Fundamental equation of information revisited

Summary This paper presents a new, shorter and more direct proof of the following result of J. Aczél and C. T. Ng: IfM: J R (J =]0, 1[ ^k ) is both multiplicative and additive, then the general solution: J R of(x) + M(1 – x)(y/1 – x) = (y) + M(1 – y)(x/1 – y) (x, y, x + y J) is given by(x) = ifM = 0,(x) = M(x)[L(x) + ] + M(1 – x)L(1 – x) ifM 0,where is an arbitrary constant andL: J R is an arbitrary solution of the logarithmic functional equationL(xy) = L(x) + L(y) (x, y J). Also, some extensions of this result to fields more general than the reals are given.     

Nice decompositions of R n entirely into nice sets are mostly impossible

While there are several interesting examples of partitions of R ³ into elements which individually are geometrically nice — circles or segments — the partitions themselves fail to be nice, in the sense of forming continuous or upper semicontinuous decompositions. We show that this is no accident: R ³ has no continuous decomposition into circles, and no open subset of R ⁿ has an upper semicontinuous decomposition into convex compact nonsingleton sets.     

Subelliptic operators on Lie groups: Variable coefficients

Let G be a Lie group with Lie algebra g and a _i,...,a _d and algebraic basic of g. Futher, if A _i=dL(a_i) are the corresponding generators of left translations by G on one of the usual function spaces over G, let% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbciab-Heaijaab2dadaaeqbqa% aiaadogadaWgaaWcbaqedmvETj2BSbacgmGae4xSdegabeaakiaadg% eadaahaaWcbeqaaiab+f7aHbaaaeaacqGFXoqycaGG6aGaaiiFaiab% +f7aHjaacYhatuuDJXwAK1uy0HMmaeXbfv3ySLgzG0uy0HgiuD3BaG% Wbbiab9rMiekaaikdaaeqaniabggHiLdaaaa!5EC1!\[H{\rm{ = }}\sum\limits_{\alpha :|\alpha | \le 2} {c_\alpha A^\alpha } \] be a second-order differential operator with real bounded coefficients c . The operator is defined to be subelliptic if% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiGacMgacaGGUbGaaiOzamXvP5wqonvsaeHbfv3ySLgzaGqbaKaz% aasacqWF7bWEcqWFTaqlkmaaqafabaGaam4yamaaBaaaleaarmWu51% MyVXgaiyWacqGFXoqyaeqaaaqaaiab+f7aHjaacQdacaGG8bGae4xS% deMaaiiFaiabg2da9iaaikdaaeqaniabggHiLdGccqWFOaakiuGacq% qFNbWzcqWFPaqkcqaH+oaEdaahaaWcbeqaamaaBaaameaacqGFXoqy% aeqaaaaakiaacUdacqqFNbWzcqGHiiIZcqqFhbWrcqqFSaalcqqFGa% aicqaH+oaEcqGHiiIZrqqtubsr4rNCHbachaGaeWxhHe6aaWbaaSqa% beaacqqFKbazcqqFNaWjcqaFaC-jaaGccaGGSaGaaiiFaiabe67a4j% aacYhacqGH9aqpjqgaGeGae8xFa0NccqGH+aGpcaaIWaGaaiOlaaaa% !7884!\[\inf \{ - \sum\limits_{\alpha :|\alpha | = 2} {c_\alpha } (g)\xi ^{_\alpha } ;g \in G, \xi \in ^{d'} ,|\xi | = \} > 0.\]We prove that if the principal coefficients {c ; ||=2} of the subelliptic operator are once left differentiable in the directions a ₁,...,a _d with bounded derivatives, then the operator has a family of semigroup generator extensions on the L _p-spaces with respect to left Haar measure dg, or right Haar measure d, and the corresponding semigroups S are given by a positive integral kernel,% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbaiab-HcaOGqbciab+nfatnaa% BaaaleaacaWG0baabeaaruqqYLwySbacgiGccaqFgpGae8xkaKIae8% hkaGIae43zaCMae8xkaKIae8xpa0Zaa8qeaeaacaqGKbaaleaacqGF% hbWraeqaniabgUIiYdGcceWGObGbaKaacaWGlbWaaSbaaSqaaiaads% haaeqaaOGae8hkaGIae43zaCMae43oaSJae4hAaGMae8xkaKIaa0NX% diab-HcaOiab+HgaOjab-LcaPiab-5caUaaa!5DFA!\[(S_t \phi )(g) = \int_G {\rm{d}} \hat hK_t (g;h)\phi (h).\]The semigroups are holomorphic and the kernel satisfies Gaussian upper bounds. If in addition the coefficients with ||=2 are three times differentiable and those with ||=1 are once differentiable, then the kernel also satisfies Gaussian lower bounds.Some original features of this article are the use of the following: a priori inequalities on L in Section 3, fractional operator expansions for resolvent estimates in Section 4, a parametrix method based on reduction to constant coefficient operators on the Lie group rather than the usual Euclidean space in Section 5, approximation theory of semigroups in Section 11 and time dependent perturbation theory to treat the lower order terms of H in Sections 11 and 12.     

A New Pentacyclic Triterpene from Ecdysanthera Rosea

D-friedours-14-en-11α, 12α-epoxy-3β-yl palmitate (1), a new pentacyclic triterpene of the ursane series, was isolated from the aerial parts of Ecdysanthera rosea, and the structure was elucidated on the basis of the spectral data. The partial synthesis of this compound from α-amyrin acetate via a few steps was also achieved.     

几种分子筛的转晶和混晶的控制及单一晶体的优化合成

 以六亚甲基亚胺作模板剂，在配料比一定的情况下，详细考察了反应温度和反应时间对MCM－22，ZSM－5，ZSM－35和丝光沸石分子筛成晶的影响．结果表明，MCM－22的最佳合成温度在低温区，ZSM－35易在提高反应温度或延长反应时间时形成，而作为中间相的ZSM－5和丝光沸石则在反应温度与反应时间合理匹配时才能以单一相生成．同时，探讨了晶种的加入对产物晶相的影响．在特定的温度和时间区间，能够合成出比例可控的ZSM－35＋MCM－22混晶，ZSM－5＋ZSM－35混晶和ZSM－35＋丝光沸石混晶，并从分子筛孔道和结构单元的特点出发，就转晶发生对温度和时间的依赖性作了解释．     

胶原纤维固化杨梅单宁对UO22+的吸附

以胶原纤维为基质，通过交联剂将杨梅单宁固化在胶原纤维上制备吸附材料．实验结果表明，所制备的吸附材料对UO2^2 具有很强的吸附能力，当溶液中UO2^2 的浓度为7．5mmol/L、pH为5．0时，吸附容量达到1．19mmol UO2^2 /g(283．3mgU／g)．UO2^2 在固化杨梅单宁上的吸附平衡符合Freurldlich方程，升高温度，平衡吸附量增大。吸附动力学可用拟二级速度方程来描述，由动力学方程计算得到的平衡吸附量与实测的平衡吸附量基本相同，误差在4％以内．pH值对吸附过程有较大影响，适宜的pH在5-8之间。所制备的吸附材料具有优良的柱动力学特性，床层的有效利用率高；经解吸后的吸附柱其吸附性能基本不变。     

Recent developments in manufacturing emulsions and particulate products using membranes

Membrane emulsification (ME) is a relatively new technique for the highly controlled production of particulates. This review focuses on the recent developments in this area, ranging from the production of simple oil-in-water (O/W) or water-in-oil (W/O) emulsions to multiple emulsions of different types, solid-in-oil-in-water (S/O/W) dispersions, coherent solids (silica particles, solid lipid microspheres, solder metal powder) and structured solids (solid lipid microcarriers, gel microbeads, polymeric microspheres, core-shell microcapsules and hollow polymeric microparticles). Other emerging technologies that extend the capabilities into different membrane materials and operation methods (such as rotating membranes, repeated membrane extrusion of coarsely pre-emulsified feeds) are introduced. The results of experimental work carried out by cited researchers in the field together with those of the current authors are presented in a tabular form in a rigorous and systematic manner. These demonstrate a wide range of products that can be manufactured using different membrane approaches. Opportunities for creation of new and novel entities are highlighted for low throughput applications (medical diagnostics, healthcare) and for large-scale productions (consumer and personal products).     

在反应温度下以1％O2对Mo／MCM－22催化剂的原位再生

In recent years, the catalytic dehydroaromatization of methane to yield aromatics has been a challenging and intriguing topic in heterogeneous catalysis. Until now, the two effective methane dehydroaromatization catalysts are Mo/HZSM-5[1] and Mo/MCM-22[2]. However, this reaction suffers from rapid catalyst deactivation due to coking[3].     

Structural and dynamical analysis of the hydration of the Alzheimer's beta-amyloid peptide

An analysis of the water molecules in the first solvation shell obtained from the molecular dynamics simulation of the amyloid beta(10-35)NH2 peptide and the amyloid beta(10-35)NH2E22Q "Dutch" mutant peptide is presented. The structure, energetics, and dynamics of water in the hydration shell have been investigated using a variety of measures, including the hydrogen bond network, the water residence times for all the peptide residues, the diffusion constant, experimentally determined HN amide proton exchange, and the transition probabilities for water to move from one residue to another or into the bulk. The results of the study indicate that: (1) the water molecules at the peptide-solvent interface are organized in an ordered structure similar for the two peptide systems but different from that of the bulk, (2) the peptide structure inhibits diffusion perpendicular to the peptide surface by a factor of 3 to 5 relative to diffusion parallel to the peptide surface, which is comparable to diffusion of bulk water, (3) water in the first solvation shell shows dynamical relaxation on fast (1-2 ps) and slow (10-40 ps) time scales, (4) a novel solvent relaxation master equation is shown to capture the details of the fast relaxation of water in the peptide's first solvation shell, (5) the interaction between the peptide and the solvent is stronger in the wild type than in the E22Q mutant peptide, in agreement with earlier results obtained from computer simulations [Massi, F.; Straub, J. E. Biophys J 2001, 81, 697] correlated with the observed enhanced activity of the E22Q mutant peptide.     

MCM-22分子筛酸性的DFT理论计算研究

本文利用量子力学中的密度泛函理论(DFT)计算，研究了MCM-22分子筛上骨架Al在8个不同的T位的分布和Br?nsted酸的落位及强度。所有计算基于分子筛的8T簇模型 (H₃SiO)₃Si-O(H)-T(OSiH₃)₃(T=Si，Al)，采用DFT的BLYP方法，所有原子均应用DNP基组。通过计算(Al，H)/Si替代能和质子亲和势，得出推论：MCM-22分子筛中骨架Al的最有利落位在T1，T4，T3和T8位。而形成Br?nsted-酸的最可能的位置为Al1-O3-Si4，Al4-O3-Si1，Al3-O11-Si2和Al8-O10-Si2桥基。Al1-O3H-Si4和Al4-O3H-Si1位的酸性强度接近，Al3-O11H-Si2和Al8-O10H-Si2位的酸性分别略低于和略高于前两个酸位。通过计算模板剂分子六次甲基亚胺(HMI)与B-酸中心的相互作用，进一步探讨了HMI对分子筛中Al落位的靶向作用。