Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

The effect of ultrasound on the structure and properties of the water-soluble corn hull heteroxylan

Ultrasonic irradiation of a water-soluble corn hull xylan fraction in neutral and alkaline aqueous medium has been found to produce significant changes in its molecular properties. Degradation is first manifested by a decrease in the large molar mass component under generation of polymer chains with about the same size as those of the main molar mass component. The latter is slightly shifted to the lower molar mass region only at stronger irradiation conditions. Ultrasonication of the xylan in neutral aqueous medium at high ultrasound power and/or long irradiation caused no significant changes in its sugar composition, primary structure and viscoelastic properties.     

On Convex Limit Sets and Brownian Motion

We prove limsup results for nonnegative functionals of convex sets determined by normalized Brownian paths in Banach spaces. This continues the interesting investigation of D. Khoshnevisan into this area, and relates to some classical unsolved isoperimetric problems for the convex hull of curves in ^d. Section 4 contains the solution of a problem similar to these classical problems.     

Study of the Photochemical Properties and Conical Intersections of [2,2′‐Bipyridyl]‐3‐amine‐3′‐ol

The two isoelectronic bipyridyl derivatives [2,2′‐bipyridyl]‐3,3′‐diamine and [2,2′‐bipyridyl]‐3,3′‐diol are experimentally known to undergo very different excited‐state double‐proton‐transfer processes, which result in fluorescence quantum yields that differ by four orders of magnitude. In a previous study, these differences were explained from a theoretical point of view, because of topographical features in the potential energy surface and the presence of conical intersections (CIs). Here, we analyze the photochemical properties of a new molecule, [2,2′‐bipyridyl]‐3‐amine‐3′‐ol [BP(OH)(NH₂)], which is, in fact, a hybrid of the former two. Our density functional theory (DFT), time‐dependent DFT (TDDFT), and complete active space self‐consistent field (CASSCF) calculations indicate that the double‐proton‐transfer process in the ground and first singlet π→π* excited state in BP(OH)(NH₂) presents features that are between those of their “parents”. The presence of two CIs and the role they may play in the actual photochemistry of BP(OH)(NH₂) and other bipyridyl derivatives are also discussed.     

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (−F) and donating (−CH₃) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the −CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to −F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with −F or −CH₃, the conversion proceeds via the conrotatory pathway.     

Antioxidant activity of different parts of Pistacia khinjuk Stocks fruit and its correlation to phenolic composition

The fruits of Pistacia khinjuk Stocks were collected from Ilam province, Iran. The aim of this study was to analyse antioxidant capacity and phenolic composition of different parts of P. khinjuk fruit. The antioxidant capacity of extracts was measured using different assays: ferric reducing ability of plasma, 2,2-diphenyl-1-picrylhydrazyl and nitric oxide radical scavenging. The phenolic composition of P. khinjuk fruit is reported for the first time. Amongst different parts of the fruit analysed in this study, hull extract contained the highest total phenolic and flavonoid contents. We observed a high correlation between different antioxidant activity and total phenolic and flavonoid contents. Therefore, antioxidant capacity can be related to total phenolic and flavonoid contents. A correlation analysis revealed that ascorbic acid, gallic acid, rutin, caffeic acid, ferulic acid and sinapic acid were the phenolic compounds mainly responsible for antioxidant power of the fruit extracts.     

A Donnell type theory for finite deflection of stiffened thin conical shells composed of composite materials

A Donnell type theory is developed for finite deflection of closely stiffened truncatedlaminated composite conical shells under arbitrary loads by using the variational calculusand smeared-stiffener theory.The most general bending-stretching coupling and the effectof eccentricity of stiffeners are considered.The equilibrium equations,boundary conditionsand the equation of compatibility are derived.The new equations.of the mixed-type ofstiffened laminated composite conical shells are obtained in terms of the transversedeflection and stress function.The simplified equations are also given for some commonlyencountered cases.     

复合材料三角形网格加筋圆锥壳体位移型稳定性方程及其总体稳定性分析

本文采用Donnell型扁壳理论,首先利用最小势能原理和广义平均筋条刚度法推导出用位移分量表示的复合材料三角形网格加筋叠层圆锥壳体的稳定性方程,考虑了蒙皮最一般的拉弯与拉扭耦合关系和加筋筋条的偏心效应,并讨论了该方程的基本性质.根据外压实验观察结果,通过选取适当的位移分量表达式,并运用Galerkin法分析了在均布外压作用下复合材料三角形网格加筋叠层圆锥壳体总体稳定性,得到了临界载荷的解析表达式,并对某一类C/E复合材料三角形内网格加筋圆锥壳体的临界外压进行了计算,所得理论值与实验结果很好地吻合.最后,讨论了有关参数对临界载荷的影响.本文所建立的新方程和所得结果对于航空航天结构非常有用.     

Non-symmetrical large deformation of a shallow thin conical shell

I.IntroductionItisimportanttoresearchnon-symmetricalquestionsofshallowcollicalshellsintheoryoronapplication.Asonekindofpressurevessel'sparts,shallowconicalshellsareverycommonlyusedillellgineerillgpractice,becausethedifficultyofmanul\lctul.illgthemis'small.AlthotlghwelookupmanyChineseandtbreignperiodicalswhicharctlblctobefound,wehavenotyeth'ulldarticlesanddocumentsfornon-symmetricalandnolllinearquestionsofshitllowconictllshells.Oval'rccelltyears,ProlbssorWangXinzhiandhiscolleagueshavedonealot…