Étale covers of affine spaces in positive characteristicRevêtements étales des espaces affines en caractéristique positive

We prove that every projective, geometrically reduced scheme of dimension n over an infinite field k of positive characteristic admits a finite morphism over some finite radicial extension k′ of k to projective n-space, étale away from the hyperplane H at infinity, which maps a chosen Weil divisor into H and a chosen smooth geometric point of X not on the divisor to some point not in H. To cite this article: K.S. Kedlaya, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 921–926.     

The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

An algebraic approach to q-partial fractions and Sylvester denumerants

The Ramanujan Journal - In 1857, Sylvester established an elegant theory that certain counting functions (which he termed denumerants) are quasi-polynomials by decomposing them into periodic and...     

The Ulam number of infinite graphs

The following is a conjecture of Ulam: In any partition of the integer lattice on the plane into uniformly bounded sets, there exists a set that is adjacent to at least six other sets. Two sets are adjacent if each contain a vertex of the same unit square. This problem is generalized as follows. Given any uniformly bounded partitionP of the vertex set of an infinite graphG with finite maximum degree, letP (G) denote the graph obtained by letting each set of the partition be a vertex ofP (G) where two vertices ofP (G) are adjacent if and only if the corresponding sets have an edge between them. The Ulam number ofG is defined as the minimum of the maximum degree ofP (G) where the minimum is taken over all uniformly bounded partitionsP. We have characterized the graphs with Ulam number 0, 1, and 2. Restricting the partitions of the vertex set to connected subsets, we obtain the connected Ulam number ofG. We have evaluated the connected Ulam numbers for several infinite graphs. For instance we have shown that the connected Ulam number is 4 ifG is an infinite grid graph. We have settled the Ulam conjecture for the connected case by proving that the connected Ulam number is 6 for an infinite triangular grid graph. The general Ulam conjecture is equivalent to proving that the Ulam number of the infinite triangular grid graph equals 6. We also describe some interesting geometric consequences of the Ulam number, mainly concerning good drawings of infinite graphs.     

Nonlinear optical study of palladium Schiff base complex using femtosecond differential optical Kerr gate and Z-scan techniques

A femtosecond differential optical Kerr gate (DOKG) and Z-scan techniques, have been applied to investigate the third-order optical nonlinearity of composite film of the coordination complex [PdLPPh₃] (L=N-(2-pyridyl)-N′-(salicylidene)hydrazine, PPh₃=triphenylphosphine). Film exhibits superior nonlinear optical properties in the near-infrared spectral region. The nonlinear response time and third-order nonlinear optical susceptibility of complex were found to be≤90 fs and 3.9×10^?10 esu, respectively. The Z-scan result shows that saturable absorption property of the film and its nonlinear absorption coefficient of the sample was found to be ?23 cm/GW.     

Isomeric pyrazolo­[3,4-d]­pyrimidine-based mol­ecules: disappearance of dimerization due to interchanged substitutions

In 5-benzyl-1,7-di­methyl-4,5,6,7-tetra­hydro-1H-pyrazolo­[3,4-d]­pyrimidine-4,6-dione, C₁₄H₁₄N₄O₂, which crystallizes in space group P, weak intermolecular C—H⋯O hydrogen bonds generate dimers. The isomeric compound 1-benzyl-5,7-di­methyl-4,5,6,7-tetra­hydro-1H-pyrazolo­[3,4-d]­pyrimidine-4,6-dione, C₁₄H₁₄N₄O₂, crystallizes in space group P2₁/n, and shows no such dimerization. Instead, it exhibits C—H⋯π interactions with the phenyl ring. In both structures, the mol­ecules are linked by aromatic π–π-stacking interactions.     

Simultaneous quantification of ondansetron and tariquidar in rat and human plasma using a high performance liquid chromatography‐ultraviolet method

Ondansetron, a widely used antiemetic agent, is a P‐glycoprotein (P‐gp) substrate and therefore expression of P‐gp at the blood–brain barrier limits its distribution to the central nervous system (CNS), which was observed to be reversed by coadministration with P‐gp inhibitors. Tariquidar is a potent and selective third‐generation P‐gp inhibitor, and coadministration with ondansetron has shown improved ondansetron distribution to the CNS. There is currently no reported bioanalytical method for simultaneously quantifying ondansetron with a third‐generation P‐gp inhibitor. Therefore, we aimed to develop and validate a method for ondansetron and tariquidar in rat and human plasma samples. A full validation was performed for both ondansetron and tariquidar, and sample stability was tested under various storage conditions. To demonstrate its utility, the method was applied to a preclinical pharmacokinetic study following coadministration of ondansetron and tariquidar in rats. The presented method will be valuable in pharmacokinetic studies of ondansetron and tariquidar in which simultaneous determination may be required. In addition, this is the first report of a bioanalytical method validated for quantification of tariquidar in plasma samples.     

Synthesis and Structural Characterization of New Divanada‐ and Diniobaboranes Containing Chalcogen Atoms

The reaction of [Cp_nMCl_4?x] (M=V: n=2, x=2; M=Nb: n=1, x=0; Cp=η⁵‐C₅H₅) with LiBH₄ ? THF followed by thermolysis in the presence of dichalcogenide ligands E₂R₂ (E=S, Te; R=2,6‐(tBu)₂‐C₆H₂OH, Ph) and 2‐mercaptobenzothiazole (C₇H₅NS₂) yielded dimetallaheteroboranes [{CpV(μ‐TePh)}₂(μ₃‐Te)BH ? thf] ( 1 ), [(CpV)₂(BH₃S)₂] ( 2 ), [(CpNb)₂B₄H₁₀S] ( 3 ), [(CpNb)₂B₄H₁₁S(tBu)₂C₆H₂OH] ( 4 ), and [(CpNb)₂B₄H₁₁TePh] ( 5 ). In cluster 1 , the V₂BTe atoms define a tetrahedral framework in which the boron atom is linked to a THF molecule. Compound 2 can be described as a dimetallathiaborane that is built from two edge‐fused V₂BS tetrahedron clusters. Cluster 3 can be considered as an edge‐fused cluster in which a trigonal‐bipyramidal unit (Nb₂B₂S) has been fused with a tetrahedral core (Nb₂B₂) by means of a common Nb₂ edge. In addition, thermolysis of an in‐situ‐generated intermediate that was produced from the reaction of [Cp₂VCl₂] and LiBH₄ ? THF with excess BH₃ ? THF yielded oxavanadaborane [(CpV)₂B₃H₈(μ₃‐OEt)] ( 6 ) and divanadaborane cluster [(CpV)₂B₅H₁₁] ( 7 ). Cluster 7 exhibits a nido geometry with C_2v symmetry and it is isostructural with [(Cp*M)₂B₅H_9+n] (M=Cr, Mo, and W, n=0; M=Ta, n=2; Cp*=η⁵‐C₅Me₅). All of these new compounds have been characterized by ¹H NMR, ¹¹B NMR, and ¹³C NMR spectroscopy and elemental analysis and the structural types were established unequivocally by crystallographic analysis of compounds  1 – 4 , 6 , and 7 .