Conditional Monte Carlo method for dynamic systems with random properties

A method is developed for calculating moments and other properties of states X(t) of dynamic systems with random coefficients depending on semi-Markov processes ξ(t) and subjected to Gaussian white noise. Random vibration theory is used to find probability laws of conditional processes X(t)∣ξ(·). Unconditional properties of X(t) are estimated by averaging conditional statistics of this process corresponding to samples of ξ(t). The method is particularly efficient for linear systems since X(t)∣ξ(·) is Gaussian during periods of constant values of ξ(t), so that and its probability law is completely defined by the process mean and covariance functions that can be obtained simply from equations of linear random vibration. The method is applied to find statistics of an Ornstein-Uhlenbeck process X(t) whose decay parameter is a semi-Markov process ξ(t). Numerical results show that X(t) is not Gaussian and that the law of this process depends essentially on features of ξ(t). A version of the method is used to calculate the failure probability for an oscillator with degrading stiffness subjected to Gaussian white noise.     

Studies regarding the formation from metal nitrates and diol of NiM 2 III O4 spinels, inside a silica matrix

The present study deals with preparation and characterization of spinel mixed oxide systems NiM ₂ ^III O₄, where M^III?=?Fe^III, Cr^III. In order to obtain 50% NiFe₂O₄/50% SiO₂ and 50% NiCr₂O₄/50% SiO₂ nanocomposite, we have used a versatile route based on the thermal decomposition inside the SiO₂ matrix, of some particular precursors, coordination compounds of the involved M^II and M^III cations with dicarboxylate ligands. The ligands form in the redox reaction between metal nitrates mixture and 1,3-propanediol at the heating around 140?°C of the gels (tetraethylorthosilicate?Cmetal nitrates?C1,3-propanediol?Cwater). The as-obtained precursors, embedded in silica gels, have been characterized by FT-IR spectrometry and thermal analysis. Both precursors thermally decompose up to 350?°C leading to the formation of the corresponding metal oxides inside the silica matrix. X-ray diffraction of the annealed powders have evidenced the formation of NiFe₂O₄ starting with 600?°C, and NiCr₂O₄ starting with 400?°C. This behavior can be explained by the fact that, by thermal decomposition of the Fe(III) carboxylate at 300?°C, the spinelic phase ??-Fe₂O₃ is formed, which interacts with the NiO, forming the ferrite nuclei. By thermal decomposition of chromium carboxylate, a nonstoichiometric chromium oxide (Cr₂O_3+x ) is formed. In the range 380?C400?°C, Cr₂O_3+x turns into Cr₂O₃ which immediately interacts with NiO leading to the formation of nickel chromites nuclei inside the pores of silica matrix. Both spinels have been obtained as nanocrystalites homogenously dispersed as resulted from XRD and TEM data.     

G-凸空间的择一原理和极大极小不等式

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.     

Thermal stresses in cylindrical Cosserat elastic shells

We consider the problem of thermal stresses in cylindrical elastic shells, modelled as Cosserat surfaces. In the theory of Cosserat shells, the thermal effects are described generally by means of two temperature fields. The problem consists in finding the equilibrium of the shell under the action of a given temperature distribution. The temperature fields are assumed to be general polynomial functions in the axial coordinate, whose coefficients depend on the circumferential coordinate.     

PEO‐b‐PCL Block Copolymers: Synthesis,Detailed Characterization,and Selected Micellar Drug Encapsulation Behavior

Summary: A series of poly(ethylene glycol)‐block‐poly(ε‐caprolactone) diblock copolymers was synthesized and fully characterized. In particular, MALDI‐TOF MS results revealed interesting new insights into their molecular architecture. Small and defined micelles could be prepared from these block copolymers. Utilizing a high‐throughput screening approach, it was observed that these micelles are able to encapsulate/solubilize different guest molecules (e.g. drugs) depending on the solubility of the guest in water. Furthermore, it could be proven that a guest is located within a micelle and that these micelles can be utilized as transport vehicles for the encapsulated guest molecules.

PEO‐b‐PCL diblock copolymers can encapsulate small guest molecules in the core of the polymeric micelles.     

Diastereoselective heterogeneous catalytic hydrogenation of 2-methyl nicotinic acid using pyroglutamate chiral auxiliary

The diastereoselective hydrogenation of 2-methyl nicotinic acid covalently bound to proline ester or pyroglutamic ester over supported metallic catalyst yielded moderate diastereoselectivity (26%). The hydrogenation of the corresponding pyridinium salt was studied and similar de's were achieved.     

Constraints on the Higgs field from black hole physics

We consider the connection between the thermal effect of a black hole and the restoration of a broken symmetry. It appears that the second law of thermodynamics could be violated in a special circumstance. It is shown that this does not happen if we impose some constraints on the Higgs field.This essay recieved Honorable Mention from the Gravity Research Foundation—Ed.     

Interaction of 1-methyl-1-({2-[4-(trifluoromethyl)phenyl]-1,3-thiazol-4-yl}methyl) piperidinium chloride with β-CD: spectroscopic,calorimetric and molecular modeling approaches

Spectroscopic investigation supported by molecular modeling methods has been used to describe the inclusion complex of β-cyclodextrin (β-CD) with 1-Methyl-1-({2-[4-(trifluoromethyl)phenyl]-1,3-thiazol-4-yl}methyl) piperidinium chloride (1MPTMPC) in solution and in solid state. The formation of inclusion complex between the β-CD and the 1MPTMPC has been investigated both in solution and in the solid state. Solution-state complexation between the 1MPTMPC and β-CD was established using ¹H NMR spectroscopy and isothermal titration calorimetry (ITC). From the ¹H NMR spectroscopic studies, 1:1 complex stoichiometry was deduced with an association constant (K) of 925 M^?1. Using an independent binding model, the ITC technique provides a K value of the same order with the one determined by NMR and the thermodynamic parameters ΔH, ΔS and ΔG which reveals driving forces involved during complex formation. The formation of the solid inclusion compound was confirmed by X-ray powder diffraction and differential scanning calorimetry. The most probable conformation of the inclusion complex obtained through a molecular docking investigation corroborates well to ROESY experiment.     

Unconstrained Polarization (Chebyshev) Problems: Basic Properties and Riesz Kernel Asymptotics

Potential Analysis - We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an N-point configuration that maximizes the minimum value of its potential...