超模的同构定理

本文利用模论导出超模的三个同构定理,同时,给出超模的Jordan-Holder定理,最后,探讨了超模的基本关系∈~*,并研究其性质．     

Spinor Field Nonlinearity and Space-Time Geometry

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI₀ type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI₀ type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI(LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Nonlinear Spinor Fields in Bianchi type-III Spacetime

Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In this case the spacetime remains locally rotationally symmetric and anisotropic all the time. It is found that depending on the sign of nonlinearity the models allows both accelerated and oscillatory modes of expansion. The non-diagonal components of energy-momentum tensor though impose some restrictions on metric functions and components of spinor field, unlike Bianchi type I, V and V I ₀ cases, they do not lead to vanishing mass and nonlinear terms of the spinor field.     

Synthesis,characterization and reactivity of electrophilic mono- and binuclear nitrosyls of osmium(II)ketoximates

The reaction of [OsX₂(HL)(L)] (1) {X = Cl or Br; HL = PhC(O)C(=NOH)Ph (HL¹) or PhC(O)C(=NOH)Me (HL2)] with n-BuONO yields mononuclear [OsX(NO)(L¹)₂] (2) or binuclear [OsX₂(NO)(L²)]₂2 (3) nitrosyls depending on L. The complexes are also obtained by reacting (1) with NaNO₂ plus HCl. Molecular weight determinations are in agreement with mono- and binuclear formulations. The diamagnetic orange-red nitrosyls exhibit (NO) at ca. 1890 cm^–1 indicating NO⁺ character of the bound nitrogen monoxide. In ¹H-n.m.r. a single sharp L² methyl signal is in line with the centrosymmetric geometry (4) of the binuclear nitrosyls. The complexes display both spin-allowed and -forbidden charge transfer transitions in the 1000–200 nm range. Both (2) and (3) are electroactive and reductions characteristic of mono- and binuclear compositions are observable on the negative side of s.c.e. They react smoothly with acetylacetone (acacH) in the presence of K2CO3 yielding K[Os(acamo)(L1)2] (5) and K[Os(acac)(acamo)(L2)] (6) [acamo = deprotonated MeC(O)C(=NOH)C(O)Me] respectively.     

Characterization of Acid-Induced Partially Folded Conformation Resembling a Molten Globule State of Polygalacturonase from a Filamentous Fungus <Emphasis Type="Italic">Tetracoccosporium</Emphasis> sp.

Acid-induced unfolding of a Tetracoccosporium sp. polygalacturonase enzyme (PG) was studied by a comprehensive series of biophysical and biochemical techniques. At pH 1.0, PG acquires partially folded state, which reveals characteristics of molten globule (MG) state, i.e., reduction of defined tertiary structure with minimal changes in the secondary structure. In this study PG unfolds exposing its hydrophobic surface to a greater extent than the native form at acidic pH with more tryptophan residues exposed to the solvent. Collectively, our data imply the presence of MG state of PG at low pH, suggesting the phenomenon of hydrophobic collapse model for folding and integration into cell membrane.     

Transition Metal Ions or Acid-induced Suppression of Photoinduced Proton Transfer and Electron Transfer Reaction in 5-(4-Fluorophenyl)-2-hydroxypyridine: A Molecule of Dual Mode Fluorosensitivity

The photophysical properties of 5-(4-fluorophenyl)-2-hydroxypyridine (FP2HP) at different pH and its fluorescence response toward different transition metal ions have been studied by steady-state absorption and emission spectroscopy in combination with quantum chemical calculations. Although keto-enol tautomerization is observed in the excited state, the molecule is weakly fluorescent due to the presence of electron-rich nitrogen atom and relatively electron-deficient fluorine atom, which may lead to photoinduced electron transfer process. In the presence of the transition metal ions, such as Zn²⁺, Cd²⁺, Hg²⁺, etc., the studied molecule exhibits changes in its absorption and emission properties. The present system shows fluorescence enhancement instead of usual quenching in presence of the transition metal ions, such as Fe²⁺ and Cu²⁺. Spectral observation leads to the interpretation that this structurally simple molecule can be effectively utilized as a chelation-enhanced fluorescence-based chemosensor for the detection of transition metal ions. The experimental findings corroborate well with theoretical calculations at Hartree–Fock level using 6-31G** and lanl2dz basis sets.     

Design and optimization of on-chip capillary electrophoresis

We present a systematic, experimentally validated method of designing electrokinetic injections for on-chip capillary electrophoresis applications. This method can be used to predict point-wise and charge-coupled device (CCD)-imaged electropherograms using estimates of species mobilities, diffusivities and initial sample plug parameters. A simple Taylor dispersion model is used to characterize electrophoretic separations in terms of resolution and signal-to-noise ratio (SNR). Detection convolutions using Gaussian and Boxcar detector response functions are used to relate optimal conditions for resolution and signal as a function of relevant system parameters including electroosmotic mobility, sample injection length, detector length scale, and the length-to-detector. Analytical solutions show a tradeoff between signal-to-noise ratio and resolution with respect to dimensionless injection width and length to the detector. In contrast, there is no tradeoff with respect to the Peclet number as increases in Peclet number favor both SNR and separation solution (R). We validate our model with quantitative epifluorescence visualizations of electrophoretic separation experiments in a simple cross channel microchip. For the pure advection regime of dispersion, we use numerical simulations of the transient convective diffusion processes associated with electrokinetics together with an optimization algorithm to design a voltage control scheme which produces an injection plug that has minimal advective dispersion. We also validate this optimal injection scheme using fluorescence visualizations. These validations show that optimized voltage scheme produces injections with a standard deviation less than one-fifth of the width of the microchannel.     

One‐pot Synthesis of Octahydroqinazolinones Derivatives Catalyzed by [C4(mim)2](FeCl4)2 under Solvent Free Conditions

In this investigation, a practical green chemistry procedure for synthesis of octahydroqinazolinones and thiones derivatives via condensation of aldehyde, 1,3‐cyclohexanedione/dimedone and urea or thiourea catalyzed by magnetic room temperature dicationic liquid under solvent free conditions is described. The catalyst was studied by UV spectroscopy, vibrating sample magnetometer, and thermogravimetric analysis. This methodology is of interest due to several advantages such as environmental benign, easy experimental procedure, good yield and reusable catalyst.