Construct non-graded bi-Frobenius algebras via quivers

Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.     

Effect of Notoginsenoside-Rg_1 on the Expression of Several Proteins in the Striatum of Rat Models with Parkinson′s Disease

Introduction Parkinson′sdisease(PD),alsocalledshaking palsy,isaneurodegenerativedisorderandfrequently occursinthepeopleabovetheageof65[1].PDisa relativelycommonneurodegenerativedisorder,which hasclinicalsymptomsincludingbradykinesia,rest tremor,rigidity,…     

Single-period Two-product Inventory Model with Reorder and Substitution

In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer's substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi's, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.     

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between "punctured" Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.     

Ab Initio Study on the Isomerization and Dehydrogenation of Methylnitrene

The ab initio calculations were performed at the RHF/4-31G level with the reaction pathways of the iso-merization and dehydrogenation of methylnitrene by the intrinsic reaction coordinate method. The results show that the transformation from methylnitrene to methylenimine would be very easy. This accountes for the experimental fact that one couldn' t find the methylnitrene, but only obtained the methylenimine in the pyrolysis of methyl azide. The mode-selective study reveals the reaction coordinates (IRC) of isomerization and dehydrogenation of methylnitrene are associated with the molecular deformation mode of 1191 cm-1 and the methyl group unsymmetrical stretch mode, respectively. The coupling between normal coordinates is favourable to select the reaction channel of isomerization.     

PRACTICAL STABILITY IN TERMS OF TWO MEASURES FOR DISCRETE SYSTEMS

Practical stability in terms of two measures for difference equations is discussed by using the Lyapunov function and a new comparison theorem.     

Absorption Complex between Porphyrin and Phenothiazine in Reverse Micelles

Porphyrin derivatives attract much more interest in photodynamic therapy (PDT). Their importance as therapeutic drugs and targeting agents has been widely recognized1, and many of the efforts have been put towards crafting new porphyrin-based molecular entities to achieve enhanced tumor localization, better tissue penetration and increased singlet oxygen quantum yield2. The states of porphyrins in tissue models such as micelles, lipid bilayers are extensively investigated focusing more or l…     

12-Ring Network Coordination Polymer——{[Cu(C_4N_2H_(10))_4]_2·H_4V_4O_(14)}_n Formed by Linking cyclo-[H_4V_4O_(14)]~(4-) with Cu(C_4N_2H_(10))~(2+)_4 Cation Clusters

IntroductionThe interest in polyoxometalates that are widelyused in medical chemistry, catalyst reactions, and ma-terial sciences stems from their complicated aggregatesformed by means of corner-, edge- and face-sha-ring[1—4]. The exploitation of new str…     

INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.     

The Newton filtration and d-determination of bifurcation problems related to C~0 contact equivalence

In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.