A note on a paper by G. Mastroianni and G. Monegato

Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral

where or or and is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70 2001, 251-267). The error bounds for the quadrature rule approximating the inner integral given in Theorems 3, 4 of that paper are not correct according to the proof. However, following a different approach, we are able to improve the pointwise error estimates given in that paper.

     

The loss of tightness of time distributions for homeomorphisms of the circle

For a minimal circle homeomorphism we study convergence in law of rescaled hitting time point process of an interval of length 0$">. Although the point process in the natural time scale never converges in law, we study all possible limits under a subsequence. The new feature is the fact that, for rotation numbers of unbounded type, there is a sequence going to zero exhibiting coexistence of two non-trivial asymptotic limit point processes depending on the choice of time scales used when rescaling the point process. The phenomenon of loss of tightness of the first hitting time distribution is an indication of this coexistence behaviour. Moreover, tightness occurs if and only if the rotation number is of bounded type. Therefore tightness of time distributions is an intrinsic property of badly approximable irrational rotation numbers.

     

How to make a triangulation of polytopal

We introduce a numerical isomorphism invariant for any triangulation of . Although its definition is purely topological (inspired by the bridge number of knots), reflects the geometric properties of . Specifically, if is polytopal or shellable, then is ``small' in the sense that we obtain a linear upper bound for in the number of tetrahedra of . Conversely, if is ``small', then is ``almost' polytopal, since we show how to transform into a polytopal triangulation by local subdivisions. The minimal number of local subdivisions needed to transform into a polytopal triangulation is at least . Using our previous results [The size of triangulations supporting a given link, Geometry & Topology 5 (2001), 369-398], we obtain a general upper bound for exponential in . We prove here by explicit constructions that there is no general subexponential upper bound for in . Thus, we obtain triangulations that are ``very far' from being polytopal. Our results yield a recognition algorithm for that is conceptually simpler, although somewhat slower, than the famous Rubinstein-Thompson algorithm.

     

The length of harmonic forms on a compact Riemannian manifold

We study -dimensional Riemannian manifolds with harmonic forms of constant length and first Betti number equal to showing that they are -step nilmanifolds with some special metrics. We also characterize, in terms of properties on the product of harmonic forms, the left-invariant metrics among them. This allows us to clarify the case of equality in the stable isosytolic inequalities in that setting. We also discuss other values of the Betti number.

     

Photoinduced Electron Transfer From Carbazole to Halomethanes in a Gas Phase

Intermolecular photoinduced electron transfer (PET) in a gas phase was studied using carbazole vapor fluorescence quenching by halomethanes (CHCl₃, CH₂Br₂, CCl₄, CHBr₃). The fluorescence quenching rate constants k _q changing from 2.3·10⁵ sec^–1·torr^–1 in mixtures with CHCl₃ to 4.6·10⁶ sec^–1·torr^–1 in mixtures with CHBr₃ at a constant temperature of 403 K were estimated. The dependence of the carbazole fluorescence decay rates in the presence of halomethanes on the free energy change G during transfer of the electron from carbazole to halomethanes is considered. It is suggested to take into account the influence of the vibrational energy of the carbazole molecule E _vib and its temperature changes in estimation of the G values. The differences between PET in the gas and liquid phases were analyzed. It is found that for mixtures with CCl₄ and CHBr₃ the negative temperature dependence of k _q is observed, when the decay rates and efficiencies of the intermolecular PET decreased with temperature increase in the range 403–573 K, i.e. these mixtures the electron transfer is not a barrier-restricted process.     

“最小键级原理”的从头算证实———苯和苯胺类硝基衍生物

感度是爆炸物对外界刺激的敏感程度 ,是火药、炸药和起爆药的基本属性 .在外界撞击作用下炸药发生爆炸的难易程度即该炸药的撞击感度 .感度通常依靠实测 ,从理论上加以判别是人们追求的目标 ,故研究炸药感度与结构的关系一直是该领域的热点 .根据撞击引起热解、热解引起爆炸、撞击感度主要与热解引发步骤相关联等思想 ,我们建议了“最小键级原理 (PSBO)”[1- 4] :对系列结构相似爆炸物 ,其热解引发键键级 (或重叠布居 )越小 ,则撞击感度越大 ;热解引发键键级越大 ,则撞击感度越小 .该判据已在多系列炸药中获得证实和应用[1- 4] .“热解引…     

Measurement of small spin-spin splittings in the presence of chemical exchange: case of deuteriated water

A new implementation of a described data processing for measuring small scalar coupling constant J is proposed. It is applied particularly to situations where the coupling constant is around the linewidth at half-height, and in the presence of chemical exchange. This modified data processing uses only a simple "one-pulse" experiment instead of a series of spin echoes experiments required by the previous processing. The FID recorded in the one pulse experiment is used by a reconstitution program to generate a set of signals, which are analyzed in the time domain to obtain a spectrum where the scalar coupling constant is apparently multiplied by n+1, where n is positive. The new processing is tested with simulated spectra. The coupling constant between proton and deuterium is measured in the proton spectrum of a solution of 80% of D(2)O and 20% of H(2)O. It was found to be J=1.54+/-0.01 Hz.     

Evaluation of radiostability of some steroid derivatives

The effect of ionising radiation (15-100 kGy) on the physico-chemical properties of 6 steroid derivatives in solid state (Hydrocortisone, Hydrocortisone acetate, Prednisolone, Prednisolone acetate, Dexamethasone and Fludrocortisone acetate) was studied by differential scanning calorimetry (DSC), differential thermal analysis (DTA), scanning electron microscopy (SEM), UV spectrophotometry, high-performance liquid chromatography (HPLC), X-ray powder diffraction and polarimetry. DSC and DTA results revealed that the irradiated compounds undergo phase transitions at lower temperatures, show lower melting points and lower enthalpy of the melting process their non-irradiated analogues. The results of HPLC measurements proved a loss in the active substance content after irradiation ranging from 0.5 to 2.88%. No significant effect of irradiation was detected by the UV spectrophotometry or polarimetry in the course of the UV spectrum, absorbancy or optical rotation, as well as in the SEM photographs and X-ray patterns. For some compounds studied a correlation was found between the irradiation dose and the shifts in DSC curves and the loss of content determined by the HPLC method. Similar, but not so much pronounced relations were established in or earlier studies of the derivatives of nitroimidazole and 1,4-dihydropyridine. In general the results have shown relatively high radiochemical stability of the compounds studied and have proved that the DSC method is a sensitive detector of irradiation-caused changes in drugs in solid phase. This revised version was published online in July 2006 with corrections to the Cover Date.     

准周期链状聚合物电子谱及特征

研究了链状聚合物的长短键结构呈准周期排列的电子谱。利用紧束缚近似和转移矩阵方法通过理论证明和计算表明：这种准周期排列聚合物的电子谱,当长短键长度相差很小时,具有类似于金属晶体的能带结构;相差很大时,具有无序系统一维能级结构;而对于一般情形,其电子谱与上两者均异,形成所谓的类Cantor集。这3类不同的谱结构反映在链状聚合物的宏观物理性质上也将有所不同,它无疑会影响聚合物的稳定性及相关(超)导电性能,深入研究这方面问题将有助于对有机超导的认识。     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.