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...     

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.     

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

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

     

Exact analytical solutions for shallow impurity states in symmetrical paraboloidal and hemiparaboloidal quantum dots

The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.     

Cleavage of the N-PChd group from protected amino acids and peptides by cathodic reduction

Amino acid and peptide esters protected by the PChd group can be deprotected cathodically under mild conditions.     

A short large scale synthesis of (±) sarkomycin esters

(±) Sarkomycin ethyl ester has been prepared in four steps from ethyl acrylate.