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1.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):243-252
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of
a group is subdirectly irreducible. For an MV-algebra
we denote by
, A and
the idempotent modification, the underlying set or the underlying lattice of
, respectively. In the present paper we prove that if
is semisimple and
is a chain, then
is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras. 相似文献
2.
The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics,
physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied
this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of
parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor
in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor
for DCGL equation in ℝ2 is detailed studied.
相似文献
3.
V. A. Solonnikov 《Journal of Mathematical Sciences》2006,135(6):3522-3528
This note is a correction of the proof of Theorem 1.2 in the paper “On a linear problem connected with equilibrium figures
of a uniformly rotating viscous liquid” published in J. Math. Sci. 132 (2006), no. 4, 502–521. The correction concerns the auxiliary problem (3.7)
. where λ ∈ C is a spectral parameter, u(x) = (u1, u2, u3), x ∈
, is a complex-valued vector field, and ρ = ρ(x), x ∈
. Bibliography: 4 titles.
__________
Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 77–83. 相似文献
4.
Stefan Neuwirth 《Journal d'Analyse Mathématique》2008,104(1):371-396
Let Γ be a set of three integers and let
be the space of 2π-periodic functions with spectrum in Γ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T ∈
and prove that x is unique unless |T| has an axis of symmetry. This enables us to compute the exposed and the extreme points of the unit ball of
, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers
on
. We obtain in particular the Sidon constant of Γ. 相似文献
5.
We study the weak hereditary class S
w
(
) of all weak subalgebras of algebras in a total variety
}. We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization
of these classes. We also consider the problem of when such a weak hereditary class is weak equational. 相似文献
6.
Wang Chengyong 《分析论及其应用》1994,10(3):17-31
In this paper we investigate the asymptotic behaviour of μ-averagen-widths of integral operatorK on the Wiener space, whereK is the inverse operator of an ordinary linear differential operatorL of orderm. For 1≤p.q<∞
. and forp∈[1, ∞),q∈[2, ∞)
.
Supported by the Fund. of Dooctoral program of NECC. 相似文献
7.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
8.
K. R. Apt 《Israel Journal of Mathematics》1978,29(2-3):221-238
The connections between inductive definability and models of comprehension are studied. Let
= 〈A, R
l, ...,R
n 〉 be an infinite structure and letI
φ
be a set inductively defined by a formulaφ of the second order language
. We prove that if
is a model of Δ
1
1
-Comprehension relativized toφ, andφ is
-absolute, then for everyη smaller than the height of
(h(
)),I
φ
is in
. If
is aβ-structure which satisfies Σ
1
1
-Comprehension relativized toφ and WF(X), and φ is
-absolute, thenI
φ
is in
and ‖φ| <h (
). These results imply that Barwise-Grilliot theorem is false in the case of uncountable acceptable structures. We also study
the notion of invariant definability over models1 of Δ
1
1
-Comprehension.
This paper is registered as Report ZW 69/76 of the Mathematical Centre. 相似文献
9.
Let f be an integrable function on the unit sphere Σ
n−1 of R
n
(n⩾3) and let σ
N
δ
be the Cesàro means of order σ of the Fourier-Laplace series of f. The special value λ:=n−2/2 of σ is known as the critical index. This paper proves that
and
where ω(f,t)p is the 1st-order modulus of continuity of f in Lp-metric which is defined in a way different than in the classical case of n=2.
In Memory of Professor M. T. Cheng
Project supported by the NSF of China under the grans # 19771009. 相似文献
10.
In this note we extend the results in [1] to high dimensions. Let f∈Hp (Tn), 0<p<1, n≥1 andσ
δ
, f denote the Riesz means of f at the critical index δ=n/p−(n+1)/2. We have the following estimate:
were 0<s≤2 and
, is the K-functional in Hp(Tn).
Supported by NSFC 相似文献
11.
I. S. Kats 《Mathematical Notes》2007,81(3-4):302-307
We establish that the problem of constructing a strictly increasing singular function is equivalent to the problem of constructing subsets and of a closed interval [a; b] ? ? such that (1) ∩ = ø; (2) ∪ = [a; b]; (3) the Lebesgue measures of the intersections of and with an arbitrary interval J ? [a; b] are positive. 相似文献
12.
S. Repin 《Journal of Mathematical Sciences》2007,142(1):1821-1827
The note is concerned with functional type a posteriori estimates of the difference between exact and approximate solutions
of the Maxwell problem
. The estimates are derived by transformations of the basic integral identity defining a generalized solution to the problem
by using the method suggested by the author. The estimates are obtained in the case ℵ > 0 and ℵ = 0. Bibliography: 10 titles.
__________
Translated from Problemy Matematicheskogo Analiza, No. 34, 2006, pp. 83–88. 相似文献
13.
A monotone structure (
;μ) consists of a structure
and a monotone systemμ over the domain of
.L(Q
n
) is
, enlarged by a newn-ary quantifierQ
n
.
says in (
;μ) that there isU ∈μ such thatϕ[ā] is valid in (
;μ) for allā ∈U
n
. If
is a class of monotone structures,
means thatϕ is valid in all expansions of monotone structures in
. We show for the class
of all ultrafilters that interpolation with respect to
holds forL(Q
n
) exactly in casen=1. Then we prove for a large class of
(e.g. the class of topological groups) thatL(Q
n
) satisfies interpolation with respect to
for alln ≧ 1. Counterexamples indicate that the class of
is sharp in some sense. Finally the results are carried over to certain topological structures and the interior quantifiersI
n
instead ofQ
n
, thereby generalizing results of Makowsky/Ziegler and Sgro, and to a multidimensional type of monotone structures including
uniform spaces. 相似文献
14.
Lin Qingquan 《高校应用数学学报(英文版)》2000,15(3):289-296
In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift
coefficient in the different method from the one with Lipschitz condition. Then by considering (ξ, g) as a parameter of BSDE, and (ξ
α, g
α) as a class of parameters for BSDE, where α belongs to a set
, for every
there exists a pair of solution {Y
a, Za} for the BSDE, the properties of
which is also a solution for some BSDE is studied. This result may be used to discuss optimal problems with recursive utility.
This work was supported by NSFC (79790130) 相似文献
15.
We show, for any operatorT from aC(K)-space into a Banach space with rank (T)≤n, the inequality
, whereC≤4.671 is a numerical constant. The factor (1+logn)1−1/p
is asymptotically correct. This inequality extends a result of Jameson top ≠ 2. Several applications are given — one is a positive solution of a conjecture of Rosenthal and Szarek: For 1≤p<q<2,
相似文献
16.
Edward W. Barankin Koiti Takahasi 《Annals of the Institute of Statistical Mathematics》1984,36(1):499-520
Summary This paper introduces terminology enabling the discussion of centerrelated betweennesses defined with respect to centers other
than the origin. Thus, it is then proved that the familiar
-betweenness in
which is origin-centered, is equivalent to a non-origin-centered
-betweenness in one lower dimension. A new betweenness inK, denoted by
, (r>0), is defined and studied, and it is shown that its restriction to
is precisely
-betweenness for a certain ν. Finally, by a method elaborated in the earlier papers, a new betweeness,
, is induced on the upper open-hemisphere-plus-a-point in 3-space, and a characterization of it is obtained which is expected
to facilitate later investigations of betweenness is complex spaces. 相似文献
17.
We prove a Schwarz lemma for a domain
in ℂ3 that arises in connection with a problem in H∞ control theory. We describe a class of automorphisms of
and determine the distinguished boundary of
We apply our Schwarz lemma to a special case of the μ-synthesis problem. 相似文献
18.
V. V. Napalkov Jr. 《Mathematical Notes》1996,60(1):42-48
We study the growth of an entire functionƒ, whose Borel transformγƒ is holomorphic outside a bounded convex regionD
ƒ with boundary curvature bounded away from 0 and ∞. The functionγƒ is assumed to belong to the Dirichlet space, i.e., it satisfies
, wheredv(ξ) is the area element. It is shown that forγƒ to satisfy the above conditions, it is necessary and sufficient to have
and the growth indicatrixh
ƒ ofƒ satisfies the relation 0<m≤h″(ϕ)+h(ϕ)≤M<∞.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 58–65, July, 1996. 相似文献
19.
Z. A. Arushanyan 《Journal of Mathematical Sciences》1981,16(3):1161-1167
One finds conditions which ensure the possibility of weighted mean-square approximation of a vector-function defined on the
boundary of an n-dimensional domain
by vector-functions of the form
, where u is, the solution of the equation Δm
u=0 in
while∂/∂v denotes differentiation along the normal. The weight function is continuous and positive everywhere on
with the point
whose relative neighborhood
is contained in some (n-1)-dimensional plane. The solution of this approximation problem is closely related with a certain
uniqueness theorem for the solution of the Cauchy problem for the polyharmonic equation, also proved in the paper.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR,
Vol. 65, pp. 164–171, 1976. 相似文献
20.
Given a self-concordant barrier function for a convex set
, we determine a self-concordant barrier function for the conic hull
of
. As our main result, we derive an “optimal” barrier for
based on the barrier function for
. Important applications of this result include the conic reformulation of a convex problem, and the solution of fractional
programs by interior-point methods. The problem of minimizing a convex-concave fraction over some convex set can be solved
by applying an interior-point method directly to the original nonconvex problem, or by applying an interior-point method to
an equivalent convex reformulation of the original problem. Our main result allows to analyze the second approach showing
that the rate of convergence is of the same order in both cases. 相似文献