The Nitsche phenomenon for weighted Dirichlet energy

2020 ◽  
Vol 13 (3) ◽  
pp. 301-323
Author(s):  
Tadeusz Iwaniec ◽  
Jani Onninen ◽  
Teresa Radice
Keyword(s):  
Mathematical Models ◽  
Weight Function ◽  
Rotational Symmetry ◽  
The Other ◽  
Dirichlet Energy ◽  
Target Domain ◽  
Dirichlet Integral ◽  
Planar Domains ◽  
Main Challenge ◽  
Minimal Mappings

AbstractThe present paper arose from recent studies of energy-minimal deformations of planar domains. We are concerned with the Dirichlet energy. In general the minimal mappings need not be homeomorphisms. In fact, a part of the domain near its boundary may collapse into the boundary of the target domain. In mathematical models of nonlinear elasticity this is interpreted as interpenetration of matter. We call such occurrence the Nitsche phenomenon, after Nitsche’s remarkable conjecture (now a theorem) about existence of harmonic homeomorphisms between annuli. Indeed the round annuli proved to be perfect choices to grasp the nuances of the problem. Several papers are devoted to a study of deformations of annuli. Because of rotational symmetry it seems likely that the Dirichlet energy-minimal deformations are radial maps. That is why we confine ourselves to radial minimal mappings. The novelty lies in the presence of a weight in the Dirichlet integral. We observe the Nitsche phenomenon in this case as well, see our main results Theorem 1.4 and Theorem 1.7. However, the arguments require further considerations and new ingredients. One must overcome the inherent difficulties arising from discontinuity of the weight. The Lagrange–Euler equation is unavailable, because the outer variation violates the principle of none interpenetration of matter. Inner variation, on the other hand, leads to an equation that involves the derivative of the weight. But our weight function is only measurable which is the main challenge of the present paper.

An Error Analysis of Hiragana and Katakana Writing Systems in the Learning of Japanese as Third Language at UiTM

2020 ◽  
Vol 4 (3) ◽  
pp. 46
Author(s):  
Norhazlina Husin ◽  
Nuranisah Tan Abdullah ◽  
Aini Aziz
Keyword(s):  
Error Analysis ◽  
Foreign Students ◽  
Teaching And Learning ◽  
Language Skills ◽  
The Other ◽  
Japanese Language ◽  
Writing System ◽  
Writing Systems ◽  
Third Language ◽  
Main Challenge

Abstract The teaching of Japanese language as third language to foreign students has its own issues and challenges. It does not merely involve only teaching the four language skills. Japanese language has its own unique values. These unique values also tend to differentiate the teaching of Japanese language as a third language from other third language acquisitions. The teaching of Japanese language as third language to foreign students also involves the teaching of its writing system. This makes the teaching of Japanese language rather complicated because Japanese language has three forms of writings, namely: Hiragana, Katakana and Kanji. Students are required to fully understand the Hiragana system of writing first before proceeding to learn the other two forms of writings. The main challenge in the teaching of Japanese writing systems is the time allocated that can be considered as very limited as other language aspects need to be taught too. This, which relates directly to students’ factor very much contribute to the challenges foreseen. Students are likely to face problems in understanding and using the writings as they simultaneously need to adhere to the findings teaching and learning schedules. This article discusses on the analysis conducted in terms of the learning of the Hiragana and Katagana systems of writing among foreign students. The discussion in this article is based on the teaching of Japanese language to students of Universiti Teknologi MARA(UiTM), Shah Alam. Keywords: Third language, Hiragana, Katakana, Kanji

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Electron drift caused by rf field gradient creates many plasma phenomena: An attempt to distinguish the cause and the effect

2011 ◽  
Vol 78 (2) ◽  
pp. 165-174 ◽  
Author(s):  
C. L. XAPLANTERIS ◽  
E. D. FILIPPAKI ◽  
I. S. MISTAKIDIS ◽  
L. C. XAPLANTERIS
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Low Temperature ◽  
Mathematical Models ◽  
Field Gradient ◽  
Collision Frequency ◽  
The Other ◽  
Frequency Effect ◽  
Electron Drift ◽  
Plasma Parameters

AbstractMany experimental data along with their theoretical interpretations on the rf low-temperature cylindrical plasma have been issued until today. Our Laboratory has contributed to that research by publishing results and interpretative mathematical models. With the present paper, two issues are being examined; firstly, the estimation of electron drift caused by the rf field gradient, which is the initial reason for the plasma behaviour, and secondly, many new experimental results, especially the electron-neutral collision frequency effect on the other plasma parameters and quantities. Up till now, only the plasma steady state was taken into consideration when a theoretical elaboration was carried out, regardless of the cause and the effect. This indicates the plasma's complicated and chaotic configuration and the need to simplify the problem. In the present work, a classification about the causality of the phenomena is attempted; the rf field gradient electron drift is proved to be the initial cause.

scholarly journals Rationales and Applications of Mutuality of Obligations in Iranian Contract Law

2016 ◽  
Vol 10 (12) ◽  
pp. 132
Author(s):  
Majid Sarbazian ◽  
Soroush Rostamzad Asli
Keyword(s):  
Contract Law ◽  
The Other ◽  
Legal Doctrine ◽  
Main Challenge

In Iranian laws, commitment is exchangeable if it is of proper and rational interest. In exchangeable contracts, it needs that parties perform their commitments mutually and in the case of not performing the commitments by one party, another one can refuse its commitments as called lien. There are also cases in which some terms are cancelled since they destroy the powers of one party to enforce the other party in performing his commitment. On this basis, the main challenge of present paper is to study the nature and status of mutuality of obligations doctrine in Iranian laws and studying its basics and implications. At the end, it is recognized that although mutuality of obligations is not raised in Iranian laws as a legal doctrine, it is effective in shaping and undertaking an exchangeable commitment.

scholarly journals Hyperbolic markers in modeling hyperbole: a scenario-based account

2021 ◽  
Vol 85 ◽  
pp. 61-71
Author(s):  
Carla Ovejas Ramírez
Keyword(s):  
Cognitive Linguistics ◽  
Language Use ◽  
Meaning Construction ◽  
The Other ◽  
Target Domain ◽  
Real Situation ◽  
Source Domain ◽  
The Real ◽  
Theoretical Context ◽  
Hypothetical Scenario

This article discusses hyperbolic markers in modeling hyperbole from the perspective of a scenario-based account of language use within the framework of Cognitive Linguistics. In this view, hyperbole is seen as a mapping across two conceptual domains (Peña y Ruiz de Mendoza, 2017), a source domain, here relabeled as the magnified scenario, which contains a hypothetical unrealistic situation based on exaggeration, and a target domain or observable scenario which depicts the real situation addressed by the hyperbolic expression. Since the hypothetical scenario is a magnified version of the observable scenario, the mapping contains source-target matches in varying degrees of resemblance. Within this theoretical context, the article explores resources available to speakers for the construction of magnified scenarios leading to hyperbolic interpretation. Among such resources, we find hyperbole markers and the setting up of domains of reference. Finally, the article also discusses hyperbole blockers, which cancel out the activity of the other hyperbolic meaning construction mechanisms.

scholarly journals Image-to-Image Translation with Multi-Path Consistency Regularization

2019 ◽  
Author(s):  
Jianxin Lin ◽  
Yingce Xia ◽  
Yijun Wang ◽  
Tao Qin ◽  
Zhibo Chen
Keyword(s):  
Machine Learning ◽  
Computer Vision ◽  
The Other ◽  
Natural Images ◽  
Original Image ◽  
Target Domain ◽  
Source Domain ◽  
Face To Face ◽  
Image Translation ◽  
The Difference

Image translation across different domains has attracted much attention in both machine learning and computer vision communities. Taking the translation from a source domain to a target domain as an example, existing algorithms mainly rely on two kinds of loss for training: One is the discrimination loss, which is used to differentiate images generated by the models and natural images; the other is the reconstruction loss, which measures the difference between an original image and the reconstructed version. In this work, we introduce a new kind of loss, multi-path consistency loss, which evaluates the differences between direct translation from source domain to target domain and indirect translation from source domain to an auxiliary domain to target domain, to regularize training. For multi-domain translation (at least, three) which focuses on building translation models between any two domains, at each training iteration, we randomly select three domains, set them respectively as the source, auxiliary and target domains, build the multi-path consistency loss and optimize the network. For two-domain translation, we need to introduce an additional auxiliary domain and construct the multi-path consistency loss. We conduct various experiments to demonstrate the effectiveness of our proposed methods, including face-to-face translation, paint-to-photo translation, and de-raining/de-noising translation.

Epistemic Opacity

2019 ◽  
pp. 98-131
Author(s):  
Johannes Lenhard
Keyword(s):  
Mathematical Models ◽  
Simulation Models ◽  
Scientific Understanding ◽  
The Other ◽  
Weak Version ◽  
Simulation Based ◽  
Lower Standard ◽  
Epistemic Standards ◽  
Epistemic Opacity ◽  
Experimental Runs

This chapter shows that—and how—simulation models are epistemically opaque. Nevertheless, it is argued, simulation models can provide a means to control dynamics. Researchers can employ a series of iterated (experimental) runs of the model and can learn to orient themselves within the model—even if the dynamics of the simulation remain (at least partly) opaque. Admittedly, such an acquaintance with the model falls short of the high epistemic standards usually ascribed to mathematical models. This lower standard is still sufficient, however, when the aim is controlled intervention in technological contexts. On the other hand, opacity has to be accepted if the option for control is to remain in any way open. This chapter closes by discussing whether epistemic opacity restricts simulation-based science to a pragmatic—“weak”—version of scientific understanding.

The property market, property valuations and property performance measurement

1985 ◽  
Vol 112 (1) ◽  
pp. 19-60 ◽  
Author(s):  
David P. Hager ◽  
David J. Lord
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Performance Measurement ◽  
The Other ◽  
Property Market ◽  
Institutional Investment ◽  
Property Valuation ◽  
Valuation Method ◽  
Property Performance

1.1. The Institute has discussed papers on most aspects of institutional investment in recent years, with the notable exception of property. This is not due to the lack of importance of this investment sector to pension funds and life offices, but perhaps to the greater role of actuaries (rather than surveyors) in the other investment media and to the interest in mathematical models for gilts and equities.1.2. In this paper we have not tried to produce a mathematical model of the property market, a new valuation method for property or solutions to the extensive problems of property performance measurement and indices. We have, however, tried to pull together, in a single paper, the volumes of material on the property market and property valuation methods. We have also tried to set down some of the pitfalls of property performance measurement, which often tend to be overlooked in the relentless pursuit for more statistics in this important area.

On the number of solutions of right-definite problems with a convergent Dirichlet integral

1982 ◽  
Vol 91 (3-4) ◽  
pp. 347-360 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
The Other ◽  
Dirichlet Integral ◽  
Number Of Solutions ◽  
Linearly Independent ◽  
Higher Order Differential Equations

SynopsisA recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M− of linearly independent solutions with a convergent Dirichlet integral, M+ and M− referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M− is maximal but not the other. Conditions are given under which M+ (say) is maximal and M− is the same, one less, and two less.

Sign in / Sign up

Export Citation Format

Share Document