Orthmodular lattices whose MacNeille completions are not orthomodular

The only known example of an orthomodular lattice (abbreviated: OML) whose MacNeille completion is not an OML has been noted independently by several authors, see Adams [1], and is based on a theorem of Ameniya and Araki [2]. This theorem states that for an inner product space V, if we consider the ortholattice ?(V,⊥) = {A \( \subseteq \) V: A = A ^⊥⊥} where A ^⊥ is the set of elements orthogonal to A, then ?(V,⊥) is an OML if and only if V is complete. Taking the orthomodular lattice L of finite or confinite dimensional subspaces of an incomplete inner product space V, the ortholattice ?(V,⊥) is a MacNeille completion of L which is not orthomodular. This does not answer the longstanding question Can every OML be embedded into a complete OML? as L can be embedded into the complete OML ?(V,⊥), where V is the completion of the inner product space V. Although the power of the Ameniya-Araki theorem makes the preceding example elegant to present, the ability to picture the situation is lost. In this paper, I present a simpler method to construct OMLs whose Macneille completions are not orthomodular. No use is made of the Ameniya-Araki theorem. Instead, this method is based on a construction introduced by Kalmbach [7] in which the Boolean algebras generated by the chains of a lattice are glued together to form an OML. A simple method to complete these OMLs is also given. The final section of this paper briefly covers some elementary properties of the Kalmbach construction. I have included this section because I feel that this construction may be quite useful for many purposes and virtually no literature has been written on it.     

Time-asymptotic boson states from infinite mean field quantum systems coupled to the boson gas

By means of cocycle techniques in a recent paper, the global dynamics of mean field-boson couplings has been studied. Here, by restricting to the bosonic system the infinite time limit (t ) for very general initial states, one obtains time-asymptotic states on the bosonicC ^*-Weyl algebra, in which one partially rediscovers the collective ordering of the infinite mean field lattice.     

Charge dynamics and optical properties of layered cobaltates

We study the charge dynamics and electronic structure by optical spectroscopy technique. Here we focus on the following four issues: (1) the evolution of optical spectra with Na content; (2) the spectral features specific to different regions in the phase diagram; (3) the c-axis optical response for crystal at the A-type antiferromagnetic region; (4) the optical response of misfit-layered Bi₂M₂Co₂O_y (M=Ba, Sr, Ca) and Ca₃Co₄O_y single crystals.     

Measurements on diproton emission from the break-up channels of ~(23)Al and ~(22)Mg

Two-proton relative momentum distributions from the break-up channels 23Al→p+p+21Na and 22Mg→p+p+20Ne at an energy of 60-70 A MeV have been measured together with two-proton opening angles at the projectile fragment separator beamline (RIPS) in the RIKEN Ring Cyclotron Facility. The results demonstrate the existence of diproton emission component from single-step 2He for highly excited 23Al and 22Mg.     

TrigonometricR matrices related to ‘dilute’ Birman-Wenzl-Murakami algebra

Explicit expressions for three series ofR matrices which are related to a dilute generalisation of the Birman-Wenzl-Murakami algebra are presented. Of those, one series is equivalent to the quantumR matrices of theD _n+1 ⁽²⁾ generalised Toda systems, whereas the remaining two series appear to be new.     

基于TMS320DM642的实时语音处理系统

设计了一种基于DSP的实时音频处理系统,介绍了音频解码芯片TLV320AIC23B的基本特点和使用方法,详细描述了该芯片与DM642的McASP接口的连接方式,使用了2个ping-pong缓存实现了输入和输出的匹配.该系统具有良好的通用性,可以广泛应用干各种音频处理应用.     

Synthesis and structure of novel derivatives of thieno[2,3-b]thiocine. An unusual product of intramolecular cycloaddition of 2-homomethallylthio-5-methyl-3-thiophenecarbonitrile oxide

9-Methyl-3,3a,4,5-tetrahydro-6H-thieno[2,3-b]thiocino[4,5-c]isoxazole and 9-hydroxyimino-2-methyl-7-methylene-6, 7,8,9-tetrahydro-5H-thieno[2,3-b]thiocine have been prepared for the first time by the oxidation of 2--alkenylthio-3-thiophenecarbaldoximes with NaOCl. X-ray structural investigations of thieno[2,3-b]thiocine and 2-homomethallylthio-5-methyl-3-thiophenecarbaldoxime have been carried out.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1262–1266, July, 1993.     

Synthesis of new pyridazino[4′,3′:4,5]-thieno[3,2-d]-1,2,3-triazine and pyrimido[4′,5′:4,5]thieno[2,3-c]pyridazine derivatives

Summary 8,9-Diphenylpyridazino[4,3:4,5]thieno[3,2-d]-1,2,3-triazin-4(3H)-one (2), 3-substituted 8,9-diphenylpyridazino[4,3:4,5]thieno[3,2-d]-1,2,3-triazin-4(3H)-ones (3a–c), 3,4-diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazin-8(7H)-one (4), 8-chloro-3,4-diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazine (5), 8-substituted 3,4-diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazines (6a–h) and 7-substituted 3,4-diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazin-8(7H)-ones(7a–c) were synthesized from 5-amino-3,4-diphenylthieno[2,3-c]pyridazine-6-carboxamide (1).

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Synthese neuer Pyridazino[4,3:4,5]thieno[3,2-d]-1,2,3-triazin-und Pyrimido[4,5:4,5]thieno[2,3-c]pyridazin-Derivate

Zusammenfassung Folgende Verbindungen wurden ausgehend von 5-Amino-3,4-diphenylthieno[2,3-c]pyridazin-6-carboxamid (1) synthetisiert: 8,9-Diphenylpyridazino[4,3:4,5]thieno[3,2-d]-1,2,3-triazin-4(3H)-on (2), 3-substituierte 8,9-Diphenylpyridazino[4,3:4,5]thieno[3,2-d]-1,2,3-triazin-4(3H)-one (3a–c), 3,4-Diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazin-8[7H]-on (4), 8-Chlor-3,4-diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazin (5), 8-substituierte 3,4-Diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazine (6a–h) und 7-substituierte 3,4-Diphenylpyrimido[4,5:4,5]thieno[2,3-c]pyridazin-8(7H)-one (7a–c).

     

Comments on the electronic properties of cyclopropane,cyclobutane, and cyclohexane

Spectral quantities of cyclopropane, cyclobutane, cyclohexane, and of several derivatives, have been calculated by a semiempirical all-valence electron SCF-CI MO method. In cyclopropane, HOMO is practically localized in the carbon-frame, and LVMO is purely so. In cyclobutane, these two MO's are based on C-H bonds, while cyclohexane holds an intermediate position. Despite the overall similarity-experimental and computed-of the spectra of these molecules, assignments are non-parallel. Like cyclopropane, cyclobutane can extend conjugation, but to a diminished degree; cyclohexane behaves in this respect like an acyclic alkane. An interpretation of this gradation, in terms of the nature of high-lying MO's, is proposed.     

Triterpene glycosides from Pulsatilla chinensis

Four triterpene glycosides were isolated from the roots of Pulsatilla chinensis (Bunge) Regel (Ranunculaceae). Two new glycosides, chinensiosides A (1a) and B (2), were identified as 3-O-[-L-rhamnopyranosyl-(12)--L-arabinopyranosyl]-28-O-[-L-rhamnopyranosyl-(14)--D-glucopyranosyl-(16)--D-glucopyranosyl]-3,23-dihydroxylup-20(29)-en-28-oic acid and 3-O-{-L-rhamnopyranosyl-(12)-[-D-glucopyranosyl-(14)]--L-arabinopyranosyl}-28-O-[-L-rhamnopyranosyl-(14)--D-glucopyranosyl-(16)--D-glucopyranosyl]-3,23-dihydroxylup-20(29)-en-28-oic acid. The other two glycosides were identified as previously known hederasaponin C (3) from Hedera helix and glycoside III (4) from Pulsatilla cernua.