Strange Term Research Articles

Mobilisation of polish into german army from occupies polish territory in Second world war

At the outbreak of the Second World War, some of the local population of the territory annexed to the German Reich were granted partial or full German citizenship by Heinrich Himmler’s decree on the Deutsche Volksliste (German People’s List). At the same time, men of draft age, like other Reich citizens, became subject to military service. However, the first mass conscriptions to the German army in the annexed territory took place even earlier, in the spring of 1940. At the time, a rather strange term Deutsch-Polen (German Pole) was used in German internal correspondence to describe conscripts from the annexed part of Poland

Aperiodical isoperimetric planar homogenization with critical diameter: universal non-local strange term for a dynamical unilateral boundary condition

Aperiodical isoperimetric planar homogenization with critical diameter: universal non-local strange term for a dynamical unilateral boundary condition

Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size

We study the homogenization of a nonlinear problem given by the Poisson equation, in a domain with arbitrarily shaped perforations (or particles) and with a dynamic unilateral boundary condition (of Signorini type), with a large coefficient, on the boundary of these perforations (or particles). This problem arises in the study of chemical reactions of zero order. The consideration of a possible asymmetry in the perforations (or particles) is fundamental for considering some applications in nanotechnology, where symmetry conditions are too restrictive. It is important also to consider perforations (or particles) constituted by small different parts and then with several connected components. We are specially concerned with the so-called critical case in which the relation between the coefficient in the boundary condition, the period of the basic structure, and the size of the holes (or particles) leads to the appearance of an unexpected new term in the effective homogenized equation. Because of the dynamic nature of the boundary condition this ``strange term'' becomes now a non-local in time and non-linear operator. We prove a convergence theorem and find several properties of the ``strange operator'' showing that there is a kind of regularization through the homogenization process.
 For more information see https://ejde.math.txstate.edu/Volumes/2024/03/abstr.html

Operator estimates for non‐periodically perforated domains with Dirichlet and nonlinear Robin conditions: Strange term

We consider a boundary value problem for a general second‐order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries of the cavities are subject either to a Dirichlet or a nonlinear Robin condition. On the perforation, certain rather weak conditions are imposed to ensure that under the homogenization, we obtain a similar problem in a non‐perforated domain with an additional potential in the equation usually called a strange term. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in ‐ and ‐norms uniformly in ‐norm of the right hand side in the equation. The estimates for the convergence rates are established, and their order sharpness is discussed.

Homogenization in perforated domains at the critical scale

We describe the asymptotic behaviour of the minimal heterogeneous d-capacity of a small set, which we assume to be a ball for simplicity, in a fixed bounded open set Ω⊆Rd, with d≥2. Two parameters are involved: ɛ, the radius of the ball, and δ, the length scale of the heterogeneity of the medium. We prove that this capacity behaves as C|logɛ|1−d, where C=C(λ) is an explicit constant depending on the parameter λ≔limɛ→0|logδ|/|logɛ|.We determine the Γ-limit of oscillating integral functionals subjected to Dirichlet boundary conditions on periodically perforated domains. Our first result is used to study the behaviour of the functionals near the perforations which, in this instance, are balls of radius ɛ. We prove that an additional strange term arises involving C(λ).

Homogenization of sound-soft and high-contrast acoustic metamaterials in subcritical regimes

We propose a quantitative effective medium theory for two types of acoustic metamaterials constituted of a large number N of small heterogeneities of characteristic size s, randomly and independently distributed in a bounded domain. We first consider a “sound-soft” material, in which the total wave field satisfies a Dirichlet boundary condition on the acoustic obstacles. In the “sub-critical” regime sN = O(1), we obtain that the effective medium is governed by a dissipative Lippmann–Schwinger equation which approximates the total field with a relative mean-square error of order O(max((sN)2N-1/3, N-1/2)). We retrieve the critical size s ~ 1/N of the literature at which the effects of the obstacles can be modelled by a “strange term” added to the Helmholtz equation. Second, we consider high-contrast acoustic metamaterials, in which each of the N heterogeneities are packets of K inclusions filled with a material of density much lower than the one of the background medium. As the contrast parameter vanishes, δ → 0, the effective medium admits K resonant characteristic sizes (si(δ))1≤i≤K and is governed by a Lippmann–Schwinger equation, which is diffusive or dispersive (with negative refractive index) for frequencies ω respectively slightly larger or slightly smaller than the corresponding K resonant frequencies (ωi (δ))1≤i≤K. These conclusions are obtained under the condition that (i) the resonance is of monopole type, and (ii) lies in the “subcritical regime” where the contrast parameter is small enough, i.e. δ = o(N−2)), while the considered frequency is “not too close” to the resonance, i.e. Nδ1/2 = O(|1 - s/si(δ)|). Our mathematical analysis and the current literature allow us to conjecture that “solidification” phenomena are expected to occur in the “super-critical” regime Nδ1/2|1 - s/si(δ)|-1 → + ∞.

Attractors of Ginzburg–Landau equations with oscillating terms in porous media: homogenization procedure

We consider the Ginzburg–Landau equation in the perforated domain, with rapidly oscillating coefficients. We derive the homogenized Ginzburg–Landau equation with a ‘strange term’ (potential) and prove that the trajectory attractors of the given equation tend in a weak sense to the trajectory attractors of the homogenized one. Assuming additional conditions to be satisfied for the coefficients, we provide also a convergence of the global attractor.

Boundary homogenization with large reaction terms on a strainer-type wall

We consider a homogenization problem for the Laplace operator posed in a bounded domain of the upper half-space, a part of its boundary being in contact with the plane {x_3=0}. On this part, the boundary conditions alternate from Neumann to nonlinear-Robin, being of Dirichlet type outside. The nonlinear-Robin boundary conditions are imposed on small regions periodically placed along the plane and contain a Robin parameter that can be very large. We provide all the possible homogenized problems, depending on the relations between the three parameters: period varepsilon , size of the small regions r_varepsilon and Robin parameter beta (varepsilon ). In particular, we address the convergence, as varepsilon tends to zero, of the solutions for the critical size of the small regions r_varepsilon =O(varepsilon ^{ 2}). For certain beta (varepsilon ), a nonlinear capacity term arises in the strange term which depends on the macroscopic variable and allows us to extend the usual capacity definition to semilinear boundary conditions.

Boundary control and homogenization: Optimal climatization through smart double skin boundaries

We consider the homogenization of an optimal control problem in which the control $v$ is placed on a part $\Gamma _{0}$ of the boundary and the spatial domain contains a thin layer of “small particles”, very close to the controlling boundary, and a Robin boundary condition is assumed on the boundary of those “small particles”. This problem can be associated with the climatization modeling of Bioclimatic Double Skin Façades which was developed in modern architecture as a tool for energy optimization. We assume that the size of the particles and the parameters involved in the Robin boundary condition are critical (and so they justify the occurrence of some “strange terms” in the homogenized problem). The cost functional is given by a weighted balance of the distance (in a $H^{1}$-type metric) to a prescribed target internal temperature $u_{T}$ and the proper cost of the control $v$ (given by its $L^{2}(\Gamma _{0})$ norm). We prove the (weak) convergence of states ${u_{\varepsilon }}$ and of the controls $ v_{\varepsilon }$ to some functions, ${u_{0}}$ and $v_{0}$, respectively, which are completely identified: ${u_{0}}$ satisfies an artificial boundary condition on $\Gamma _{0}$ and $v_{0}$ is the optimal control associated to a limit cost functional $J_{0}$ in which the “boundary strange term” on $\Gamma _{0}$ arises. This information on the limit problem makes much more manageable the study of the optimal climatization of such double skin structures.

Strong convergence of attractors of reaction-diffusion system with rapidly oscillating terms in an orthotropic porous medium

A system of reaction-diffusion equations in a perforated domain with rapidly oscillating terms in the equations and in the boundary conditions is considered. It is not assumed that the uniqueness theorem conditions are satisfied for the corresponding initial-boundary value problem. We have proved the strong convergence of the trajectory attractors of this system to the trajectory attractors of the homogenized reaction-diffusion system with a ‘strange term’ (potential).

Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case

Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case

Homogenization of Attractors of Reaction–Diffusion System with Rapidly Oscillating Terms in an Orthotropic Porous Medium

In a perforated domain, we consider a reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so the uniqueness of a solution to the corresponding initial-boundary value problem is not guaranteed. We prove that the trajectory attractors of the system weakly converge to the trajectory attractors of the homogenized reaction-diffusion systems with a strange term (potential).

On the convergence of controls and cost functionals in some optimal control heterogeneous problems when the homogenization process gives rise to some strange terms

We consider the convergence of solutions and cost functional in some optimal control problems arising in the study of the adsorption chemical phenomenon in which some microscopic reactant particles are placed over an internal manifold γ of the chemical reactor Ω. The chemical reaction is given by some Robin-type boundary condition on the boundary of the periodic set of particles. We consider the special case in which there is a critical relation between the coefficient of the reaction, the size of the particles and the dimension of the space. This gives rise to a “strange term”, which is not occurring for other scales, and thus the limit cost functional must be suitably defined. In a last section, we use this type of technique to prove a similar “energy convergence” result (improving the H01(Ω)-weak convergence) for the problem without control for the critical scale case.

A simple justification of effective models for conducting or fluid media with dilute spherical inclusions

We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of n ≫ 1 spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as n → + ∞ by simple arguments.

To Be ‘An Out-of-the-Synagoguer’

Since J. Louis Martyn proposed that John reflected a two-level drama, there has been much criticism of his (anachronistic?) use of the Birkat Ha-Minim to explain the expulsion of Christians from the synagogue. Adele Reinhartz maintains that this is really a case of anti-synagogue propaganda on the part of the evangelist. Yet, in all the exegetical discussion, one aspect which is rarely examined is the nominal form of ἀποσυνάγωγος (Jn 9.22; 12.42; 16.2a), a strange term which Bible translations have to turn into a verb. This label appears to come from a Greek-speaking Jewish milieu, and its negativity is re-appropriated by the author of this Christian text. Social identity research provides an insight into how a positive approach to stigmatizing labels can allow a community to thrive. This can be applied to ἀποσυνάγωγος in John, an insult which actually demonstrates the validity of one’s faith and identity. It is good to be a reject.

Attractors and a “strange term” in homogenized equation

Attractors and a “strange term” in homogenized equation

“Strange term” in homogenization of attractors of reaction–diffusion equation in perforated domain

Abstract We consider reaction–diffusion equation in perforated domain, with rapidly oscillating coefficient in boundary conditions. We do not assume any Lipschitz condition for the nonlinear function in the equation, so, the uniqueness theorem for the corresponding initial boundary value problem may not hold for the considered reaction-diffusion equation. We prove that the trajectory attractors of this equation tend in a weak sense to the trajectory attractors of the homogenized reaction-diffusion equation with a “strange term” (potential). Bibliography: 48 titles.

ISTIQOMAH IN AL-QUR’AN: THE CONCEPT, TERMINOLOGY, AND IT’S APPLICATION

This paper is aimed to describe the most spoken concept in alQur’an, namely istiqomah and its application. The description of this important concept covers some aspects: 1) the definition and meaning of istiqomah both etimologically and terminologically, 2) the interpretations of the Muslim scholars dealing with the concept, 3) the answer to the question if it is the strange term to Muslim, 4) the significance of the implementation of the term istiqomah, and 5) the ways to implement the concept of istiqomah. Based on the descriptions above, it can be concluded that the concept of istiqomah covers some aspects as follows: 1) istiqomah deals with tauhid purity and not false worship, 2) istiqomah deals with doing the duties, either compulsory or optional, physically or mentally, 2) istiqomah deals with leaving out all the prohibitions, 3) istiqomah deals with being a pious to worship Allah The Almighty, 4) istiqomah deals with the continuation of worshipping Allah The Almighty, and 5) istiqomah deals with the implementation of the rightness in social life

A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case

A strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is considered. A problem with dynamic boundary conditions given on the union of some boundary subsets of critical size arranged e-periodically along the boundary and with homogeneous Neumann conditions given on the rest of the boundary is studied. It is proved that the homogenized boundary condition is a Robin-type containing a nonlocal term depending on the trace of the solution u(x, t) on the boundary $$\partial \Omega $$ .

Ikhtiyār dalam Pemikiran Ekonomi Islam; Perspektif Teologi

Ikhti yā r is not a strange term in Indonesian language . T his word has been absorbed from Arabic language and being an important concept which has a place in Indonesian society worldview. Ikhti yā r as a key terminology in Islamic tradition has a close relationship with the discipline of economics . B oth are speaking about ‘choice’ and human behavior . Comprehending the meaning of ikhtiyār as Syed Muhammad Naquib al-Attas has conveyed generates influences in viewing some concepts and ideas in the modern economy which certainly implicate Islamic economics thought . Furthermore , t his study is conforming that the difference s between Islamic economy and Western one could not only lie at the macro economy level, but also relating to the ideas and activities in microeconom y as well . I n fact , b oth are inseparable at all.