Modelling the CPI using a lognormal diffusion process and implications on forecasting inflation

The Maximum Likelihood estimator is used within a lognormaldiffusion process and closed form analytical solutions are obtained.The monthly CPI forecasts are estimated for the period between1970 and 2002. The quarterly estimates of inflation rates areobtained from monthly forecasts rather than from quarterly data.This has significantly improved the estimates of inflation rates.The model also produced a superior fit as compared to randomwalk and GARCH(p,q)-M models. The adopted approach is foundto be simple, economical and generally suitable for modellingstochastic processes that reflect aggregation over time stemmingfrom many factors, and in which the transition path betweenconsecutive states is relatively smooth.     

Analytical sequences of upper and lower solutions for a class of elliptic equations

Comparison arguments are applied to derive decreasing sequences of upper solutions and increasing sequences of lower solutions for a class of nonlinear elliptic equations. The monotonicity of the two sequences is proven. These polynomial sequences are obtained by applying new algorithms and solving linear differential equations. The obtained upper and lower solutions are analytic and have closed forms. Different examples are presented to explore the effectiveness of the new algorithms. The presented ideas and algorithms can be extended to deal with different classes of equations.     

6-Chlorothieno[2,3-<Emphasis Type="Italic">e</Emphasis>]-1,4,2-dithiazine-3(2<Emphasis Type="Italic">H</Emphasis>)-thione-1,1-dioxide,Ammonium Salt Sesquihydrate: Synthesis,Crystal Structure and Density Functional Calculations

Abstract  

The title compound crystallizes in the monoclinic space group C2/c space group, with unit cell dimensions of a = 15.6684(3) ?, b = 7.3974(2) ?, c = 21.2669(5) ?; β = 106.7770(10)° (Z = 8). In the title compound, NH₄ ⁺·C₅HClNO₂S₄ ^–·1.5 H₂O, the 1,4,2-dithiazine ring adopts a distorted half-chair conformation. The structure displays several cooperative intermolecular N/O–H···N/O/S hydrogen-bonding interactions, giving rise to a two-dimensional layers packing motif. The layers are built up from seven component entities formed via extensive intermolecular N/O–H···N/O/S hydrogen bonds involving 6-chlorothieno[2,3-e]-1,4,2-dithiazine-3(2H)-thione-1,1-dioxide anions, ammonium cations and water molecules. The geometry of the title compound was fully optimized using a Density functional B3LYP/6-31G(d) and B3LYP/6-31+G(d) methods and the results were consistent with experimental values. The binding energy and associated basis set superposition as well as the thermodynamic quantities were calculated.     

Convergence analysis for an iterative method for solving nonlinear parabolic systems

In a recent work, we have proposed a new iterative method based on the eigenfunction expansion to integrate nonlinear parabolic systems sequentially. In this paper, we prove that the method is convergent and give analytical rate for its convergence. Moreover, we determine the number of iterations needed to obtain a solution with a pre-determined level of accuracy. We then illustrate the convergence analysis with a problem in combustion theory. It is expected that the convergence analysis can be used for similar systems with time dependence.     

An efficient method for analyzing the solutions of the Korteweg-de Vries equation

A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.     

Monotone iterative sequences for nonlinear boundary value problems of fractional order

In this paper we extend the maximum principle and the method of upper and lower solutions to boundary value problems with the Caputo fractional derivative. We establish positivity and uniqueness results for the problem. We then introduce two well-defined monotone sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. A numerical iterative scheme is introduced to obtain an accurate approximate solution for the problem. The accuracy and efficiency of the new approach are tested through two examples.     

Synthesis,characterization, inequivalency of methylene proton and proton lability in the amino ligand of trans-[dichloro[(N-ferrocenyl methyl)amine](eta2-ethene)platinum] complexes

A series of complexes of the type trans-[PtCl(2)(eta(2)-ethene)(N-ferrocenyl methyl)amine)] complexes, N-ferrocenylmethylamine=[(eta(5)-C(5)-H(5))Fe(eta(5)-C(5)-H(4)CH(2)NHR], R=(Me, Pr(i), Bu(s), Bu(t), CH(2)Ph, (p-OCH(3))Ph, (o-(OCH(3))Ph, (p-CH(3))Ph, (o-CH(3))Ph, (m-CH(3))Ph, (p-Cl)Ph) have been synthesized and characterized on the basis of elemental analysis, IR, 1H and 13C NMR spectroscopic methods. The CpCH(2)NHR (Cp=(eta(5)-C(5)H(5))Fe(eta(5)-C(5)H(4)), region of the 1H NMR spectrum of the complexes has been investigated and shown to contain inequivalent methylene protons, NH-CH and 195Pt-N-CH coupling take place.