Asymptotic distributions of non-central studentized statistics

Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applicati...     

On <Emphasis Type="Italic">Saaty</Emphasis>’s and <Emphasis Type="Italic">Koczkodaj</Emphasis>’s inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 ×  3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4  ×  4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n ×  n PRM is formulated, the elements a _ij (i < j) of which were randomly chosen from the ratio scale

On relations for the multiple <Emphasis Type="Italic">q</Emphasis>-zeta values

We prove a new relation for the multiple q-zeta values (MqZV’s). It is a q-analogue of the Ohno-Zagier relation for the multiple zeta values (MZV’s). We discuss the problem of determining the dimension of the space spanned by MqZV’s over ℚ, and present an application to MZV. The first author is supported by Grant-in-Aid for Young Scientists (B) No. 17740026 and the second author is supported by Grant-in-Aid for Young Scientists (B) No. 17740089.     

Applications of Klee’s Dehn–Sommerville Relations

We use Klee’s Dehn–Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove Kalai’s conjecture providing lower bounds on the f-vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that gives an upper bound on the middle Betti number of a 2k-dimensional manifold in terms of k and the number of vertices, and (iii) partially prove Kühnel’s conjecture providing upper bounds on other Betti numbers of odd- and even-dimensional manifolds. For manifolds with boundary, we derive an extension of Klee’s Dehn–Sommerville relations and strengthen Kalai’s result on the number of their edges. I. Novik research partially supported by Alfred P. Sloan Research Fellowship and NSF grant DMS-0500748. E. Swartz research partially supported by NSF grant DMS-0600502.     

Integral Points of Small Height Outside of a Hypersurface

Let F be a non-zero polynomial with integer coefficients in N variables of degree M. We prove the existence of an integral point of small height at which F does not vanish. Our basic bound depends on N and M only. We separately investigate the case when F is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel’s Lemma as well as to Faltings’ version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem.     

Equivariant isospectrality and Sunada’s method

We construct pairs and continuous families of isospectral yet locally non-isometric orbifolds via an equivariant version of Sunada’s method. We also observe that if a good orbifold ${\mathcal{O}}We construct pairs and continuous families of isospectral yet locally non-isometric orbifolds via an equivariant version of Sunada’s method. We also observe that if a good orbifold O{\mathcal{O}} and a smooth manifold M are isospectral, then they cannot admit non-trivial finite Riemannian covers M₁ ?O{M_1 \to\mathcal{O}} and M ₂ → M where M ₁ and M ₂ are isospectral manifolds.     

Foliations with leaves of nonpositive curvature

We answer a question of Gromov ([G2]) in the codimension 1 case: ifF is a codimension 1 foliation of a compact manifoldM with leaves of negative curvature, thenπ ₁(M) has exponential growth. We also prove a result analogous to Zimmer’s ([Z2]): ifF is a codimension 1 foliation on a compact manifold with leaves of nonpositive curvature, and ifπ ₁(M) has subexponential growth, then almost every leaf is flat. We give a foliated version of the Hopf theorem on surfaces without conjugate points. Partially supported by NSF Grant #DMS 9403870.     

S-convexity revisited (fuzzy): long version

In this revisional article, we criticize (strongly) the use made by Medar et al., and those whose work they base themselves on, of the name ‘convexity’ in definitions which intend to relate to convex functions, or cones, or sets, but actually seem to be incompatible with the most basic consequences of having the name ‘convexity’ associated to them. We then believe to have fixed the ‘denominations’ associated with Medar’s (et al.) work, up to a point of having it all matching the existing literature in the field [which precedes their work (by long)]. We also expand his work scope by introducing s ₁-convexity concepts to his group of definitions, which encompasses only convex and its proper extension, s ₂-convex, so far. This article is a long version of our previous review of Medar’s work, published by FJMS (Pinheiro, M.R.: S-convexity revisited. FJMS, 26/3, 2007).     

A multivalued version of Sharkovskiĭ’s theorem holds with at most two exceptions

A multivalued version of Sharkovskiĭ’s theorem is formulated for M-maps on linear continua and, more generally, for triangular M-maps on a Cartesian product of linear continua. This improves the main result of [AP1] in the sense that our multivalued analogue holds with at most two exceptions. A further specification requires some additional restrictions. For instance, 3- orbits of m-maps imply the existence of k-orbits for all k ? \mathbbNk \in {\mathbb{N}} , except possibly for k ?k \in {4, 6}. It is also shown that, on every connected linearly ordered topological space, an M-map with orbits of all periods can always be constructed. This demonstrates that Baldwin’s classification of linear continua in terms of admissible periods [Ba] is useless for multivalued maps.     

Compactification of a class of conformally flat 4-manifold

In this paper we generalize Huber’s result on complete surfaces of finite total curvature. For complete locally conformally flat 4-manifolds of positive scalar curvature with Q curvature integrable, where Q is a variant of the Chern-Gauss-Bonnet integrand; we first derive the Cohn-Vossen inequality. We then establish finiteness of the topology. This allows us to provide conformal compactification of such manifolds. Oblatum 3-III-1999 & 18-II-2000?Published online: 8 May 2000     

An effective version of the Bombieri–Vinogradov theorem, and applications to Chen’s theorem and to sums of primes and powers of two

In this paper we give an effective version of the Bombieri–Vinogradov theorem of Bombieri, Friedlander, and Iwaniec. As applications, we refine Chen’s theorem on primes with difference h for h ≤ x ^1/56, with a consequence on integers of the form p + 2 ^k .     

Minimum winning coalitions and endogenous status quo

I analyze a stochastic bargaining game in which a renewable surplus is divided among n ≥ 5 committee members in each of an infinite number of periods, and the division implemented in one period becomes the status quo allocation of the surplus in the ensuing period. I establish existence of equilibrium exhibiting minimum winning coalitions, assuming sufficiently mild concavity of stage preferences. The analysis highlights the role of proposal power in committee deliberations and yields a fully strategic version of McKelvey’s (J Econ Theory 12:472–482, 1976; Econometrica 47:1086–1112, 1979) dictatorial agenda setting.     

Asymptotic expansions for the conditional sojourn time distribution in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1-PS queue

We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison (SIAM J. Appl. Math. 45:152–167, [1985]) and Flatto (Ann. Appl. Probab. 7:382–409, [1997]). This work was partly supported by NSF grant DMS 05-03745.     

On the multi-phase M/G/1 queueing system with random feedback

In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general distribution. After the completion of the i-th phase, with probability θ _i the (i + 1)-th phase starts, with probability p _i the customer feedback to the tail of the queue and with probability 1 − θ _i − p _i  = q _i departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p _k feedback to the tail of the queue and with probability 1 − p _k departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue size at departure epoch is obtained.     

Peripheral fillings of relatively hyperbolic groups

In this paper a group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group G we define a peripheral filling procedure, which produces quotients of G by imitating the effect of the Dehn filling of a complete finite volume hyperbolic 3-manifold M on the fundamental group π₁(M). The main result of the paper is an algebraic counterpart of Thurston’s hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of G ‘almost’ have the Congruence Extension Property and the group G is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings. Mathematics Subject Classification (2000) 20F65, 20F67, 20F06, 57M27, 20E26     

Additivity of the two-dimensional Miller ideal

Let J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is bigger than the covering number of the ideal of the meager subsets of ^ω ω. We also show that Martin’s Axiom implies that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is 2 ^ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of \mathfrakP(w)/fin{\mathfrak{P}{(\omega)}/{\rm fin}} .     

Generalized connected sum construction for scalar flat metrics

In this paper we construct constant scalar curvature metrics on the generalized connected sum M = M₁  \sharp_K  M₂{M = M_1 \, \sharp_K \, M_2} of two compact Riemannian scalar flat manifolds (M ₁, g ₁) and (M ₂, g ₂) along a common Riemannian submanifold (K, g _K ) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M ₁ and M ₂. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the (1₊) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction.     

Rigid geometric structures,isometric actions,and algebraic quotients

By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure σ. It generalizes Gromov’s centralizer and representation theorems to the case where R(G) is split solvable and G/R(G) has no compact factors, strengthens a special case of Gromov’s open dense orbit theorem, and implies that for smooth M and simple G, if Gromov’s representation theorem does not hold, then the local Killing fields on [(M)\tilde]{\widetilde{M}} are highly non-extendable. As applications of the generalized centralizer and representation theorems, we prove (1) a structural property of Iso(M) for simply connected compact analytic M with unimodular σ, (2) three results illustrating the phenomenon that if G is split solvable and large then π ₁(M) is also large, and (3) two fixed point theorems for split solvable G and compact analytic M with non-unimodular σ.     

A Simple Proof of Perelman’s Collapsing Theorem for 3-manifolds

We will simplify earlier proofs of Perelman’s collapsing theorem for 3-manifolds given by Shioya–Yamaguchi (J. Differ. Geom. 56:1–66, 2000; Math. Ann. 333: 131–155, 2005) and Morgan–Tian ( [math.DG], 2008). A version of Perelman’s collapsing theorem states: “Let {M³_i}\{M^{3}_{i}\} be a sequence of compact Riemannian 3-manifolds with curvature bounded from below by (−1) and $\mathrm{diam}(M^{3}_{i})\ge c_{0}>0$\mathrm{diam}(M^{3}_{i})\ge c_{0}>0 . Suppose that all unit metric balls in M³_iM^{3}_{i} have very small volume, at most v _i →0 as i→∞, and suppose that either M³_iM^{3}_{i} is closed or has possibly convex incompressible toral boundary. Then M³_iM^{3}_{i} must be a graph manifold for sufficiently large i”. This result can be viewed as an extension of the implicit function theorem. Among other things, we apply Perelman’s critical point theory (i.e., multiple conic singularity theory and his fibration theory) to Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds.