1,720,992 research outputs found
On the relaxation of some types of Dirichlet minimum problems for unbounded functionals
No full textIn this paper, considered a Borel function g on Rn taking its values in [0,+∞], verifying some weak hypothesis of continuity, such that (domg)^{o}=∅ and domg is convex, we obtain an integral representation result for the lower semicontinuous envelope in the L1(Ω)-topology of the integral functional G0(u0,Ω,u)=∫_{Ω}g(∇u)dx, where u∈W_{loc}^{1,∞}(Rn), u=u0 only on suitable parts of the boundary of Ω that lie, for example, on affine spaces orthogonal to aff(domg), for boundary values u0 satisfying suitable compatibility conditions and Ω is geometrically well situated respect to domg. Then we apply this result to Dirichlet minimum problems
Asymptotic approximation of the solution to the Robin problem in a thick multi-structure
No full textWe consider a mixed boundary value problem for the Poisson equation in a thick multistructure Ωɛ, which is the union of a domain Ω0 and a large number N of ɛ-periodically situated thin rings with variable thickness of order ɛ = O(N-1): The Robin conditions are given on the lateral boundaries of the thin rings. The leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H1(Ωɛ) are proved (as ɛ-> 0) with minimal conditions for the right-hand side
A Tabulation of Absorbed Dose per Unit Fluence Conversion Coefficients for Slab Phantoms of Three Tissue Equivalent Materials for Electron Energies from 70 keV to 10 MeV
No full textOn Optimal L1-Control in Coefficients for Quasi-Linear Dirichlet Boundary Value Problems with BMO-Anisotropic p-Laplacian
No full textWe study an optimal control problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principal part and L1-control in coefficient of the low-order term. We assume that the matrix of anisotropy belongs to BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space, we introduce a suitable functional class in which we look for solutions and prove existence of optimal pairs using an approximation procedure and compactness arguments in variable spaces
Optimal boundary control problem for ill-posed elliptic equation in domains with rugous boundary. Existence result and optimality conditions
No full textThe main purpose is the study of optimal control problem in a domain with rough boundary for the mixed Dirichlet-Neumann boundary value problem for the strongly nonlinear elliptic equation with exponential nonlinearity. A density of surface traction u acting on a part of rough boundary is taken as a control. The optimal control problem is to minimize the discrepancy between a given distribution and the current system state. We deal with such case of nonlinearity when we cannot expect to have a solution of the state equation for a given control. After having defined a suitable functional class in which we look for solutions, we prove the consistency of the original optimal control problem and show that it admits a unique optimal solution. Then we derive a first-order optimality system assuming the optimal solution is slightly more regular
Absorbed Dose per Unit Fluence for Tissue Equivalent Slab Phantoms for Electrons from 50 keV to 10 MeV
No full textMicrogeometrical design of lightweight bioinspired nacre-like composite materials for wave attenuation tuning
No full textAn Indirect Approach to the Existence of Quasi-optimal Controls in Coefficients for Multi-dimensional Thermistor Problem
No full textThe paper studies a problem of an optimal control in coefficients for the system of two coupled elliptic equations also known as thermistor problem which provides a simultaneous description of the electric field u= u(x) and temperature θ(x). The coefficient b of operator div(b(x)∇θ(x)) is used as the control in W1,q(Ω) with q> N. The optimal control problem is to minimize the discrepancy between a given distribution θd∈ L1(Ω) and the temperature of thermistor θ∈W01,γ(Ω) by choosing an appropriate anisotropic heat conductivity b(x). Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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