Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.     

Effective non-vanishing of global sections of multiple adjoint bundles for polarized 3-folds

Let X be a smooth complex projective variety of dimension 3 and let L be an ample line bundle on X. In this paper, we provide a lower bound for h⁰(m(K_X+L)) under the assumption that κ(K_X+L)≥0. In particular, we get the following: (1) if 0≤κ(K_X+L)≤2, then h⁰(K_X+L)>0 holds. (2) If κ(K_X+L)=3, then h⁰(2(K_X+L))≥3 holds. Moreover we get a classification of (X,L) with κ(K_X+L)=3 and h⁰(2(K_X+L))=3 or 4.     

Functional monomers and polymers. LXXI. Conformation and interaction studies of poly-L-lysine derivatives with pendant nucleic acid bases

Copolymers of L -lysine and L -lysine derivatives which contained nucleic acid bases substituted on the N^ε position were synthesized by grafting nucleic acid derivatives onto poly-L -lysine. The conformation and interaction of these copolymers in solution were studied by using spectroscopic measurements. They existed in helical conformation at neutral pH values, and the polymer complex formation among them was examined by ultraviolet (UV) measurements in organic solvents. A decrease in the nucleic acid base content of the copolymers resulted in a decrease in helical structures and also in interactions with the polymer-containing complementary bases.     

Polymerization of cyclic derivatives of uracil and thymine

Cyclic derivatives of uracil and thymine were synthesized from their corresponding 1-(2′-chloroethyl) derivatives by dehydrochlorination. These compounds were found to undergo a variety of reactions, giving many valuable derivatives of uracil and thymine. The cyclic derivatives, as monomers, were polymerized with a cationic initiator by a unique ring-opening process. The polymerization proceeded by ring opening with isomerization of the pyrimidine ring to give a polymer in which pyrimidine rings were connected with ethylene between N-1 and N-3 or O-4 in the pyrimidine ring. The structure of these polymers was determined by nuclear magnetic resonance (NMR), ultraviolet (UV), infrared (IR), and mass spectra. The structure was affected by polymerization temperature.     

Linear free energy relationships for carbon-13 NMR chemical shifts of substituted benzoic acids1

In order to examine ¹³C-SCS of substituted benzoic acids, chemical shifts of the acid form (I) and the dissociated form (II) have been obtained separately. Single substituent parameters, σ⁰ or σ⁺ are correlated with the shifts for the carboxyl (δ_co) or ipso carbons (δ_ipso), respectively. Among the available five equations which are developed for the analysis with dual (or divided) substituent parameters (DSP), the Swain-Lupton equation (eqn 3) and the Taft-Swain-Lupton equation (eqn 4) give much better correlations, not only for δ_co and δ_ipso but also for the results for ring carbons (C(2), C(5), C(6)), except for those attached to or neighboured by substituents. It is concluded that the SCS of aromatic compounds are best analyzed with substituent parameters derived from reactions or equilibria on the basis of linear free energy relationships.     

Oxidation of alcohols with oxoperoxobis(N-phenylbenzohydroxamato)molybdenum(VI)

The title complex oxidizes primary and secondary alcohols to the corresponding carbonyl compounds. Stereoselective epoxidation of allylic alcohols is also described.     

New global stability conditions for a class of difference equations

In this paper we consider some classes of difference equations, including the well-known Clark model, and study the stability of their solutions. In order to do that we introduce a property, namely semicontractivity, and study relations between ‘semi-contractive’ functions and sufficient conditions for the solution of the difference equation to be globally asymptotically stable. Moreover, we establish new sufficient conditions for the solution to be globally asymptotically stable, and we improve the ‘3/2 criteria’ type stability conditions.      

Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space R2n up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.