共查询到20条相似文献,搜索用时 31 毫秒
1.
S. Yu. Antonov 《Russian Mathematics (Iz VUZ)》2012,56(5):9-22
We estimate the least degree of identities of subspaces M
1(m,k) (F) of the matrix superalgebra M
(m,k)(F) over the field F for arbitrary m and k. For subspaces M
1(m,1) (F) (m≥1) and M
1(2,2) (F) we obtain concrete minimal identities. 相似文献
2.
For any atomless positive measure μ, the space L 1(μ) has the polynomial Daugavet property, i.e., every weakly compact continuous polynomial ${P:L_1(\mu)\longrightarrow L_1(\mu)}For any atomless positive measure μ, the space L
1(μ) has the polynomial Daugavet property, i.e., every weakly compact continuous polynomial P:L1(m)? L1(m){P:L_1(\mu)\longrightarrow L_1(\mu)} satisfies the Daugavet equation ||Id + P||=1 + ||P||{\|{\rm Id} + P\|=1 + \|P\|}. The same is true for the vector-valued spaces L
1(μ, E), μ atomless, E arbitrary. 相似文献
3.
Let f(x)=(x-a1)?(x-am){f(x)=(x-a_1)\cdots (x-a_m)}, where a
1, . . . , a
m
are distinct rational integers. In 1908 Schur raised the question whether f(x) ± 1 is irreducible over the rationals. One year later he asked whether (f(x))2k+1{(f(x))^{2^k}+1} is irreducible for every k ≥ 1. In 1919 Pólya proved that if
P(x) ? \mathbbZ[x]{P(x)\in\mathbb{Z}[x]} is of degree m and there are m rational integer values a for which 0 < |P(a)| < 2−N
N! where N=ém/2ù{N=\lceil m/2\rceil}, then P(x) is irreducible. A great number of authors have published results of Schur-type or Pólya-type afterwards. Our paper contains
various extensions, generalizations and improvements of results from the literature. To indicate some of them, in Theorem
3.1 a Pólya-type result is established when the ground ring is the ring of integers of an arbitrary imaginary quadratic number
field. In Theorem 4.1 we describe the form of the factors of polynomials of the shape h(x) f(x) + c, where h(x) is a polynomial and c is a constant such that |c| is small with respect to the degree of h(x) f(x). We obtain irreducibility results for polynomials of the form g(f(x)) where g(x) is a monic irreducible polynomial of degree ≤ 3 or of CM-type. Besides elementary arguments we apply methods and results
from algebraic number theory, interpolation theory and diophantine approximation. 相似文献
4.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献
5.
In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some
congruences concerning Fibonacci and Lucas numbers such as L
2mn+k
≡ (−1)(m+1)n
L
k
(mod L
m
), F
2mn+k
≡ (−1)(m+1)n
F
k
(mod L
m
), L
2mn+k
≡ (−1)
mn
L
k
(mod F
m
) and F
2mn+k
≡ (−1)
mn
F
k
(mod F
m
). By the achieved identities, divisibility properties of Fibonacci and Lucas numbers are given. Then it is proved that there
is no Lucas number L
n
such that L
n
= L
2
k
t
L
m
x
2 for m > 1 and k ≥ 1. Moreover it is proved that L
n
= L
m
L
r
is impossible if m and r are positive integers greater than 1. Also, a conjecture concerning with the subject is given. 相似文献
6.
Anders Bj?rner 《Combinatorica》2011,31(2):151-164
Let L be a finite distributive lattice and μ: L → ℝ+ a log-supermodular function. For functions k: L → ℝ+ let
Em (k;q)def ?x ? L k(x)m(x)qrank(x) ? \mathbbR+ [q] .E_\mu (k;q)^{\underline{\underline {def}} } \sum\limits_{x \in L} {k(x)\mu (x)q^{rank(x)} \in \mathbb{R}^ + [q]} . 相似文献
7.
Parameterizing above Guaranteed Values: MaxSat and MaxCut 总被引:1,自引:0,他引:1
Meena Mahajan Venkatesh Raman 《Journal of Algorithms in Cognition, Informatics and Logic》1999,31(2):335
In this paper we investigate the parameterized complexity of the problems MaxSat and MaxCut using the framework developed by Downey and Fellows. LetGbe an arbitrary graph havingnvertices andmedges, and letfbe an arbitrary CNF formula withmclauses onnvariables. We improve Cai and Chen'sO(22ckcm) time algorithm for determining if at leastkclauses of ac-CNF formulafcan be satisfied; our algorithm runs inO(|f| + k2φk) time for arbitrary formulae and inO(cm + ckφk) time forc-CNF formulae, where φ is the golden ratio
. We also give an algorithm for finding a cut of size at leastk; our algorithm runs inO(m + n + k4k) time. We then argue that the standard parameterization of these problems is unsuitable, because nontrivial situations arise only for large parameter values (k ≥ m/2), in which range the fixed-parameter tractable algorithms are infeasible. A more meaningful question in the parameterized setting is to ask whether m/2 + kclauses can be satisfied, or m/2 + kedges can be placed in a cut. We show that these problems remain fixed-parameter tractable even under this parameterization. Furthermore, for up to logarithmic values of the parameter, our algorithms for these versions also run in polynomial time. 相似文献
8.
L∞ estimates are derived for the oscillatory integral ∫+0∞e−i(xλ + (1/m) tλm)a(λ) dλ, where 2 ≤ m
and (x, t)
×
+. The amplitude a(λ) can be oscillatory, e.g., a(λ) = eit
(λ) with
(λ) a polynomial of degree ≤ m − 1, or it can be of polynomial type, e.g., a(λ) = (1 + λ)k with 0 ≤ k ≤
(m − 2). The estimates are applied to the study of solutions of certain linear pseudodifferential equations, of the generalized Schrödinger or Airy type, and of associated semilinear equations. 相似文献
9.
Donald St. P. Richards 《Annals of the Institute of Statistical Mathematics》1982,34(1):119-121
Summary LetC
κ(S) be the zonal polynomial of the symmetricm×m matrixS=(sij), corresponding to the partition κ of the non-negative integerk. If ∂/∂S is them×m matrix of differential operators with (i, j)th entry ((1+δij)∂/∂sij)/2, δ being Kronecker's delta, we show that Ck(∂/∂S)Cλ(S)=k!δλkCk(I), where λ is a partition ofk. This is used to obtain new orthogonality relations for the zonal polynomials, and to derive expressions for the coefficients
in the zonal polynomial expansion of homogenous symmetric polynomials. 相似文献
10.
Kirill A. Kopotun 《Journal of Approximation Theory》1998,94(3):481-493
It is shown that an algebraic polynomial of degree k−1 which interpolates ak-monotone functionfatkpoints, sufficiently approximates it, even if the points of interpolation are close to each other. It is well known that this result is not true in general for non-k-monotone functions. As an application, we prove a (positive) result on simultaneous approximation of ak-monotone function and its derivatives inLp, 0<p<1, metric, and also show that the rate of the best algebraic approximation ofk-monotone functions (with bounded (k−2)nd derivatives inLp, 1<p<∞, iso(n−k/p). 相似文献
11.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
Folowing [7], we consider a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ε ∈ ℂ, is said to have a parametric center, if for any ɛ and for any solutiony(ɛ,x) of (**)y(ɛ, 0)≡y(ɛ, 1)..
We give another proof of the fact, shown in [6], that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and generalize a “canonical representation” ofm
k
(x) given in [7]. On this base we prove in some additional cases a composition conjecture, stated in [6, 7] for a parametric
center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
12.
A. S. Sivatski 《Israel Journal of Mathematics》2011,186(1):273-284
Let k be a field, char k ≠ 2, p(t) a monic irreducible polynomial over k, and k
p
= k[t]/pk[t] the corresponding residue field. For a regular quadratic form φ over k we investigate the relationship between two conditions:
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