共查询到20条相似文献,搜索用时 46 毫秒
1.
A. V. Kotikov L. N. Lipatov A. I. Onishchenko V. N. Velizhanin 《Theoretical and Mathematical Physics》2007,150(2):213-224
We present results for the universal anomalous dimension γun(j) of Wilson twist-2 operators in the
supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting
the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis
of the integrability of the
supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 249–262, February, 2007. 相似文献
2.
Generalizing earlier results, it is shown that if are “large” subsets of a finite field F
q
, then the equations a + b = cd, resp. ab + 1 = cd can be solved with . Other algebraic equations with solutions restricted to “large” subsets of F
q
are also studied. The proofs are based on character sum estimates proved in Part I of the paper.
Research partially supported by the Hungarian National Foundation for Scientific Research, Grants No. T 043623, T 043631 and
T 049693. 相似文献
3.
We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators
at a large spin s in the supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels
analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions
ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the
Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT
correspondence.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 117–129, April, 2008. 相似文献
4.
Y. Nishimura 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):212-224
For a simple complete multipolytope
in ℝn, Hattori and Masuda defined a locally constant function
on ℝn minus the union of hyperplanes associated with
, which agrees with the density function of an equivariant complex line bundle over a Duistermaat-Heckman measure when
arises from a moment map of a torus manifold. We improve the definition of
and construct a convex chain
on ℝn. The well-definiteness of this convex chain is equivalent to the semicompleteness of the multipolytope
. Generalizations of the Pukhlikov-Khovanskii formula and an Ehrhart polynomial for a simple lattice multipolytope are given
as corollaries. The constructed correspondence ⨑ub;simple semicomplete multipolytopes⫂ub; →; ⨑ub;convex chains⫂ub; is surjective
but not injective. We will study its “kernel.” 相似文献
5.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献
6.
Djemaïa Bensikaddour Sadek Gala Amina Lahmar-Benbernou 《Periodica Mathematica Hungarica》2008,57(1):1-22
The most important result stated in this paper is to show that the solutions of the Poisson equation −Δu = f, where f ∈ (Ḣ1(ℝ
d
) → (Ḣ−1(ℝ
d
)) is a complex-valued distribution on ℝ
d
, satisfy the regularity property D
k
u ∈ (Ḣ1 → Ḣ−1) for all k, |k| = 2. The regularity of this equation is well studied by Maz’ya and Verbitsky [12] in the case where f belongs to the class of positive Borel measures.
相似文献
7.
Changguo Wei 《Proceedings Mathematical Sciences》2008,118(4):517-524
Some results on A
-algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A
-algebras are A
-algebras or A
-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A
-algebra being an A
-algebra. 相似文献
8.
P. C. Allaart 《Acta Mathematica Hungarica》2008,121(3):243-275
This paper concerns the maximum value and the set of maximum points of a random version of Takagi’s continuous, nowhere differentiable
function. Let F(x):=∑
n=1∞
ε
n
ϕ(2
n−1
x), x ∈ R, where ɛ
1, ɛ
2, ... are independent, identically distributed random variables taking values in {−1, 1}, and ϕ is the “tent map” defined by ϕ(x) = 2 dist (x, Z). Let p:= P (ɛ
1 = 1), M:= max {F(x): x ∈ R}, and := {x ∈ [0, 1): F(x) = M}. An explicit expression for M is given in terms of the sequence {ɛ
n
}, and it is shown that the probability distribution μ of M is purely atomic if p < , and is singular continuous if p ≧ . In the latter case, the Hausdorff dimension and the multifractal spectrum of μ are determined. It is shown further that the set is finite almost surely if p < , and is topologically equivalent to a Cantor set almost surely if p ≧ . The distribution of the cardinality of is determined in the first case, and the almost-sure Hausdorff dimension of is shown to be (2p − 1)/2p in the second case. The distribution of the leftmost point of is also given. Finally, some of the results are extended to the more general functions Σa
n − 1
ɛ
n
ϕ(2
n − 1
x), where 0 < a < 1.
相似文献
9.
It is proved that the Stokes operator in Lq -space on an infinite cylindrical domain of
,
, with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded
-calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight
cylinder with bounded cross-section
is studied in L
q
where
and
is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on
-boundedness of operator families and on square function estimates involving Muckenhoupt weights. 相似文献
10.
Let A: V → V′ be a strongly elliptic operator on a d-dimensional manifold D (polyhedra or boundaries of polyhedra are also allowed). An operator equation Au = f with stochastic data f is considered. The goal of the computation is the mean field and higher moments
of the solution.
We discretize the mean field problem using a FEM with hierarchical basis and N degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment
for k⩾1.
The key tool in both algorithms is a “sparse tensor product” space for the approximation of
with O(N(log N)
k−1) degrees of freedom, instead of N
k
degrees of freedom for the full tensor product FEM space.
A sparse Monte-Carlo FEM with M samples (i.e., deterministic solver) is proved to yield approximations to
with a work of O(M N(log N)
k−1) operations. The solutions are shown to converge with the optimal rates with respect to the Finite Element degrees of freedom
N and the number M of samples.
The deterministic FEM is based on deterministic equations for
in D
k
⊂ ℝkd. Their Galerkin approximation using sparse tensor products of the FE spaces in D allows approximation of
with O(N(log N)
k−1) degrees of freedom converging at an optimal rate (up to logs).
For nonlocal operators wavelet compression of the operators is used. The linear systems are solved iteratively with multilevel
preconditioning. This yields an approximation for
with at most O(N (log N)
k+1) operations.
This work was supported under IHP Network “Breaking Complexity” by the Swiss BBW under grant No. 02.0418 相似文献
11.
In the article [2] Ennio De Giorgi conjectured that any compact n-dimensional regular submanifold M of ℝ
n+m
,moving by the gradient of the functional
where ηM is the square of the distance function from the submanifold M and Hn is the n-dimensional Hausdorff measure in ℝ n+m, does not develop singularities in finite time provided k is large enough, depending on the dimension n.
We prove this conjecture by means of the analysis of the geometric properties of the high derivatives of the distance function
from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its
covariant derivatives of independent interest. 相似文献
12.
13.
A. P. Kombarov 《Journal of Mathematical Sciences》2005,131(4):5738-5764
Topological properties similar to normality are considered in subspaces of products and powers of topological spaces, of spaces
of closed subsets, and of spaces having the form
(X), where
is a normal functor.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 2, pp. 57–98, 2003. 相似文献
14.
Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids 总被引:1,自引:0,他引:1
The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety
of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain
the structure theorems of various generalized orthogroups.
Partially supported by a UGC (HK) grant #2060123 (04-05). 相似文献
15.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
16.
Manuel Falconi Ernesto A. Lacomba Jaume Llibre 《Rendiconti del Circolo Matematico di Palermo》2004,53(2):153-164
We consider the topological classification of cubic surfaces which are obtained as intersection of the sphere
with the algebraic variety defined by the zeroes of a homogeneous cubic polynomial in Arnold’s normal form. This classification
is based on the parameters appearing in this normal form, obtaining a correspondence between the parameters of the surface
and its topological type. General classifications of cubic surfaces are made in the projective space ℙ3(ℝ), but our method, based on a very simple combinatorial procedure is easier to implement in
. We split the cubic surfaces parameter space into ten equivalence classes. 相似文献
17.
We construct the category of quotients of
-spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990. 相似文献
18.
Ivan Ginchev Angelo Guerraggio Matteo Rocca 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):137-156
In this paper the constrained vector optimization problem mic
C
f(x), g(x) ∃ − K, is considered, where and are locally Lipschitz functions and and are closed convex cones. Several solution concepts are recalled, among them the concept of a properly efficient point (p-minimizer) and an isolated minimizer (i-minimizer). On the base of certain first-order optimalitty conditions it is shown that there is a close relation between
the solutions of the constrained problem and some unconstrained problem. This consideration allows to “double” the solution
concepts of the given constrained problem, calling sense II optimality concepts for the constrained problem the respective
solutions of the related unconstrained problem, retaining the name of sense I concepts for the originally defined optimality
solutions. The paper investigates the stability properties of thep-minimizers andi-minimizers. It is shown, that thep-minimizers are stable under perturbations of the cones, while thei-minimizers are stable under perturbations both of the cones and the functions in the data set. Further, it is shown, that
sense I concepts are stable under perturbations of the objective data, while sense II concepts are stable under perturbations
both of the objective and the constraints. Finally, the so called structural stability is discused. 相似文献
19.
Given two vectors x, y in a Hilbert space and a weakly closed -module , we provide a necessary and sufficient condition for the existence of a compact operator T in satisfying Tx = y. 相似文献
20.
V. V. Makeev 《Journal of Mathematical Sciences》2005,131(1):5395-5400
Let ABCDE be a pentagon inscribed in a circle. It is proved that if
is a C4-generic smooth convex planar oval with four vertices (stationary points of curvature), then there are two similarities φ
such that the quadrangle φ(ABCD) is inscribed in
and the point φ(E)lies inside
, as well as two similarities ψ such that the quadrangle ψ(ABCD) is inscribed in
and ψ(E)lies outside
. Itisalsoprovedthatif n is odd, then any smoothly embedded circle γ ↪ ℝn contains the vertices of an equilateral (n + 1)-link polygonal line lying in a hyperplane of ℝn. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 241–251. 相似文献