Formation of heterocyclic rings containing nitrogen: Part XXVI—Condensation of pyridine 2, 3-diamine with aromatic aldehydes

Preparation of 3-arylideneamino-2-aminopyridines (I), 2-aryl-1H-2, 3-dihydroimidazo (4, 5-b) pyridines (III) and 2-aryl-1H-imidazo (4, 5-b) pyridines (IV), by the condensation of pyridine-2, 3-diamine with aromatic aldehydes under different conditions is described.     

Studies in the formation of heterocyclic rings containing nitrogen: Part XXIII. Condensation ofo-aminobenzamide with aldehydes and schiff bases

N-Arylidene orthanilamides undergo isomeric cyclisation in acetic acid to the corresponding 2-aryl-1, 2, 3, 4-tetrahydro-4-oxoquinazolines. The u.v. and n.m.r. spectra of some of the arylidene derivatives and their isomeric tetrahydroquinazolines have neeb studied. Condensation ofo-aminobenzamide either with aromatic aldehydes in nitrobenzene or Schiff bases in acetic acid has yielded 2-aryl-4 (3H)-quinazolinones.     

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.     

The D2Σ+ − X2Σ+ system of A10

Eleven bands of A10 belonging to the system (D² Σ ⁺-X² Σ ⁺) in the ultra-violet region have been analysed for their rotational structure. These are the 0-2, 1-3, 2-4, 0-3, 1-4, 3-0, 4-1, 3-1, 4-0, 5-1 and 6-1 bands lying at 2611.8Å, 2620.7Å, 2629.4Å, 2677.4Å, 2685.7Å, 2347.7Å, 2358.3Å, 2402.2Å, 2305.8Å, 2316.7Å and 2277.3Å respectively. The spin-splitting for the D² Σ ⁺ state has been determined from the doubling of the rotational lines observed for the bands 0-2, 1-3, 2-4 and 1-4. The rotational and vibrational constants (in cm^?1) evaluated for the D² Σ ⁺ state are: $$\begin{gathered} T_a = 40267 \cdot 6 \hfill \\ G(V) = 817 \cdot 47 (v + 1/2) - 4 \cdot 795 (v + 1/2)^2 - 0 \cdot 1107 (v + 1/2)^3 \hfill \\ B_v = 0 \cdot 56522 - 0 \cdot 0046 (v + 1/2) - 0 \cdot 00005 (v + 1/2)^2 \hfill \\ \gamma = 0 \cdot 004 \pm 0 \cdot 002 \hfill \\ \sigma = - 0 \cdot 4 \pm 0 \cdot 1 \times 10^{ - 6} \hfill \\ \end{gathered} $$      

Classifying 2-groups by coclass

Now that the conjectures of Leedham-Green and Newman have been proved, we probe deeper into the classification of -groups using coclass. We determine the pro--groups of coclass at most 3 and use these to classify the 2-groups of coclass at most 3 into families. Using extensive computational evidence, we make some detailed conjectures about the structure of these families. We also conjecture that the 2-groups of arbitrary fixed coclass exhibit similar behaviour.

     

A study of the Mannich reaction in the isoxazole series

3 : 5-Dimethyl-4-nitro isoxazole and 3-aryl-2-isoxazolin-5-ones were found to undergo the Mannich reaction readily at room temperature, affording in most cases unstable products. While the 5-methyl group was the active site with the former, the latter underwent reaction exclusively at the 4-position. The structures of the products were confirmed by spectral data. The Mannich bases from the isoxazolones were found to exist in three tautomeric modifications, contrary to earlier observations. Most of the products exhibited a high degree of antibacterial activity.     

Electron paramagnetic resonance of mn2+ in single crystals of Cesium Sulphate

Electron paramagnetic resonance (EPR) of divalent manganese ion has been studied at 9.5 KMc/sec. These studies reveal that Mn²⁺ ion substitutes at a β-Cs⁺ site and gets associated with a vacancy at a neighbouring β-Cs⁺ site in the aft-plane. Thez-axis of this ββ complex makes an angle of 25° with the crystallographicb-axis. The spectra observed have been described by the spin-Hamiltonian for Mn²⁺ in rhombic crystalline field. The temperature dependence of the parameters D and E has been studied in the range 293°–77° K. The spectra for the observed complex along its three-principal axes have been analysed using second order perturbation equations. The spin-Hamiltonian parameters obtained from the spectra taken at room temperature are: $$\begin{gathered} g_z = 2 \cdot 000 \pm 0 \cdot 003, g_x = 2 \cdot 015 \pm 0 \cdot 003, g_y = 2 \cdot 000 \pm 0 \cdot 003; \hfill \\ A_z = - 93 \pm 1, A_x = - 91 \pm 1, and A_y = - 91 \pm 1 G; \hfill \\ D = - 941 \pm 3 and E = - 14 \pm 4 G; \hfill \\ b^\circ _4 = \left( {0 \cdot 0} \right), b_4 ^2 = \left( {13} \right), and b_4 ^4 = - 77 \pm 5 G \hfill \\ \end{gathered} $$      

Cubic edge-transitive graphs of order $$2^np$$ 2 n p

Journal of Algebraic Combinatorics - Let p be a prime. Cubic edge-transitive graphs of order $$2^np$$ have been classified for $$1\le n\le 4$$ in the literature. This paper is devoted to a general...     

Rotational analysis of the C2Σ+ — X2Σ+ system of AlO

The 2-0, 1-0, 0-0 and 0-1 bands of the C²Σ⁺-X²Σ⁺ system of AlO, lying at 2391.88 Å, 2438.35 Å, 2487.32 Å and 2548.51 Å respectively were excited in a low pressure arc and photographed on a 6.6-metre concave grating spectrograph in the third order at a dispersion of 0.37 Å/mm. From the rotational analysis of these bands, the following constants have been determined: B_e′ = 0.565₃ cm.^?1 a_e′ = 0.004₈ cm.^?1 T_e =40267.0 cm.^?1 B_e″ = 0.641₃ cm.^?1 a_{″ = 0.005 7} cm.^?1     

The 2-(9, 4, 3) and 3-(10, 5, 3) designs

It is shown that there is a unique 2-(9, 4, 3) design with three different extensions to a 3-(10, 5, 3) design. Two of the extensions are isomorphic and have a further extension to the unique 4-(11, 6, 3) design. There is another 2-(9, 4, 3) design with just two extensions to a 3-design. There are 11 2-(9, 4, 3) designs in all, as announced by van Lint, et al. and Stanton et al. There are seven 3-(10, 5, 3) designs of which one is triply transitive, another transitive, and the rest are not transitive but are self-complementary. The transitive 3-designs each have one restriction to a 2-design. Of the non-transitive 3-designs 4 each have two restrictions and the fifth has three.     

The 2-characters of a group and the group determinant

A new look at Frobenius' original papers on character theory has produced the following: (a) the group determinant determines the group (Formanek-Sibley); (b) the group is determined by the 1-, 2- and 3-characters of the irreducible representations (Hoehnke-Johnson); and (c) pairs of non-isomorphic groups exist with the same irreducible 1- and 2-characters (Johnson-Sehgal). The examples produced in Johnson and Sehgal have large orders but, recently, McKay and Sibley have proved that the ten Brauer pairs of order 256 have the same irreducible 2-characters. It is shown here that the pairs of non-isomorphic groups of order p³, p and odd prime, have the same irreducible 2-characters. Further results are given on the k-characters of the regular representation/rod a shorter proof of the result mentioned in (c) is indicated. A criterion is given which is sufficient for the 3-character of an arbitrary representation to determine the group.     

On 2-(45, 12, 3) designs

Under the assumption that the incidence matrix of a 2-(45, 12, 3) design has a certain block structure, we determine completely the number of nonisomorphic designs involved. We discover 1136 such designs with trivial automorphism group. In addition we analyze all 2-(45, 12, 3) designs having an automorphism of order 5 or 11. Altogether, the total number of nonisomorphic 2-(45, 12, 3) designs found in 3752. Many of these designs are self-dual and each of these self-dual designs possess a polarity. Some have polarities with no absolute points, giving rise to strongly regular (45, 12, 3, 3) graphs. In total we discovered 58 pairwise nonisomorphic strongly regular graphs, one of which has a trivial automorphism group. Further, we analyzed completely all the designs for subdesigns with parameters 2-(12, 4, 3), 2-(9, 3, 3), and 2-(5, 4, 3). In the first case, the number of 2-(12, 4, 3) subdesigns that a design possessed, if non-zero, turned out to be a multiple of 3, whereas 2-(9, 3, 3) subdesigns were so abundant it was more unusual to find a design without them. Finally, in the case of 2-(5, 4, 3) subdesigns there is a design, unique amongst the ones discovered, that has precisely 9 such subdesigns and these form a partition of the point set of the design. This design has a transitive group of automorphisms of order 360. © 1996 John Wiley & Sons, Inc.     

β-delayed proton decays of 81Zr and 85Mo

β-delayed proton decays of Tz=1/2 series nuclei 81Zr and 85Mo have been studied in detail by using p-γ coincidence measurement. The β-delayed proton spectra populating the first excited states of the daughter nuclei have been obtained. Half-life of 81Zr has been measured to be 5.3 s±0.5 s and that of 85Mo 3.2 s±0.2 s. By using statistical model calculations and systematic analyses, spins and parities for the ground states of 81Zr and 85Mo have been tentatively assigned to be 3/2- and 1/2-, respectively. Mass excess of 81Zr is -58.3 MeV±0.2 MeV and that of 85Mo -59.1 MeV±0.4 MeV. Combining the measured half-lives with the calculated partial ones yields the branches of β-delayed proton decay for 81Zr and 85Mo of (1.2±0.2)×10-3 and (1.4±0.2)×10-3, respectively.     

Reactivity of 2-hydroxy-ω-nitroacetophenones: Synthesis of 2-oximinocoumaranones

2-Hydroxy-ω-nitroacetophenones prepared by the hydrolysis of 3-nitro-4-hydroxycoumarins were found to undergo a facile intramolecular cyclisation when heated with pyridine. The structures of the reaction products have been established by spectral characteristics and chemical methods as 2-oximinocoumaranones and comparison with an authentic synthetic sample in one case.     

A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

Numerical Algorithms - Null-space methods have long been used to solve large sparse n × n symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on...     

求解大型稀疏最小二乘问题的2—块PSD型迭代法

１引言假设Ａ为大型稀疏的ｍ×ｎ实矩阵（ｍ＞ｎ）,ｒａｎｋ（Ａ）＝ｎ,在实际中,常常需要求解Ａｘ＝ｂ,（１．１）其中ｂ为给定的ｍ维向量．求（１．１）的欧氏范数最小二乘解等价于求解其中ｒ为ｍ维向量,不失一般性,可令其中Ａ;为ｎ×ｎ满秩方阵,且把ｂ和ｒ也相应地分块为其中ｒ１和ｂ１都是ｎ维向量,用（１．３）和（１．４）的符号,（１．２）可写成等价形式如下相应的块Ｊａｃｏｂｉ迭代矩阵Ｂ２和Ｂ３,定义为Ｃ相应于ＢＬ的分块形式是Ｌ循环阵或是ＧＣＯ（１,Ｌ—１）阵或Ｔ（１,ｌ—１）阵,ＢＬ是指标为Ｌ的弱循环阵（…     

Characterization of allA-stable methods of order 2m-4

The characterization ofA-stable methods is often considered as a very difficult task (see e.g. [1]). In recent years, simple proofs have been found for methods of orderp2m-2 (see [2], [3], [7]). In this paper, we characterize theA-acceptable approximations of orderp 2m-4 and apply the result to 12-parameter families of implicit Runge-Kutta methods.     

自同构群基柱为~3D_4(q)的2-(v,k,1)设计

2-(v,k,1)设计的存在性问题是组合设计理论中重要的问题,当这类设计具有一个有意义自同构群时,讨论其存在性是尤其令人感兴趣的.30年前,一个6人团队基本上完成了旗传递的2-(v,k,1)设计分类.此后,人们开始致力于研究区传递但非旗传递的2-(v,k,1)设计的分类课题.本文证明了自同构群基柱为~3D_4(q)的区传递及点本原非旗传递的2-(v,k,1)设计是不存在的.     

2-Spreads and Transitive and Orthogonal 2-Parallelisms of PG(5, 2)

A 2-spread is a set of two-dimensional subspaces of PG(d, q), which partition the point set. We establish that up to equivalence there exists only one 2-spread of PG(5, 2). The order of the automorphism group preserving it is 10584. A 2-parallelism is a partition of the set of two-dimensional subspaces by 2-spreads. There is a one-to-one correspondence between the 2-parallelisms of PG(5, 2) and the resolutions of the 2-(63,7,15) design of the points and two-dimensional subspaces. Sarmiento (Graphs and Combinatorics 18(3):621–632, 2002) has classified 2-parallelisms of PG(5, 2), which are invariant under a point transitive cyclic group of order 63. We classify 2-parallelisms with automorphisms of order 31. Among them there are 92 2-parallelisms with full automorphism group of order 155, which is transitive on their 2-spreads. Johnson and Montinaro (Results Math 52(1–2):75–89, 2008) point out that no transitive t-parallelisms of PG(d, q) have been constructed for t > 1. The 92 transitive 2-parallelisms of PG(5, 2) are then the first known examples. We also check them for mutual orthogonality and present a set of ten mutually orthogonal resolutions of the geometric 2-(63,7,15) design.     

A characterization of Buekenhout-Metz unitals in PG(2, q 2), q even

The known examples of embedded unitals (i.e. Hermitian arcs) in PG(2, q ²) are B-unitals, i.e. they can be obtained from ovoids of PG(3, q) by a method due to Buekenhout. B-unitals arising from elliptic quadrics are called BM-unitals. Recently, BM-unitals have been classified and their collineation groups have been investigated. A new characterization is given in this paper. We also compute the linear collineation group fixing the B-unital arising from the Segre-Tits ovoid of PG(3, 2 ^r ), r3 odd. It turns out that this group is an Abelian group of order q ².Research supported by MURST.