Search for physiologically active compounds

7-Hydroxy-3-methyl 4-phenylcoumarin andα-methyl dihydrofurano,α andγ-pyrono ring systems have been built on 7, 8-position of 4-phenylcoumarin. The bacteriostatic activity of these compounds as well as that of mammeisin and mesuol isolated fromMesua ferrea seeds has been evaluated. Structure-activity relationship among these compounds is discussed.     

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.     

Search for physiologically active compounds

α-Methyldihydrofurano,γ andα-pyrono ring systems have been built on 7, 8-position of 2-(2-furyl)-3-methyl chromone. The structure-activity relationship among 2-(2-furyl)-chromones is discussed.     

Heats of combustion of some symmetrical dialkyl ureas and their corresponding alkyl carbamates

The standard heats of combustion of the disubstituted ureas, N, N′-diheptyl urea, N, N′-dioctyl urea and N, N′-didecyl urea and the carbamates,n-heptyl ammoniumn-heptyl carbamate,n-octylammoniumn-octyl carbamate andn-decyl ammoniumn-decyl carbamate have been determined. The values found are 2353±1·3, 2658·4±1·1, 3268·5±1·7, 2349·8±1·6, 2654·4±1·2, 3264·6±1·8, K.cals. mole^?1 respectively. The heats of formation of these compounds have been calculated.     

Synthesis of some chromono (7, 8) oxazoles and their antibacterial activity

The synthesis of a few 2-substituted aryl-8-methyl-chromono (7, 8) oxazoles is described. A study of the antibacterial activities of these compounds has revealed that 2-(p-nitrophenyl) 8-methyl-chromono (7, 8) oxazole is active in 1 in 10,000 parts concentration.     

Search for physiologically active compounds

The synthesis of a few (7, 8) oxazolo-flavones has been carried out starting from 7-hydroxy-8-amino flavone. The ultraviolet and infrared spectra of these new class of heterocyclic compounds have been studied. The anti-bacterial and anti-fungal activities of these compounds have been reported.     

Structure and analysis of some bands of theβ-system of PO molecule

Rotational analysis of (4–4), (7–6), (7–8) bands of the² Σ?² II _1/2 sub-system and (3–3) band of² Σ–² II _3/2 sub-system of theβ-system of PO have been made. Vibrational assignments of fifteen new bands of this system have also been reported.     

Classification of partitions of all triples on ten points into copies of Fano and affine planes

We continue our study of partitions of the full set of triples chosen from a v-set into copies of the Fano plane PG(2,2) (Fano partitions) or copies of the affine plane AG(2,3) (affine partitions) or into copies of both of these planes (mixed partitions). The smallest cases for which such partitions can occur are v=8 where Fano partitions exist, v=9 where affine partitions exist, and v=10 where both affine and mixed partitions exist. The Fano partitions for v=8 and the affine partitions for v=9 and 10 have been fully classified, into 11, two and 77 isomorphism classes, respectively. Here we classify (1) the sets of i pairwise disjoint affine planes for i=1,…,7, and (2) the mixed partitions for v=10 into their 22 isomorphism classes. We consider the ways in which these partitions relate to the large sets of AG(2,3).     

On non-antipodal binary completely regular codes

Binary non-antipodal completely regular codes are characterized. Using a result on nonexistence of nontrivial binary perfect codes, it is concluded that there are no unknown nontrivial non-antipodal completely regular binary codes with minimum distance d?3. The only such codes are halves and punctured halves of known binary perfect codes. Thus, new such codes with covering radius ρ=6 and 7 are obtained. In particular, a half of the binary Golay [23,12,7]-code is a new binary completely regular code with minimum distance d=8 and covering radius ρ=7. The punctured half of the Golay code is a new completely regular code with minimum distance d=7 and covering radius ρ=6. The new code with d=8 disproves the known conjecture of Neumaier, that the extended binary Golay [24,12,8]-code is the only binary completely regular code with d?8. Halves of binary perfect codes with Hamming parameters also provide an infinite family of binary completely regular codes with d=4 and ρ=3. Puncturing of these codes also provide an infinite family of binary completely regular codes with d=3 and ρ=2. Both these families of codes are well known, since they are uniformly packed in the narrow sense, or extended such codes. Some of these completely regular codes are new completely transitive codes.     

Multiple scattering measurements on high energy protons with long cell lengths

Scattering measurements on individual tracks and relative scattering measurements on pairs of tracks have been made in two stacks exposed to 6·2 and 5·7 BeV protons respectively from the Berkeley Bevatron. Spurious scattering was determined in these two stacks for cell lengths ranging from 1 mm. to 8 mm. In one stack the magnitude of spurious scattering was very low while in the other it was fairly high. Our results indicate that:

1. (a)
   Spurious scattering varies with cell lengtht, as t^x, wherex is about 0·8 fort = 1 mm. to 3 mm. and about 0·5 fort = 3 mm. to 8 mm.     
   
   

Monotonic positive solution of a nonlinear quadratic functional integral equation

The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in [4], [5], [6], [7] and [8]. Here we are concerning with a nonlinear quadratic integral equation of Volterra type and we shall prove the existence of at least one L₁-positive monotonic solution for that equation under Carathèodory condition.     

Synthesis of benzodipyrandiones

The reaction of hydroxycoumarins, flavones, isoflavones and chromones with α, β-unsaturated acids, in the presence of PPA has been found to give a number of compounds whose structures have been elucidated on the basis of spectral data and the formation of 2, 4-DNP derivatives.     

On the Orthogonal Tableaux of Koike and Terada

Many different definitions have been given for semistandard odd and even orthogonal tableaux which enumerate the corresponding irreducible orthogonal characters. Weightpreserving bijections have been provided between some of these sets of tableaux (see [3], [8]). We give bijections between the (semistandard) odd orthogonal Koike-Terada tableaux and the odd orthogonal Sundaram-tableaux and between the even orthogonal Koike-Terada tableaux and the even orthogonal King-Welsh tableaux. As well, we define an even version of orthogonal Sundaram tableaux which enumerate the irreducible characters of O(2n).     

Vertex-transitive triangulations of compact orientable 2-manifolds

In this note we construct two infinite families of vertex-transitive triangulations of compact orientable 2-manifolds. Included in these families are two of the best known “classical” examples, viz., the triangulation of the genus 3 surface admitting the group PSL(2, 7) and the triangulation of the genus 7 surface admitting SL(2, 8).     

Synthetic investigation on testosterone and its analogues— II

The total synthesis of the anthracene analogue of 8-iso-19-nortestosterone has been described.dl-Dihydroequilenin and the ethylene ketal ofd-equilenin have been converted todl- andd-8-iso-17β-hydroxy-19-nor-androst-5 (10)-en-3-one respectively, which were isomerized todl- andd-8-iso-10-iso-19-nortestosterone, the ORD data of the latter confirming the configuration.     

Nonisomorphic Maximum Packing and Minimum Covering of K v with 8-Cycles

The maximum packing C ₈-max PD(v) and minimum covering C ₈-minCD(v) of K _v with 8-cycles are studied, all structures with the nonisomorphic leave (excess) are presented. In Li et al. (Graphs Combin 25:735–752, 2009), C ₈-max PD(v) and C ₈-minCD(v) have been determined for odd v. In this paper, we introduce the enumeration of nonisomorphic ${(v,\frac{v}{2}+s)}$ -graphs (s = 4, 6), give complete solution of the maximum packing and minimum covering designs of K _v with 8-cycles for any even v with all possible leaves (excesses).     

Magic square spectra

To study the eigenvalues of low order singular and non-singular magic squares we begin with some aspects of general square matrices. Additional properties follow for general semimagic squares (same row and column sums), with further properties for general magic squares (semimagic with same diagonal sums). Parameterizations of general magic squares for low orders are examined, including factorization of the linesum eigenvalue from the characteristic polynomial.For nth order natural magic squares with matrix elements 1,…,n² we find examples of some remarkably singular cases. All cases of the regular (or associative, or symmetric) type (antipodal pair sum of 1+n²) with n-1 zero eigenvalues have been found in the only complete sets of these squares (in fourth and fifth order). Both the Jordan form and singular value decomposition (SVD) have been useful in this study which examines examples up to 8th order.In fourth order these give examples illustrating a theorem by Mattingly that even order regular magic squares have a zero eigenvalue with odd algebraic multiplicity, m. We find 8 cases with m=3 which have a non-diagonal Jordan form. The regular group of 48 squares is completed by 40 squares with m=1, which are diagonable. A surprise finding is that the eigenvalues of 16 fourth order pandiagonal magic squares alternate between m=1, diagonable, and m=3, non-diagonable, on rotation by π/2. Two 8th order natural magic squares, one regular and the other pandiagonal, are also examined, found to have m=5, and to be diagonable.Mattingly also proved that odd order regular magic squares have a zero eigenvalue with even multiplicity, m=0,2,4,... Analyzing results for natural fifth order magic squares from exact backtracking calculations we find 652 with m=2, and four with m=4. There are also 20, 604 singular seventh order natural ultramagic (simultaneously regular and pandiagonal) squares with m=2, demonstrating that the co-existence of regularity and pandiagonality permits singularity. The singular odd order examples studied are all non-diagonable.     

Investigations on multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsions

The charge spectrum obtained from measurements made on tracks of 1329 nuclei of the cosmic radiation of Z?6 and E?7·5 GeV/n has been studied in detail using emulsion stacks exposed over Hyderabad, India (cut off rigidity=16·8 GV) at a depth of 6·8 g/cm² of air for 7¼ hrs. This spectrum has been compared with that available for nuclei of E≥1·5 GeV/n. Within the limits of experimental errors, no dependence of the flux values or ratios of intensities with energy are noticed. This result has important implications on the origin and history of the cosmic radiation. Integral energy spectra of M and H-nuclei have been derived making use of the flux values at the two locations; the spectra thus derived have the least errors associated with these.