Diastereoselective Synthesis of Functionalized Tetrahydropyrimidin‐2‐thiones via ZnCl2 Promoted One‐pot Reactions

In the presence of zinc chloride, the in situ generated β‐enamino ester from the reaction of morpholine, piperidine and pyrrolidine with methyl propiolate reacted, with aromatic aldehydes and thiourea in ethanol resulting in the functionalized tetrahydropyrimidin‐2‐thiones in satisfactory yields and with good diastereoselectivity. When aromatic aldehydes bearing electron‐withdrawing group were used in the reaction, the 4‐hydroxytetrahydropyrimidin‐2‐thione derivatives were obtained as the main product.     

Synthesis of Functionalized 1‐Benzamido‐1,4‐dihydropyridines via a One‐Pot Two‐Step Four‐Component Reaction

The one‐pot four‐component reaction of benzohydrazide, acetylenedicarboxylate, aromatic aldehydes and malononitrile in ethanol with triethylamine as base catalyst afforded functionalized 1‐benzamido‐1,4‐dihydropyridines in satisfactory yields. Under similar conditions, picolinohydrazide or nicotinohydrazide can also be successfully utilized in the reactions to give corresponding functionalized 1,4‐dihydropyridines. ¹H NMR data indicated that an equilibrium of cis/trans‐conformations exist in 1‐benzamido‐1,4‐dihydropyridines.     

Multi-guasiparticle excitations of ~(91)Ru

The level structure in neutron-deficient nucleus 91Ru was investigated via the 58Ni(36Ar,2 plnγ)Ru reaction at a beam energy of 111 MeV.Charged particles,neutrons,and y-rays were emitted in this reaction and detected by the DIAMANT CsI ball,Neutron Wall,and the EXOGAM Ge clover array,respectively.In addition to the previously reported levels in 91Ru,new low-to-medium spin states were observed.Angular correlation and linear polarization measurements were performed to unambiguously determine spins and parities of the excited states in 91 Ru.The low-spin states of 91 Ru exhibit a scheme of multi-quasiparticle excitations,which is very similar to that of the neighboring N=47 isotone.These excitations have been interpreted in terms of the shell model.The calculations performed in the configuration space(p3/2,f5/2,p1/2,g9/2)reproduce the experimental excitation energies reasonably well,supporting the interpretation of the newly assigned positive-parity states in terms of the three quasiparticle configurationsπ(g9/2)^-2v(g9/2^-1 and v(g9/2)^-3.     

A strengthened Barvinok-Pataki bound on SDP rank

The Barvinok-Pataki bound provides an upper bound on the rank of extreme points of a spectrahedron. This bound depends solely on the number of affine constraints of the problem, i.e., on the algebra of the problem. Specifically, the triangular number of the rank r is upper bounded by the number of affine constraints. We revisit this bound and provide a strengthened upper bound on the rank using the singularity degree of the spectrahedron. Thus we bring in the geometry and stability of the spectrahedron, i.e., increased instability as seen by higher singularity degree, yields a lower, strengthened rank bound.     

具有三个公共值的亚纯函数(Ⅱ)

本文研究了具有三个公共值的亚纯函数的唯一性问题，改进了Ueda，H．,叶寿桢和仪洪勋的有关定理，并且纠正了Gross和Yang的一个结果．     

The Minimum Rank of a 3 × 3 Partial Block Matrix

After recalling the definition and some basic properties of finite hypergroups—a notion introduced in a recent paper by one of the authors—several non-trivial examples of such hypergroups are constructed. The examples typically consist of n n×n matrices, each of which is an appropriate polynomial in a certain tri-diagonal matrix. The crucial result required in the construction is the following: ‘let A be the matrix with ones on the super-and sub-diagonals, and with main diagonal given by a ₁…a _n which are non-negative integers that form either a non-decreasing or a symmetric unimodal sequence; then A_k =P_k (A) is a non-negative matrix, where p_k denotes the characteristic polynomial of the top k× k principal submatrix of A, for k=1,…,n. The matrices A_k as well as the eigenvalues of A, are explicitly described in some special cases, such as (i) a_i =0 for all ior (ii) a_i =0 for i<n and a_n =1. Characters ot finite abelian hypergroups are defined, and that naturally leads to harmonic analysis on such hypergroups.     

New inequalities for subspace arrangements

For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.     

分式化时模理论的一些稳定性性质的保持性

本文讨论了将分式环S－1R上的模归约到R上的模时包（hull）、类（class）、界（bound）、秩（rank）的保持性,证明了：1）NR是A在MR中的包当且仅当NS－1R是A在MS－1R中的包;2）还讨论了分式模（S－1M）S－1R与MR之间上述性质存在单向或双向保持性的条件．     

On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem

Let A be a u by v matrix, and let M and N be u by p and v by q matrices, where p may not be equal to q or rank(M^′AN)<min(p,q). Recently, Galantai [A. Galantai, A note on the generalized rank reduction, Acta Math. Hungarica 116 (2007) 239–246] presented what he claimed to be the necessary and sufficient condition for rank(A-AN(M^′AN)^-M^′A)=rank(A)-rank(AN(M^′AN)^-M^′A) to hold. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn–Guttman theorem. In this paper, we show that some of Galantai’s assertions are incorrect.     

Skew codes of prescribed distance or rank

In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40, 23, 10]₄ code by imposing a distance and a [42,14,21]₈ code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal length and dimension over those fields. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section.