共查询到20条相似文献,搜索用时 15 毫秒
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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. 相似文献
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Sergio A. Pérez 《Archiv der Mathematik》2017,109(5):471-475
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. 相似文献
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Permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics
and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper,
six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over are presented. These polynomials have simple shapes, and they are related to planar functions.
This work was supported by Australian Research Council (Grant No. DP0558773), National Natural Science Foundation of China
(Grant No. 10571180) and the Research Grants Council of the Hong Kong Special Administrative Region of China (Grant No. 612405) 相似文献
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Tao Feng 《Designs, Codes and Cryptography》2012,62(3):253-258
In 1976, Helleseth conjectured that two binary m-sequences of length 2
m
− 1 can not have a three-valued crosscorrelation function when m is a power of 2. We show that this conjecture is true when −1 is a correlation value. In other words, if C1,k{{\mathcal{C}}_{1,k}} is the cyclic code of length 2
m
− 1 with two zeros α, α
k
, where α is a primitive element of
\mathbbF2m{{\mathbb{F}}_{2^m}} and gcd(k, 2
m
− 1) = 1, then its dual C1,k^{{\mathcal{C}}_{1,k}^{\perp}} can not have three weights when m is a power of 2. 相似文献
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We prove that for each prime p, positive integer \(\alpha \), and non-negative integers \(\beta \) and \(\gamma \), the Diophantine equation \(X^{2N} + 2^{2\alpha }5^{2\beta }{p}^{2\gamma } = Z^5\) has no solution with N, X, \(Z\in \mathbb {Z}^+\), \(N > 1\), and \(\gcd (X,Z) = 1\). 相似文献
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We determine the exact values and asymptotic decompositions of upper bounds of approximations by biharmonic Poisson integrals on classes of periodic differentiable functions. 相似文献
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The Marcinkiewicz integral is essentially a Littlewood-Paley g-function, which plays a very important role in harmonic analysis. In this paper we give weaker smoothness conditions assumed
on Ω to imply the
boundedness of the Marcinkiewicz integral operator μΩ, where w belongs to the Muckenhoupt weight class. 相似文献
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A. Melakhessou K. Guenda T. A. Gulliver M. Shi P. Solé 《Journal of Applied Mathematics and Computing》2018,57(1-2):375-391
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring \(R=\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}\), where \(v^{3}=v\), for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over \(\mathbb {F}_q\) and extend these to codes over R. 相似文献
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Bounds are obtained for the \(L^p\) norm of the torsion function \(v_{\varOmega }\), i.e. the solution of \(-\varDelta v=1,\, v\in H_0^1(\varOmega ),\) in terms of the Lebesgue measure of \(\varOmega \) and the principal eigenvalue \(\lambda _1(\varOmega )\) of the Dirichlet Laplacian acting in \(L^2(\varOmega )\). We show that these bounds are sharp for \(1\le p\le 2\).
相似文献15.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
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Corentin Pontreau 《Monatshefte für Mathematik》2009,157(3):267-281
We prove a sharper so-called Mordell-Lang plus Bogomolov type result for curves lying in the two-dimensional linear torus.
We mainly follow the approach of Rémond in (Comp Math 134:337–366, 2002), using Vojta and Mumford type inequalities. In the
special case we consider, we improve Rémond’s main result using a better Bogomolov property and an elementary arithmetic Bézout
theorem.
相似文献
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Mathematical Notes - We construct a family of flat isotropic nonhomogeneous tori in $$\mathbb{H}^n$$ and $$\mathbb{C}\mathrm{P}^{2n+1}$$ and find necessary and sufficient conditions for their... 相似文献
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Minjia Shi Zahra Sepasdar Adel Alahmadi Patrick Solé 《Designs, Codes and Cryptography》2018,86(6):1201-1209
We determine the possible homogeneous weights of regular projective two-weight codes over \(\mathbb {Z}_{2^k}\) of length \(n>3\), with dual Krotov distance \(d^{\lozenge }\) at least four. The determination of the weights is based on parameter restrictions for strongly regular graphs applied to the coset graph of the dual code. When \(k=2\), we characterize the parameters of such codes as those of the inverse Gray images of \(\mathbb {Z}_4\)-linear Hadamard codes, which have been characterized by their types by several authors. 相似文献
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For \(\alpha , \beta \in L^{\infty } (S^1),\) the singular integral operator \(S_{\alpha ,\beta }\) on \(L^2 (S^1)\) is defined by \(S_{\alpha ,\beta }f:= \alpha Pf+\beta Qf\), where P denotes the orthogonal projection of \(L^2(S^1)\) onto the Hardy space \(H^2(S^1),\) and Q denotes the orthogonal projection onto \(H^2(S^1)^{\perp }\). In a recent paper, Nakazi and Yamamoto have studied the normality and self-adjointness of \(S_{\alpha ,\beta }\). This work has shown that \(S_{\alpha ,\beta }\) may have analogous properties to that of the Toeplitz operator. In this paper, we study several other properties of \(S_{\alpha ,\beta }\). 相似文献
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Chris Pollett 《Archive for Mathematical Logic》2011,50(3-4):367-393
Conservative subtheories of ${{R}^{1}_{2}}$ and ${{S}^{1}_{2}}$ are presented. For ${{S}^{1}_{2}}$ , a slight tightening of Je?ábek??s result (Math Logic Q 52(6):613?C624, 2006) that ${T^{0}_{2} \preceq_{\forall \Sigma^{b}_{1}}S^{1}_{2}}$ is presented: It is shown that ${T^{0}_{2}}$ can be axiomatised as BASIC together with induction on sharply bounded formulas of one alternation. Within this ${\forall\Sigma^{b}_{1}}$ -theory, we define a ${\forall\Sigma^{b}_{0}}$ -theory, ${T^{-1}_{2}}$ , for the ${\forall\Sigma^{b}_{0}}$ -consequences of ${S^{1}_{2}}$ . We show ${T^{-1}_{2}}$ is weak by showing it cannot ${\Sigma^{b}_{0}}$ -define division by 3. We then consider what would be the analogous ${\forall\hat\Sigma^{b}_{1}}$ -conservative subtheory of ${R^{1}_{2}}$ based on Pollett (Ann Pure Appl Logic 100:189?C245, 1999. It is shown that this theory, ${{T}^{0,\left\{2^{(||\dot{id}||)}\right\}}_{2}}$ , also cannot ${\Sigma^{b}_{0}}$ -define division by 3. On the other hand, we show that ${{S}^{0}_{2}+open_{\{||id||\}}}$ -COMP is a ${\forall\hat\Sigma^{b}_{1}}$ -conservative subtheory of ${R^{1}_{2}}$ . Finally, we give a refinement of Johannsen and Pollett (Logic Colloquium?? 98, 262?C279, 2000) and show that ${\hat{C}^{0}_{2}}$ is ${\forall\hat\Sigma^{b}_{1}}$ -conservative over a theory based on open cl-comprehension. 相似文献