ℓ-Divisibility of ℓ-regular partition functions

We give exact criteria for the ℓ-divisibility of the ℓ-regular partition function b _ℓ (n) for ℓ∈{5,7,11}. These criteria are found using the theory of complex multiplication. In each case the first criterion given corresponds to the Ramanujan congruence modulo ℓ for the unrestricted partition function, and the second is a condition given by J.-P. Serre for the vanishing of the coefficients of ∏ _m=1^∞(1−q ^m ) ^ℓ−1.      

Fibonacci Lengths of Certain Nilpotent 2-Groups

In this paper, we study two classes of 2-generated 2-groups of nilpotency class 2 classified by Kluempen in 2002 and also a class of finite 2-groups of high nilpotency class for their Fibonacci lengths. Their involvement in certain interesting sequences of Tribonacci numbers gives us some explicit formulas for the Fibonacci lengths and this adds to the small class of finite groups for which the Fibonacci length are known.     

The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes

This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively.     

Maximal ℓ-Frattini quotients of ℓ-Poincaré duality groups of dimension 2

Any morphism of profinite groups has maximal ℓ-Frattini quotients

Decomposition of ℓ-group-valued measures

We deal with decomposition theorems for modular measures µ: L → G defined on a D-lattice with values in a Dedekind complete ?-group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete ?-groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for ?-group-valued modular measures on D-lattices. Recall that D-lattices (or equivalently lattice ordered effect algebras) are a common generalization of orthomodular lattices and of MV-algebras, and therefore of Boolean algebras. If L is an MV-algebra, in particular if L is a Boolean algebra, then the modular measures on L are exactly the finitely additive measures in the usual sense, and thus our results contain results for finitely additive G-valued measures defined on Boolean algebras.     

Convergence of the reweighted ℓ 1 minimization algorithm for ℓ 2–ℓ p minimization

The iteratively reweighted ? ₁ minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the ? ₂–? _p minimization problem with 0<p<1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.     

Classes of generalized ∗-modules

We study the class, STAR , of all ?-modules by means of the classes, S_λ, of all ?λ-modules, λ> 0 being a cardinal. Since STAR, equals the intersection of the decreasing chain S_λ, λ > 0, our approach ‘from above’ complements the usual approach ‘from below’ consisting in the study of quasi-progenerators and tilting modules. We present relations between categorical properties of ?-;modules and those of ?-modules. Answering a question of Menini, we use the solution of the Artin's problem to show that the chain Sλ,λ > No, is strictly decreasing in general.     

On Some Classes of Interpolating Splines

In this article, we consider some classes of interpolating spline with difference. derivative and integral interpolating conditions respectively. Let Δ_π:a=x_o相似文献   

Two Wider Classes of Combinatorial Identities

Here introduced are two general classes of combinatorial identities that may be defined via inverse relations due to Gould and Hsu(cf.Duke Math J. 40(1973), 885 891). Classes(∑) and(∑~*). Any identity is said to belong to the class(∑) if it can be embedded in either of the forms(reciprocal relations)     

Calculation of ℓ-adic local Fourier transformations

We calculate the local Fourier transformations for a class of ${\overline{\mathbb Q}_\ell}$ -sheaves. In particular, we verify a conjecture of Laumon and Malgrange [18, 2.6.3]. As an application, we calculate the local monodromy of ?-adic hypergeometric sheaves introduced by Katz [15]. We also discuss the characteristic p analogue of the Turrittin-Levelt Theorem for D-modules.     

M-ideals of compact operators into ℓp

We show for 2 p < and subspaces X of quotients of L _p with a 1-unconditional finite-dimensional Schauder decomposition that K(X, _p) is an M-ideal in L(X, _p).     

Recovery of sparsest signals via ℓq-minimization

In this paper, it is proved that every s-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ can be exactly recovered from the measurement vector $\mathbf{z}=\mathbf{Ax}\in {\mathbb{R}}^m$ via some ${?}^q$-minimization with $0<q?1$, as soon as each s-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the ${?}^q$-minimization can be so chosen to be about $0.6796\times (1?{\delta }_{2s}(\mathbf{A}))$, where ${\delta }_{2s}(\mathbf{A})$ is the restricted isometry constant of order 2s for the measurement matrix A.     

ℓ1-summability of higher-dimensional Fourier series

It is proved that the maximal operator of the ${?}_1$-Fejér means of a $d$-dimensional Fourier series is bounded from the periodic Hardy space $H_p\left({\mathbb{T}}^d\right)$ to $L_p\left({\mathbb{T}}^d\right)$ for all $d/(d+1)<p\le \infty$ and, consequently, is of weak type (1, 1). As a consequence we obtain that the ${?}_1$-Fejér means of a function $f\in L_1\left({\mathbb{T}}^d\right)$ converge a.e. to $f$. Moreover, we prove that the ${?}_1$-Fejér means are uniformly bounded on the spaces $H_p\left({\mathbb{T}}^d\right)$ and so they converge in norm $(d/(d+1)<p<\infty )$. Similar results are shown for conjugate functions and for a general summability method, called $\theta$-summability. Some special cases of the ${?}_1–\theta$-summation are considered, such as the Weierstrass, Picard, Bessel, Fejér, de la Vallée Poussin, Rogosinski and Riesz summations.     

Subspaces of Lp Isometric to Subspaces of ℓ p

We present three results on isometric embeddings of a (closed, linear) subspace X of L_p=L_p[0,1] into _p . First we show that if p 2N, then X is isometrically isomorphic to a subspace of _p if and only if some, equivalently every, subspace of L_p which contains the constant functions and which is isometrically isomorphic to X, consists of functions having discrete distribution. In contrast, if p 2N; and X is finite-dimensional, then X is isometrically isomorphic to a subspace of _p , where the positive integer N depends on the dimension of X, on p , and on the chosen scalar field. The third result, stated in local terms, shows in particular that if p is not an even integer, then no finite-dimensional Banach space can be isometrically universal for the 2-dimensional subspaces of L_p .