Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

Optimization of the Production Medium for Biosynthesis of Antifungal Antibiotic Ak-111-81 by Phosphate-Deregulated Mutant of <Emphasis Type="Italic">Streptomyces hygroscopicus</Emphasis>

Experimental mathematical designs were applied for optimization of a nutrient medium for biosynthesis of the antifungal antibiotic AK-111-81 by phosphate-deregulated mutant of Streptomyces hygroscopicus 111-81. Antifungal antibiotic AK-111-81 possesses well-expressed activity against Fusarium graminearum and other phytopathogenic fungi. The level of the production of the antibiotic AK-111-81 on this medium is more than three times higher than on the initial medium. The optimized quantitative composition of the nutrient culture media is (g/l): glucose, 20; soy meal, 18; ammonium succinate, 3; CaCO₃, 1.     

Formation of hexagonal shaped wurtzite zinc sulphide nano rods

Zinc sulfide nanorods with good photoluminescence have been successfully fabricated using a simple sol-gel process via ultrasonication, with mercaptoethanol as capping agent. The formation of ZnS nucleation, followed by subsequent growth, is significant in obtaining highly oriented ZnS nanorods. Temperature, time, and capping agent also proved to be significant factors in the growth of ZnS nanorods and greatly affect their photo luminescent properties. X-ray diffraction (XRD) analysis, low and high-resolution transmission electron microscopy (TEM & HRTEM), selected-area electron diffraction (SAED) pattern, and scanning electron microscopy (SEM) indicated that the ZnS nanorods were single crystal in nature and that they had grown up preferentially along the [0001] direction. This simple method of nucleation, followed by their successive growth, resulted in the development of an effective and low-cost fabrication process for high-quality ZnS nanorods with good photo luminescent properties that can be applied to luminescent sensors and optoelectronic devices.     

Functional integration and gauge ambiguities in generalized abelian gauge theories

We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n$n$-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger–Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger–Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized p$p$-form Maxwell theory closed expressions for all physical observables are obtained. The Green’s functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operator for singular p$p$-cycles of the manifold, are computed and selection rules are derived.     

Number of Bound States of Schrödinger Operators with Matrix-Valued Potentials

We give a Cwikel–Lieb–Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

R245fa基于MH81方程的热物性计算模型

R245fa作为替代CFC的新型工质,在高温热泵,低温发电系统等工程领域中有着广泛的使用。为满足仿真计算的需要,提出一种基于MH81方程的R245fa物性计算模型。该模型在过热区符合良好,在过冷区修正为六参数的拟合式之后,其精度与过热区相当。将计算式与物性数据进行对比,结果表明平均相对误差小于8%,最大相对误差小于13%。     

Casimir effect in source theory III

A proper-energy method is used to find the energy of attraction between two dielectric slabs. Independent derivations of the attractive force are also presented.     

A time- and spaceadaptive algorithm for the linear time-dependent Schrödinger equation

Summary. We prove an a posteriori error estimate for the linear time-dependent Schr?dinger equation in . From this, we derive a residual based local error estimator that allows us to adjust the mesh and the time step size in order to obtain a numerical solution with a prescribed accuracy. As a special feature, the error estimator controls localization and size of the finite computational domain in each time step. An algorithm is described to compute this solution and numerical results in one space dimension are included. Received March 17, 1995