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1.
Let {c
n
(St
k
)} and {c
n
(C
k
)} be the sequences of codimensions of the T-ideals generated by the standard polynomial of degreek and by thek-th Capelli polynomial, respectively. We study the asymptotic behaviour of these two sequences over a fieldF of characteristic zero. For the standard polynomial, among other results, we show that the following asymptotic equalities
hold:
whereM
k
(F) is the algebra ofk×k matrices andM
k×l
(F) is the algebra of (K+l)×(k+l) matrices having the lastl rows and the lastk columns equal to zero. The precise asymptotics ofc
n
(M
k
(F)) are known and those ofM
k×2k
(F) andM
2k×k
(F) can be easily deduced. For Capelli polynomials we show that also upper block triangular matrix algebras come into play.
The first author was partially supported by MURST of Italy.
The second author was partially supported by RFBR grants 99-01-00233 and 00-15-96128. 相似文献
2.
Ilijas Farah 《Israel Journal of Mathematics》2006,154(1):235-246
We prove two results about the quotient over the asymptotic density zero ideal. First, it is forcing equivalent to
% MathType!End!2!1!, where
% MathType!End!2!1! is the homogeneous probability measure algebra of characterc. Second, if it has analytic Hausdorff gaps, then they look considerably different from proviously known gaps of this form.
Partially supported by NSERC. 相似文献
3.
Nguyen Canh Luong 《Advances in Applied Clifford Algebras》2001,11(2):171-180
The factorization of the Laplacian by means of first order systems and of second order operators was considered by several
authors (see, e.g [2],[3],[4]).
In the paper the definition of Cauchy-Riemann system (CR-system) of ordern is given by their symbols.
We prove that ifD
(n) is the symbol andD
(s, n) is the sign-matrix of CR-system, then
and
where Δ denotes teh Laplacian operator inR
n. We show that(CN)
n ≠ ϕ if and only ifn ∈ {2, 4, 8}.
This work was supported in part by N.B.R.P in N.S. Vietnam 相似文献
4.
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. 相似文献
5.
We prove the existence of a positive and smooth solution for the following semilinear elliptic problem:
% MathType!End!2!1! for anya∈R
N
, 1<p<1+2/N andq=(p+1)/2. This solution decays exponentially as |x|→+∞. Moreover, if |a| is sufficiently small, this positive and rapidly decaying solution is unique.
The existence of a positive, self-similar solution
% MathType!End!2!1! follows for the following convection-diffusion equation with absorption:
% MathType!End!2!1!. It is also a very singular solution. This solution decays as |x|→+∞ for anyt>0 fixed.
Because of the nonvariational nature of the elliptic problem, a fixed point method is used for proving the existence result.
The uniqueness is proved applying the Implicit Function Theorem.
The work of the first author has been partially supported by Grant 1273/00003/88 of the University of the Basque Country.
The work of the second author has been supported by Grant PB 86-0112-C02-00 of the Dirección General de Investigación Científica
y Técnica. 相似文献
6.
7.
K. F. Cheng 《Periodica Mathematica Hungarica》1983,14(2):177-187
The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model $$Y = R(X) + Z$$ , where the random variableZ has mean zero and is independent ofX. The regression functionR(x) is the conditional expectation ofY givenX = x. For an estimator of the form $$R_n (x) = \sum\limits_{i = 1}^n {Y_i K{{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} \mathord{\left/ {\vphantom {{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} $$ , we obtain the rate of strong uniform convergence $$\mathop {\sup }\limits_{x\varepsilon C} \left| {R_n (x) - R(x)} \right|\mathop {w \cdot p \cdot 1}\limits_ = o({{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } \mathord{\left/ {\vphantom {{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } {\beta _n \log n}}} \right. \kern-\nulldelimiterspace} {\beta _n \log n}}),\beta _n \to \infty $$ . HereX is ad-dimensional variable andC is a suitable subset ofR d . 相似文献
8.
Summary Let
be a sequence of independent identically distributed random variables withθ
1∼G and the conditional distribution ofx
1 givenθ
1=θ given by
. HereG is unknown andF
θ(·) is known. This paper provides estimators
ofG based onx
1, …,x
n such that the random variable sup
has an asymptotic distribution asn→∞ under certain on conditionsG and for certain choices ofF
θ. A simulation model has been discussed involving the uniform distribution on (0, θ) forF
θ and an exponential distribution forG.
Research supported by the National Science Foundation under Grant #MCS77-26809. 相似文献
9.
Volker Turau 《Israel Journal of Mathematics》1988,62(2):206-212
For a finite groupG and some prime powerp
n
, the
-subgroup
is defined by
. Meixner proved that ifG is a finite solvable group and
for somen≧1, then the Fitting length of
is bounded by 4n. In the following note it is shown that the 2-length of
is at mostn. This result cannot be derived from Meixner’s paper, since his result implies only that the 2-length is bounded by 2n. 相似文献
10.
Global Existence of Positive
Periodic Solutions for a Distributed Delay Competition Model 总被引:3,自引:0,他引:3
Xian-yi Li De-ming ZhuDepartment of Mathematics East China Normal University Shanghai China Department of Mathematics Physics Nanhua University Hengyang China 《应用数学学报(英文版)》2003,19(3):491-498
By using the continuation theorem of Mawhin's coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition modelwhere ri and r2 are continuous w-periodic functions in R+=[0,∞) with ,ai,ci(i =1,2) are positive continuous w-periodic functions in R+=[0,∞),bi (i = 1,2) is nonnegative continuous w-periodic function in R+=[0,∞), w and T are positive constants. Ki,Lt ∈ C([-T,0], (01 88)) and Ki(s)ds = 1,ds - 1. i = 1,2. Some known results are improved and extended. 相似文献
11.
Zhi-Wei Sun 《Israel Journal of Mathematics》2002,128(1):135-156
In this paper we study [
r
n
]
m
=Σ
k≡r(modm) (
k
n
) wherem>0,n≥0 andr are integers. We show that [
r
n
]
m
(m>2) can be expressed in terms of some linearly recurrent sequences with orders not exceeding ϕ(m)/2. In particular, we determine [
r
n
]
12
explicitly in terms of first order and second order recurrences. It follows that for any primep>3 we have
and
.
The research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions
of MOE, and the National Natural Science Foundation of P. R. China. 相似文献
12.
Amitai Regev 《Israel Journal of Mathematics》1999,113(1):15-28
The numbers
% MathType!End!2!1!, λ ⊢n appear in the enumeration of various objects, as well as coefficients inS
nrepresentations associated with products of higher commutators. We study their asymptotics asn→∞ and show that if (λ1, λ2, …)≈(α
1,α
2, …)n, if (λ′1, λ′2, …)≈(β
1,β
2, …)n and ifγ=1− Σ
k⩽1(α
k⩽1+β
k⩽1), then
% MathType!End!2!1!.
Work partially supported by N.S.F. Grant No. DMS 94-01197. 相似文献
13.
Peter Allen 《Israel Journal of Mathematics》2007,161(1):311-346
Bollobás, Brightwell and Leader [2] showed that there are at most
2-SAT functions on n variables, and conjectured that in fact the number of 2-SAT functions on n variables is
. We prove their conjecture.
As a corollary of this, we also find the expected number of satisfying assignments of a random 2-SAT function on n variables. We also find the next largest class of 2-SAT functions and show that if k = k(n) is any function with k(n) < n
1/4 for all sufficiently large n, then the class of 2-SAT functions on n variables which cannot be made unate by removing 25k variables is smaller than
for all sufficiently large n. 相似文献
14.
ShuJunDANG LiZhongPENG 《数学学报(英文版)》2004,20(2):255-260
This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators Tn:L^2(R)→L^2(C,e^-|z|^2/2dzd-↑z/4πi), s.t. TnL^2(R) lontain in L^2(C,e^-|z|^2/2dzd-↑z/4πi) are reproducing subspaces (n=0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of TnL^2(R), Furthermore, it shows the orthogonal spaces decomposition of L^2(C,e^-|z|^2/2dzd-↑z/4πi). Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6]. 相似文献
15.
For measuresμ on the circleT the quantities
,
need not be equal; it is shown, however, that they are continuous with respect to each other whenμ varies on bounded subsets ofM(T), the space of measures onT. It is also shown that measuresμ which areɛ-almost idempotent (i.e.
) are the sum of an idempotent measure and of a measureυ satisfying
providedɛ is small enough (as a function of ‖μ‖). 相似文献
16.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
where R
m
(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in
is homogeneous of degree zero, the authors prove that T
A
is bounded from L
p
(ℝ
n
) to
and from L
1(ℝ
n
) to L
n/(n−β),∞(ℝ
n
) with the bound
And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T
A
is also bounded from L
p
(ℝ
n
) to
with the bound
Supported by the National 973 Project (G1990751) and SEDF of China (20010027002) 相似文献
17.
Let u = (u
n
) be a sequence of real numbers whose generator sequence is Cesàro summable to a finite number. We prove that (u
n
) is slowly oscillating if the sequence of Cesàro means of (ω
n
(m−1)(u)) is increasing and the following two conditions are hold:
$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered}$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered} 相似文献
18.
Yan-ling Tian Pei-xuan Weng~ Jin-ji Yang~ Department of Mathematics South China Normal University Guangzhou China Department of Computer Sciences South China Normal University Guangzhou China 《应用数学学报(英文版)》2004,20(1):101-114
A group of necessary and sufficient conditions for the nonoscillation of a second order linear delayequation with impulses(r(t)u')'=-p(t)u(t-τ)are obtained in this paper,where p(t)=sum from ∞to n=1 a_n δ(t-t_n),δ(t) is a Dirac δ-unction,and for each n∈N,a_n>0,t_n→∞as n→∞.Furthermore,the boundedness of the solutions is also investigated if the equationis nonoscillatory.An example is given to illustrate the use of the main theorems. 相似文献
19.
Consider the probability spaceW={−1, 1}
n
with the uniform (=product) measure. Letf: W →R be a function. Letf=Σf
IXI be its unique expression as a multilinear polynomial whereX
I=Π
i∈I
x
i. For 1≤m≤n let
=Σ|I|=m
f
IXI. LetT
ɛ
(f)=Σf
Iɛ|I|
X
I where 0<ɛ<1 is a constant. A hypercontractive inequality, proven by Bonami and independently by Beckner, states that
20.
Let PG2(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained
in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is
|