On Cesàro Means of Double Trigonometric Fourier Series

Zhizhiashvili studied questions associated with the approximation properties of Cesàro means of trigonometric Fourier series for functions of two variables in the spaces H. It is proved here that the corresponding estimate cannot be improved for p = 1 or p = .     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

A Modal Logic Based on Linearly Ordered f-Spaces

A modal logic associated with the -spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered -frames, and the class of all strictly linearly ordered -frames.     

Free and Sulfated Sterols of Two Far-East Leptasterias Starfish

NMR spectroscopy, capillary GLC, and GLC-MS are used to study the composition of free and sulfated sterols from the far-east starfishLeptasterias alaskensis asiatica(Fischer) andL. Fisheri(Djakonov). The total free sterols of both species are shown to have similar qualitative and quantitative compositions and contain mainly⁷ -sterols. Sterol sulfate fractions contain cholesterol sulfate as the main component but differ in the ratios of⁵ :⁰ :⁷ -sterol derivatives. Possible reasons for these differences are discussed. A new steroid, 3-hydroxycholest-5-en-7-one sulfate, was isolated.     

Novel Synthesis of 2β,3β,20β-Triacetoxy-5 -pregnan-6-one

Pregnenolone (2) is used in a novel synthesis of 2,3,20-triacetoxy-6-ketosteroid (6), a key intermediate in the preparation of 20-hydroxyecdysone (1)     

Chemical Composition of Certain Sedum Species of Kazakhstan

The chemical composition of sevenSedumspecies growing in Kazakhstan was studied by chromatography. The contents of seven groups of natural compounds were determined. Comparison with markers and literature data identified 24 compounds including 9 that have not been described previously inSedumspecies     

Partial Molar Volumes of Transfer of Some Amino Acids from Water to Aqueous Glycerol Solutions at 25°C

Apparent molar volumes of glycine, DL--alanine, L-valine, L-leucine, and L-phenylalanine in 0.5, 1.0, 2.0, 3.5, and 5.0 m _B (mol-kg^–1) aqueous solutions of glycerol have been obtained from solution densities at 25°C using precise vibrating-tube digital densimeter. The estimated partial molar volumes at infinite dilution V ^o ₂ have been used to obtain the corresponding transfer volumes _tr V ₂ ^o from water to different glycerol–water mixtures. The transfer volumes are positive for glycine and DL--alanine, and both positive and negative for the other amino acids over the concentration range studied. Interaction coefficients have been obtained from McMillan–Mayer approach and the data have been interpreted in terms of solute–cosolute interactions.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Pseudo-Anosov Flows and Incompressible Tori

We study incompressible tori in 3-manifolds supporting pseudo-Anosov flows and more generally ZZ subgroups of the fundamental group of such a manifold. If no element in this subgroup can be represented by a closed orbit of the pseudo-Anosov flow, we prove that the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus. In particular it is non singular and is an Anosov flow. It follows that either a pseudo-Anosov flow is topologically conjugate to a suspension Anosov flow, or any immersed incompressible torus can be realized as a free homotopy from a closed orbit of the flow to itself. The key tool is an analysis of group actions on non-Hausdorff trees, also known as R-order trees – we produce an invariant axis in the free action case. An application of these results is the following: suppose the manifold has an R-covered foliation transverse to a pseudo-Anosov flow. If the flow is not an R-covered Anosov flow, then it follows that the manifold is atoroidal.     

Function Spaces of Posets with Projections

This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p _i ) _iI ) with (D,) a poset and (p _i ) _iI a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D -construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus.