Sample-path solution of stochastic variational inequalities

Received July 30, 1997 / Revised version received June 4, 1998 Published online October 21, 1998     

Synthesis, characterization and catalytic behavior of functionalized mesoporous SBA-15 with various organo-silanes

Mesoporous silica SBA-15 has been synthesized and functionalized by one-step synthesis method to widen their various application possibilities. In this study, phenyltrimethoxysilane (PTMS), 3-mercaptopropyltrimethoxysilane (MPTMS) and trimethoxypropylsilane (TMPS) were used as silane precursors for the functionalization, and after treated with HCl solution, their catalytic activities were evaluated in the lactic acid-methanol esterification. The presence of anchoring of functional groups on SBA-15 was proved by XRD, FT-IR, BET surface area and pore size distributions. Good catalytic activity was observed especially for SBA-15-SO(3)H-MPTMS, and the catalytic activity order was determined as follows: SBA-15-SO(3)H-MPTMS>SBA-15-TMPS>SBA-15-PTMS, which is directly associated with the surface area, pore size and pore volume. As compared with homogeneous catalyst, SBA-15-SO(3)H-MPTMS heterogeneous catalyst shows remarkable performance, such as separation, recovery and reusability.     

Modular photoinduced grafting onto approach by ketene chemistry

A modular approach for the synthesis of graft copolymers by the combination of reversible addition–fragmentation chain‐transfer (RAFT) polymerization and photoinduced acylation processes is described. In the two‐step approach, first the copolymers of benzodioxinone containing monomer, namely, 4‐oxo‐2,2‐diphenyl‐4H‐benzo[d][1,3]dioxin‐7‐yl methacrylate (BDMA) and methyl methacrylate (MMA) in different feed ratios were prepared by RAFT polymerization. In the subsequent step, dichloromethane solutions of these copolymers (PMMA‐co‐PBDMA) were irradiated at λ = 300 nm in the presence of independently prepared hydroxyl functional polymers such as poly(ethylene glycol) (MeO‐PEG‐OH) and poly(?‐caprolactone) (PCL‐OH). Side‐chain esterification reaction between photochemically generated ketene groups and hydroxyl functionalities resulted in the formation graft copolymers. The intermediates and final graft copolymers were characterized by ¹H NMR, UV, IR, fluorescence, and GPC measurements. The success of the process was also confirmed by a model reaction using pyrene methanol. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 274–280     

Modeling of an insurance system and its large deviations analysis

We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R². The claim sizes {X_i} are an iid sequence with light tails. The interarrival times {τ_i} between claims are also iid and exponentially distributed. There is a fixed premium rate c₁ that the customers pay; c<c₁ of this rate goes to the reinsurance company. If a claim size is greater than R the reinsurance company pays for the claim. We study the bankruptcy of this system before it is able to handle N number of claims. It is assumed that each company has initial reserves that grow linearly in N and that the reinsurance company has a larger reserve than the insurance company. If c and c₁ are chosen appropriately, the probability of bankruptcy decays exponentially in N. We use large deviations (LD) analysis to compute the exponential decay rate and approximate the bankruptcy probability. We find that the LD analysis of the system decouples: the LD decay rate γ of the system is the minimum of the LD decay rates of the companies when they are considered independently and separately. An analytical and numerical study of γ as a function of (c,R) is carried out.     

Numerical solution of a class of complex differential equations by the Taylor collocation method in elliptic domains

An approximate method for solving higher‐order linear complex differential equations in elliptic domains is proposed. The approach is based on a Taylor collocation method, which consists of the matrix represantation of expressions in the differential equation and the collocation points defined in an elliptic domain. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

An integrated numerical method with error analysis for solving fractional differential equations of quintic nonlinear type arising in applied sciences

In this study, fractional differential equations having quintic nonlinearity are considered by proposing an accurate numerical method based on the matching polynomial and matrix‐collocation system. This method provides an integration between matrix and fractional derivative, which makes it fast and efficient. A hybrid computer program is designed by making use of the fast algorithmic structure of the method. An error analysis technique consisting of the fractional‐based residual function is constructed to scrutinize the precision of the method. Some error tests are also performed. Figures and tables present the consistency of the approximate solutions of highly stiff model problems. All results point out that the method is effective, simple, and eligible.     

A Taylor method for numerical solution of generalized pantograph equations with linear functional argument

This paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this paper, we introduce a numerical method based on the Taylor polynomials for the approximate solution of the pantograph equation with retarded case or advanced case. The method is illustrated by studying the initial value problems. The results obtained are compared by the known results.     

Non‐perturbative solution of three‐dimensional Navier–Stokes equations for the flow near an infinite rotating disk

In this paper, we present Homotopy perturbation method (HPM) and Padé technique, for finding non‐perturbative solution of three‐dimensional viscous flow near an infinite rotating disk. We compared our solution with the numerical solution (fourth‐order Runge–Kutta). The results show that the HPM–Padé technique is an appropriate method in solving the systems of nonlinear equations. The mathematical technique employed in this paper is significant in studying some other problems of engineering. Copyright © 2009 John Wiley & Sons, Ltd.