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1.
For an embedding i : X ? M of smooth manifolds and a Fourier integral operator Φ on M defined as the quantization of a canonical transformation g: T*M \ {0} → T*M \ {0}, we consider the operator ii* on the submanifold X, where i* and i* are the boundary and coboundary operators corresponding to the embedding i. We present conditions on the transformation g under which such an operator has the form of a Fourier integral operator associated with the fiber of the cotangent bundle over a point. We obtain an explicit formula for calculating the amplitude of this operator in local coordinates.  相似文献   

2.
It is known that critical fluctuations can change the effective anisotropy of a cubic ferromagnet near the Curie point. If the crystal undergoes a phase transition into the orthorhombic phase and the initial anisotropy is not too strong, then the effective anisotropy acquires the universal value A* = v*/u* at T c, where u* and v* are the coordinates of the cubic fixed point of the renormalization group equations in the scaling equation of state and expressions for nonlinear susceptibilities. Using the pseudo-?-expansion method, we find the numerical value of the anisotropy parameter A at the critical point. Padé resummation of the six-loop pseudo-?-expansions for u*, v*, and A* leads to the estimate A* = 0.13 ± 0.01, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.  相似文献   

3.
We obtain bivariate forms of Gumbel’s, Fréchet’s and Chung’s linear inequalities for P(Su, Tv) in terms of the bivariate binomial moments {S i, j }, 1 ≤ ik,1 ≤ jl of the joint distribution of (S, T). At u = v = 1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k, l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.  相似文献   

4.
Given a sequence A = (a 1, …, a n ) of real numbers, a block B of A is either a set B = {a i , a i+1, …, a j } where ij or the empty set. The size b of a block B is the sum of its elements. We show that when each a i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B 1, …, B k with |b i ?b j | ≤ 1 for every i, j. We extend this result in several directions.  相似文献   

5.
Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call AC-injective complexes, showing that K(AC-Inj), the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DGinjective complexes are AC-injective and in fact there is a recollement linking K(AC-Inj) to the usual derived category D(R). This is based on the author’s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.  相似文献   

6.
Let N0 be the set of natural numbers whose binary expansions have an even number of 1’s, and let N1 = N\N0. In this paper, we obtain asymptotic formulas for the number of primes p not exceeding X and such that p ∈ Ni, p + 1 ∈ Nj, where i and j take values 0 and 1 independently of each other.  相似文献   

7.
Let (F′, F, F″) be a comparison of left recollements of triangulated categories such that F′ and F″ are equivalences. We prove that if F is full then F is an equivalence; and on the other hand, we construct a class of examples via the derived categories of Morita rings, showing that there really exists such a comparison (F′, F, F″) so that F is not an equivalence. This is in contrast to the case of a recollement. We also give a class of examples of left recollements of homotopy categories, which can not sit in recollements.  相似文献   

8.
Clifford Smyth 《Order》2018,35(2):393-402
We present a probabilistic characterization of the dominance order on partitions. Let ν be a partition and Y ν its Ferrers diagram, i.e. a stack of rows of cells with row i containing ν i cells. Let the cells of Y ν be filled with independent and identically distributed draws from the random variable X = B i n(r, p) with r ≥ 1 and p ∈ (0, 1). Given j, t ≥ 0, let P(ν, j, t) be the probability that the sum of all the entries in Y ν is j while the sum of the entries in each row of Y ν is no more than t. It is shown that if ν and μ are two partitions of n, ν dominates μ if and only if P(ν, j, t) ≤ P(μ, j, t) for all j, t ≥ 0. It is shown that the same result holds if X is any log-concave integer valued random variable with {i : P(X = i) > 0} = {0, 1,…,r} for some r ≥ 1.  相似文献   

9.
For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Finite-dimensional (not necessarily associative) k-algebras of general type of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent (over k) rational functions of the structure constants. (2) There exists an “algebraic normal form” to which the set of structure constants of every such algebra can be uniquely transformed by means of passing to its new basis—namely, there are two finite systems of nonconstant polynomials on the space of structure constants, {fi}i∈I and {bj}j∈J, such that the ideal generated by the set {fi}i∈I is prime and, for every tuple c of structure constants satisfying the property bj(c) ≠ 0 for all jJ, there exists a unique new basis of this algebra in which the tuple c′ of its structure constants satisfies the property fi(c′) = 0 for all iI.  相似文献   

10.
A (v, β o , μ)-design over regular graph G = (V, E) of degree d is an ordered pair D = (V, B), where |V| = v and B is the set of maximum independent sets of G called blocks such that if i, jV, ij and if i and j are not adjacent in G then there are exactly μ blocks containing i and j. In this paper, we study (v, β o , μ)-designs over the graphs K n × K n , T(n)-triangular graphs, L 2(n)-square lattice graphs, Petersen graph, Shrikhande graph, Clebsch graph and the Schläfli graph and non-existence of (v, β o , μ)-designs over the three Chang graphs T 1(8), T 2(8) and T 3(8).  相似文献   

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