A series of search designs for 2m factorial designs of resolution V which permit search of one or two unknown extra three-factor interactions

In the absence of four-factor and higher order interactions, we present a series of search designs for 2^m factorials (m6) which allow the search of at most k (=1,2) nonnegligible three-factor interactions, and the estimation of them along with the general mean, main effects and two-factor interactions. These designs are derived from balanced arrays of strength 6. In particular, the nonisomorphic weighted graphs with 4 vertices in which two distinct vertices are assigned with integer weight (13), are useful in obtaining search designs for k=2. Furthermore, it is shown that a search design obtained for each m6 is of the minimum number of treatments among balanced arrays of strenth 6. By modifying the results for m6, we also present a search design for m=5 and k=2.     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

On the equation of similar profiles

Summary Considerf+ ff+ (1–f²)+ f=0 together with the boundary conditionsf(0)=f(0)=0,f ()=1. If=–1,>0, arbitrary there is at least one solution which satisfies 0<f<1 on (0, ). By the additional conditionf>0 on (0, ) or, alternately 0<1, the uniqueness of the solution is demonstrated.If=1,<0, arbitrary the existence of solutions for which –1<f<0 in some initial interval (0,t) and satisfying generallyf>1 is established. In both problems, bounds forf (0) and qualitative behavior of the solutions are shown.

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Sommario Si consideri il problema definito dall'equazionef+ f f+ (1–f²)+ f=0 e dalle condizioni al contornof(0)=f (0)=0,f()=1. Assumendo=–1,>0, arbitrario si dimostra che esiste almeno una soluzione che soddisfa 0<f<1 nell'intervallo (0, ). Se in aggiunta si ipotizzaf>0 in (0, ), oppure 0<=1, l'unicità délia soluzione è assicurata.Successivamente si considéra il problema di valori al contorno con=1,<0, arbitrario. In questo caso esiste un'intera classe di soluzioni che soddisfano –1<f<0 in un intorno dell'origine e tali chef>1, in generale.Di detti problemi viene studiato il comportamento délle soluzioni e vengono determinate dalle maggiorazioni e minorazioni del valoref(0).

     

Absolut stetige Maße auf lokalkompakten Halbgruppen

LetS be a locally compact semigroup. It is shown that if a measure is absolutely continuous and ifS is cancellative, then the measure concentrated on a Borel subsetB ofS (i. e. =(B.)) is also absolutely continuous. Other properties of absolutely continuous measures will be obtained. Moreover we will answer the question when absolutely continuous probability measures exist. This is the case ifS admits an invariant integral on the space of all continuous functions onS with compact support. Another result is the following: If the compact semigroupS has a connected kernel then there exist absolutely continuous probability measures if and only ifS is amenable.     

Embeddings of Banach Spaces Into Banach Lattices and the Gordon–Lewis Property

In this paper we first show that if X is a Banach space and is a left invariant crossnorm on lX, then there is a Banach lattice L and an isometric embedding J of X into L, so that I J becomes an isometry of lX onto l_m J(X). Here I denotes the identity operator on l and l_m J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices.     

On convex multipliers of convergence of some classes of bivariate fourier series

- ()N²,L _F ( ) — , 2- , {s _m() f} -L. — . (L _F( ),L _F( ) ={(k)} (kZ²) , fL_F( ) f , , L _F( ). - ={()} ={()} , n(())m()n(()+()) . R() , .. - . , . (L _F ( ),L _F ( )) , R(,)=O(1) (x).

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The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper.     

Bounds for optimalα-β binary trees

In this paper we consider a special kind of binary trees where each right edge is associated with a positive number and each left edge with a positive number( ). Given, and the number of nodesn, an optimal tree is one which minimizes the total weighted path length. An algorithm for constructing an optimal tree for given, , n is presented, based on which bounds for balances and total weighted path lengths of optimal trees are derived.     

The convolution operator in weighted spaces with asymptotic conditions

We consider the operation of convolution with a homogeneous function in ^m that has a discontinuity on the subspace ^m–n , 1 n m–1.We exhibit a scale of weighted function spaces in which the convolution is continuous. The weight function is taken as a certain power of the distance to ^m–n.Bibliography: 5 titles. Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 186–213.     

On the Structure of Cimpact Simply Connected Manifolds of Positive Sectional Curvature

We present a first structure theorem for compact simply connected positively curved manifolds with arbitrarily small pinching constants: For each nN and 0<1, there exists a positive number V = V(n,) such that if (M,g) is a compact simply connected n-dimensional Riemannian manifold with sectional curvature 0相似文献   

Some functional inequalities and their Baire category properties

Summary In the paper we consider, from a topological point of view, the set of all continuous functionsf:I I for which the unique continuous solution:I – [0, ) of(f(x)) (x, (x)) and(x, (x)) (f(x)) (x, (x)), respectively, is the zero function. We obtain also some corollaries on the qualitative theory of the functional equation(f(x)) = g(x, (x)). No assumption on the iterative behaviour off is imposed.     

Markuševič decompositions and quasireflexivity of Banach spaces

. , , . .     

Minimal Blocking Sets in Projective Spaces of Square Order

In this paper minimal m-blocking sets of cardinality at most in projective spaces PG(n,q) of square order q, q 16, are characterized to be (t, 2(m-t-1))-cones for some t with . In particular we will find the smallest m-blocking sets that generate the whole space PG(n,q) for 2m n m.     

Block LU factorization is stable for block matrices whose inverses are block diagonally dominant

Let A M_n (C) and let the inverse matrix B = A^–1 be block diagonally dominant by rows (columns) w.r.t. an m × m block partitioning and a matrix norm. We show that A possesses a block LU factorization w.r.t. the same block partitioning, and the growth factor for A in this factorization is bounded above by 1 + , where = max _{1im i} and _i, 0 _i 1, are the row (column) block dominance factors of B. Further, the off-diagonal blocks of A (and of its block Schur complements) satisfy the inequalities

The geometric structure of Chebyshev sets in ℓ<Superscript>∞</Superscript>(<Emphasis Type="Italic">n</Emphasis>)

A subset M of a normed linear space X is called a Chebyshev set if each x X has a unique nearest point in M. We characterize Chebyshev sets in (n) in geometric terms and study the approximative properties of sections of Chebyshev sets, suns, and strict suns in (n) by coordinate subspaces.__________Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 1–10, 2005Original Russian Text Copyright © by A. R. AlimovSupported by RFBR grant No.02-01-00248.Translated by A. R. Alimov     

A note on threshold theorems for epidemics with bunching

This note begins by reviewing the Kermack-McKendrick and Whittle Threshold Theorems for the general epidemic. It then extends these results to the case of the general epidemic with bunching where thexy homogeneous mixing term is replaced byxy/(x+y), 01.Research supported by Office of Naval Research Contract N00014-84-K-0568.     

Notes on best constants in some Sobolev inequalities

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Liftings for abstract valued functions and separable stochastic processes

Summary In this paper we extend the notion of lifting from real-valued functions to abstract-valued functions (functions with values in a completely regular space). We prove the existence and uniqueness of the abstract lifting associated with a given real lifting. As an application we show that given a stochastic process with values in a completely regular space, the modification of this process obtained by applying a lifting is always separable.Research supported by the U.S. Army Research Office (Durham) under contract DA-31-124-ARO(D)-288.     

Über die Häufigkeit großer Differenzen konsekutiver Primzahlen

The following theorem is going to be proved. Letp _m be them-th prime and putd _m :=p _m+1–p _m . LetN(,T), 1/21,T3. denote the number of zeros =+i of the Riemann zeta function which fulfill and ||T. Letc2 andh0 be constants such thatN(,T)T ^c(1–) (logT) ^h holds true uniformly in 1/21. Let >0 be given. Then there is some constantK>0 such that      

Non removable edges in 3-connected cubic graphs

LetG be a cyclicallyk-edge-connected cubic graph withk 3. Lete be an edge ofG. LetG be the cubic graph obtained fromG by deletinge and its end vertices. The edgee is said to bek-removable ifG is also cyclicallyk-edge-connected. Let us denote by S _k (G) the graph induced by thek-removable edges and by N _k (G) the graph induced by the non 3-removable edges ofG. In a previous paper [7], we have proved that N ₃(G) is empty if and only ifG is cyclically 4-edge connected and that if N ₃(G) is not empty then it is a forest containing at least three trees. Andersen, Fleischner and Jackson [1] and, independently, McCuaig [11] studied N ₄(G). Here, we study the structure of N _k (G) fork 5 and we give some constructions of graphs such thatN _k (G) = E(G). We note that the main result of this paper (Theorem 5) has been announced independently by McCuaig [11].

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Résumé SoitG un graphe cubique cyliquementk-arête-connexe, aveck 3. Soite une arête deG et soitG le graphe cubique obtenu à partir deG en supprimante et ses extrémités. L'arêtee est ditek-suppressible siG est aussi cycliquementk-arête-connexe. Désignons par S _k (G) le graphe induit par les arêtesk-suppressibles et par N _k (G) celui induit par les arêtes nonk-suppressibles. Dans un précédent article [7], nous avons montré que N ₃(G) est vide si et seulement siG est cycliquement 4-arête-connexe et que si N ₃(G) n'est pas vide alors c'est une forêt possédant au moins trois arbres. Andersen, Fleischner and Jackson [1] et, indépendemment, McCuaig [11] ont étudié N ₄(G). Ici, nous étudions la structure de N _k (G) pourk 5 et nous donnons des constructions de graphes pour lesquelsN _k (G) = E(G). Nous signalons que le résultat principal de cet article (Théorème 5) a été annoncé indépendamment par McCuaig [11].

     

О числе Делителей “Сдвинутых” Простых чисел-Близнецов

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