Minimum energy states of the plasma pinch in standard and Hall magnetohydrodynamics

Axisymmetric relaxed states of a cylindrical plasma column are found analytically in both standard and Hall magnetohydrodynamics (MHD) by complete minimization of energy with constraints imposed by invariants inherent in corresponding models. It is shown that the relaxed state in Hall MHD is the force-free magnetic field with uniform axial flow and/or rigid azimuthal rotation. The relaxed states in standard MHD are more complex due to the coupling between velocity and magnetic field. Application of these states for reversed-field pinches (RFP) is discussed

ZIF-8 Modified Polypropylene Membrane: A Biomimetic Cell Culture Platform with a View to the Improvement of Guided Bone Regeneration.

PurposeDespite the significant advances in modeling of biomechanical aspects of cell microenvironment, it remains a major challenge to precisely mimic the physiological condition of the particular cell niche. Here, the metal-organic frameworks (MOFs) have been introduced as a feasible platform for multifactorial control of cell-substrate interaction, given the wide range of physical and mechanical properties of MOF materials and their structural flexibility.ResultsIn situ crystallization of zeolitic imidazolate framework-8 (ZIF-8) on the polydopamine (PDA)-modified membrane significantly raised surface energy, wettability, roughness, and stiffness of the substrate. This modulation led to an almost twofold increment in the primary attachment of dental pulp stem cells (DPSCs) compare to conventional plastic culture dishes. The findings indicate that polypropylene (PP) membrane modified by PDA/ZIF-8 coating effectively supports the growth and proliferation of DPSCs at a substantial rate. Further analysis also displayed the exaggerated multilineage differentiation of DPSCs with amplified level of autocrine cell fate determination signals, like BSP1, BMP2, PPARG, FABP4, ACAN, and COL2A. Notably, osteogenic markers were dramatically overexpressed (more than 100-folds rather than tissue culture plate) in response to biomechanical characteristics of the ZIF-8 layer.ConclusionHence, surface modification of cell culture platforms with MOF nanostructures proposed as a powerful nanomedical approach for selectively guiding stem cells for tissue regeneration. In particular, PP/PDA/ZIF-8 membrane presented ideal characteristics for using as a barrier membrane for guided bone regeneration (GBR) in periodontal tissue engineering

Hopf algebras in dynamical systems theory

The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this long-established theme, through the tinted glasses of a (Hopf and Rota-Baxter) algebraic point of view. By reviewing, reformulating and strengthening known results, we give evidence for the claim that the use of Hopf algebra allows for a refined analysis of differential equations. We revisit the renowned Campbell-Baker-Hausdorff-Dynkin formula by the modern approach involving Lie idempotents. Approximate solutions to differential equations involve, on the one hand, series of iterated integrals solving the corresponding integral equations; on the other hand, exponential solutions. Equating those solutions yields identities among products of iterated Riemann integrals. Now, the Riemann integral satisfies the integration-by-parts rule with the Leibniz rule for derivations as its partner; and skewderivations generalize derivations. Thus we seek an algebraic theory of integration, with the Rota-Baxter relation replacing the classical rule. The methods to deal with noncommutativity are especially highlighted. We find new identities, allowing for an extensive embedding of Dyson-Chen series of time- or path-ordered products (of generalized integration operators); of the corresponding Magnus expansion; and of their relations, into the unified algebraic setting of Rota-Baxter maps and their inverse skewderivations. This picture clarifies the approximate solutions to generalized integral equations corresponding to non-autonomous linear (skew)differential equations.Comment: International Journal of Geometric Methods in Modern Physics, in pres

Comment on: Modular Theory and Geometry

In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.Comment: 13 pages, corrected versio

Functional representations of integrable hierarchies

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as `noncommutative' analogs of `Fay identities' for the KP hierarchy.Comment: 21 pages, version 2: equations (3.28) and (4.11) adde

From AKNS to derivative NLS hierarchies via deformations of associative products

Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed method to obtain 'functional representations' can be applied. We actually consider hierarchies with dependent variables in any (possibly noncommutative) associative algebra, e.g., an algebra of matrices of functions. This also covers the case of hierarchies of coupled DNLS equations.Comment: 22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of section 2 rewritten, taking account of previously overlooked references. To appear in J. Physics A: Math. Ge

Prognostic and therapeutic significance of carbohydrate antigen 19-9 as tumor marker in patients with pancreatic cancer

In pancreatic cancer ( PC) accurate determination of treatment response by imaging often remains difficult. Various efforts have been undertaken to investigate new factors which may serve as more appropriate surrogate parameters of treatment efficacy. This review focuses on the role of carbohydrate antigen 19- 9 ( CA 19- 9) as a prognostic tumor marker in PC and summarizes its contribution to monitoring treatment efficacy. We undertook a Medline/ PubMed literature search to identify relevant trials that had analyzed the prognostic impact of CA 19- 9 in patients treated with surgery, chemoradiotherapy and chemotherapy for PC. Additionally, relevant abstract publications from scientific meetings were included. In advanced PC, pretreatment CA 19- 9 levels have a prognostic impact regarding overall survival. Also a CA 19- 9 decline under chemotherapy can provide prognostic information for median survival. A 20% reduction of CA 19- 9 baseline levels within the first 8 weeks of chemotherapy appears to be sufficient to define a prognostic relevant subgroup of patients ('CA 19- 9 responder'). It still remains to be defined whether the CA 19- 9 response is a more reliable method for evaluating treatment efficacy compared to conventional imaging. Copyright (c) 2006 S. Karger AG, Basel

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde