Regiospecificity of nucleophilic substitution in 4,6-dinitro-1-phenyl-1H-indazole

The reactions of 4,6-dinitro-1-phenyl-1H-indazole with anionic nucleophiles RS^– and N₃ ^– lead to the regiospecific replacement of the nitro group at position 4. The reaction with N₂H₄·H₂O + FeCl₃ also results in reduction of only the 4-NO₂ group. Based on this fact, a procedure was developed for the preparation of previously unknown 3-unsubstituted 4-X-6-nitro-1-phenyl-1H-indazoles (X is a residue of a nucleophile or NH₂). Comparison of the data on the selective nucleophilic substitution (4-NO₂ group) in 3-Z-1-aryl-4,6-dinitro-1H-indazoles shows that in the case of Z = H, the regiospecificity of substitution is determined by the electronic effect of the annelated pyrazole ring.     

Production of submicron-size monodisperse polymer particles having aldehyde groups by the seeded aldol condensation polymerization of glutaraldehyde (II)

Submicron-size monodisperse polystyrene/polyglutaraldehyde (PS/PGLA) composite particles having aldehyde groups at the surfaces were produced by the seeded aldol condensation polymerization of glutaraldehyde at various temperatures of 040°C. Since a part of aldehyde groups was consumed by the Cannizzaro reaction (hemiacetal formation) as a intermolecular reaction of PGLA, the amount of aldehyde groups on PS/PGLA composite particles was varied by the competition between the aldol condensation reaction and the Cannizzaro reaction at the various temperatures.Part CXXXIX of the series Studies on Suspension and Emulsion     

A characterization ofL n (q) by the normalizers' orders of their sylow subgroups

LetG be a finite group. If for every primer, whereR ₁ Syl _r G andR ₂ Syl _r (L _n (q)), thenG L _n (q).     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Conjectures on the Quotient Ring by Diagonal Invariants

We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring in two sets of variables by the ideal generated by all S _n invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x ₁, ..., x _n} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.     

Stories about groups and sequences

The main theme of this article is that counting orbits of an infinite permutation group on finite subsets or tuples is very closely related to combinatorial enumeration; this point of view ties together various disparate stories. Among these are reconstruction problems, the relation between connected and arbitrary graphs, the enumeration of N-free posets, and some of the combinatorics of Stirling numbers.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

On representations of affine Kac-Moody groups and related loop groups

We demonstrate a one to one correspondence between the irreducible projective representations of an affine Kac-Moody group and those of the related loop group, which leads to the results that every non-trivial representation of an affine Kac-Moody group must have its degree greater than or equal to the rank of the group and that the equivalence appears if and only if the group is of type for some . Moreover the characteristics of the base fields for the non-trivial representations are found being always zero.

     

Algebraic surfaces with log canonical singularities and the fundamental groups of their smooth parts

Let be a log surface with at worst log canonical singularities and reduced boundary such that is nef and big. We shall prove that either has finite fundamental group or is affine-ruled. Moreover, and the structure of are determined in some sense when .

     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.