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1.
In this paper the invariance criterion is applied for the nonlinear equation
where g(u) is a smooth function on u. Some particular set of Lie generators are given. In the case of inviscid Burger’s equation [1]
the Lie projectable symmetry algebra is determined, and the inviscid Burger’s equation will be connected to some order differential
equations. The obtained differential equations are solved and some exact solutions of (2) are found.
E.H. El Kinani, Junior Associate at The Abdus Salam ICTP, Trieste, Italy. 相似文献
(0.1) |
(0.2) |
2.
3.
We consider solutions of functional-differential equations
in both real and complex variables. We characterize entire solutions g when f is a meromorphic function in the complex plane and a ≠ 0, b, c are constants or polynomials. We also examine questions of existence and uniqueness of the solutions in the real variable
for initial value problems and provide theorems that are valid “in the large”. 相似文献
4.
5.
Let K be a field of characteristic 0 and let p, q, G 0 , G 1 , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G n (x)) n=0 ∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G n (x) = G m (P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set
相似文献
6.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
7.
本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果. 相似文献
8.
Ayelet Lindenstrauss 《K-Theory》1996,10(3):239-265
Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x
n) and [x]/(x
n–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra. 相似文献
9.
We consider the projective line over the finite quotient ring R⋄ ≡ GF(2)[x]/〈x
3 − x〉. The line is endowed with 18 points, spanning the neighborhoods of three pairwise distant points. Because R⋄ is not a local ring, the neighbor (or parallel) relation is not an equivalence relation, and the sets of neighbors for two
distant points hence overlap. There are nine neighbors of any point on the line, forming three disjoint families under the
reduction modulo either of the two maximal ideals of the ring. Two of the families contain four points each, and they swap
their roles when switching from one ideal to the other, the points in one family merging with (the image of) the point in
question and the points in the other family passing in pairs into the remaining two points of the associated ordinary projective
line of order two. The single point in the remaining family passes to the reference point under both maps, and its existence
stems from a nontrivial character of the Jacobson radical
of the ring. The quotient ring
is isomorphic to GF(2) ⊗ GF(2). The projective line over
features nine points, each of them surrounded by four neighbors and four distant points, and any two distant points share
two neighbors. We surmise that these remarkable ring geometries are relevant for modeling entangled qubit states, which we
will discuss in detail in Part II of this paper.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 44–53, April, 2007. 相似文献
10.
The equation
(t) − c(t)x(t − τ) is considered in the critical case. For it, the asymptotic behavior of dominant and subdominant solutions is studied. A generalization is made and connections with known results are discussed. 相似文献
11.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
12.
M. H. M. Rashid 《Ukrainian Mathematical Journal》2012,63(8):1256-1267
If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum
of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations
by finite-rank operators. 相似文献
13.
Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials
in some classes of functions and for the Kolmogorov N-widths of these classes. These results find applications in numerical analysis.
Original Russian Text ? V.A. Abilov, M.K. Kerimov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi
Fiziki, 2009, Vol. 49, No. 8, pp. 1364–1368. 相似文献
14.
Here we solve two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for
solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal.
68 (2008) 3504–3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of
the form x
Δ = f (t,x,x
σ
) on time scales by using the Banach’s fixed-point theorem. Some examples are presented to illustrate the efficiency of the
proposed results. 相似文献
15.
Sergey K. Bagdasarov 《Journal of Approximation Theory》1997,90(3):340-378
The main result of this paper characterizes generalizationsof Zolotarev polynomials as extremal functions in the Kolmogorov–Landauproblemwhereω(t) is a concave modulus of continuity,r, m: 1?m?r,are integers, andB?B0(r, m, ω). We show that theextremal functionsZBhaver+1 points of alternance andthe full modulus of continuity ofZ(r)B: ω(Z(r)B; t)=ω(t) for allt∈[0, 1]. This generalizesthe Karlin's result on the extremality of classical Zolotarevpolynomials in the problem () forω(t)=tand allB?Br. 相似文献
16.
CertainSolutionsofEquationf(z,0,…,0,u_k,0,…,0)=0LiuGuangmin(刘光民)(KaifengTeacher'sCollege)LiuGuangmin(KaifengTeacher'sCollege)?.. 相似文献
17.
18.
19.
Alexander A. Davydov Stefano Marcugini Fernanda Pambianco 《Designs, Codes and Cryptography》2009,50(3):359-372
An infinite family of complete (q
2 + q + 8)/2-caps is constructed in PG(3, q) where q is an odd prime ≡ 2 (mod 3), q ≥ 11. This yields a new lower bound on the second largest size of complete caps. A variant of our construction also produces
one of the two previously known complete 20-caps in PG(3, 5). The associated code weight distribution and other combinatorial properties of the new (q
2 + q + 8)/2-caps and the 20-cap in PG(3, 5) are investigated. The updated table of the known sizes of the complete caps in PG(3, q) is given. As a byproduct, we have found that the unique complete 14-arc in PG(2, 17) contains 10 points on a conic. Actually, this shows that an earlier general result dating back to the Seventies fails
for q = 17.
相似文献
20.
We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best
uniform polynomial approximation of |x|
p
on two symmetric intervals. Note that, in addition, we get asymptotics for the polynomials themselves under a certain renormalization.
Also, we solve a problem on asymptotics of the best approximation of sgn(x) on [−1,−a]∪[a,1] by Laurent polynomials.
相似文献