共查询到20条相似文献,搜索用时 656 毫秒
1.
Kris Coolsaet 《Designs, Codes and Cryptography》2013,68(1-3):179-194
As a first step in the classification of nonsingular 2×2×2×2 hypercubes up to equivalence, we resolve the case where the base field is finite and the hypercubes can be written as a product of two 2×2×2 hypercubes. (Nonsingular hypercubes were introduced by D. Knuth in the context of semifields. Where semifields are related to hypercubes of dimension 3, this paper considers the next case, i.e., hypercubes of dimension 4.) We define the notion of ij-rank (with 1 ≤ i < j ≤ 4) and prove that a hypercube is the product of two 2×2×2 hypercubes if and only if its 12-rank is at most 2. We derive a ‘standard form’ for nonsingular 2×2×2×2 hypercubes of 12-rank less than 4 as a first step in the classification of such hypercubes up to equivalence. Our main result states that the equivalence class of a nonsingular 2×2×2×2 hypercube M of 12-rank 2 depends only on the value of an invariant δ 0(M) which derives in a natural way from the Cayley hyperdeterminant det0 M and another polynomial invariant det M of degree 4. As a corollary we prove that the number of equivalence classes is (q + 1)/2 or q/2 depending on whether the order q of the field is odd or even. 相似文献
2.
Peter Zhidkov 《Rendiconti del Circolo Matematico di Palermo》2009,58(3):427-440
Let w and µ be respectively the conditional Wiener measure in C 0([0, 1]) and the centered Gaussian measure in L 2[0, 1] with the correlation operator (?d 2/dx 2)?1. We prove the equivalence of these two measures in the following sense: for any Borel set A ? L 2[0, 1] the set A ∩ C 0([0, 1]) is a Borel subset of C 0([0, 1]) and µ(A) = w(A∩C 0([0, 1])). 相似文献
3.
4.
We prove that the simplest four-fermion Gross-Neveu model with the dimensional regularization d=2+2ɛ is not multiplicatively
renormalizable. This is due to the counter-term, generated by the three-loop vertex diagrams, that is proportional to the
evanescent operator
. Here
is the totally antisymmetric product of n γ-matrices, which is not zero in a noninteger dimension as well. Therefore, calculations
of the (2+ɛ)-expansion of the critical indices η and ν in the framework of the simple Gross-Neveu model are correct only up
to ε4 for η and to ɛ3 for ν. In higher orders, one must take into consideration the generation of other (not only V3) evanescent operators.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 85–99, October, 1997. 相似文献
5.
Yu. A. Neretin 《Functional Analysis and Its Applications》2016,50(2):160-162
It is shown that the group PSL2(?) is a spherical subgroup in the group of C3-diffeomorphisms of the circle. 相似文献
6.
We show that every incomplete Σ
2
0
enumeration degree is meet-reducible in the structure of the enumeration degrees of the Σ
2
0
sets.
The first author was partially supported by NSF-grant DMS-9500983.
The second author was partially supported by the HC&M research networkComplexity, Logic and Recursion Theory (COLORET), contract no. ERBCHRXCT930415, and by MURST 60%. 相似文献
7.
We quantize the W-algebra W(2, 2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated
and determined in a series of papers recently. 相似文献
8.
In [1], Eells and Lemaire arise a problem of the existence of harmonic mapsfrom R~2 into H~2. Using the fact that H~2 = {x = (x_1,x_2,x_3)∈R~(2,1):x_1~2+x_2~2- x_3~2= - 1,x_3≥1}, we can rewrite maps into H~2 as maps from R~2 into R~(2,1) valued in H~2.Then, we can write the equation of harmonic map as follows:φ:R~2→H~2 R~(2,1), 相似文献
9.
Murray R. Bremner 《Linear and Multilinear Algebra》2013,61(8):921-932
We use the representation theory of Lie algebras and computational linear algebra to determine the simplest non-constant invariant polynomial in the entries of a general 2?×?2?×?3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients ±1, ±2 in the 12 indeterminates x ijk where i, j?=?1,?2 and k?=?1,?2,?3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2?×?2?×?2 arrays. 相似文献
10.
Xu Kong 《Linear and Multilinear Algebra》2013,61(10):1348-1362
Using rank-1 reduction formula and the vector space spanned by the real rank-1 matrices, we present a different way to show that the maximum possible rank of the 2?×?2?×?2 tensors over the real field is 3. Following, we obtain that the maximum rank of the 2?×?2?×?2?×?2 tensors over the real field is less than or equal to 5 and propose another way to show that the maximum rank of the 2?×?2?×?2?×?2 tensors over the complex field is 4, except one special case. 相似文献
11.
Viviane Ribeiro Tomaz da Silva 《代数通讯》2013,41(9):3342-3359
Let E be the infinite-dimensional Grassmann algebra over a field F of characteristic zero, and consider L the F-vector space spanned by all generators of E. Let ? l be any fixed automorphism of E of order 2 such that L is an homogeneous subspace. Our goal is to finish the computation of the sequences of ? l -codimensions, by finding its exact value for the unique open case, that is, when the subspace of L corresponding to the eigenvalue 1 is finite-dimensional. As a consequence we get the ?-codimensions for a large amount of arbitrary automorphisms ? of E of order 2. 相似文献
12.
13.
The impetus for this study is the work of Dumas and Rigal on the Jordanian deformation of the ring of coordinate functions on 2×2 matrices. We are also motivated by current interest in birational equivalence of noncommutative rings. Recognizing the construction of the Jordanian matrix algebra as a skew polynomial ring, we construct a family of algebras relative to differential operator rings over a polynomial ring in one variable which are birationally equivalent to the Weyl algebra over a polynomial ring in two variables. 相似文献
14.
WEI DaSheng 《中国科学 数学(英文版)》2013,56(2):227-238
We propose a method to determine the solvability of the diophantine equation x2-Dy2=n for the following two cases:(1) D = pq,where p,q ≡ 1 mod 4 are distinct primes with(q/p)=1 and(p/q)4(q/p)4=-1.(2) D=2p1p2 ··· pm,where pi ≡ 1 mod 8,1≤i≤m are distinct primes and D=r2+s2 with r,s ≡±3 mod 8. 相似文献
15.
D. P. Novikov 《Theoretical and Mathematical Physics》2009,161(2):1485-1496
We show that the Belavin-Polyakov-Zamolodchikov equation of the minimal model of conformal field theory with the central charge
c = 1 for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with 2×2 tmatrices. This generalizes Suleimanov’s result on the Painlevé equations. We consider the properties of the solutions, which
are expressible in terms of the Riemann theta function. 相似文献
16.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1969-1975
The lower bound
l1 (A) - ln (A) \geqslant 2||A12 ||\lambda _1 (A) - \lambda _n (A) \geqslant 2\parallel A_{12} \parallel 相似文献
17.
18.
Various generalizations of the inequality mentioned in the title are given. The estimates obtained are of pointwise as well as of integral character. In addition to non-negative functions, also those without simple zeros are considered. 相似文献
19.
YuanYI WenPengZHANG 《数学学报(英文版)》2004,20(1):75-180
The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums,and give a sharper asymptotic formula. 相似文献
20.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,129(2):3772-3786
Let an n × n Hermitian matrix A be presented in block 2 × 2 form as
, where A12 ≠ 0, and assume that the diagonal blocks A11 and A22 are positive definite. Under these assumptions, it is proved that the extreme eigenvalues of A satisfy the bounds
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