Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Abstract

In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise.     

Synthesis,structural characterization and in vitro cytotoxic activity of novel polymeric triorganotin(IV) complexes of urocanic acid

Two novel triorganotin carboxylate complexes of the biologically active urocanic acid have been synthesized and characterized. Elemental analysis, melting point, spectroscopic techniques – IR, ¹H, ¹³C and ¹¹⁹Sn NMR – mass spectrometry and X‐ray diffraction studies have been used for structural characterization. Crystal structures of the tin(IV) derivatives show that urocanic acid acts as a bridging bidentate ligand through its imidazole nitrogen atom and its carboxylic group, producing a polymeric one‐dimensional chain. The molecular structures of the complexes, catena‐poly‐tri(n‐butyl)tin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (1) and catena‐poly‐triphenyltin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (2), present a distorted trigonal–bipyramidal configuration. This is further confirmed by ¹¹⁹Sn NMR in the solid state. The tin(IV) derivatives form double‐stranded ribbons via N―H^…O―H bonds. Nevertheless, the compounds are essentially monomeric in solution, with a tetrahedral configuration as observed by ¹¹⁹Sn NMR in solution. The cytotoxic activity of the titled compounds has been tested against six human cell lines and the corresponding IC₅₀ values are reported. Both tin(IV) compounds have a high to very high in vitro cytotoxic activity against the tumor cell lines K562, HCT‐15 and MCF‐7. Compound 1 is 86 times more active than cisplatin in the HTC‐15 cell line. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis and characterization of intrinsic high‐barrier polyimide derived from a novel diamine monomer containing rigid planar moiety

A new diamine monomer containing rigid planar fluorenone moiety, 2,7‐bis(4‐aminophenyl)‐9H‐fluoren‐9‐one, was synthesized through Suzuki coupling reaction. Then it was reacted with pyromellitic dianhydride to obtain a polyimide (FOPPI) via a conventional two‐step polymerization process. The prepared FOPPI exhibits excellent barrier properties, with the oxygen transmission rate and water vapor transmission rate low to 3.2 cm³·m^?2·day^?1 and 2.9 g·m^?2·day^?1, respectively. The results of wide angle X‐ray diffractograms, positron annihilation lifetime spectroscopy, and molecular dynamics simulations reveal that the excellent barrier properties of FOPPI are mainly ascribed to the crystallinity, high chain rigidity, and low free volume, which are resulted from the rigid planar moiety. FOPPI also shows outstanding thermal stability and mechanical properties with a glass transition temperature up to 420 °C, 5% loss temperature of 607 °C, coefficient of thermal expansion of 1.28 ppm K^?1, and tensile strength of 150.8 MPa. The polyimide has an attractive potential application prospect in the flexible electronics encapsulation area. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 2373–2382     

Multiple Statistical models for simulation and prediction of nonlinear processes

The paper describes a parameterisation procedure for multiple nonlinear equations with intercepts. These equations may consist of numerous members with few practical limitations on their structure. Examples are given on the application of the procedure to simulation in the areas of chemical technology and hydrology. Advantages of the proposed method are simplicity of the fitting procedure, high accuracy of simulations and more reliable simulations beyond the calibration range     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Monotonicity of certain integrals involving gamma distributions and their applications in multiple comparisons

Barlow and Gupta (1969) and Alam (1970) studied the monotonicity of two integrals, involving gamma distributions, that arise in certain ranking and selection problems. In this paper, we shall unify their results by studying the monotonicity of two generalized versions of integrals considered by them. We will also provide applications of derived results in study of certain multiple comparison procedures.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

A novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.