The H\"older-Poincar\'e Duality for Lq,pL_{q,p}-cohomology

We prove the following version of Poincare duality for reduced $L_{q,p}$-cohomology: For any $1<q,p<\infty$, the $L_{q,p}$-cohomology of a Riemannian manifold is in duality with the interior $L_{p',q'}-cohomology for$1/p+1/p'=1$,$1/q+1/q'=1$.Comment: 21 page

Joint characteristic timescales and entropy production analyses for model reduction of combustion systems

The reduction of chemical kinetics describing combustion processes remains one of the major topics in the combustion theory and its applications. Problems concerning the estimation of reaction mechanisms real dimension remain unsolved, this being a critical point in the development of reduction models. In this study, we suggest a combination of local timescale and entropy production analyses to cope with this problem. In particular, the framework of skeletal mechanism is in the focus of the study as a practical and most straightforward implementation strategy for reduced mechanisms. Hydrogen and methane/dimethyl ether reaction mechanisms are considered for illustration and validation purposes. Two skeletal mechanism versions were obtained for methane/dimethyl ether combustion system by varying the tolerance used to identify important reactions in the characteristic timescale analysis of the system. Comparisons of ignition delay times and species profiles calculated with the detailed and the reduced models are presented. The results of the application show transparently the potential of the suggested approach to be automatically implemented for the reduction of large chemical kinetic models

Sobolev Inequalities for Differential Forms and Lq,pL_{q,p}-cohomology

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space of closed differential forms in $L^p(M)$ modulo the exact forms which are exterior differentials of forms in $L^q(M)$.Comment: This paper has appeared in the Journal of Geometric Analysis, (only minor changes have been made since verion 1

Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the dirichlet energy

In this paper we show a striking contrast in the symmetries of equilibria and extremisers of the total elastic energy of a hyperelastic incompressible annulus subject to pure displacement boundary conditions.Indeed upon considering the equilibrium equations, here, the nonlinear second order elliptic system formulated for the deformation u=(u1,…,uN) : EL[u,X]=⎧⎩⎨⎪⎪Δu=div(P(x)cof∇u)det∇u=1u≡φinX,inX,on∂X, where X is a finite, open, symmetric N -annulus (with N≥2 ), P=P(x) is an unknown hydrostatic pressure field and φ is the identity mapping, we prove that, despite the inherent rotational symmetry in the system, when N=3 , the problem possesses no non-trivial symmetric equilibria whereas in sharp contrast, when N=2 , the problem possesses an infinite family of symmetric and topologically distinct equilibria. We extend and prove the counterparts of these results in higher dimensions by way of showing that a similar dichotomy persists between all odd vs. even dimensions N≥4 and discuss a number of closely related issues

Identification of candidate disease genes by integrating Gene Ontologies and protein-interaction networks: case study of primary immunodeficiencies

Disease gene identification is still a challenge despite modern high-throughput methods. Many diseases are very rare or lethal and thus cannot be investigated with traditional methods. Several in silico methods have been developed but they have some limitations. We introduce a new method that combines information about protein-interaction network properties and Gene Ontology terms. Genes with high-calculated network scores and statistically significant gene ontology terms based on known diseases are prioritized as candidate genes. The method was applied to identify novel primary immunodeficiency-related genes, 26 of which were found. The investigation uses the protein-interaction network for all essential immunome human genes available in the Immunome Knowledge Base and an analysis of their enriched gene ontology annotations. The identified disease gene candidates are mainly involved in cellular signaling including receptors, protein kinases and adaptor and binding proteins as well as enzymes. The method can be generalized for any disease group with sufficient information

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic–elliptic duality of surface and interfacial waves is established, along with the parabolic–elliptic duality of the dispersive edge wave on a Kirchhoff plate. The effects of anisotropy, piezoelectricity, thin elastic coatings, and mixed boundary conditions are taken into consideration. The advantages of the developed approach are illustrated by steady-state and transient problems for a moving load on an elastic half-space