This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop our analysis are: (i) new density result G S B V p $GSBV^{p}$ functions satisfying maximal-rank constraint on subgradients, which can be approximated by C1-local immersions regular subdomains cracked set, and (ii) construction recovery sequence...

Nickel-rich cathode materials with small amounts of tungsten (W) dopants have attracted extensive attention in recent years. However, the chemical state, crystalline form, compound chemistry, and location W these layered cathodes are still not well-understood. In this study, missing structural properties determined through a combination macro-, to atomic-sensitive characterization techniques de...

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a g...

Reference 1. Reddy PS, Legault HM, Sypek JP, Collins MJ, Goad E, Goldman SJ, Liu W, Murray S, Dorner AJ, O’Toole M: Mapping similarities in mTOR pathway perturbations in mouse lupus nephritis models and human lupus nephritis. Arthritis Res Ther 2008, 10:R127. Correction Correction: Mapping similarities in mTOR pathway perturbations in mouse lupus nephritis models and human lupus nephritis Padma...

Let W denote a family of probability distributions with parameter space Γ, and WG be a subfamily of W depending on a mapping G : Θ→ Γ. Extremum estimations of the parameter vector θ ∈ Θ are considered. Some sufficient conditions are presented to ensure the uniqueness with probability one. As important applications, the maximum likelihood estimation in curved exponential families and nonlinear r...

X id → X → 0→ · For any morphism u : X → Y , there is an object Z (called a mapping cone of the morphism u) fitting into a distinguished triangle X u − → Y → Z → · Any triangle isomorphic to a distinguished triangle is distinguished. This means that if X u − → Y v − → Z w −→ X[1] is a distinguished triangle, and f : X → X, g : Y → Y , and h : Z → Z are isomorphisms, then X′ gu f −1 −−−−→ Y ′ hv...

T 2 are the only closed Riemann surfaces admitting nonconstant conformal mappings from the complex plane. The same rigidity is present in higher dimensions; closed manifolds admitting conformal mappings from Rn are quotients of Sn and Tn, see e.g. [2, Prop. 1.4]. However, if distortion is allowed, simple examples show that the spaces Sk1 × Sk2 × · · · × Skl (k1 + · · ·+ kl = n) receive nonconst...

PURPOSE To improve image registration accuracy in neurodegenerative populations. MATERIALS AND METHODS This study used primary progressive aphasia, aged control, and young control T1-weighted images. Mapping to a template image was performed using single-channel Large Deformation Diffeomorphic Metric Mapping (LDDMM), a dual-channel method with ventricular anatomy in the second channel, and a ...

Equilibrium problems theory provides us with a natural, novel and unified framework for studying a wide class of problems arising in economics, finance, transportation, network and structural analysis, elasticity and optimization. The ideas and techniques of this theory are being used in a variety of diverse areas and proved to be productive and innovative. Let H be a Hilbert space with inner p...