On the concept of matrix derivative

We discuss how to generalize the concept of vector derivative to matrix derivative, propose two definitions, a ‘broad’ and a ‘narrow’ one, compare the two definitions, and argue in favor of the narrow definition.     

Kirchhoff systems with dynamic boundary conditions

We are interested in the study of the global non-existence of solutions of hyperbolic nonlinear problems, governed by the p-Kirchhoff operator, under dynamic boundary conditions, when p>p_n with p_n<2. The systems involve nonlinear external forces and may be affected by a perturbation of the type |u|^p−2u. Several models already treated in the literature are covered in special subcases, and concrete examples are provided for the source term f and the external nonlinear boundary damping Q.     

L-fuzzy ⋎ and ⋏ hyperoperations and the associated l-fuzzy hyperalgebras

In this paper we study two fuzzy hyperoperations, denoted by ⋎ (which can be seen as a generalization of ∨) and ⋏ (which can be seen as a generalization of ∧). ⋎ is obtained from a family of crisp ∨; _p hyperoperations and ⋏ is obtained from a family of crisp ∧ _p hyperoperations. The hyperstructure (X, ⋎, ∧) resembles ahyperlattice and the hyperstructure (X, ∨, ⋏) resembles adual hyperlattice     

Thermodynamic data for nonmesomorphic solutes at infinite dilution in the nematic and isotropic phases of hexylcyanobiphenyl

Infinite dilution solute activity coefficients 72/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0"> _o ² , partial molar excess enthalpies 72/10953_2005_Article_BF01036378_TeX2GIFIE1.gif" alt=" $$\overline H ^e$$ " align="middle" border="0"> and entropies 72/10953_2005_Article_BF01036378_TeX2GIFIE2.gif" alt=" $$\overline S ^e$$ " align="middle" border="0"> , and partial molar enthalpies ( 72/10953_2005_Article_BF01036378_TeX2GIFIE3.gif" alt=" $$(\Delta \overline H ^e )$$ " align="middle" border="0"> ) and entropies ( 72/10953_2005_Article_BF01036378_TeX2GIFIE4.gif" alt=" $$(\Delta \overline S )$$ " align="middle" border="0"> ) of solution, obtained using gas-liquid chromatography (GLC), are reported for thirty nonmesomorphic solutes in the nematic and isotropic phases of p-n-hexyl-p72/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-cyanobiphenyl (6CB). The solutes studied include normal and branched alkanes, alkenes and hexadienes (with some cis and trans isomers), and benzene. The results corroborate earlier studies on other members of the p-n-alkyl-p72/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-cyanobiphenyl homologous series of liquid crystals. The results demonstrate the effect that solute structure (size, shape, flexibility, polarizability and polarity) has on the solution process. Thermodynamic data for the cis and trans isomers of 2-pentene and 2-hexene are examined. A method for the simultaneous examination of the effects of both solute and solvent structures on the solution process is suggested.     

Enthalpy, heat of fusion and specific electrical resistivity of pure silver, pure copper and the binary Ag-28Cu alloy

Within the present work, recent investigation carried out with a fast pulse-heating technique on silver, copper and the Ag-28Cu binary alloy in the solid and the molten states are presented.Properties like enthalpy or electrical resistivity of a pulse-heated sample can be obtained for a wide temperature range (solid state up into the liquid state) from the directly measured base quantities, namely: current through the sample, voltage drop across the specimen and pyrometric determined temperature. As a further result, enthalpy of fusion is computable from the enthalpy values at the melting transition or the solidus/liquidus transition. These thermophysical properties (mainly of the melting transition and the subsequent liquid phase) are commonly used as input data for numerical casting simulations.The measurements presented within this work deal with group¹ 11 elements silver, copper and the binary eutectic 72-28 (wt.%) alloy of the two elements, respectively. One of the main goals of this work is to investigate to which extent the thermophysical properties of the two pure materials influence or determine the properties of its corresponding alloy. It is to proof if data for pure materials can be used to predict the thermophysical properties of simple alloys. For this specific copper-silver alloy, there is a certain mutual solid solubility with a quite large miscibility gap. Ag-28Cu is not a single phase alloy but an eutectic alloy with two phases.     

A short, simple and general approach for the synthesis of (3S,4S)-3-methoxy-4-methylamino pyrrolidine and (3S,4R)-3-methoxy-4-methylamino pyrrolidine

A general and efficient stereoselective approach for the synthesis of (3S,4S) and (3S,4R)-3-methoxy-4-methylamino pyrrolidines, a part of the structure of AG-7352, a naphthyridine antitumor agent and quinoline antibacterial compounds has been described.     

辅助配体调控的荧光Cd-MOFs: 乙酰丙酮的荧光增强和Cr(Ⅵ)的荧光猝灭

将柔性苄氨基三羧酸配体5-(3-羧基-4-甲氧基苄氨基)间苯二甲酸(H₃L)与硝酸镉和不同含氮配体在溶剂热条件下反应, 制得了配合物{[Cd(HL)(bpea)·H₂O]·H₂O·DMF}_n(1)、 {[Cd(HL)(bpp)·H₂O]·2H₂O·DMF}_n(2)和 {[Cd(HL)(dmbpy)]·DMF}_n(3)[bpea=bis(4-pyridyl)ethane; bpp=1,3-bis(4-pyridyl)propane; dmbpy=5,5′-dimethyl-2,2′-bipyridine]. 3个配合物分别表现出有趣的2D→2D穿插结构和一维带状结构. 荧光性质测试结果表明, 所有配合物的荧光均可被Cr₂O₇^2?猝灭, 而在乙酰丙酮的DMF溶液中, 只有配合物1表现出明显的荧光增强. 羧酸配体的柔性、 含氮配体的类型和结构可以调控配合物的结构和荧光性能.     

A comparative study of Gaussian geostatistical models and Gaussian Markov random field models

Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GMRFs) are two distinct approaches commonly used in spatial models for modeling point-referenced and areal data, respectively. In this paper, the relations between GGMs and GMRFs are explored based on approximations of GMRFs by GGMs, and approximations of GGMs by GMRFs. Two new metrics of approximation are proposed : (i) the Kullback-Leibler discrepancy of spectral densities and (ii) the chi-squared distance between spectral densities. The distances between the spectral density functions of GGMs and GMRFs measured by these metrics are minimized to obtain the approximations of GGMs and GMRFs. The proposed methodologies are validated through several empirical studies. We compare the performance of our approach to other methods based on covariance functions, in terms of the average mean squared prediction error and also the computational time. A spatial analysis of a dataset on PM_2.5 collected in California is presented to illustrate the proposed method.     

A fuzzy clustering application to precise orbit determination

In recent years, fuzzy logic techniques have been successfully applied in geodesy problems, in particular to GPS. The aim of this work is to test a fuzzy-logic method with an enhanced probability function as a tool to provide a reliable criteria for weighting scheme for satellite-laser-ranging (SLR) station observations, seeking to optimize their contribution to the precise orbit determination (POD) problem. The data regarding the stations were provided by the International Laser Ranging Service (ILRS), NASA/Crustal Dynamics Data Information System (CDDIS) provided the satellite data for testing the method. The software for processing the data is GEODYN II provided by NASA/Goddard Space Flight Center (GSFC). Factors to be considered in the fuzzy-logic clustering are: the total number of LAGEOS passes during the past 12 months, the stability measure of short- and long-term biases, the percentage of LAGEOS normal points that were accepted in CSR weekly LAGEOS analysis, and the RMS uncertainty of the station coordinates. A fuzzy-logic statistical method allows classifying the stations through a clear ‘degree of belonging’ to each station group. This degree of belonging translates into a suitable weight to be assigned to each station in the global solution. The first tests carried out showed improvements in the RMS of the global POD solution as well as individual stations, to within a few millimeters. We expect further work would lead to further improvements.