Hamiltonization of theories with degenerate coordinates

We consider a class of Lagrangian theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it is reasonable to reconsider the conventional definition of singularity based on the usual Hessian and, moreover, to simplify the conventional hamiltonization procedure. In particular, in such a procedure, it is not necessary to complete the degenerate coordinates with the corresponding conjugate momenta.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

三氟化硼引发四氢呋喃聚合的研究——Ⅳ.1,4-丁二醇的影响

前报中已证明用三氟化硼-环氧氯丙烷(ECH)引发四氢呋喃(THF)聚合具有较高的引发效率,并对在Ac_2O、水和无水存在下的聚合反应进行了研究。本文报道1,4-丁二醇(BG)对BF_3引发THF聚合反应的影响。通常认为在BG存在下,BF_3是不能引发THF聚合的,但本工作证明BG是有效的分子量调节剂,制备分子量在     

Heterocyclization of 1,1-dicyano-2-(trifluoromethyl)ethylenes with 1,3,3-trimethyl-3,4-dihydroisoquinoline and its derivatives

1,3,3-Trimethyl-3,4-dihydroisoquinolines react with 1,1-dicyano-2,2-bis(trifluoromethyl)ethylene to give 4-amino-6,6-dimethyl-2,2-bis(trifluoromethyl)-3-cyano-6,7-dihydro-2H-benzo[a]quinolizines. The reaction of 3,3-dimethyl-1-cyanomethylidene-1,2,3,4-tetrahydroisoquinoline and the methyl ester of 3,3-dicyano-2-(trifluoromethyl)acrylic acid leads to 5,5-dimethyl-3-oxo-2-(trifluoromethyl)-2-(dicyanomethyl)-2,3,5,6-tetrahydropyrrolo[2,1-a]isoquinoline.A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 8, pp. 1888–1892, August, 1992.     

以硫醚为主链的螯合树脂研究Ⅳ．含硫代硫酸根、叠氮基树脂的合成及吸附性能

聚环硫氯丙烷或环硫氯丙烷与环氧氯丙烷共聚物，在少量二乙烯三胺存在下制得交联预聚物，将交联预聚物分别与硫代硫酸钠，叠氮化钠反应，制得四种侧链带有硫代硫酸根或叠氮基的新型螯合树脂。它们对贵金属离子具有较高的吸附容量和较好的吸附选择性。     

Generalized oscillator representations for generalized Calogero Hamiltonians

We construct generalized oscillator representations for all generalized Calogero Hamiltonians with the potential V (x) = g ₁ /x ² + g ₂ x ² , g ₁ ≥ ?1/4, g ₂ > 0. These representations are generically nonunique, but for each Hamiltonian, there exists an optimum representation explicitly determining the ground state and its energy. For generalized Calogero Hamiltonians with coupling constants g ₁ < ?1/4 or g ₂ < 0, generalized oscillator representations do not exist, which agrees with the fact that the corresponding Hamiltonians are not bounded from below.     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.     

IN AQUA SYNTHESIS OF A HIGH MOLECULAR WEIGHT ARYLETHYNYLENE POLYMER EXHIBITING REVERSIBLE HYDROGEL PROPERTIES

ABSTRACT

A high molecular weight poly(aryleneethynylene) (M_w ～ 60,000) is prepared by the palladium catalyzed copolymerization of 3,5-diiodobenzoic acid and acetylene gas in a basic aqueous medium. The polymer has a “zig-zag”, fully conjugated backbone. The polymer has been characterized by a variety of methods and exhibits high thermal stability. Furthermore, the polymer is readily soluble in aqueous base and is reversibly switchable from the solution state to a hydrogel state, in water, by changing the pH of the solvent.