mean curvatures in the family by the Gauss curvature of the metric.

Given a convex body in the plane, we define the isoptic curve of angle \(\alpha \), for an arbitrary but fixed angle \(\alpha ,\) as the curve from which K is always seen under an angle \(\alpha \) In this article we prove an inequality between the perimeter of any convex body in the plane and its isotopic curve. Moreover, we also prove some characterizations of the Euclidean disc by means of the constancy

This is a survey of results from the rich theory of medial and more general quasigroups and its close connection with the geometry of point-reflections. The emphasis is on questions regarding the simplest axiomatization, in the sense of the minimal number of variables appearing in the identtties, on dependence or independence of axioms, and on representation theorems in the style of Toyoda.

We show generic existence of power series \(a = \sum \nolimits _{n = 0}^{\infty }a_nz^n, a_n \in \mathbb {C}\), such that the sequence \(T_N(a)(z) = \sum \nolimits _{n=0}^{N}b_n(a_0, \ldots , a_n)z^n, N = 0, 1, 2 \ldots \) approximates every polynomial uniformly on every compact set \(K \subset \mathbb {C}{\setminus }\{0\}\) with connected complement. The functions \(b_n : \mathbb {C}^{n + 1}\rightarrow

Linear canonical transform (LCT), which is of importance in solving differential equations and analyzing optical systems, extends the conventional Fourier transform to the time-frequency domain characterized by a parameter matrix \(\mathbf{A }=(a,b;c,d)\). The main objective of this paper is to study the Balian–Low theorem in the LCT domain. We first state a Balian–Low theorem associated with the LCT

We present a new Kantorovich modification of Szász–Mirakjan operators which reproduce affine functions. We present an upper estimate for the rate of convergence of the new operators in polynomial weighted spaces and characterized all functions for which there is convergence.

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns out to be equivalent to the property of being unitary. The result reveals a dichotomy identifying a specific family of weighted Hardy spaces as the only ones that

In the present paper we continue to study almost geodesic curves and determine in \({\mathbb {R}}^n\) the form of curves \({\mathcal {C}}\) for which every image under an \((n-1)\)-dimensional algebraic torus is also an almost geodesic with respect to an affine connection \(\nabla \) with constant coefficients. We also calculate explicitly the components of \(\nabla \). For the explicit calculation

In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean \(C^2\)-smooth surface in the BCV spaces and the twisted Heisenberg group away from characteristic points and signed geodesic curvature for Euclidean \(C^2\)-smooth curves on surfaces. We get Gauss–Bonnet theorems in the BCV spaces and the twisted Heisenberg group.

In this paper, new criteria for zero dimensional rings, Gelfand rings, clean rings and mp-rings are given. A new class of rings is introduced and studied, we call them purified rings. Specially, reduced purified rings are characterized. New characterizations for pure ideals of reduced Gelfand rings and mp-rings are provided. It is also proved that if the topology of a scheme is Hausdorff, then the

If a K-contact manifold (M, g) and a D-homothetically deformed K-contact manifold \((M,{\bar{g}})\) are both Ricci almost solitons with the same associated vector field V, then we show (i) that (M, g) and (\(M, {\bar{g}}\)) are both D-homothetically fixed \(\eta \)-Einstein Ricci solitons, and (ii) V preserves \(\phi \). We also show that, if the associated vector field V of a complete K-contact Ricci

A new and elementary proof of the Artin–Zorn theorem that finite alternative division rings are fields is given. The characterisation of finite fields of Glauberman and Heimbeck is also extended to a broader class of fields, the two subjects being connected via geometry.

We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.

The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincaré lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract derivative and the homotopy operator plays the role of an abstract integral. This operator calculus can be used to formulate abstract differential equations. An example of

In this paper we consider complex form of a modified (perturbed) Bernstein operators attached to an analytic function in a disk of radius \(R>1\) centered at the origin. We obtain quantitative estimates of the convergence in compact disks and exact degree of simultaneous approximation with the help of upper estimates in quantitative form, and of lower estimates obtained from a qualitative Voronovskaja

In this note, using the spinorial description of SU(3) and \(G_2\)-structures obtained recently by other authors, we give necessary and sufficient conditions for harmonicity of the above mentioned structures. We describe the results on appropriate homogeneous spaces. Here, harmonicity means harmonicity of a certain unique section induced by the G-structure in consideration.

In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series \((I_{w}^{\chi })_{w>0}.\) Further, we establish a representation formula and an inverse result of approximation for these operators. Finally, we give some examples of kernel functions to which the theory

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when \(\lambda \) is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

An oriented sphere in \({\mathbb {R}}^n\) is a sphere for which one side (inside or outside) is distinguished as its positive side. Two oriented spheres are said to be properly tangent if they are tangent and the positive side of one sphere is contained in the positive side of the other. A set of 2k spheres \(\{\alpha _1,\dots ,\alpha _k,\beta _1,\dots ,\beta _k\}\) in \({\mathbb {R}}^n\) is called

For an entire function \(f(z) = \sum _{k=0}^\infty a_k z^k, a_k>0\), we show that if f belongs to the Laguerre–Pólya class, and the quotients \(q_k:= \frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots \) satisfy the condition \(q_2 \le q_3\), then f has at least one zero in the segment \([-\frac{a_1}{a_2},0]\). We also give necessary conditions and sufficient conditions of the existence of such a zero in

Because all the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange–Hermite interpolation formula, in this paper we obtain semi-discrete quantitative Voronovskaya-type theorems based on various other Lagrange–Hermite interpolation formulas. Applications to Bernstein–Kantorovich and

Magnetic curves with respect to the almost cosymplectic structure of the \(\mathrm {Sol}_3\) space are determined and curvature properties of these curves are investigated.

In this paper, we construct a topology on the vector space \(\delta \mathcal F_{m,\chi }(\Omega )\). We also prove that with this topology it is quasi-Banach, non-separable and non-reflexive. We also give a characterization for the class \(\mathcal F_{m, \min \{\chi _1, \chi _2\}}(\Omega )\).