On some stochastic singular integro-partial differential equations and the parabolic transform

Some stochastic singular integro-partial differential equations are studied without any restrictions on the characteristic forms of the partial differential operators. Linear and nonlinear cases are studied. Using the parabolic transform, existence and stability results are obtained. The Cauchy problem of fractional stochastic partial differential equations can be considered as a special case from the obtained results. Key words: Singular integral equations, Stochastic partial differential equations, Existence and stability of solutions, Fractional stochastic partial differential equations

Generalized random processes and Cauchy's problem for some partial differential systems

In this paper we consider a parabolic partial differential system of the form DtHt=L(t,x,D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained

Cross-border corporate insolvency: a modest proposal for an enhanced international approach

PhDThe ongoing process of globalisation has witnessed an increase in cross-border corporate insolvencies involving multinational enterprises (MNEs). Yet, national insolvency laws have proven themselves ill-equipped to handle such matters in an international setting. Responsible policy-makers and academics argue for the creation of a viable international insolvency approach. This debate has revolved around an "either-or" spectrum of (1) the theory of "Universality" that proposes a single court charged with implementing a single bankruptcy law to worldwide claimants, and (2) the theory of "Territoriality" that asserts each jurisdiction can only adjudicate the debtor's insolvency on a territorial basis and distribute local assets to local claimants. But, this debate yet has yielded no practical solution. This thesis suggests that these two theories are not mutually exclusive, and both may be utilized in developing a pragmatic and "better" international insolvency framework. To date, there has been one non-binding international instrument based on moderate choice of forum/law provisions: the UNCITRAL Model Law on Cross-Border Insolvency (the Model Law). Although the Model Law has significant merits, it falls short of the broader expectations minimally acceptable international insolvency system should fulfill. In addition, the regional European Union Council Regulation on Insolvency Proceedings (the Regulation) has recently been enacted. This thesis will argue that, while recognizing the special sui generic nature of the EU framework, important lessons can be learned from this Regulation, and when combined with certain elements from a revamped Model Law approach, a "better" international insolvency framework may be found. The concluding observations of this thesis will touch upon a range of existing international vehicles that may be complementary or alternative vehicles to channel interim reforms. Unless otherwise expressly indicated, this thesis speaks as of 1 January 2006

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders

Toeplitz matrix method and nonlinear integral equation of Hammerstein type

AbstractThe existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated

Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation

In this paper, the existence and uniqueness about the solution for a class of abstract stochastic fractional-order differential equations                                           where  in and  are given functions, are investigated, where the fractional derivative is described in Caputo sense. The fractional calculus, stochastic analysis techniques and the standard $Picard's$ iteration method are used to obtain the required

A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition

In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,We shall use the Yamada-Watanabe condition for ”pathwise uniqueness” of the solutions of the stochastic differential equation; this condition is weaker than the usual Lipschitz condition. The proof is based on Bihari’sinequality

Fractional integrated semi groups and nonlocal Cauchy problem for abstract nonlinear fractional differential equations

Some classes of fractional abstract differential equations with α-integrated semi groups are studied in Banach space. The existence of a unique solution of the nonlocal Cauchy problem is studied. Some properties are given

Pleuropulmonary Blastoma: A Case Report and Review of the Literature

The case of 38-month-old boy is being reported who was brought to the pediatrics clinic with fever, cough, hemoptysis, and breathing difficulty. Imaging studies revealed a right lower chest mass. Lobectomy and histopathological examination revealed it to be predominantly solid pleuropulmonary blastoma type II. It is a rare pediatric pleuropulmonary tumor with aggressive behavior and tendency to spread to the brain. The case is being presented to make the general histopathologist aware of this rare entity and to highlight to the pediatric physicians/surgeons, radiologists, and histopathologists the fact that lung cysts in infants and young children should be evaluated seriously and sampled thoroughly to diagnose cases of type I pleuropulmonary blastoma which will progress over time to type II or type III tumors. Also the siblings and first degree relatives of the patient should be screened for associated pulmonary and extrapulmonary benign and malignant conditions