Parameter Estimates in Random Intercept Mixed Effects Model for Repeated Measures

In this article the following random intercept mixed effects model will be considered： yij = vi =v^τijβ＋ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality.     

On Two Variable Jordan Block (II)

On the Hardy space over the bidisk H²(D²), the Toeplitz operators and are unilateral shifts of infinite multiplicity. A closed subspace M is called a submodule if it is invariant for both and . The two variable Jordan block (S₁, S₂) is the compression of the pair to the quotient H²(D²) ⊖M. This paper defines and studies its defect operators. A number of examples are given, and the Hilbert-Schmidtness is proved with good generality. Applications include an extension of a Douglas-Foias uniqueness theorem to general domains, and a study of the essential Taylor spectrum of the pair (S₁, S₂). The paper also estabishes a clean numerical estimate for the commutator [S₁*, S₂] by some spectral data of S₁ or S₂. The newly-discovered core operator plays a key role in this study.     

On a Poincaré-type Inequality for Energy Forms in L p

We consider Dirichlet spaces ( ) in L ² and more general energy forms in L ^p , . For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that , resp. , are compactly embedded in L ², resp. L ^p , we prove a Poincaré inequality for transient (Dirichlet) forms. If both and its adjoint are sub-Markovian semigroups, we show that the transience of T _t is independent of ) and that it is implied by the transience of the energy form of and the form belonging to .     

Uniform Mixed Hypergraphs: The Possible Numbers of Colors

For a mixed hypergraph , where and are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every meets some class in more than one vertex, and every has a nonempty intersection with at least two classes. The feasible set of , denoted , is the set of integers k such that admits a coloring with precisely k nonempty color classes. It was proved by Jiang et al. [Graphs and Combinatorics 18 (2002), 309–318] that a set S of natural numbers is the feasible set of some mixed hypergraph if and only if either or S is an ‘interval’ for some integer k ≥ 1. In this note we consider r-uniform mixed hypergraphs, i.e. those with |C| = |D| = r for all and all , r ≥ 3. We prove that S is the feasible set of some r-uniform mixed hypergraph with at least one edge if and only if either for some natural number k ≥ r − 1, or S is of the form where S′′ is any (possibly empty) subset of and S′ is either the empty set or {r − 1} or an ‘interval’ {k, k + 1, ..., r − 1} for some k, 2 ≤ k ≤ r − 2. We also prove that all these feasible sets can be obtained under the restriction , i.e. within the class of ‘bi-hypergraphs’. Research supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613.     

On the graph of a function in two variables over a finite field

We show that if the number of directions not determined by a pointset of , of size q² is at least p^e q then every plane intersects in 0 modulo p^e+1 points and apply the result to ovoids of the generalised quadrangles and .     

Ratios of Norms for Polynomials and Connected n-width Problems

Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:

Generalized self-duality of 2-forms

Self-dual 2–forms on play a fundamental role in gauge theory. For generalized Seiberg-Witten theory (and for some other purposes in mathematical physics) a notion of self-duality of 2–forms on is needed. There are several definitions, but the one given by [Bilge, Dereli, Ko?ak ; JMP 38(9), 1997] is intimately related with Clifford algebras. They defined a 2–form to be self-dual if the anti-symmetric matrix Ω = (ω_ij) satisfies Ω² = λ I for a scalar λ and proved that the space of such forms is non-linear with dimension n² − n + 1, but contains maximal linear subspaces with dimension the Radon-Hurwitz number of (2n). It is important to have an algorithm for construction of such maximal linear subspaces and we give an explicit one with the help of representations of Clifford algebras on whereby we show that the representations given by the standart recursion formulas are anti-symmetric.     

Non- (Quantum) Differentiable C 1-Functions in the Spaces with Trivial Boyd Indices

If E is a separable symmetric sequence space with trivial Boyd indices and is the corresponding ideal of compact operators, then there exists a C¹-function f_E, a self-adjoint element and a densely defined closed symmetric derivation δ on such that , but      

Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel

We show that the algebra of functions on the scheme of monic linear second-order ordinary differential operators with prescribed n + 1 regular singular points, prescribed exponents at the singular points, and having the kernel consisting of polynomials only, is isomorphic to the Bethe algebra of the Gaudin model acting on the vector space Sing of singular vectors of weight Λ^(∞) in the tensor product of finite-dimensional polynomial -modules with highest weights .      

High Order Singular Rank One Perturbations of a Positive Operator

In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space with inner product 〈·,·〉, α is a real parameter, and φ in the rank one perturbation is a singular element belonging to with n ≥ 3, where is the scale of Hilbert spaces associated with L in      

Elements of Prescribed Order,Prescribed Traces and Systems of Rational Functions Over Finite Fields

Let k 1 and be a system of rational functions forming a strongly linearly independent set over a finite field . Let be arbitrarily prescribed elements. We prove that for all sufficiently large extensions , there is an element of prescribed order such that is the relative trace map from onto We give some applications to BCH codes, finite field arithmetic and ordered orthogonal arrays. We also solve a question of Helleseth et~al. (Hypercubic 4 and 5-designs from Double-Error-Correcting codes, Des. Codes. Cryptgr. 28(2003). pp. 265–282) completely.classification 11T30, 11G20, 05B15     

Ultraproducts of real interpolation spaces between L p -spaces

Let , be a family of compatible couples of L^p-spaces. We show that, given a countably incomplete ultrafilter in , the ultraproduct of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type , an intermediate K?the space between and being a purely atomic measure space, and a K?the function space K(Ω₃) defined on some purely non atomic measure space (Ω₃, ν₃) in such a way that Ω₂ ∪ Ω₃ ≠∅. The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group 03/050.     

Maximally singular functions in Besov spaces

Assuming that 0 < α p < N, p, q ∈(1,∞), we construct a class of functions in the Besov space such that the Hausdorff dimension of their singular set is equal to N − α p. We show that these functions are maximally singular, that is, the Hausdorff dimension of the singular set of any other Besov function in is ≦ N − α p. Similar results are obtained for Lizorkin-Triebel spaces and for the Hardy space . Some open problems are listed. Received: 5 July 2005; revised: 18 October 2005     

Spherical Monogenics: An Algebraic Approach

The space of spherical monogenics in can be regarded as a model for the irreducible representation of Spin(m) with weight . In this paper we construct an orthonormal basis for . To describe the symmetry behind this procedure, we define certain Spin(m − 2)-invariant representations of the Lie algebra (2) on . Received: October, 2007. Accepted: February, 2008.     

Strong Approximation by Cesàro Means with Critical Index in the Hardy Spaces H p (\mathbb{S}^{{d - 1}} ) (0 < p ≤ 1)

Let be a unit sphere of the d–dimensional Euclidean space ℝ ^d and let (0 < p ≤ 1) denote the real Hardy space on For 0 < p ≤ 1 and let E _j (f,H ^p ) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or equal to j, in the space Given a distribution f on its Cesàro mean of order δ > –1 is denoted by For 0 < p ≤ 1, it is known that is the critical index for the uniform summability of in the metric H ^p . In this paper, the following result is proved: Theorem Let 0<p<1 and Then for

Properties of Auto- and Antiautomorphisms of Maximal Chain Structures and their Relations to i-Perspectivities

Let E be a non empty set, let P : = E × E, := {x × E|x ∈ E}, := {E × x|x ∈ E}, and := {C ∈ 2 ^P |∀X ∈ : |C ∩ X| = 1} and let . Then the quadruple resp. is called chain structure resp. maximal chain structure. We consider the maximal chain structure as an envelope of the chain structure . Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes. Here we study in detail the groups of automorphisms , , , related to a maximal chain structure . The set of all chains can be turned in a group such that the subgroup of generated by the left-, by the right-translations and by ι the inverse map of is isomorphic to (cf. (2.14)).     

Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks

We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial （finite） number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n（·） = Znt（√n·）, where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^（2β-1/2）Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit.     

Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes

In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.     

Convexities of partial monounary algebras

In the present paper we prove that the collection of all convexities of partial monounary algebras is finite; namely, it has exactly 23 elements. Further, we show that for each element there exists a subset of such that is generated by and card . This work was supported by the Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by Grant VEGA 1/3003/06.     

Second-Order Efficient Test for Inhomogeneous Poisson Processes

We observe a realization X ⁽ⁿ⁾ of a Poisson process on the set with intensity function depending on the unknown real parameter . Based on X ⁽ⁿ⁾ we test simple null hypothesis against one sided alternative for given . We improve the level of the well-known locally asymptotically uniformly most powerful (LAUMP) test by using the Edgeworth type expansion for stochastic integral. We show that the improved test is second-order efficient under certain regularity conditions.