NMR studies of solvent-solute interactions of OH,SH and CH protons in dimethyl formamide and dimethyl acetamide

The H-bonding of CH₃OH, C₆H₅SH and CHCl₃ with N:N Dimethyl formamide and N:N Dimethyl acetamide has been studied using proton magnetic resonance. It has been observed that the strength of interaction is greater for dimethyl acetamide than for dimethyl formamide for the same solvent. For the same solute, however, the strength increases in the order chloroform, thiol and alcohol. The equilibrium constant for 1:1 complex of these solutes in the chloroform solvent has been estimated. In the case of benzene thiol, complex formation between the pi-electrons of the phenyl ring and the amides has been detected. It has also been observed that the exchange rate of OH proton of CH₃OH in the dimethyl formamide decreases considerably.     

Free group factors and factors with some decompositions

In this paper, we show that if type von Neumann factors have some decompositions introduced by Liming Ge and Sorin Popa, then these von Neumann factors are not isomorphic to free group factors . Thus we have proved the number defined by Ge and Popa bigger than 3 for all free group factors and we also extend some results of M. Stefan.

     

Subgroups of the general symplectic group containing the group of diagonal matrices

There are described the subgroups of the general symplectic group =GSp(2n, R) over a commutative semilocal ring R, containing the group of symplectic diagonal matrices. For each such subgroup P there is uniquely defined a symplectic D-net a such that ()pN(), where () is the net subgroup in corresponding to (cf. RZhMat, 1977, 5A288), and N() is its normalizer. The quotient group N × ()/() is calculated. There are also considered subgroups in Sp(2n, R). Analogous results for subgroups of the general linear group were obtained earlier in RZhMat, 1978, 9A237.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 31–47, 1980.     

On the structure of some group codes

In this paper, we study the following problem: Which characteristics does a codeC possess when the syntactic monoidsyn(C ^*) of the star closureC ^* ofC is a group? For a codeC, if the syntactic monoidsyn(C ^*) is a group, then we callC a group code. This definition of a group code is different from the one in [1] (see [1], 46–47). Schützenberger had characterized the structure of finite group codes and had proved thatC is a finite group code if and only ifC is a full uniform code (see [5], [8]). Fork-prefix andk-suffix codes withk≥2,k-infix,k-outfix,p-infix,s-infix, right semaphore codes and left semaphore codes, etc., we obtain similar results. It is proved that the above mentioned codes are group codes if and only if they are uniform codes.     

Every finite group is the automorphism group of some perfect code

In this paper we prove the every finite group is isomorphic to the full automorphism group of some perfect binary single error correcting code.     

Computer studies of interactions of particles with differing masses

In this paper a new type of modeling of physical phenomena is developed for systems of particles of differing masses. Initial value problems must be solved by means of modern, high speed digital computation. Of basic importance is a natural, self-reorganization property of any particle system so modeled. Extensive computer examples are given.     

On the fundamental group of some open manifolds

We study fundamental groups of noncompact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.     

On the Galois group of some Fuchsian systems

In this paper, we give a new result ofn the differential Galois theory of linear ordinary differential equations. In particular, we compute the differential Galois group for a special type of nonresonant Fuchsian system.     

Idempotents and the multiplicative group of some totally bounded rings

In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2^ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.     

On the fundamental group of hyperelliptic fibrations and some applications

We prove that for a hyperelliptic fibration on a surface of general type with irreducible fibers over a (possibly) non-complete curve, the image of the fundamental group of a general fiber in the fundamental group of the surface is finite. Examples show that the result is optimal. As a corollary of this result we prove two conjectures; the Shafarevich conjecture on holomorphic convexity for the universal cover of these surfaces, and a conjecture of Nori on the finiteness of the fundamental groups of some surfaces. We also prove a striking general result about the multiplicities of multiple fibers of a hyperelliptic fibration on a smooth, projective surface.     

Algebraic reflexivity of some subsets of the isometry group

Let X be a compact first countable space. In this paper we show that the set of isometries of C(X) that are involutions is algebraically reflexive. As a consequence of a recent work of Botelho and Jamison this leads to the conclusion that the set of generalized bi-circular projections on C(X) is also algebraically reflexive. We also consider these questions for the space C(X,E) where E is a uniformly convex Banach space.