Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One

By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$.     

On the homogeneity of additive mappings

LetK be a ring with an identity 1 0 andM, L two unitaryK-modules. Then, for any additive mappingf:M L, the setH _f :={ K f(x)=f(x) for allx M} forms a subring ofK, the homogeneity ring off. It is shown that, forM {0},L {0} and any subringS ofK for whichM is a freeS-module, there exists an additive mappingf:ML such thatH _f =S. This result is applied to the four Cauchy functional equations, and it leads also to an answer to the question as to whether it is possible to introduce onM a multiplication ·:M × M M makingM into a ring but not into aK-algebra.     

One pot synthesis of chromium incorporated SBA-16 under acid medium-Application in the selective oxidation of benzyl alcohol derivatives

Cr-SBA-16 mesoporous silica heterogeneous catalysts (Si/Cr = 7, 14, and 28) were successfully synthesized by one-pot hydrothermal method at low acidic medium. The catalysts were characterized by means of X-ray diffraction (XRD), N₂ adsorption-desorption at 77 K, Fourier Transform Infrared (FTIR), X-ray photoelectron (XPS) and Diffuse Reflectance UV–Vis (DRS) Spectroscopies, Thermogravimetric analysis (TGA), Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM) techniques. Herein, Cr-SBA-16 catalysts are evaluated in the selective catalytic oxidation of benzyl alcohol derivatives using H₂O₂ as oxidant. From XPS and UV–Vis (DRS) spectroscopies the molar ratios between Cr⁶⁺/Cr³⁺ are found to increase versus chromium loading in the following order: Cr-SBA-16(28) < Cr-SBA-16(14) < Cr-SBA-16(7). Hence the highest Cr⁶⁺ in tetrahedrally environment is observed for Si/Cr = 7. We demonstrated for the first time that the selective catalytic oxidation of benzyl alcohol (BzOH) using H₂O₂ over Cr-SBA-16 occurs through noncompetitive adsorption mechanism and the reaction is pseudo-first order to BzOH. The activity of the reaction depends on the symmetry of chromium species, herein, high activity is observed for tetrahedral chromium species in Cr-SBA-16(7). The absence of any chromium ions in the filtrate shows no chromium leaching from the silica framework.     

Micellization and mixed micellization of cationic gemini (dimeric) surfactants and cationic conventional (monomeric) surfactants: Conductometric,dye solubilization,and surface tension studies

In the present study, we have investigated the self-association, mixed micellization, and thermodynamic studies of a cationic gemini (dimeric) surfactant, hexanediyl-1,6-bis(dimethylcetylammonium bromide (16-6-16)) and a cationic conventional (monomeric) surfactant, cetyltrimethylammonium bromide (CTAB). The critical micelle concentration (CMC) of pure (16-6-16 and CTAB) and mixed (16-6-16+CTAB) surfactants was measured by electrical conductivity, dye solubilization, and surface tension measurements. The surface properties (viz., C₂₀ (the surfactant concentration required to reduce the surface tension by 20 mN/m), Π_CMC (the surface pressure at the CMC), Γ_max (maximum surface excess concentration at the air/water interface), A_min (the minimum area per surfactant molecule at the air/water interface), etc.) of micellar (16-6-16 or CTAB) and mixed micellar (16-6-16+CTAB) surfactant systems were evaluated. The thermodynamic parameters of the micellar (16-6-16 and CTAB) and mixed micellar (16-6-16+CTAB) surfactant systems were also evaluated.     

氮化SBA-16负载镍基催化剂的制备及其对甲烷二氧化碳重整反应的催化性能

通过软模板法合成了SBA-16分子筛,采用高温氨气氮化的方法使有序介孔硅材料中的氧原子部分被氮原子取代,得到氮化的SBA-16载体(SBA-16-N)。采用满孔浸渍法制备了镍基催化剂,并将制得的Ni/SBA-16和Ni/SBA-16-N催化剂用于甲烷二氧化碳重整反应。通过透射电镜、氮气物理吸附、X射线衍射、X射线光电子能谱和二氧化碳程序升温脱附等手段研究了载体和催化剂的结构,并利用热重分析对反应之后回收催化剂进行了表征。结果表明,高温氮化后的分子筛中掺入了氮元素,增加了载体的碱性,改善了载体对反应气体的吸附活化能力,增强了载体与金属之间的相互作用,从而提高了催化剂的活性和抗积炭性能。     

Simple and Convenient Synthesis of 21‐Thioalkylether Derivatives of Methyl 16‐Prednisolone Carboxylates

The antedrug approach for corticosteroids has been described as a fundamentally sound approach for the development of safer anti‐inflammatory and anti‐asthmatic therapy. However, the derivatization of prednisolone and its congeners have been considered to be major pitfalls, because their syntheses are complicated by the presence of numerous carboxylate esters and hydroxyl functions in the steroid nucleus. A simple and direct synthesis of 21‐thioalkylether derivatives of methyl 16‐prednisolonecarboxylates is described. The 21‐mesylate of the methyl 16‐prednisolonecarboxylate and 9‐fluoro‐17‐dehydro methyl 16‐prednisolonecarboxylate were reacted with Na‐thioalkoxides to furnish the desired thioethers in good yields. A previously published method for the methanolysis of 16‐cyanoprednisolone to methylcarboxylate has been reexamined, and the conditions are explained clearly. The reaction conditions for all these reactions were critical.     

The Zassenhaus variety of a reductive Lie algebra in positive characteristic

Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let Z be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus variety of g. We show that, under certain mild assumptions on G, the field of fractions Frac(Z) of Z is G-equivariantly isomorphic to the function field of the dual space g^∗ with twisted G-action. In particular Frac(Z) is rational. This confirms a conjecture of J. Alev. Furthermore we show that Z is a unique factorisation domain, confirming a conjecture of A. Braun and C. Hajarnavis. Recently, A. Premet used the above result about Frac(Z), a result of Colliot-Thelene, Kunyavskii, Popov and Reichstein and reduction mod p arguments to show that the Gelfand-Kirillov conjecture cannot hold for simple complex Lie algebras that are not of type A, C or G₂.     

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant's Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras.     

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.