共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM~k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M~j(s), M~k(t)) for s, t ≤ n, M~j, M~k are g-twisted V modules, if V is g-rational. 相似文献
2.
T. M. Tovstik 《Vestnik St. Petersburg University: Mathematics》2009,42(1):37-45
The paper considers cubature formulas for calculating integrals of functions f(X), X = (x 1, …, x n ) which are defined on the n-dimensional unit hypercube K n = [0, 1] n and have integrable mixed derivatives of the kind \(\partial _{\begin{array}{*{20}c} {\alpha _1 \alpha _n } \\ {x_1 , \ldots , x_n } \\ \end{array} } f(X)\), 0 ≤ α j ≤ 2. We estimate the errors R[f] = \(\smallint _{K^n } \) f(X)dX ? Σ k = 1 N c k f(X(k)) of cubature formulas (c k > 0) as functions of the weights c k of nodes X(k) and properties of integrable functions. The error is estimated in terms of the integrals of the derivatives of f over r-dimensional faces (r≤n) of the hypercube K n : |R(f)| ≤ \(\sum _{\alpha _j } \) G(α j )\(\int_{K^r } {\left| {\partial _{\begin{array}{*{20}c} {\alpha _1 \alpha _n } \\ {x_1 , \ldots , x_n } \\ \end{array} } f(X)} \right|} \) dX r , where coefficients G(α j ) are criteria which depend only on parameters c k and X(k). We present an algorithm to calculate these criteria in the two- and n-dimensional cases. Examples are given. A particular case of the criteria is the discrepancy, and the algorithm proposed is a generalization of those used to compute the discrepancy. The results obtained can be used for optimization of cubature formulas as functions of c k and X(k). 相似文献
3.
José Trashorras 《Journal of Theoretical Probability》2008,21(2):397-412
In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures \(\frac{1}{n}\sum_{i=1}^{n}\delta_{(X^{n}_{i},X^{n}_{\sigma_{n}(i)})}\) where σ n is a random permutation and ((X i n )1≤i≤n ) n≥1 is a triangular array of random variables with suitable properties. As an application we show how this result allows to improve the Large Deviation Principles for symmetrised initial-terminal conditions bridge processes recently established by Adams, Dorlas and König. 相似文献
4.
Let v 1,…,v n be unit vectors in ? n such that v i ?v j =?w for i≠j, where \(-1. The points ∑ i=1 n λ i v i (1≥λ 1≥???≥λ n ≥0) form a “Hill-simplex of the first type,” denoted by \(\mathcal {Q}_{n}(w)\). It was shown by Hadwiger in 1951 that \(\mathcal {Q}_{n}(w)\) is equidissectable with a cube. In 1985, Schöbi gave a three-piece dissection of \(\mathcal {Q}_{3}(w)\) into a triangular prism \(c\mathcal {Q}_{2}(\frac{1}{2})\times I\), where I denotes an interval and \(c=\sqrt{2(w+1)/3}\). In this paper, we generalize Schöbi’s dissection to an n-piece dissection of \(\mathcal {Q}_{n}(w)\) into a prism \(c\mathcal {Q}_{n-1}(\frac{1}{n-1})\times I\), where \(c=\sqrt{(n-1)(w+1)/n}\). Iterating this process leads to a dissection of \(\mathcal {Q}_{n}(w)\) into an n-dimensional rectangular parallelepiped (or “brick”) using at most n! pieces. The complexity of computing the map from \(\mathcal {Q}_{n}(w)\) to the brick is O(n 2). A second generalization of Schöbi’s dissection is given which applies specifically in ?4. The results have applications to source coding and to constant-weight binary codes. 相似文献
5.
D. Ranganatha 《印度理论与应用数学杂志》2017,48(3):449-465
Let b ? (n) denote the number of ?-regular partitions of n. In 2012, using the theory of modular forms, Furcy and Penniston presented several infinite families of congruences modulo 3 for some values of ?. In particular, they showed that for α, n ≥ 0, b 25 (32α+3 n+2 · 32α+2-1) ≡ 0 (mod 3). Most recently, congruences modulo powers of 5 for c5(n) was proved by Wang, where c N (n) counts the number of bipartitions (λ1,λ2) of n such that each part of λ2 is divisible by N. In this paper, we prove some interesting Ramanujan-type congruences modulo powers of 5 for b25(n), B25(n), c25(n) and modulo powers of 7 for c49(n). For example, we prove that for j ≥ 1, \({c_{25}}\left( {{5^{2j}}n + \frac{{11 \cdot {5^{2j}} + 13}}{{12}}} \right) \equiv 0\) (mod 5 j+1), \({c_{49}}\left( {{7^{2j}}n + \frac{{11 \cdot {7^{_{2j}}} + 25}}{{12}}} \right) \equiv 0\) (mod 7 j+1) and b 25 (32α+3 · n+2 · 32α+2-1) ≡ 0 (mod 3 · 52j-1). 相似文献
6.
The uncertain system is considered, where the coefficients a ij (n) of the m×m matrix A n are functionals of any nature subject to the constraints
Such systems include, in particular, switched-type systems, whose matrix A can take values in a given finite set.By using a special Lyapunov function, a bound δ ≤ δ(α0,α*) ensuring the global asymptotic stability of the system is found. In particular, the system is stable if the last inequality is replaced by a i,j (n) = 0 for j < i.It is shown that pulse-width modulated systems reduce to the uncertain systems under consideration; moreover, in the case of a pulse-width modulation of the first kind, the coefficients of the matrix A are functions of x(n), and in the case of a modulation of the second kind, they are functionals. 相似文献
$x_{n + 1} = A_n x_n , n = 0,1,2, \ldots ,$
$\begin{array}{*{20}c} {\left| {a_{i,i} (n)} \right| \leqslant \alpha _ * < 1,} \\ {\left| {a_{i,j} (n)} \right| \leqslant \alpha _0 for j \geqslant i + 1,} \\ {\left| {a_{i,j} (n)} \right| \leqslant \delta for j < i.} \\ \end{array} $
7.
Let i=1+q+???+q i?1. For certain sequences (r 1,…,r l ) of positive integers, we show that in the Hecke algebra ? n (q) of the symmetric group \(\mathfrak{S}_{n}\), the product \((1+\boldsymbol{r}_{\boldsymbol{1}}T_{r_{1}})\cdots (1+\boldsymbol{r}_{\boldsymbol{l}}T_{r_{l}})\) has a simple explicit expansion in terms of the standard basis {T w }. An interpretation is given in terms of random walks on \(\mathfrak{S}_{n}\). 相似文献
8.
LetX be a complex projective algebraic manifold of dimension 2 and let D1, ..., Du be distinct irreducible divisors onX such that no three of them share a common point. Let\(f:{\mathbb{C}} \to X\backslash ( \cup _{1 \leqslant i \leqslant u} D_i )\) be a holomorphic map. Assume thatu ? 4 and that there exist positive integers n1, ... ,nu,c such that ninJ D i.Dj) =c for all pairsi,j. Thenf is algebraically degenerate, i.e. its image is contained in an algebraic curve onX. 相似文献
9.
Herbert E. Salzer 《Numerische Mathematik》1964,6(1):68-77
Divided differences forf (x, y) for completely irregular spacing of points (x i ,y i ) are developed here by a natural generalization of Newton's scheme. Existing bivariate schemes either iterate the one-dimensional scheme, thus constraining (x i ,y i ) to be at corners of rectangles, or give polynomials Σa jk x j y k having more coefficients than interpolation conditions. Here the generalizedn th divided difference is defined by (1)\(\left[ {01... n} \right] = \sum\limits_{i = 0}^n {A_i f\left( {x_i , y_i } \right)} \) where (2)\(\sum\limits_{i = 0}^n {A_i x_i^j , y_i^k = 0} \), and 1 for the last or (n+1)th equation, for every (j, k) wherej+k=0, 1, 2,... in the usual ascending order. The gen. div. diff. [01...n] is symmetric in (x i ,y i ), unchanged under translation, 0 forf (x, y) an, ascending binary polynomial as far asn terms, degree-lowering with respect to (X, Y) whenf(x, y) is any polynomialP(X+x, Y+y), and satisfies the 3-term recurrence relation (3) [01...n]=λ{[1...n]?[0...n?1]}, where (4) λ= |1...n|·|01...n?1|/|01...n|·|1...n?1|, the |...i...| denoting determinants inx i j y i k . The generalization of Newton's div. diff. formula is (5)
$$\begin{gathered} f\left( {x, y} \right) = f\left( {x_0 , y_0 } \right) - \frac{{\left| {\alpha 0} \right|}}{{\left| 0 \right|}}\left[ {01} \right] + \frac{{\left| {\alpha 01} \right|}}{{\left| {01} \right|}}\left[ {012} \right] - \frac{{\left| {\alpha 012} \right|}}{{\left| {012} \right|}}\left[ {0123} \right] + \cdots + \hfill \\ + \left( { - 1} \right)^n \frac{{\left| {\alpha 01 \ldots n - 1} \right|}}{{\left| {01 \ldots n - 1} \right|}}\left[ {01 \ldots n} \right] + \left( { - 1} \right)^{n + 1} \frac{{\left| {\alpha 01 \ldots n} \right|}}{{\left| {01 \ldots n} \right|}}\left[ {01 \ldots n} \right], \hfill \\ \end{gathered} $$ 相似文献
10.
On <Emphasis Type="Italic">s</Emphasis>-Elementary Super Frame Wavelets and Their Path-Connectedness
A super wavelet of length n is an n-tuple (ψ 1,ψ 2,…,ψ n ) in the product space \(\prod_{j=1}^{n} L^{2}(\mathbb{R})\), such that the coordinated dilates of all its coordinated translates form an orthonormal basis for \(\prod_{j=1}^{n} L^{2} (\mathbb{R})\). This concept is generalized to the so-called super frame wavelets, super tight frame wavelets and super normalized tight frame wavelets (or super Parseval frame wavelets), namely an n-tuple (η 1,η 2,…,η n ) in \(\prod_{j=1}^{n}L^{2} (\mathbb{R})\) such that the coordinated dilates of all its coordinated translates form a frame, a tight frame, or a normalized tight frame for \(\prod_{j=1}^{n} L^{2}(\mathbb{R})\). In this paper, we study the super frame wavelets and the super tight frame wavelets whose Fourier transforms are defined by set theoretical functions (called s-elementary frame wavelets). An m-tuple of sets (E 1,E 2,…,E m ) is said to be τ-disjoint if the E j ’s are pair-wise disjoint under the 2π-translations. We prove that a τ-disjoint m-tuple (E 1,E 2,…,E m ) of frame sets (i.e., η j defined by \(\widehat{\eta_{j}}=\frac{1}{\sqrt{2\pi}}\chi_{E_{j}}\) is a frame wavelet for L 2(?) for each j) lead to a super frame wavelet (η 1,η 2,…,η m ) for \(\prod_{j=1}^{m} L^{2} (\mathbb{R})\) where \(\widehat{\eta_{j}}=\frac{1}{\sqrt{2\pi}}\chi_{E_{j}}\). In the case of super tight frame wavelets, we prove that (η 1,η 2,…,η m ), defined by \(\widehat{\eta_{j}}=\frac{1}{\sqrt{2\pi}}\chi_{E_{j}}\), is a super tight frame wavelet for ∏1≤j≤m L 2(?) with frame bound k 0 if and only if each η j is a tight frame wavelet for L 2(?) with frame bound k 0 and that (E 1,E 2,…,E m ) is τ-disjoint. Denote the set of all τ-disjoint s-elementary super frame wavelets for ∏1≤j≤m L 2(?) by \(\mathfrak{S}(m)\) and the set of all s-elementary super tight frame wavelets (with the same frame bound k 0) for ∏1≤j≤m L 2(?) by \(\mathfrak{S}^{k_{0}}(m)\). We further prove that \(\mathfrak{S}(m)\) and \(\mathfrak{S}^{k_{0}}(m)\) are both path-connected under the ∏1≤j≤m L 2(?) norm, for any given positive integers m and k 0. 相似文献
11.
In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H_(|x|α)~1(R~2) ( -1 ≤α≤0), defined by H_(Φ,A)f(x)=∫R~2Φ(u)f(A(u)x)du,where Φ∈L_loc~1(R~2),A(u) = (α_(ij)(u))_(i,j=1)~2 is a 2×2 matrix, and each α_(i,j) is a measurablefunction.We obtain that HΦ,A is bounded from H_(|x|~α)~1(R~2) ( -1≤α≤0) to itself, if∫R2|Φ(u)‖det A~(-1)(u)|‖A(u)‖~(-α)ln(1+‖A~(-1)(u)‖~2/|det A~(-1)(u)|)du∞.This result improves some known theorems, and in some sense it is sharp. 相似文献
12.
Let M n be an n-dimensional closed submanifold of a sphere with parallel normalized mean curvature vector. Denote by S and H the squared norm of the second fundamental form and the mean curvature of M n , respectively. Assume that the fundamental group \({\pi_{1}(M^{n})}\) of M n is infinite and \({S\, \leqslant\, S(H)=n+\frac{n^{3}H^{2}}{2(n-1)}-\frac{n(n-2)H}{2(n-1)}\sqrt{n^{2}H^{2}+4(n-1)}}\), then S is constant, S = S(H), and M n is isometric to a Clifford torus \({S^{1}(\sqrt{1-r^{2}})\times S^{n-1}(r)}\) with \({r^{2}\leqslant \frac{n-1}{n}}\). 相似文献
13.
N. Baccar 《Periodica Mathematica Hungarica》2007,55(2):197-213
For P ? \(\mathbb{F}_2 \)[z] with P(0) = 1 and deg(P) ≥ 1, let \(\mathcal{A}\) = \(\mathcal{A}\)(P) (cf. [4], [5], [13]) be the unique subset of ? such that Σ n≥0 p(\(\mathcal{A}\), n)z n ≡ P(z) (mod 2), where p(\(\mathcal{A}\), n) is the number of partitions of n with parts in \(\mathcal{A}\). Let p be an odd prime and P ? \(\mathbb{F}_2 \)[z] be some irreducible polynomial of order p, i.e., p is the smallest positive integer such that P(z) divides 1 + z p in \(\mathbb{F}_2 \)[z]. In this paper, we prove that if m is an odd positive integer, the elements of \(\mathcal{A}\) = \(\mathcal{A}\)(P) of the form 2 k m are determined by the 2-adic expansion of some root of a polynomial with integer coefficients. This extends a result of F. Ben Saïd and J.-L. Nicolas [6] to all primes p. 相似文献
14.
Let L2 be the space of 2π-periodic square-summable functions and E(f, X)2 be the best approximation of f by the space X in L2. For n ∈ ? and B ∈ L2, let \({{\Bbb S}_{B,n}}\) be the space of functions s of the form \(s\left( x \right) = \sum\limits_{j = 0}^{2n - 1} {{\beta _j}B\left( {x - \frac{{j\pi }}{n}} \right)} \). This paper describes all spaces \({{\Bbb S}_{B,n}}\) that satisfy the exact inequality \(E{\left( {f,{S_{B,n}}} \right)_2} \leqslant \frac{1}{{^{{n^r}}}}\parallel {f^{\left( r \right)}}{\parallel _2}\). (2n–1)-dimensional subspaces fulfilling the same estimate are specified. Well-known inequalities are for approximation by trigonometric polynomials and splines obtained as special cases. 相似文献
15.
V. G. Karapetyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(3):180-191
The paper studies a class of almost hypoelliptic equations P(D)U = ? in a strip. It is proved that for \(\mathcal{H}\) great enough and for δ > 0 small enough all solutions of this equation, which are square summable with the weight e ?δ|x| and for which \(D_2^{\alpha _2 } U\), where α 2 = 0, …, \(ord_{\alpha _2 } P\), are infinitely differentiable in x 1 functions, provided D 1 j ? ∈ L 2(\(\Omega _\mathcal{H} \)) for any j. 相似文献
16.
Konstantin E. Tikhomirov 《Israel Journal of Mathematics》2016,212(1):289-314
Let δ > 1 and β > 0 be some real numbers. We prove that there are positive u, v, N0 depending only on β and δ with the following property: for any N,n such that N ≥ max(N0, δn), any N × n random matrix A = (aij) with i.i.d. entries satisfying \({\sup _{\lambda \in \mathbb{R}}}P\left\{ {\left| {{a_{11}} - \lambda } \right| \leqslant 1} \right\} \leqslant 1 - \beta \) and any non-random N × n matrix B, the smallest singular value sn of A + B satisfies \(P\left\{ {{s_n}\left( {A + B} \right) \leqslant u\sqrt N } \right\} \leqslant \exp \left( { - vN} \right)\). The result holds without any moment assumptions on the distribution of the entries of A. 相似文献
17.
In this paper we consider the Schrödinger type operators \(H_2=(-\Delta)^2 +V^2\), where the nonnegative potential V belongs to the reverse Hölder class \(B_{q_{_1}}\) for \(q_{_1}\geq \frac{n}{2}, n\geq 5\). The L p and weak type (1, 1) estimates of higher order Riesz transform \(\nabla^2H^{-\frac{1}{2}}_2 \) related to Schrödinger type operators H 2 are obtained. In particular, \(\nabla^2H^{-\frac{1}{2}}_2 \) is a Calderón-Zygmund operator if V?∈?B 2n or \(V\in B_\frac{n}{2}\) and there exists a constant C such that V(x)?≤?Cm(x,V)2. 相似文献
18.
In this paper, we study Toeplitz operators T μ from one Fock space \({F^{p}_{\alpha}}\) to another \({F^{q}_{\alpha}}\) for 1 < p, q < ∞ with positive Borel measures μ as symbols. We characterize the boundedness (and compactness) of \({T_\mu: F^{p}_{\alpha} \to F^{q}_{\alpha}}\) in terms of the averaging function \({\widehat{\mu}_r}\) and the t-Berezin transform \({\widetilde{\mu}_t}\) respectively. Quite differently from the Bergman space case, we show that T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for some p ≤ q if and only if T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for all p ≤ q. In order to prove our main results on T μ , we introduce and characterize (vanishing) (p, q)-Fock Carleson measures on C n . 相似文献
19.
Huan Liu 《Frontiers of Mathematics in China》2017,12(3):655-673
Let g be a holomorphic or Maass Hecke newform of level D and nebentypus χD, and let a g (n) be its n-th Fourier coefficient. We consider the sum \({S_1} = \sum {_{X < n \leqslant 2X}{a_g}\left( n \right)e\left( {\alpha {n^\beta }} \right)}\) and prove that S 1 has an asymptotic formula when β = 1/2 and α is close to \(\pm 2\sqrt {q/D}\) for positive integer q ≤ X/4 and X sufficiently large. And when 0 < β < 1 and α, β fail to meet the above condition, we obtain upper bounds of S 1. We also consider the sum \({S_2} = \sum {_{n > 0}{a_g}\left( n \right)e\left( {\alpha {n^\beta }} \right)\phi \left( {n/X} \right)}\) with ø(x) ∈ C c ∞ (0,+∞) and prove that S 2 has better upper bounds than S 1 at some special α and β. 相似文献
20.
We consider a fractional Adams method for solving the nonlinear fractional differential equation \(\,^{C}_{0}D^{\alpha }_{t} y(t) = f(t, y(t)), \, \alpha >0\), equipped with the initial conditions \(y^{(k)} (0) = y_{0}^{(k)}, k=0, 1, \dots , \lceil \alpha \rceil -1\). Here, α may be an arbitrary positive number and ?α? denotes the smallest integer no less than α and the differential operator is the Caputo derivative. Under the assumption \(\,^{C}_{0}D^{\alpha }_{t} y \in C^{2}[0, T]\), Diethelm et al. (Numer. Algor. 36, 31–52, 2004) introduced a fractional Adams method with the uniform meshes t n = T(n/N),n = 0,1,2,…,N and proved that this method has the optimal convergence order uniformly in t n , that is O(N ?2) if α > 1 and O(N ?1?α ) if α ≤ 1. They also showed that if \(\,^{C}_{0}D^{\alpha }_{t} y(t) \notin C^{2}[0, T]\), the optimal convergence order of this method cannot be obtained with the uniform meshes. However, it is well-known that for y ∈ C m [0,T] for some \(m \in \mathbb {N}\) and 0 < α < m, the Caputo fractional derivative \(\,^{C}_{0}D^{\alpha }_{t} y(t) \) takes the form “\(\,^{C}_{0}D^{\alpha }_{t} y(t) = c t^{\lceil \alpha \rceil -\alpha } + \text {smoother terms}\)” (Diethelm et al. Numer. Algor. 36, 31–52, 2004), which implies that \(\,^{C}_{0}D^{\alpha }_{t} y \) behaves as t ?α??α which is not in C 2[0,T]. By using the graded meshes t n = T(n/N) r ,n = 0,1,2,…,N with some suitable r > 1, we show that the optimal convergence order of this method can be recovered uniformly in t n even if \(\,^{C}_{0}D^{\alpha }_{t} y\) behaves as t σ ,0 < σ < 1. Numerical examples are given to show that the numerical results are consistent with the theoretical results. 相似文献