Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Molar heat capacities and volumes of transfer of cytosine,thymine, caffeine and 1,3-diethylthymine to aqueous solutions of glycyl-glycine and L-α-alanyl-L-α-alanine at 25°C

Densities and specific heat capacities of ternary aqueous systems containing dipeptides (glycyl-glycine or L--alanyl-L--alanine) and nucleic acid bases (cytosine or thymine) or their alkyl derivatives (1,3-diethylthymine or caffeine) were determined at 25°C by flow calorimetry and flow densimetry. The partial molar volumes and heat capacities of transfer at infinite dilution of the different nucleic acid bases from water to water+dipeptide solutions were obtained therefrom. Except for the case of the transfer of cytosine to aqueous glycyl-glycine solutions where a small positive dependence of the transfer quantities was observed with the dipeptide concentration, the values of the heat capacities of transfer were in general low, positive or negative, depending on the compensation of hydrophobic-hydrophilic interactions between the dipeptide and the base. The volumes of transfer of most of the bases are very small, within the limit of the experimental error.     

X-ray emission spectroscopy with EPMA applied to high Tc Superconductors using new spectrometer crystals

The High Temperature Superconductors are characterized by a very anisotropical structure and by typical arrangements of Cu- and O-atoms within CuO₂-planes. In studying the electronic structure of these compounds there is a strong demand for high resolution valence band spectroscopy. Using an electron probe microanalyzer we study the X-ray emission of O-K_ga and Cu-L emerging from polycrystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₂Cu₃O₁₀. The O-K emission band is analyzed using a chlinochlore crystal in (001) orientation (2d = 28.4 Å). For the Cu-L emission band we use a beryl crystal in (10¯10) orientation (2d = 15.9 Å). Furthermore, orientation dependent X-ray emission spectroscopy of single-crystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₁Cu₂O₈ specimens was performed. We present the partial O-K spectra which represent the O-2p ( = x, y, z) electronic densities of states of the valence band and compare them with calculated data.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

Geometric indices and the Alexander polynomial of a knot

It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

The theoretical basis of column chromatography in multicomponent separations. Part 2: Peak capacity. Column systems with good selectivity

The selectivity of a column system, S, defined by equation 28, includes a variation coefficient (β) of plate number with capacity ratio which has a large influence on the peak capacity, as shown in Fig. 18. Some typical chromatograms are given. In order to predict S for a column system from Kovat's Index, equations 40 and 41 are given to calculate the constant of the carbon number rule for squalane at different temperatures or for different stationary phases. The specific retention value of heptane on squalane at different temperatures can be calculated from equation 42. The nonpolarity index, defined by equation 43, was used to calculate the retention value of heptane on various stationary phases. In liquid chromatography, the order of elution may be reversed by changing the composition of the eluent on the same chemically bonded silica (manufactured in China). The linear relations between the log retention values of different kinds of solutes or of a single solute on the silicas of different surface areas when using the same eluent are given.     

校正峰电位漂移偏最小二乘极谱催化波同时测定轻稀土

应用Ｍ２７３．Ａ电化学系统中的线性扫描技术，确定了８．０×１０－５ｍｏｌ／Ｌ二甲酚橙及ｐＨ４．０ＨＡｃ－ＮａＡｃ缓冲体系为偏最小二乘极谱法同时测定Ｌａ、Ｃｅ、Ｐｒ、Ｎｄ、Ｓｍ、Ｅｕ的最佳极谱体系。６种稀土元素的线性范围均在１．０× １０－７～１．２ × １０－５ｍｏｌ／Ｌ。并对极谱峰电位随浓度漂移进行了校正，提高了方法的准确度。