Homotopical algebra in homotopical categories

We develop here a version of abstract homotopical algebra based onhomotopy kernels andcokernels, which are particular homotopy limits and colimits. These notions are introduced in anh-category, a sort of two-dimensional context more general than a 2-category, abstracting thenearly 2-categorical properties of topological spaces, continuous maps and homotopies. A setting which applies also, at different extents, to cubical or simplicial sets, chain complexes, chain algebras, ... and in which homotopical algebra can be established as a two-dimensional enrichment of homological algebra.Actually, a hierarchy of notions ofh-,h1-, ...h4-categories is introduced, through progressive enrichment of thevertical structure of homotopies, so that the strongest notion,h4-category, is a sort of relaxed 2-category. After investigating homotopy pullbacks and homotopical diagrammatical lemmas in these settings, we introduceright semihomotopical categories, ash-categories provided with terminal object and homotopy cokernels (mapping cones), andright homotopical categories, provided also with anh4-structure and verifying second-order regularity properties forh-cokernels.In these frames we study the Puppe sequence of a map, its comparison with the sequence of iterated homotopy cokernels and theh-cogroup structure of the suspension endofunctor. Left (semi-) homotopical categories, based on homotopy kernels, give the fibration sequence of a map and theh-group of loops. Finally, the self-dual notion of homotopical categories is considered, together with their stability properties.Lavoro esequito nell'ambito dei progetti di ricerca del MURST.     

Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Right distributive quasigroups on algebraic varieties

In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x ^–1 ax, fora , is an automorphism of (as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups.     

Dimension and entropy of a non-ergodic Markovian process and its relation to Rademacher Riesz Products

Given a Markov chain (not necessarily stationary or homogeneous) with finite state space and an initial distribution, we can construct a measure on the unit interval [0, 1]. In this work we examine the equality (up to a constant) of the Hausdorff dimension of and of a suitably defined entropy for the Markovian process. The results are applied to the so-called Rademacher-Riesz Products.     

Confirmation of far infrared laser assignments from CH3-deformation and CH3-rocking states of optically pumped methanol

High-resolution Fourier transform spectroscopy has been applied to confirm previously proposed assignments for nine far infrared (FIR) laser lines from the CH₃-deformation state of CH₃OH and one line from the CH₃-rocking state. Accurate frequencies are deduced for the observed and other predicted FIR laser transitions. FIR torsional branch frequencies in the ground state which were used in the confirmation are presented. Comments are also made on the OH-bending mode of CH₃OH.     

Carbon-13 Assignments and Revision of the Stereostructures of the Cadinanes 2-Hydroxy-8α-angeloyloxycalamenene and 2-Hydroxy-8α-hydroxycalamenene

The two known cadinanes 2-hydroxy-8α-hydroxycalamenene and 2-hydroxy-8α-angeloyloxycalamenene were isolated from a Louisiana population of Heterotheca subaxillaris.

Their ¹³C NMR spectra were fully assigned by the application of HETCOR, COLOC, COSY, NOESY and DEPT experiments. It was shown on the basis of NOESY experiments that both cadinanes require revision at the stereogenic centre C-7.     

Determination of NAD(P)H by A Bioluminescent Enzyme Fiber Optic Probe

Abstract

A fiber optic probe was interfaced to a photon counting system for the determination of nicotinamide adenine dinucleotide reduced [NAD(P)H] by a bioluminescence method. The reagents employed in a bacterial luciferase/flavin mononucleotide /decanal system were optimized. Attempts were made to increase the quantum yield of the system. Dodecanal, tridecanal, and tetradecanal were evaluated as alternative aldehyde reagents for decanal, and hydrogen peroxide was added to the system. Neither attempt increased the quantum yield of the system. However, a relatively low detection limit of 1.6 × 10^?9 M for NAD(P)H was obtained with a linear dynamic range of 3.8 orders of magnitude. These results demonstrate the sensitivity of this instrumentation and assay.     

氮－14远程核四极共振谱仪

为了满足检测与探头有一定距离的含氮化合物的核四极共振信号，本文研制了一台结构简单，造价低廉的核四极共振操测仪．它利用了脉冲付里叶变换技术，可将获得的核自由感应衰减信号或者回波信号进行相干累加．整个系统分硬件和软件两大部分．前者由射频脉冲放大器（约５００Ｗ脉冲输出功率），探头，接收机，ＭＣＳ－９６型单片机和ＰＣ机构成．后者由单片机上的脉冲序列程序与ＰＣ机上的数值信号处理程序组成．利用这台谱仪，可以在几十秒时间内得到距离探头线圈１０ｃｍ内的典型￣（１４）Ｎ样品的核四极共振谱．     

Methodik und Ergebnisse von Tracerexperimenten über katalytische Reaktionen von Kohlenwasserstoffen

Tracermethoden können wichtige Beiträge zur Aufklärung katalytischer Kohlenwasserstoffreaktionen liefern. In dieser Arbeit werden einige Ergebnisse mehrjähriger Untersuchungen mit ¹⁴C-markierten Verbindungen zusammenfassend dargestellt. Es wird speziell auf Benzenbildungsreaktionen bei der Leichtbenzin-Reformierung und auf Reaktionsmechanismen bei der Isomerísierung von C₈-Aromaten eingegangen.