On $${\mathcal {I}}_{

Tóth  János T.  Filip  Ferdinánd  Bukor  József  Zsilinszky  László 《Periodica Mathematica Hungarica》2021,82(2):125-135

Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in $$L_2$$

Mathematical Notes - Exact constants in Jackson–Stechkin type inequalities are found for the smoothness characteristics $$\Lambda_m (f)$$ , $$ m\in\mathbb N$$ , determined by averaging the...     

Sharp Inequalities between the Best Root-Mean-Square Approximations of Analytic Functions in the Disk and Some Smoothness Characteristics in the Bergman Space

Mathematical Notes - In Jackson–Stechkin type inequalities for the smoothness characteristic $$\Lambda_m(f)$$ , $$m\in\mathbb N$$ , we find exact constants determined by averaging the norms...     

Estimates of Derivatives in Sobolev Spaces in Terms of Hypergeometric Functions

Mathematical Notes - The paper deals with sharp estimates of derivatives of intermediate order $$k\le n-1$$ in the Sobolev space $$\mathring W^n_2[0;1]$$ , $$n\in\mathbb N$$ . The functions...     

Additive and multiplicative Sidon sets

Acta Mathematica Hungarica - We give a construction of a set $$A \subset \mathbb N$$ such that any subset $${A' \subset A}$$ with $$|A'| \gg |A|^{2/3}$$ is neither an additive nor...     

On the average number of subgroups of the group $${\mathbb {Z}}_m \times {\mathbb {Z}}_n$$ Z m × Z n with k-th power sequence

The Ramanujan Journal - Let $$\mathbb {Z}_{n}$$ be the additive group of residue classes modulo n. Let s(m, n) denote the total number of subgroups of the group $$\mathbb {Z}_{m} \times...     

On p-adic valuations of certain m colored p-ary partition functions

The Ramanujan Journal - Let $$k\in \mathbb {N}_{\ge 2}$$ and for given $$m\in \mathbb {Z}{\setminus }\{0\}$$ consider the sequence $$(S_{k,m}(n))_{n\in \mathbb {N}}$$ defined by the power series...     

A note on certain integral equations associated with non-linear time series analysis

Probability Theory and Related Fields - We consider the integral equation inh $$h(y) = \int\limits_{\mathbb{R}^n } {f(y - \hat Tx)h(x)dx,} $$ wheref is a p.d.f. and $$\hat T:\mathbb{R}^n \to...     

Mapping of Least ρ-Dirichlet Energy between Doubly Connected Riemann Surfaces

In this note, we consider the mappings h : X → Y between doubly connected Riemann surfaces having least ρ-Dirichlet energy. For a pair of doubly connected Riemann surfaces, in which X has finite conformal modulus, we establish the following principle: A mapping h in the class ■(X, Y)of strong limits of homeomorphisms in Sobolev space W1,2(X, Y) is ρ-energy-minimal if and only if its Hopf-differential is analytic in X and real along ?X. It improves and extends the result of Iwaniec et al.(see Theorem 1.4 in [Arch. Ration. Mech. Anal., 209, 401–453(2013)]). Furthermore, we give an application of the principle. Any ρ-energy minimal diffeomorphism is ρ-harmonic, however, we give a 1/|w|~2-harmonic diffemorphism which is not 1/|w|~2-energy minimal diffeomorphism. At last, we investigate the necessary and sufficient conditions for the existence of 1/|w|~2-harmonic mapping from doubly connected domain Ω to the circular annulus A(1, R).     

Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum - Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ , let $$S_n\subseteq \mathbb {N}$$ be the numerical semigroup generated by...     

On the structure of partition which the difference of their representation function is a constant

Periodica Mathematica Hungarica - Let $$\mathbb {N}$$ be the set of nonnegative integers. For any set $$A \subset \mathbb {N}$$ , let $$R_1(A, n)$$ , $$R_2(A, n)$$ and $$R_3(A, n)$$ be the number...     

A note on the Lebesgue–Ljunggren–Nagell equation $$ax^2+b^{2m}=4y^n$$ a x 2 + b 2 m = 4 y n

Periodica Mathematica Hungarica - Let a, b be fixed positive integers such that $$2\not \mid {ab}$$ , $$\gcd (a,b)=1$$ and a is square-free, and let $$h(-a)$$ denote the class number of...     

The classification of maximal inverse monoids of matrices

Semigroup Forum - Let $${\mathbb {F}}$$ be a field. The set $$M_{n}({\mathbb {F}})$$ of all $$n \times n$$ matrices over $${\mathbb {F}}$$ forms a monoid under usual matrix multiplication. We...     

Numerical semigroups bounded by the translation of a plane monoid

Aequationes mathematicae - Let $$\mathbb {N}$$ be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$ . Let M be a plane monoid and $$p,q\in \mathbb {N}$$...     

On some properties of the number of permutations being products of pairwise disjoint d-cycles

Monatshefte für Mathematik - Let $$d\ge 2$$ be an integer. In this paper we study arithmetic properties of the sequence $$(H_d(n))_{n\in \mathbb {N}}$$, where $$H_{d}(n)$$ is the number of...     

The Spectrality of a Class of Fractal Measures on $$\mathbb{R}^{n}$$

Acta Mathematica Sinica, English Series - Let $$M=\rho^{-1}I\in M_{n}(\mathbb{R})$$ be an expanding matrix with 0 < ∣ ρ ∣ < 1 and $$D\subset\mathbb{Z}^{n}$$ be a...     

Menon-type identities with respect to sets of units

The Ramanujan Journal - Let $$n\ge 1$$ and let $$\mathbb {Z}_n^\star $$ be the group of units in the ring of residual classes modulo n, let $$m\ge 0$$ , $$k\ge 0$$ , $$m+k\ge 1$$ , $$u_1,\ldots...     

On the structure of submanifolds in the hyperbolic space

Monatshefte für Mathematik - Let $$M^n$$ be a complete submanifold in the hyperbolic space $$\mathbb {H}^{n+m}$$ . We show the vanishing of the Betti numbers $$\beta _p(M)$$ , $$1 \le p \le...     

Interpolation Problems for Functions with Zero Integrals over Balls of Fixed Radius

Doklady Mathematics - Let $${{V}_{r}}({{\mathbb{R}}^{n}})$$, n ≥ 2, be the set of functions $$f \in {{L}_{{{\text{loc}}}}}({{\mathbb{R}}^{n}})$$ with zero integrals over all balls in...     

Widened derangements and generalized Laguerre polynomials

The Ramanujan Journal - Let $$D_h$$ , $$E_k$$ and $$F_{\alpha }$$ be sets of size $$h,k,\alpha $$ respectively, with $$k \le h$$ . We define a strongly widened derangement to be a permutation of...