A new family of differentially 4-uniform permutations over $$\mathbb{F}_{2^{2k} }$$ for odd k

We study the differential uniformity of a class of permutations over \(\mathbb{F}_{2^n } \) with n even. These permutations are different from the inverse function as the values x^?1 are modified to be (γx)^? on some cosets of a fixed subgroup 〈γ〉 of \(\mathbb{F}_{2^n }^* \). We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent (CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.     

The extension of the $$D(-k)$$ D ( - k ) -pair $$\{k,k+1\}$$ { k,k + 1 } to a quadruple

Periodica Mathematica Hungarica - Let $$n\ne 0$$ be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ is called a D(n)-m-tuple if $$a_ia_j + n$$ is a perfect square for...     

Nonexistence of generalized bent functions from $$\mathbb {Z}_{2}^{n}$$ to $$\mathbb {Z}_{m}$$Zm

In this paper, several nonexistence results on generalized bent functions \(f:\mathbb {Z}_{2}^{n} \rightarrow \mathbb {Z}_{m}\) are presented by using the knowledge on cyclotomic number fields and their imaginary quadratic subfields.     

Lattices of topologies of unary algebras of the variety $$ \mathcal{A}_{1,1} $$

We consider the variety of unary algebras 〈A, f, g〉 defined by the identities f(g(x)) = g(f(x)) = x. We describe algebras of this variety, whose topology lattices are modular, distributive, linearly ordered, complemented, or pseudocomplemented.     

Boundary Properties of First-Order Partial Derivatives of the Poisson Integral for the Half-Space $$\mathbb{R}_{k + 1}^ + (k >1)$$

Boundary properties of first-order partial derivatives of the Poisson integral are studied in the half-space .     

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...     

On the structure of level sets of uniform and Lipschitz quotient mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{R} $$

We study two questions posed by Johnson, Lindenstrauss, Preiss, and Schechtman, concerning the structure of level sets of uniform and Lipschitz quotient mappings from . We show that if , is a uniform quotient mapping then for every has a bounded number of components, each component of separates and the upper bound of the number of components depends only on and the moduli of co-uniform and uniform continuity of .Next we prove that all level sets of any co-Lipschitz uniformly continuous mapping from to are locally connected, and we show that for every pair of a constant and a function with , there exists a natural number , so that for every co-Lipschitz uniformly continuous map with a co-Lipschitz constant and a modulus of uniform continuity , there exists a natural number and a finite set with card so that for all has exactly components, has exactly components and each component of is homeomorphic with the real line and separates the plane into exactly 2 components. The number and form of components of for are also described - they have a finite tree structure.     

A note on lattice points in model domains of finite type in $${mathbb{R}^d}$$

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.     

On the reflexivity of $$\mathcal {P}_{w}(^{n}E;F)$$

In this paper we prove that if E and F are reflexive Banach spaces and G is a closed linear subspace of the space \(\mathcal {L}_{K}(E;F)\) of all compact linear operators from E into F, then G is either reflexive or non-isomorphic to a dual space. This result generalizes (Israel J Math 21:38-49, 1975, Theorem 2) and gives the solution to a problem posed by Feder (Ill J Math 24:196-205, 1980, Problem 1). We also prove that if E and F are reflexive Banach spaces, then the space \(\mathcal {P}_{w}(^{n}E;F)\) of all n-homogeneous polynomials from E into F which are weakly continuous on bounded sets is either reflexive or non-isomorphic to a dual space.     

Two-Sided Estimates of the $$L^infty$$ -Norm of the Sum of a Sine Series with Monotone Coefficients $${b_k}$$ via the $$ell^infty$$ -Norm of the Sequence $${kb_k}$$

Mathematical Notes - We refine the classical boundedness criterion for sums of sine series with monotone coefficients $$b_k$$ : the sum of a series is bounded on $$mathbb R$$ if and only if the...     

Quasi-optimal Nonconforming Approximation of Elliptic PDEs with Contrasted Coefficients and $$H^{1+{r}}$$ , $${r}>0$$ , Regularity

Foundations of Computational Mathematics - In this paper, we investigate the approximation of a diffusion model problem with contrasted diffusivity for various nonconforming approximation methods....     

Additive properties of product sets in the field $$ \mathbb{F}_{p^2 } $$

For given positive integer n and ε > 0 we consider an arbitrary nonempty subset A of a field consisting of p ² elements such that its cardinality exceeds p ^2/n?ε . We study the possibility to represent an arbitrary element of the field as a sum of at most N(n, ε) elements from the nth degree of the set A. An upper estimate for the number N(n, ε) is obtained when it is possible.     

On the Exponential Dichotomy on $$\mathbb{R}$$ of Linear Differential Equations in $$\mathbb{R}^n$$

We present new results on the exponential dichotomy on the entire axis of linear differential equations in .     

On the varieties of ai-semirings satisfying $${x^{3}\approx x}$$

The aim of this paper is to study the varieties of ai-semirings satisfying \({x^{3}\approx x}\) . It is shown that the collection of all such varieties forms a distributive lattice of order 179. Also, all of them are finitely based and finitely generated. This generalizes and extends the main results obtained by Ghosh et al., Pastijn and Ren and Zhao.