Boundary-domain integro-differential equation of elastic damage mechanics model of stationary drilling

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Fragments of Boethius: The Reconstruction of the Cotton Manuscript of the Alfredian Text

‘These fragments I have shored against my ruins’: T. S. Eliot's metaphor in The Waste Land evokes the evanescent frailty of human existence and worldly endeavour with a poignancy that the Anglo-Saxons would surely have appreciated. Such a concept lies at the heart of Boethius's De consolatione Philosophiae, and perhaps prompted King Alfred to include this work amongst those which he considered most necessary for all men to know. Written in the early sixth century, Boethius's work was translated from Latin into Old English at the end of the ninth century, possibly by Alfred himself. It survives in two versions, one in prose (probably composed first) and the other in prose and verse, containing versifications of Boethius's Latin metres which had originally been rendered as Old English prose. It is the latter of these versions which will be the focus of my discussion here. Damaged beyond repair by fire and water, the set of fragments which contains this copy will be seen to epitomize the ideas imparted by the work in ways that Alfred could never have envisaged

Analysis of extended boundary-domain integral and integro-differential equations of some variable-coefficient BVP

For a function from the Sobolev space H1(Ω) definitions of non-unique external and unique internal co-normal derivatives are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domain Ω, where they are prescribed, to the domain boundary, where they are not. The notions are then applied to formulation and analysis of direct boundary-domain integral and integro-differential equations (BDIEs and BDIDEs) based on a specially constructed parametrix and associated with the Dirichlet boundary value problems for the "Laplace" linear differential equation with a variable coefficient and a rather general right hand side. The BDI(D)Es contain potential-type integral operators defined on the domain under consideration and acting on the unknown solution, as well as integral operators defined on the boundary and acting on the trace and/or co-normal derivative of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, and equivalence of the BDIEs/BDIDEs/BDIDPs to the original BVP are investigated in appropriate Sobolev spaces

Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

Copyright @ 2006 Tech Science PressA quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Using a cut-off function approach, the corresponding localized parametrix of the auxiliary problem is constructed to reduce the problem to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations for the displacement increments

Cancer vaccines: uses of HLA transgenic mice compared to genetically modified mice

Many tumor antigens have been identified that can be targeted by the immune system. Animal models that have been genetically modified to express human HLA molecules instead of their own MHC antigens have shown to be valuable in the discovery of peptides derived from tumor antigens many of which have since been used in clinical trials with varying degrees of success. Although these models are not perfect, they nonetheless allow transplantable tumor models to be developed to evaluate novel vaccination strategies that can then be applied in humans. In addition animals that have been genetically modified to “spontaneously” generate tumors that will grow within their correct environment are of greater value for studying angiogenesis, metastasis and the relationship between the immune system and tumor in a physiological setting. In this review, mice genetically modified to express HLA genes or to spontaneously develop tumors are discussed, highlighting their advantages and limitations as preclinical models for cancer immunotherapy

Localized direct boundary–domain integro–differential formulations for scalar nonlinear boundary-value problems with variable coefficients

Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered. Localized parametrices of auxiliary linear partial differential equations along with different combinations of the Green identities for the original and auxiliary equations are used to reduce the BVPs to direct or two-operator direct quasi-linear localized boundary-domain integro-differential equations (LBDIDEs). Different parametrix localizations are discussed, and the corresponding nonlinear LBDIDEs are presented. Mesh-based and mesh-less algorithms for the LBDIDE discretization are described that reduce the LBDIDEs to sparse systems of quasi-linear algebraic equations