Conformations of 2-C:1-N-carbonyl-2-deoxy-d-glycopyranosylamines

Geometry and molecular conformation of theN-toluenesulfonyl1 andN-acetyl-2 derivatives of peracetylated 2-C:1-N-carbonyl-2-deoxy--d-glucopyranosylamine were investigated with the use of X-ray diffraction methods. Compound1 (C₂₀H₂₃NSO₁₀) crystallizes in the monoclinic P2₁ space group, withZ=2 anda=8.238(1),b=7.988(1),c=16.928(2)Å, =99.12(1)°. Compound2 (C₁₅H₁₉NO₉) crystallizes in orthorhombic P2₁2₁2₁ space group withZ=4 anda=8.385(1),b=8.550(1),c=24.000(2) Å. Analysis of differences in bond lengths and angles between compounds1 and2 and other compounds of this class showed that the electronwithdawing effect by the residue located at the nitrogen atom can be manifested by lengthening of the -lactam C-N bonds, with simultaneous shortening of the distance between two carbon atoms at the ring fusion. Semi-empirical calculations suggested that the title compounds displayed two positively charged centers, susceptible for attack of nucleophiles, one at the carbonyl group of -lactam and the second at the anomeric carbon atom. Atomic charges, however, calculated for compounds1 and2 did not explain their different reaction directions during alcoholysis.Part 3. For part 1 and 2, see Refs. 5 and 6.     

Molecular structure of N-(2-phenylethyl)amide of α-(1,1-ethylenedioxy)-ethyl γ-hydroxybutyric acid (I) and1H NMR spectra of (I) and N-(p-methoxybenzyl)derivative (III)

The spectroscopic and X-ray investigation of the N-(2-phenylethyl) amide of -(1,1-ethylenedioxy)-ethyl--hydroxybutyric acid are reported. The¹H NMR spectra for the title structure and for the N-(p-methoxybenzyl) amide of -(1,1-ethylenedioxy)-ethyl--hydroxybutyric acid are given. The N-(2-phenylethyl)amide of -(1,1-ethylenedioxy)-ethyl--hydroxybutyric acid, C₁₆H₂₃O₄N, crustallizes in the monoclinic space groupP2 ₁/c witha=21.547(5),b=6.333(2),c=11.822(3) Å and =101.01(2)°. The dioxolane ring has a half-chair conformation with C₂(O3)=2.4° and ||_av=18.2°. The inconsiderable deviations from planarity of the six atoms of the amide group are caused mainly by twist around the C4–N1 bond and out-of-plane bending at the N1 atom ((C4–N1)=4°, X_N =7°, X_c =0.4° ). The amide group plane is nearly coplanar with the phenyl ring. The molecules are connected by two intermolecular hydrogen bonds.     

A multivariate approach for the simultaneous determination of losartan potassium and hydrochlorothiazide in a combined pharmaceutical tablet formulation

A convenient new method for the simultaneous determination of losartan potassium and hydrochlorothiazide, with minimum sample pretreatment, is described. The procedure, based on the multivariate analysis of spectral data in the 220−274 nm region by the partial least squares algorithm, is linear in the concentration range 1.06−5.70 mg L⁻¹ for hydrochlorothiazide and 4.0−22.2 mg L⁻¹ for losartan. It is simple, rapid and robust, allowing accurate and precise results, with drug recovery rates of 99.3 and 100.4% and relative standard deviations of 1.7 and 1.0% obtained for hydrochlorothiazide and losartan, respectively. The method was applied to the simultaneous determination of both analytes in tablets, and it provided good results which were in statistical agreement with those provided by independent HPLC analyses of the samples. The method has also been successfully applied for the construction of drug dissolution profiles of a commercial pharmaceutical preparation containing both analytes. Figure A UV-PLS method for the simultaneous determination of losartan potassium and hydrochlorothiazide in pharmaceutical tablet formulations has been developed and validated     

On a theorem of Cantor-Bernstein type for algebras

Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices. This work was supported by Science and Technology Assistance Agency under the contract No APVT-51-032002.     

Failure of hypoellipticity for the canonical solution to $${\bar\partial_b}$$ on some nilpotent Lie groups

In this paper we show that Kohn’s solution to the \({\bar\partial_b}\) problem fails to be hypoelliptic on some class of high codimension submanifolds of \({\mathbb{C}^n}\). The examples presented here carry a Lie group structure which generalize the one-dimensional Heisenberg group.     

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces. The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.     

Maximal subclasses of local fitting classes

A Fitting class $ \mathfrak{F} A Fitting class is said to be π-maximal if is an inclusion maximal subclass of the Fitting class of all finite soluble π-groups. We prove that is a π-maximal Fitting class exactly when there is a prime p ∊ π such that the index of the -radical in G is equal to 1 or p for every π-subgroup of G. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba’s conjecture that there are no maximal Fitting subclasses in a local Fitting class (see [1, Question 13.50]). Original Russian Text Copyright ? 2008 Savelyeva N. V. and Vorob’ev N. T. __________ Vitebsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1411–1419, November–December, 2008.     

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ _c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ _c . This algorithm is employed for finding the minimum cardinality clique-transversal of [`(3K₂)]\overline{3K_{2}} -free circular-arc graphs in O(n ⁴) time. Further we describe an algorithm for determining τ _c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n ²) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n ²) time.     

Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids

The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups. Partially supported by a UGC (HK) grant #2060123 (04-05).     

Structural information content of networks: graph entropy based on local vertex functionals

In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating j-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties.