Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints

In this paper, we are concerned with a set-valued fractional extremal programming problem under inclusion constraints. Our approach consists of using the extremal principle (an approach initiated by Mordukhovich, which does not involve any convex approximations and convex separation arguments) for the study of necessary optimality conditions.     

A mortar element method for hyperbolic problems

A non-conforming finite element method based on non-overlapping domain decomposition is extended to linear hyperbolic problems. The method is based on streamline-diffusion/discontinuous Galerkin methods and the mortar element method. A weak flux continuity condition at the inflow interface is enforced by means of Lagrange multipliers. This weak flux continuity condition replaces the usual mortar condition for elliptic problems, and allows non-matching grids at the subdomain interfaces. To cite this article: Y. Bourgault, A. El Boukili, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Critical potentials of the eigenvalues and eigenvalue gaps of Schrödinger operators

Let M be a compact Riemannian manifold with or without boundary, and let −Δ be its Laplace-Beltrami operator. For any bounded scalar potential q, we denote by λi(q) the ith eigenvalue of the Schrödinger type operator −Δ+q acting on functions with Dirichlet or Neumann boundary conditions in case ∂M≠∅. We investigate critical potentials of the eigenvalues λi and the eigenvalue gaps Gij=λj−λi considered as functionals on the set of bounded potentials having a given mean value on M. We give necessary and sufficient conditions for a potential q to be critical or to be a local minimizer or a local maximizer of these functionals. For instance, we prove that a potential q∈L^∞(M) is critical for the functional λ₂ if and only if q is smooth, λ₂(q)=λ₃(q) and there exist second eigenfunctions f₁,…,fk of −Δ+q such that . In particular, λ₂ (as well as any λi) admits no critical potentials under Dirichlet boundary conditions. Moreover, the functional λ₂ never admits locally minimizing potentials.     

Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach

Positivity - In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019. https://doi.org/10.1007/s11117-019-00685-1 ) is erroneous. Using...     

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Cheese whey tangential filtration using tubular mineral membranes

Membrane separation techniques are extensively used in dairy industry both for milk and cheese whey processing. However, cheese whey might still be considered as a problematic waste despite its high content of many valuable substances, such as proteins, lactose or minerals, which can be further used, e.g. in human nutrition, pharmacy or biotechnologies. Another problem, which food technologists have to face, is variable quality, composition and properties of food materials bringing high demands on manufacturing industry. In this paper, filtration kinetics and separation efficiency during purification and fractionation of cheese whey (sweet and salty) from Czech dairies by pilot-plant filtration (Bollene, France) was studied using tubular membranes (Membralox, USA). Various mineral membranes’ cut-offs were tested and all experiments ran in the retentate recycling mode. The obtained mass concentration factors were between 1.9 and 16.5. Steady state fluxes were calculated from the experimental data using a mathematical model. Fine ultrafiltration on a 5 kDa membrane gave steady state fluxes of 14–19 L m^?2 h^?1. The coarse pre-filtration on 100 nm, 200 nm or 500 nm membranes showed various permeate fluxes between 22 L m^?2 h^?1 and 153 L m^?2 h^?1. Despite the high pore sizes of the used membranes, lactose was partially rejected by all membranes tested.     

A general analysis of the electromagnetic wake-fields due to a relativistic electron beam moving through a cold plasma

Summary Detailed electromagnetic analysis of the wake-field accelerator is presented. Particular attention is given to the two-dimensional dynamics model to understand how the wake-field affects the self-consistent radial dynamics of the beam. The corrent fields, in zeroth and first order, are obtained by using Fourier transform in the radial field. The self-focusing of the driving beam in a plasma is a result of the transverse wake. The ratio of the transverse wake-field to the longitudinal wake-field within the beam is calculated for small and large radii beams.     

On quasinormal,subnormal, and hyponormal Toeplitz operators

Let ? be a non-constant function inL ^∞(D) such thatφ=φ ₁+φ ₂, whereφ ₁ is an element in the Bergman spaceL _a ² (D), and \(\phi _2 \in \overline {L_a^2 (D)} \) , the space of all complex conjugates of functions inL _a ² (D). In this paper, it is shown that if 1 is an element in the closure of the range of the self-commutator ofT _?, \(T_{\bar \phi } T_\phi - T_\phi T\phi \) , then the Toeplitz operatorT _? defined ofL _a ² (D) is not quasinormal. Moreover, if \(\phi = \psi + \lambda \bar \psi \) , whereψ∈ H ^∞(D), and λεC, it is proved that ifT _? is quasinormal, thenT _? is normal. Also, the spectrum of a class of pure hyponormal Toeplitz operators is determined.     

Note on faithful representations and a local property of Lie groups

Let be any analytic group, let be a maximal toroid of the radical of , and let be a maximal semisimple analytic subgroup of . If is the Lie algebra of , is the radical of , and is the center of , we show that has a faithful representation if and only if (i) , and (ii) has a faithful representation.