On the relation between cluster and classical tilting

Let be a triangulated category with a cluster tilting subcategory U. The quotient category is abelian; suppose that it has finite global dimension.We show that projection from to sends cluster tilting subcategories of to support tilting subcategories of , and that, in turn, support tilting subcategories of can be lifted uniquely to weak cluster tilting subcategories of .     

On the Wiener integral with respect to a sub-fractional Brownian motion on an interval

The domain of the Wiener integral with respect to a sub-fractional Brownian motion , , k≠0, is characterized. The set is a Hilbert space which contains the class of elementary functions as a dense subset. If , any element of is a function and if , the domain is a space of distributions.     

Higher Kurtz randomness

A real x is -Kurtz random (-Kurtz random) if it is in no closed null set ( set). We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.     

Kirillov-Reshetikhin crystals for nonexceptional types

We provide combinatorial models for all Kirillov-Reshetikhin crystals of nonexceptional type, which were recently shown to exist. For types , , we rely on a previous construction using the Dynkin diagram automorphism which interchanges nodes 0 and 1. For type we use a Dynkin diagram folding and for types , a similarity construction. We also show that for types and the analog of the Dynkin diagram automorphism exists on the level of crystals.     

Finite-sample inference with monotone incomplete multivariate normal data, II

We continue our recent work on inference with two-step, monotone incomplete data from a multivariate normal population with mean and covariance matrix . Under the assumption that is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of and of the estimated regression matrix, . We represent in terms of independent matrices; derive its exact distribution, thereby generalizing the Wishart distribution to the setting of monotone incomplete data; and obtain saddlepoint approximations for the distributions of and its partial Iwasawa coordinates. We prove the unbiasedness of a modified likelihood ratio criterion for testing , where is a given matrix, and obtain the null and non-null distributions of the test statistic. In testing , where and are given, we prove that the likelihood ratio criterion is unbiased and obtain its null and non-null distributions. For the sphericity test, , we obtain the null distribution of the likelihood ratio criterion. In testing we show that a modified locally most powerful invariant statistic has the same distribution as a Bartlett-Pillai-Nanda trace statistic in multivariate analysis of variance.     

Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices

Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form

     

Existence of smooth attractors for the Navier-Stokes-omega model of turbulence

We consider the Navier-Stokes- model, given by

     

How to play the Majority game with a liar

The Majority game is played by a questioner () and an answerer (). holds n elements, each of which can be labeled as 0 or 1. is trying to identify some element holds as having the Majority label or, in the case of a tie, claim there is none. To do this asks questions comparing whether two elements have the same or different label. ’s goal is to ask as few questions as possible while ’s goal is to delay as much as possible. Let q^∗ denote the minimal number of questions needed for to identify a Majority element regardless of ’s answers.In this paper we investigate upper and lower bounds for q^∗ in a variation of the Majority game, where is allowed to lie up to t times. We consider two versions of the game, the adaptive (where questions are asked sequentially) and the oblivious (where questions are asked in one batch).     

A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees

We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property .In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber ℵ₁ and for forcing notions with the property fails. This negatively answers a part of one of the classical problems about implications between fragments of .     

New applications of Besov-type and Triebel-Lizorkin-type spaces

In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces . The authors also establish an equivalent characterization of when τ∈[0,1/p). These Besov-type spaces and Triebel-Lizorkin-type spaces were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces and , the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ=0.     

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Denote by , k=1,…,n, the zeros of the Laguerre-Sobolev-type polynomials orthogonal with respect to the inner product

     

Chow groups of the moduli spaces of weighted pointed stable curves of genus zero

The moduli space of weighted pointed stable curves of genus zero is stratified according to the degeneration types of such curves. We show that the homology groups of are generated by the strata of and give all additive relations between them. We also observe that the Chow groups and the homology groups are isomorphic. This generalizes Kontsevich-Manin's and Losev-Manin's theorems to arbitrary weight data A.     

Quadratic prediction problems in multivariate linear models

Linear and quadratic prediction problems in finite populations have become of great interest to many authors recently. In the present paper, we mainly aim to extend the problem of quadratic prediction from a general linear model, of form , to a multivariate linear model, denoted by with . Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the optimal invariant quadratic (potentially) biased (OIQB) predictor of for any particular symmetric nonnegative definite matrix satisfying are derived. Secondly, we consider predicting and . The corresponding restricted OIQU predictor and restricted OIQB predictor for them are given. In addition, we also offer four concluding remarks. One concerns the generalization of predicting and , and the others are concerned with three possible extensions from multivariate linear models to growth curve models, to restricted multivariate linear models, and to matrix elliptical linear models.     

Weighted estimates for a class of multilinear fractional type operators

In this paper, a class of multiple fractional type weights is defined as

     

Polar syzygies in characteristic zero: The monomial case

Given a set of forms , where k is a field of characteristic zero, we focus on the first syzygy module Z of the transposed Jacobian module , whose elements are called differential syzygies of . There is a distinct submodule P⊂Z coming from the polynomial relations of through its transposed Jacobian matrix, the elements of which are called polar syzygies of . We say that is polarizable if equality P=Z holds. This paper is concerned with the situation where are monomials of degree 2, in which case one can naturally associate to them a graph with loops and translate the problem into a combinatorial one. The main result is a complete combinatorial characterization of polarizability in terms of special configurations in this graph. As a consequence, we show that polarizability implies normality of the subalgebra and that the converse holds provided the graph is free of certain degenerate configurations. One main combinatorial class of polarizability is the class of polymatroidal sets. We also prove that if the edge graph of has diameter at most 2 then is polarizable. We establish a curious connection with birationality of rational maps defined by monomial quadrics.     

Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix

Let , where is a random symmetric matrix, a random symmetric matrix, and with being independent real random variables. Suppose that , and are independent. It is proved that the empirical spectral distribution of the eigenvalues of random symmetric matrices converges almost surely to a non-random distribution.     

Exact rates in log law for positively associated random variables

Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively.     

On the number of graphs with a given endomorphism monoid

For a given finite monoid , let be the number of graphs on n vertices with endomorphism monoid isomorphic to . For any nontrivial monoid we prove that where and are constants depending only on with .For every k there exists a monoid of size k with , on the other hand if a group of unity of has a size k>2 then .