Synthesis of some chromono (6, 7) oxazoles and their physiological activity

The synthesis of a few chromono (6, 7) oxazoles has been carried out by condensing 6-amino-8-bromo-7-hydroxy-2-methyl chromone with various aromatic aldehydes in nitrobenzene medium. The ultraviolet and infrared spectral characteristics of these compounds have been described. A study of antibacterial and antifungal activities of these compounds has revealed that 2-m-hydroxyphenyl-7-methyl-9-bromo-chromono (6, 7) oxazole and 2-p-Anisyl-7-methyl-9-bromo-chromono (6, 7) oxazole possess antifungal activity.     

The mixed irredundant Ramsey numbers t(3, 7) = 18 and t(3, 8) = 22

Abstract

The mixed irredundant Ramsey number t(m, n) is the smallest natural number t such that if the edges of the complete graph K_t on t vertices are arbitrarily bi-coloured using the colours blue and red, then necessarily either the subgraph induced by the blue edges has an irredundant set of cardinality m or the subgraph induced by the red edges has an independent set of cardinality n (or both). Previously it was known that 18 ≤ t(3, 7) ≤ 22 and 18 ≤ t(3, 8) ≤ 28. In this paper we prove that t(3, 7) = 18 and t(3, 8) = 22.     

Synthesis,spectra and physiological activity of pyrono (2, 3-e) benzoxazoles

A few 2-aryl and 2-heterocyclic substituted pyrono (2, 3-e) benzoxazoles have been synthesized by condensing 8-amino-7-hydroxy-2-methyl chromone with aromatic or heterocyclic carboxylic acids employing polyphosphoric acid as the condensing agent. The ultraviolet, infrared, NMR and mass spectra of these compounds have been presented. Antibacterial evaluation revealed that the 2-naphthyl and 2-(3-coumarinyl) derivatives exhibit considerable activity.     

Embeddings ofU 3(8),Sz(8) and the Rudvalis group in algebraic groups of typeE 7

Oblatum 5-XII-1991 & 24-II-1993     

An infinite family of antiprimitive cyclic codes supporting Steiner systems $$S(3,8, 7^m+1)$$ S ( 3 , 8 , 7 m + 1 )

Designs, Codes and Cryptography - Coding theory and combinatorial t-designs have close connections and interesting interplay. One of the major approaches to the construction of combinatorial...     

Existence of (2, 8) GWhD( v) and (4, 8) GWhD( v) with $${ v \equi v 0,1 (mod 8)}$$

(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional cases. For there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.      

Coeffective Numbers of Riemannian 8-Manifolds with Holonomy in Spin(7)

We introduce a differential complex of coeffective type for anySpin(7)-manifold M locally conformal to aRiemannian 8-manifold with holonomy contained in Spin(7).Local properties of this complex, such as ellipticity and acyclicity,are studied. The relationship between the coeffective cohomology ofM and the topology of the manifold is discussed in the caseof M having a subgroup of Spin(7) as aholonomy group.     

Minimal Blocking Sets in PG(2, 8) and Maximal Partial Spreads in PG(3, 8)

We prove that PG(2, 8) does not contain minimal blocking sets of size 14. Using this result we prove that 58 is the largest size for a maximal partial spread of PG(3, 8). This supports the conjecture that q ²–q+ 2 is the largest size for a maximal partial spread of PG(3, q), q>7.     

不动点集为RP(8)(U) P(8,2n-1)的对合

设(M,T)是一个带有光滑对合T的光滑闭流形,T的不动点集为RP(8)() P(8,2n-1).本文证明了(M,T)必协边于(RP(8)×RP(8),twist)和(P(8,RP(2n)),T')之一.     

Quasi-symmetric 2-(31, 7, 7) designs and a revision of Hamada's conjecture

It is proved by use of the classification of the doubly even (32, 16) codes, that in addition to the design formed by the planes in PG(4, 2), there are exactly four other nonisomorphic quasi-symmetric 2-(31, 7, 7) designs, and they all have 2-rank 16. This shows that the “only if” part of the following conjecture due to Hamada, is not true in general: “If N(D) is an incidence matrix of a design D with the parameters of a design G defined by the flats of a given dimension in PG(t, q) or AG(t, q), then rank_q N(D) ⩾ rank_q N(G), with equality if and only if D is isomorphic with G.” The five quasi-symmetric 2-(31, 7, 7) designs are extendable to nonisomorphic 3-(32, 8, 7) designs having 2-rank 16, one of which is formed by the 3-flats in AG(5, 2), thus the designs arising from a finite affine geometry also are not characterized by their ranks in general. A quasi-symmetric 2-(45, 9, 8) design yielding a pseudo-geometric strongly regular graph with parameters (r, k, t) = (15, 10, 6) is also constructed on the base of the known extremal doubly even (48, 24) code.     

On the Ramsey numbers R(3, 8) and R(3, 9)

Using methods developed by Graver and Yackel, and various computer algorithms, we show that 28 ≤ R(3, 8) ≤ 29, and R(3, 9) = 36, where R(k, l) is the classical Ramsey number for 2-coloring the edges of a complete graph.     

Formation constants of chelates of 7-nitro-8-hydroxyquinoline-5-sulphonic acid with yttrium and some lanthanides

Formation constants and thermodynamic parameters of chelation ΔF, ΔH and ΔS for chelates of 7-nitro-8-hydroxyquinoline-5-sulphonic acid with yttrium, lanthanum, praseodymium, neodymium, gadolinium, terbium, dysprosium and holmium are reported.     

Classification of the (n, 3)-arcs in PG(2, 7)

In this paper the classification of the (n, 3)-arcs in PG(2, 7) is presented. It has been obtained using a computer-based exhaustive search that exploits projective equivalence and produces exactly one representative of each equivalence class. For each (n, 3)-arc, the automorphism group and the maximal size of a contained k-arc have been found.