Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems

Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach applied to Poisson algebras. A proof, that Poisson operators constructed near different points of Laurent expansion of Lax functions are equal, is given. All results are illustrated by several examples.Comment: 28 page

Bi-Hamiltonian structures for integrable systems on regular time scales

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors is given by the use of the recursion operators of the Lax hierarchies. The theory is illustrated by $\Delta$-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer hierarchies.Comment: 18 page

The antiapoptotic gene survivin is highly expressed in human chondrosarcoma and promotes drug resistance in chondrosarcoma cells in vitro

Background Chondrosarcoma is virtually resistant to chemotherapy and radiation therapy. Survivin, the smallest member of the inhibitor of apoptosis protein family, is a critical factor for tumor progression and resistance to conventional therapeutic approaches in a wide range of malignancies. However, the role of survivin in chondrosarcoma has not been well studied. We examined the importance of survivin gene expression in chondrosarcoma and analysed its influences on proliferation, apoptosis and resistance to chemotherapy in vitro. Methods Resected chondrosarcoma specimens from which paraffin-embedded tissues could be extracted were available from 12 patients. In vitro experiments were performed in human chondrosarcoma cell lines SW1353 and Hs819.T. Immunohistochemistry, immunoblot, quantitative PCR, RNA interference, gene-overexpression and analyses of cell proliferation and apoptosis were performed. Results Expression of survivin protein was detected in all chondrosarcoma specimens analyzed, while undetectable in adult human cartilage. RNA interference targeting survivin resulted in a G2/M-arrest of the cell cycle and led to increased rates of apoptosis in chondrosarcoma cells in vitro. Overexpression of survivin resulted in pronounced resistance to doxorubicin treatment. Conclusions These findings indicate that survivin plays a role in the pathogenesis and pronounced chemoresistance of high grade chondrosarcoma. Survivin antagonizing therapeutic strategies may lead to new treatment options in unresectable and metastasized chondrosarcoma

Soft network composite materials with deterministic and bio-inspired designs

Hard and soft structural composites found in biology provide inspiration for the design of advanced synthetic materials. Many examples of bio-inspired hard materials can be found in the literature; far less attention has been devoted to soft systems. Here we introduce deterministic routes to low-modulus thin film materials with stress/strain responses that can be tailored precisely to match the non-linear properties of biological tissues, with application opportunities that range from soft biomedical devices to constructs for tissue engineering. The approach combines a low-modulus matrix with an open, stretchable network as a structural reinforcement that can yield classes of composites with a wide range of desired mechanical responses, including anisotropic, spatially heterogeneous, hierarchical and self-similar designs. Demonstrative application examples in thin, skin-mounted electrophysiological sensors with mechanics precisely matched to the human epidermis and in soft, hydrogel-based vehicles for triggered drug release suggest their broad potential uses in biomedical devices. © 2015 Macmillan Publishers Limited. All rights reservedopen7

Classical R-matrix theory for bi-Hamiltonian field systems

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The theory is developed for (1+1)-dimensional case where the space variable belongs either to R or to various discrete sets. Then, the extension onto (2+1)-dimensional case is made, when the second space variable belongs to R. The formalism presented contains many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.Comment: review article, 39 page

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations

Armeniens et Byzantins a L'epoque de Photius : Deux Debats Theologiques apres le Triomphe de L'orthodoxie

Face au conflit qui allait en s'aggravant entre les sièges de Constantinople et de Rome en 862, le patriarche Photius se tourna vers l'Arménie pour y chercher un soutien. Il espérait devenir lui-même facteur d'unité chrétienne au moment où la reconquête byzantine de l'Est anatolien paraissait imminente. L'auteur démontre que Photius a influencé non seulement les relations de Byzance avec l'Occident, mais aussi les débats doctrinaux avec l'Orient. Il explore les sources patristiques de la politique ecclésiastique de Photius afin d'expliquer comment l'attitude de ce patriarche à l'égard des hétérodoxes a permis la formulation d'un accord aussi singulier que celui de Sirakawan. La traduction commentée des documents arméniens concernant ce concile et la controverse qui le suivit est basée sur une nouvelle collation de manuscrits et accompagnée d'un lexique extensif. L'analyse du langage technique développé par les auteurs arméniens lors de la domination arabe permet d'exposer comment évoluait l'articulation de la doctrine de l'Incarnation depuis les grandes controverses de l'époque de Justinien. L'interprétation de ces textes et de leurs sources représente la première étude systématique de la christologie arménienne. Les divergences dogmatiques entre les Arméniens et les Byzantins sont mises en relation avec les différents critères de l'orthodoxie soutenus par les deux Églises