The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation

We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong L^p{\cal L}^{p} space is the null solution, infinitely many self-similar solutions do exist in weak- L^p{\cal L}^{p} spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained.     

Clustering of spectra and fractals of regular graphs

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labeled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind.     

Differentiation of species of the Baccharis genus by HPLC and chemometric methods.

Phytochemical investigation of the aerial parts of three Baccharis species (Asteraceae family) was performed using HPLC and chemometric methods, with the objective of distinguishing between three morphologically very similar species: Baccharis genistelloides Persoon var. trimera (Less.) DC, B. milleflora (Less.) DC and B. articulata (Lam.) Persoon. With the help of Principal Component Analysis (PCA) and variance weights, it was possible to characterize the chromatographic profiles of the alcoholic extracts of the three species. Application of Soft Independent Modeling of Class Analogy (SIMCA) and K-Nearest Neighbor (KNN) methods on a training set of 74 extracts resulted in models that correctly classified all eight samples in an independent test set.     

Making equation of state models predictive: Part 2: An improved PCP-SAFT equation of state

We use the PCP-SAFT equation of state, which is of the Van der Waals type and has a sound physical basis, to predict mixture properties, such as vapor–liquid and liquid–liquid equilibria, as well as excess enthalpies. We use molecular properties, such as dipole moment, quadrupole moment, polarizability and dispersion interaction coefficients, that have been determined quantum mechanically in Part I of this publication and adjust the remaining three pure compound parameters to pure compound data. We finally present a new combination rule for the dispersion energy parameter ? that is based on the quantum mechanically determined data. The predictions based on quantum mechanically determined pure compound properties along with the new combination rule show an improved performance compared to the original PCP-SAFT combination rule.     

Voltammetric determination of methyl parathion, ortho, meta and para nitrophenol with a carbon paste electrode modified with C18

Summary The determination of methyl-parathion (MPT), ortho (ONP), meta (MNP) and para nitrophenol (PNP) has been studied by differential pulse voltammetry with a carbon-paste electrode modified with 50% (w/w) of C₁₈. A study of the influence of the pH in the preconcentration cell and the measurement cell was carried out for an electrode with 50% modifier and an accumulation time of 5 min. The voltammograms were recorded with a sweep rate of 40 mV s^–1 and a pulse amplitude of 50 mV. With the optimum conditions of pH for both of the steps, various other variables were studied. The variables for each compound were optimized and the possibility of application to the determination of a mixture of the four compounds was investigated. The determination limits found for all the compounds are: 2 ng ml^–1 for ONP, 5 ng ml^–1 for MNP, 4.3 ng ml^–1 for PNP and 7.9 ng ml^–1 for MPT. The method was applied to samples of a small lake which gathers rain water and water filtered from land on which cereals are grown.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

3,3,6,6-四甲基-9-邻氯苯基-1,8-二氧代-3,4,5,6,7,9-六氧化氧杂蒽的合成和晶体结构

标题化合物C23H25对O3Cl是由邻氯苯甲醛与5，5-二甲基1，3-环己二酮在N，N-二甲基甲酸腹中反应而得。结构通过单晶X-射线衍射法确定，其晶体属于单科晶系，空间群=1632。晶体结构用直接法解出，使用全矩阵最小二乘法对原子参数进行修正，最后的偏离因子为R=0．054，Rw一0．063。在晶体结构中，吡喃环与苯环之间的两面角为92．43°。     

Efficient palladium-catalyzed nucleophilic addition of triorganoindium reagents to carbocyclic derivatives

Palladium (0)-catalyzed allylic substitution reactions employing triorganoindium reagents have been investigated. In situ generated vinyl- and arylindiums react with substituted and unsubstituted cyclohex-2-enyl esters in the presence of 1-3 mol % Pd(2)(dba)(3) to produce vinyl- or arylcyclohexenes in moderate to excellent yields. The stereoselectivity of this process was also examined, and evidence is presented that the reaction proceeds with inversion of stereochemical configuration.