Some greedyt-intersecting families of finite sequences

Letn, s ₁,s ₂, ... ands _n be positive integers. Assume is an integer for eachi}. For , , and , denotes _p (a)={j|1jn,a _j p}, , and . is called anI _t ^p -intersecting family if, for any a,b ,a _i b _i =min(a _i ,b _i )p for at leastt i's. is called a greedyI _t ^P -intersecting family if is anI _t ^p -intersecting family andW _p (A)W _p (B+A ^c ) for anyAS _p ( ) and any with |B|=t–1.In this paper, we obtain a sharp upper bound of | | for greedyI _t ^p -intersecting families in for the case 2ps _i (1in) ands ₁>s ₂>...>s _n .This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China.     

Hyponormality of Toeplitz Operators with Polynomial and Symmetric-Type Symbols

Suppose that is a trigonometric polynomial of the form (z) = ^N_n=-N a_n zⁿ. It is well-known that T is normal if and only if | a_{– N}| =  | a_N| and the Fourier coefficients of satisfy the following symmetry condition:

Subcoercivity and subelliptic operators on Lie groups II: The general case

Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (, ,dU) denote the representation of the Lie algebra obtained by differentiation. Ifa ₁, ...,a _d is a Lie algebra basis of ,A _i =dU (a _i ) and whenever =(i ₁, ...,i _k ) we reconsider the operators

On a conditional Gołab-Schinzel equation

Let We show that for every function satisfying the conditional equation

Nonabelian K-theory: The nilpotent class of K1 and general stability

A functorial filtration GL _n =S^–1L _n S⁰L _n S ⁱ L _n E _n of the general linear group GL _{n, n} 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S^–1 L _n (A)/S⁰L _n (A) is abelian, that S⁰L _n (A) S¹L _n (A) is a descending central series, and that S ⁱ L _n (A) = E _n(A) whenever i the Bass-Serre dimension of A. In particular, the K-functors k ₁ S ⁱ L _n =S ⁱ L _n /E _n are nilpotent for all i 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S ⁱ L _n (A)/S ⁱ⁺¹ L _n (A)S ⁱ L _{n+ 1}(A)/S ⁱ⁺¹ L _{n + 1} (A) is injective whenever n i + 3, so that one has stability results without stability conditions, and if A is commutative then S⁰L _n (A) agrees with the special linear group SL _n (A), so that the functor S⁰L _n generalizes the functor SL _n to noncommutative rings. Applying the above to subgroups H of GL _n (A), which are normalized by E _n(A), one obtains that each is contained in a sandwich GL _n (A, ) H E _n(A, ) for a unique two-sided ideal of A and there is a descending S⁰L _n (A)-central series GL _n (A, ) S⁰L _n (A, ) S¹L _n (A, ) S ⁱ L _n (A, ) E _n(A, ) such that S ⁱ L _n (A, )=E _n(A, ) whenever i Bass-Serre dimension of A.Dedicated to Alexander Grothendieck on his sixtieth birthday     

On the metric theory of the nearest integer continued fraction expansion

Supposek _n denotes either (n) or (p _n) (n=1,2,...) where the polynomial maps the natural numbers to themselves andp _k denotes thek ^th rationals prime. Also let denote the sequence of convergents to a real numberx and letc _n(x)) _n=1 be the corresponding sequence of partial quotients for the nearest integer continued fraction expansion. Define the sequence of approximation constants _n(x)) _n=1 by

The boundedness below of 2×2 upper triangular operator matrices

Wen and are given we denote byM _C an operator acting on the Hilbert space of the form

On the Weak Limiting Behavior of Almost Surely Convergent Row Sums from Infinite Arrays of Rowwise Independent Random Elements in Banach Spaces

For an array {V _nk ,k1,n1} of rowwise independent random elements in a real separable Banach space with almost surely convergent row sums , we provide criteria for S _n –A _n to be stochastically bounded or for the weak law of large numbers to hold where {A _n ,n1} is a (nonrandom) sequence in .     

BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups

For a Hopf algebra , we define the structures of differential complexes on two dual exterior Hopf algebras: (1) an exterior extension of and (2) an exterior extension of the dual algebra ^*. The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on . The first differential complex is an analogue of the de Rham complex. When ^* is a universal enveloping algebra of a Lie (super)algebra, the second complex coincides with the standard complex. The differential is realized as an (anti)commutator with a BRST operator Q. We give a recursive relation that uniquely defines the operator Q. We construct the BRST and anti-BRST operators explicitly and formulate the Hodge decomposition theorem for the case of the quantum Lie algebra U _q(gl(N)).     

Bounds for Non-Gaussian Approximations of U-Statistics

Let X, ,X ₁,...,X _n be i.i.d. random variables taking values in a measurable space ( ). Consider U-statistics of degree two

Hilbert Functions, Residual Intersections, and Residually S2 Ideals

Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and I an ideal generated by s forms of degrees d ₁,...,d _s so that codim( :I)s. We give broad conditions for when the Hilbert function of R/ or of R/( :I) is determined by I and the degrees d ₁,...,d _s . These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S ₂ ideals. We prove that the residually S ₂ property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property.     

Feynman-Kac propagators and viscosity solutions

The aim of this paper is to study viscosity solutions to the following terminal value problem on [0, t] × E:

A geometric approach to the cascade approximation operator for wavelets

This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let be a Hilbert space, and let be a representation ofL ( ) on . LetR be a positive operator inL ( ) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on (bounded, but noncontractive) such that

Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics

Let or . Givenf: ⁿ , we establish convergence orders of interpolation where the cardinal functionx withx(j)=_0j is a linear combination of integer shifts, of a fast decaying function

Towards a model theory for 2-hyponormal operators

We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension ofT we only require that hold forf ; in this case we call a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let { _n } _n=0 be a weight sequence and letW denote the associated unilateral weighted shift on . IfW is 2-hyponormal thenW is weakly subnormal. Moreover, there exists a partially normal extension on such that (i) is hyponormal; (ii) ; and (iii) . In particular, if is strictly increasing then can be obtained as

Small Ball Estimates in <Emphasis Type="Italic">p</Emphasis>-Variation for Stable Processes

Let Z _t , t 0 be a strictly stable process on with index (0, 2]. We prove that for every p > , there exists = _{, p} and such that

Gamma limits in some Bernoulli free boundary problem

We study the limit cases p   and p  1 of the functionals

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as

Asymptotic expansion of norm associated with conjugate trigonometric polynomial

LetT _n (x) be trigonometric polynomial of degreen, and be conjugation ofT _n (x). In this paper we obtain the complete asymptotic expansion for

Skorohod stochastic differential equations of diffusion type

Leta, b beC ²(R ¹)-functions with bounded derivatives of first and second order. We study stochastic differential equations