The $${\mathbb {Q}}$$ Q -Korselt set of $$\mathrm {pq}$$ pq

Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus...     

Sufficient conditions for local equivalence of mappings

Let $$f,g:({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^m,0)$$ be $$C^{r+1}$$ mappings and let $$Z=\{x\in \mathbf {\mathbb {R}}^n:\nu (df (x))=0\}$$ , $$0\in Z$$ , $$m\le n$$ . We will show that if there exist a neighbourhood U of $$0\in {\mathbb {R}}^n$$ and constants $$C,C'>0$$ and $$k>1$$ such that for $$x\in U$$ $$\begin{aligned}&\nu (df(x))\ge C{\text {dist}}(x,Z)^{k-1}, \\&\left| \partial ^{s} (f_i-g_i)(x) \right| \le C'\nu (df(x))^{r+k-|s|}, \end{aligned}$$ for any $$i\in \{1,\dots , m\}$$ and for any $$s \in \mathbf {\mathbb {N}}^n_0$$ such that $$|s|\le r$$ , then there exists a $$C^r$$ diffeomorphism $$\varphi :({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^n,0)$$ such that $$f=g\circ \varphi $$ in a neighbourhood of $$0\in {\mathbb {R}}^n$$ . By $$\nu (df)$$ we denote the Rabier function.     

Tangencies and polynomial optimization

Mathematical Programming - Given a polynomial function $$f :{\mathbb {R}}^n \rightarrow {\mathbb {R}}$$ and an unbounded closed semi-algebraic set $$S \subset {\mathbb {R}}^n,$$ we show that the...     

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...     

Indefinite Stein fillings and $$\text {PIN}(2)$$PIN(2)-monopole Floer homology

Let $$W(z_1, \ldots , z_n): ({\mathbb {C}}^*)^n \rightarrow {\mathbb {C}}$$ be a Laurent polynomial in n variables, and let $${\mathcal {H}}$$ be a generic smooth fiber of W. Ruddat et al. (Geom Topol 18:1343–1395, 2014) give a combinatorial recipe for a skeleton for $${\mathcal {H}}$$. In this paper, we show that for a suitable exact symplectic structure on $${\mathcal {H}}$$, the RSTZ-skeleton can be realized as the Liouville Lagrangian skeleton.     

On the linearity and classification of $${\mathbb {Z}}_{p^s}$$ Z p s -linear generalized hadamard codes

Designs, Codes and Cryptography - $${\mathbb {Z}}_{p^s}$$ -additive codes of length n are subgroups of $${\mathbb {Z}}_{p^s}^n$$ , and can be seen as a generalization of linear codes over...     

Note on a result of Chen and Lev

Periodica Mathematica Hungarica - Let $${\mathbb {N}}$$ be the set of all nonnegative integers. For a given set $$S\subset {\mathbb {N}}$$ the representation function $$R_S(n)$$ is defined as the...     

On the distribution of the van der Corput sequences

Archiv der Mathematik - For an integer $$p\ge 2$$ , let $$\{x_n\}_{n\in {\mathbb {N}}}\subset {\mathbb {T}}$$ be the p-adic van der Corput sequence. For intervals $$[0,\alpha )\subset {\mathbb...     

A proof from the book,perchance

Journal of Algebraic Combinatorics - The fact that the groups $${\mathbb {Z}}_{2^m} \times {\mathbb {Z}}_{2^m}$$ contain difference sets was first established by induction by Jim Davis in his...     

A Trudinger–Moser inequality for a conical metric in the unit ball

Archiv der Mathematik - In this note, we prove a Trudinger–Moser inequality for a conical metric in the unit ball. Precisely, let $${\mathbb {B}}$$ be the unit ball in $${\mathbb {R}}^N$$...     

Lattice closures of polyhedra

Mathematical Programming - Given $$P\subset {\mathbb {R}}^n$$, a mixed-integer set $$P^I=P\cap ({\mathbb {Z}}^{t}\times {\mathbb {R}}^{n-t}$$), and a k-tuple of n-dimensional integral vectors...     

Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Let be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings and which characterize the compactness of differences of two weighted composition operators on the space . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.      

Bicomplex Quantum Mechanics: I. The Generalized Schrödinger Equation

We introduce the set of bicomplex numbers which is a commutative ring with zero divisors defined by where We present the conjugates and the moduli associated with the bicomplex numbers. Then we study the bicomplex Schr?dinger equation and found the continuity equations. The discrete symmetries of the system of equations describing the bicomplex Schr?dinger equation are obtained. Finally, we study the bicomplex Born formulas under the discrete symmetries. We obtain the standard Born’s formula for the class of bicomplex wave functions having a null hyperbolic angle.     

Iterated sumsets and setpartitions

The Ramanujan Journal - Let $$G\cong {\mathbb {Z}}/m_1{\mathbb {Z}}\times \cdots \times {\mathbb {Z}}/m_r{\mathbb {Z}}$$ be a finite abelian group with $$m_1\mid \cdots \mid m_r=\exp (G)$$ . The...     

Non-free isometric immersions of Riemannian manifolds

Let (V, g) be a Riemannian manifold and let be the isometric immersion operator which, to a map , associates the induced metric on V, where denotes the Euclidean scalar product in . By Nash–Gromov implicit function theorem is infinitesimally invertible over the space of free maps. In this paper we study non-free isometric immersions . We show that the operator (where denotes the space of C ^∞- smooth quadratic forms on ) is infinitesimally invertible over a non-empty open subset of and therefore is an open map in the respective fine topologies.      

The Generalized k-Resultant Modulus Set Problem in Finite Fields

Journal of Fourier Analysis and Applications - Let $${\mathbb {F}}_q^d$$ be the d-dimensional vector space over the finite field $${\mathbb {F}}_q$$ with q elements. Given k sets $$E_j\subset...     

The universal minimal one parameter system with quasi-discrete spectrum

The universal minimal one parameter system will be characterized as the space $$\Gamma ^{\infty }$$, in which $$\Gamma$$ is the Bohr compactification of the additive group $${\mathbb {R}}$$ of real numbers. In this way, we need to show that $$\Gamma ^\infty$$ is isomorphic to the spectrum of $$W({\mathbb {R}})$$, the norm closure of the invariant algebra generated by the maps $$\exp q(t)$$, where q(t) is a real polynomial on $${\mathbb {R}}$$.     

Quasi-Cauchy quotients and means

Aequationes mathematicae - Let $$I\subset {\mathbb {R}}$$ be an interval that is closed under addition, and $$ k\in {\mathbb {N}}$$ , $$k\ge 2\,$$ . For a function $$f:I\rightarrow \left( 0,\infty...     

Some permutations over $$\pmb {\mathbb {F}}_p$$ F p concerning primitive roots

The Ramanujan Journal - Let p be an odd prime and let $${\mathbb {F}}_p$$ denote the finite field with p elements. Suppose that g is a primitive root of $${\mathbb {F}}_p$$ . Define the permutation...