On Descartes’ rule for polynomials with two variations of signs

Lithuanian Mathematical Journal - For sequences of d + 1 signs + and ? beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence...     

KINETICS AND MECHANISM OF THE REACTION BETWEEN OLIGOSILOXANES AND P-TRICHLORO-N-DICHLOROPHOSPHORYL MONOPHOSPHAZENE (Cl3P[dbnd]N-POCl2)

Abstract

³¹P NMR investigation has been made of the action of Cl₃P[dbnd]N-POCl₂(I) first on hexamethyldisiloxane (Me₃Si)₂O and then on oligosiloxanes Me₃Si-(OSiMe₂)_n-OSiMe₃ n = 2 and n=3. The reactions were carried out in bulk or in solution with molar ratios siloxane/(I) varying from I to 5. It was demonstrated that only the monosubstitution of a chlorine atom by the -(OSiMe₂)_n,-OSiMe₃ species n = 0, 2, 3 with elimination of trimethylchlorosilane occurred leading to the derivatives Cl₂OP-N[dbnd]PCl₂O(SiMe₂-O)_nSiMe₃ (II). For n=2, 3 the siloxane redistribution reactions were observed by ²⁹Si NMR analysis. A two steps mechanism is proposed. consisting in a nucleophilic substitution, involving a tricoordinate phosphazenium intermediate, followed by the formation of an active ionic centre probably an oxonium ion, arising from the solvatation by the siloxane of this phosphazeniurn ion and /or of (II) leading to the redistribution reactions. The influences of the solvent, of trimethylchlorosilane, of the temperature, and of the addition of a protonated species (MDH) were investigated.     

Efficient and green syntheses of novel γ-aminophosphonate and phosphine oxide derivatives

Two synthetic protocols leading to novel γ-aminophosphonate and phosphine oxide derivatives, by reductive amination of γ-phosphonylketones, are reported. The first method involved a two-step procedure. Imine intermediates were first isolated from the p-toluenesulfonic acid-catalyzed reaction of primary amines with γ-ketophosphonates and phosphine oxides, then reduced with NaBH₄ in refluxing ethanol. The second method consists of a one-pot procedure which includes the condensation of γ-ketophosphonates and phosphine oxides with primary amines, in the presence of molecular sieves, followed by reduction with NaBH₄. These methods offer significant advantages over prior reports, such as efficiency, generality, and good yields. Furthermore, they are green protocols avoiding hazardous hydrides and solvents.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras

In this paper, we study the tensor product structure of the category of finite dimensional modules over Drinfeld doubles of Taft Hopf algebras. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.     

Purification and characterization of a new Bacillus thuringiensis bacteriocin active against Listeria monocytogenes, Bacillus cereus and Agrobacterium tumefaciens

This study reports on the identification, characterization and purification of a new bacteriocin, named Bacthuricin F103, from a Bacillus thuringiensis strain BUPM103. Bacthuricin F103 production began in the early exponential phase and reached a maximum in the middle of the same phase. Two chromatographic methods based on high performance liquid chromatography and fast protein liquid chromatography systems were used to purify Bacthuricin F103. Sodium dodecyl sulphate-polyacrylamide gel electrophoresis revealed that this bacteriocin had a molecular weight of approximately 11 kDa. It also showed a wide range of thermostability of up to 80 °C for 60 min and a broad spectrum of antimicrobial activity over a pH range of 3.0–10.0. This bacteriocin was noted, and for the first time, to exhibit potent antimicrobial activity against Agrobacterium subsp. strains, the major causal agents of crown gall disease in tomato and vineyard crops, and against several challenging organisms in food, such as Listeria monocytogenes and Bacillus cereus. Complete killing with immediate impact on cells was observed within a short period of time. The sequence obtained for Bacthuricin F103 by direct N-terminal sequencing shared considerable homology with hemolysin. Bacthuricin F103 was noted to act through the depletion of intracellular ions, which suggest that the cell membrane was a possible target to Bacthuricin F103.     

Quantitative and sensitive detection of rare mutations using droplet-based microfluidics

Somatic mutations within tumoral DNA can be used as highly specific biomarkers to distinguish cancer cells from their normal counterparts. These DNA biomarkers are potentially useful for the diagnosis, prognosis, treatment and follow-up of patients. In order to have the required sensitivity and specificity to detect rare tumoral DNA in stool, blood, lymph and other patient samples, a simple, sensitive and quantitative procedure to measure the ratio of mutant to wild-type genes is required. However, techniques such as dual probe TaqMan(?) assays and pyrosequencing, while quantitative, cannot detect less than ～1% mutant genes in a background of non-mutated DNA from normal cells. Here we describe a procedure allowing the highly sensitive detection of mutated DNA in a quantitative manner within complex mixtures of DNA. The method is based on using a droplet-based microfluidic system to perform digital PCR in millions of picolitre droplets. Genomic DNA (gDNA) is compartmentalized in droplets at a concentration of less than one genome equivalent per droplet together with two TaqMan(?) probes, one specific for the mutant and the other for the wild-type DNA, which generate green and red fluorescent signals, respectively. After thermocycling, the ratio of mutant to wild-type genes is determined by counting the ratio of green to red droplets. We demonstrate the accurate and sensitive quantification of mutated KRAS oncogene in gDNA. The technique enabled the determination of mutant allelic specific imbalance (MASI) in several cancer cell-lines and the precise quantification of a mutated KRAS gene in the presence of a 200,000-fold excess of unmutated KRAS genes. The sensitivity is only limited by the number of droplets analyzed. Furthermore, by one-to-one fusion of drops containing gDNA with any one of seven different types of droplets, each containing a TaqMan(?) probe specific for a different KRAS mutation, or wild-type KRAS, and an optical code, it was possible to screen the six common mutations in KRAS codon 12 in parallel in a single experiment.     

Convergence of Global and Bounded Solutions of Some Nonautonomous Second Order Evolution Equations with Nonlinear Dissipation

In this paper we study the asymptotic behavior of solutions of the following nonautonomous wave equation with nonlinear dissipation.

$\left\{\begin{array}{ll} u_{tt}+\vert u_{t}\vert^{\alpha}u_{t}-\Delta u +f(u)=g(t,x),\quad{\rm in}\,\mathbb{R}_{+}\times\Omega,\\ \qquad\qquad u(t,x)=0,\quad\, {\rm on}\,\mathbb{R}_{+}\times\partial\Omega,\end{array}\right.$

where f is an analytic function, α is a small positive real and g(t, ·) tends to 0 sufficiently fast in L ²(Ω) as t tends to ∞.

We also obtain a general convergence result and the rate of decay of solutions for a class of second order ODE containing as a special case

$\left\{\begin{array}{ll} \ddot{U}(t)+\Vert\dot{U}(t)\Vert^{\alpha}\dot{U}(t)+\nabla F(U(t))=g(t),\quad t \in \mathbb{R}_+,\\ \qquad U(0)=U_{0}\,\in \mathbb{R}^{N},\quad\dot{U}(0)=U_{1}\in \mathbb{R}^{N}. \end{array}\right.$

     

Acid promoted enantioselective oxygen-atom transfer from N-alkyl binaphthyl-derived oxaziridines onto sulfides

Acid-promoted asymmetric sulfoxidations of prochiral sulfides using binaphthyl-derived oxaziridines have been studied. The reactions of dialkyl or aryl-alkyl sulfides gave good yields of the corresponding sulfoxides with enantiopurities ranging from 20% to 80%. The influence of temperature and strength of the acid catalyst on enantioselectivity was studied. The absolute configuration of the resulting major enantiomer varied with the structure of the sulfide.