Linear silver clusters in aqueous solution (clusterites): radiation-induced chemical synthesis and properties

The formation and properties of the products of the radiation-induced chemical reduction of silver ions in aqueous solutions containing sodium polyacrylate were investigated. The absorption spectra of these species exhibit a band at 290 mn and a band in the visible region. The latter shifts from 470 nm to -800 nm with time or after the addition of silver ions. The species obtained (clusterites) arc linear silver clusters bound to the carboxyl groups of the ion exchanger. The red shift of the visible band is due to the increase in their size. The mechanism of the formation and the structure of the clusterites are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1429–1435, June, 1996.     

Triterpenoids from plants of the genus Tamarix

The taraxeran-14-ene-type triterpenoids methyl 3-β-al-D-fridoolean-14-en-28-oate (1), 3-α-[3″,4′-dihydroxytrans-cinnamoyl]-oxy-D-fridoolean-14-en-28-oic acid (2), and β-sitosterol (3) were isolated from the aerial part of plants from the genus Tamarix (T. laxa, T. elongata) (Tamaricaceae). The structures of the triterpenoids were proved using spectral data (IR, UV, PMR, ¹³C NMR, 2D NMR ¹H-¹H COSY, HMQC, HMBC, mass). Compound 1 is new and not previously described in the literature. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 271–273, May–June, 2006.     

Genomic variation and point mutations analysis of Indian COVID-19 patient samples submitted in GISAID database

Corona virus disease 2019 (COVID-19) endemic has havoc on the world; the causative virus of the pandemic is SARS CoV-2. Pharmaceutical companies and academic institutes are in continuous efforts to identify anti-viral therapy or vaccines, but the most significant challenge faced is the highly evolving genome of SARS CoV-2, which is imparting evolutionary selective benefits to the virus. To understand the viral mutations, we have retrieved nine hundred and thirty-four samples from different states of India via the GISAID database and analyzed the frequency of all types of point mutation in all structural, non-structural proteins, and accessory factors of SARS CoV-2. Spike glycol protein, nsp3, nsp6, nsp12, N and NS3 were the most evolving proteins. High frequency point mutations were Q496P (nsp2), A380V (nsp4), A994D (nsp3), L37F (nsp6), P323L & A97V (nsp12), Q57H (ns3), D614G (S), P13L (N), R203K (N), G204R (N) and S194L (N).     

Rearrangement during cyclisation of some 3-(2-pyrrolyl) propionic acids and related compounds

Cyclisation of the title compounds leads to mixtures of the expected 4H-cyclopental[b]pyrrol-4-ones (1), the corresponding 6-ones (3) by a single rearrangement, and the cyclopenta[c]pyrrol-4-ones (4) by a double rearrangement, the proportions depending upon the substituents.The ¹H NMR spectra of 2-methyl-4H-cyctopenta[b]thiophen-6-one (3f) shows 6J long range $\text{CH}{}_3\text{CH}{}_2$ coupling, but this is absent in the corresponding pyrroles (3c,d). The ¹³C spectra of 1 and 3 cannot be interpreted on the basis of substituent chemical shifts in pyrroles and thiophens, and are clearly -CH = CH-X (X = NMe, NPh, S) bridged derivatives of cyclopent-2-enone.     

Nonalkaloid Constituents from Stemona japonica

Five new nonalkaloid constituents, a neolignan, japonin A ( 1 ), a macrocyclic lactone, japonin B ( 2 ), a (phenylethyl)benzoquinone, japonin C ( 3 ), a phenanthraquinone, japonin D ( 4 ), as well as a dihydrostilbene, stilbostemin M ( 5 ), were isolated from the roots of Stemona japonica, together with eight known compounds. Their structures were established by spectroscopic analyses.     

Some graphs with small second eigenvalue

For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). En route we give, for any integerk>1, a simple Cayley graph onp ^k nodes of degreep of second eigenvalue . The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788, and the Office of Naval Research under Grant N00014-87-K-0467.     

An approximate max-flow min-cut relation for undirected multicommodity flow,with applications

In this paper, we prove the first approximate max-flow min-cut theorem for undirected multicommodity flow. We show that for a feasible flow to exist in a multicommodity problem, it is sufficient that every cut's capacity exceeds its demand by a factor ofO(logClogD), whereC is the sum of all finite capacities andD is the sum of demands. Moreover, our theorem yields an algorithm for finding a cut that is approximately minimumrelative to the flow that must cross it. We use this result to obtain an approximation algorithm for T. C. Hu's generalization of the multiway-cut problem. This algorithm can in turn be applied to obtain approximation algorithms for minimum deletion of clauses of a 2-CNF formula, via minimization, and other problems. We also generalize the theorem to hypergraph networks; using this generalization, we can handle CNF clauses with an arbitrary number of literals per clause.Most of the results in this paper were presented in preliminary form in Approximation through multicommodity flow,Proceedings, 31th Annual Symposium on Foundations of Computer Science (1990), pp. 726–737.Research supported by the National Science Foundation under NSF grant CDA 8722809, by the Office of Naval and the Defense Advanced Research Projects Agency under contract N00014-83-K-0146, and ARPA Order No. 6320, Amendament 1.Research supported by NSF grant CCR-9012357 and by an NSF Presidential Young Investigator Award.     

A family of (n−1)! Diagonal polynomial orders ofN n

Letn>0 be an element of the setN of nonnegative integers, and lets(x)=x ₁+...+x _n , forx=(x ₁, ...,x _n ) N _n . Adiagonal polynomial order inN _n is a bijective polynomialp:N _n N (with real coefficients) such that, for allx,y N _n ,p(x)<p(y) whenevers(x)<s(y). Two diagonal polynomial orders areequivalent if a relabeling of variables makes them identical. For eachn, Skolem (1937) found a diagonal polynomial order. Later, Morales and Lew (1992) generalized this polynomial order, obtaining a family of 2 ^n–2 (n>1) inequivalent diagonal polynomial orders. Here we present, for eachn>0, a family of (n – 1)! diagonal polynomial orders, up to equivalence, which contains the Morales and Lew diagonal orders.     

Symmetries and generalizedW∞ algebra of the modified KP equation

The infinitely many symmetries with arbitrary functions of timet for the potential modified Kadomtsev-Petviashvilli equation are obtained by using a simple direct method. These symmetries constitute a generalization of the well-knownW algebra.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.