Integral Norm Research Articles

Perturbative stability of the approximate Killing field eigenvalue problem

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity.

The Production of 'Local Culture' in Post-socialist Poland

At a time when European cities redefine themselves through 'culture' in an attempt to attract tourists, investors and potential residents, policymakers have to negotiate different notions of 'local culture' defined by state governments on the one hand and by the EU on the other. Drawing upon research conducted in the Polish city of Gdańsk in the context of the redevelopment of its urban landscape, the article illustrates how 'local culture' is redefined as 'culture of freedom' by municipal and state institutions in order to establish a relationship of historical continuity between the time when Gdańsk was a thriving multicultural city and the post-socialist present. The article puts forward the argument that while the reformulation of local culture as 'culture of freedom' involves reconciling notions of national identity with new norms of local, regional and European integration, it does not necessarily entail the supersession of nationalism.

An integral equations method combined minimum norm solution for 3D elastostatics Cauchy problem

In this paper, we establish new density results for the equilibrium equations. Based on the denseness result of the elastic potential functions, the Cauchy problem for the equilibrium equations is investigated. For this ill-posed problem, we construct a regularizing solution using the single-layer potential function. The well-posedness of the regularizing solution as well as the convergence property is rigorously analyzed. The advantage of the proposed scheme is that the regularizing solution is of the explicit analytic solution and therefore is easy to be implemented. The method combines minimum norm solution with Morozov discrepancy principle to solve an inverse problem. Convergence and stability estimates are then given with some examples for numerical verification on the efficiency of the proposed method. The numerical convergence, accuracy, and stability of the method with respect to the discretisation about the integral equations on pseudo-boundary and the distance between the pseudo-boundary and the real boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are also analysed with some examples.

CONSTRUCTION OF THE POLYGONAL FUZZY NEURAL NETWORK AND ITS APPROXIMATION BASED ON <em>K</em>-INTEGRAL NORM

The concept of an n-equidistant polygonal fuzzy number is introduced to avoid the complexity of the operations between fuzzy numbers. Firstly, the properties of linear operations and the convergence of n-equidistant polygonal fuzzy numbers are discussed, the method how to change a fuzzy number into an n-equidistant polygonal fuzzy number is shown. Next, for given a ˆ polygonal fuzzy valued function, an n-equidistant polygonal fuzzy valued function is constructed. By introducing the definition of K-quasi-additive integral and K- integral norm, the universal approximation of polygonal fuzzy neural network are studied. The final result indicates that the polygonal fuzzy neural network still possess universal approximation to an integrable system.

Sovereignty and self-determination: Where are we?

This article discusses the historical evolution of norms of sovereignty, non-intervention, territorial integrity, and self-determination in international relations. It shows the degree to which their meanings and weight have varied and considers the bumpy historical relationship between international norms and practice. The twentieth century witnessed increasing tension between the hardening of sovereignty and non-intervention norms and the development of international human rights norms. The article then discusses normative inconsistencies and the variability of application of norms in practice in the post-Cold War era. It concludes by suggesting ways in which international society might mitigate these inconsistencies and the confusion that attends them.

Sharp estimates of best approximations by deviations of Weierstrass-type integrals

We establish the estimates $$ {A_{\sigma }}{(f)_p}\leq KP\left( {f-f*W} \right), $$ where W is a kernel of special type that is integrable on R and A σ(f) P is the best approximation of a function f with respect to a seminorm P by entire functions of exponential type not greater than σ. For the uniform and integral norms, we find the least possible constant K. The estimates are obtained by linear methods of approximation. Bibliography: 7 titles.

Characterization for Fock-Type Space via Higher Order Derivatives and its Application

The space of entire functions \(\mathcal {F}_{\alpha }^{\infty }\) is mentioned in the paper of S. Janson, J. Peetre, and R. Rochberg. In this paper, we establish a characterization for the space \(\mathcal {F}_{\alpha }^{\infty }\) by \(n\)-th derivatives of entire functions. As an application of this result, we study the boundedness of Li-Stevic’s integral operators and estimate essential norms of these operators acting on \(\mathcal {F}_{\alpha }^{\infty }\). Furthermore we describe complete characterizations for boundedness and compactness of the Volterra-type integral operators on \(\mathcal {F}_{\alpha }^{\infty }\).

A Note on Rational $$L^p$$ L p Approximation on Jordan Curves

The precise asymptotics for the error of best rational approximation of meromorphic functions in integral norm is shown to be a consequence of a result of Gonchar and Rakhmanov. This reproves and extends a recent result of Baratchart, Stahl and Yattselev.

Sharp estimates of best approximations in terms of holomorphic functions of weierstrass-type operators

Estimates of the form $$ {A_{\sigma }}{(f)_P}\leq KP\left( {\varPhi \left( \mathcal{W} \right)f} \right), $$ where W is a kernel of a special type summable on $ \mathbb{R} $ , a function Φ is holomorphic in a neighborhood of the spectrum of W, and A σ(f ) P is the best approximation of a function f by entire functions of exponential type not greater than σ with respect to a seminorm P, are established. In some cases, for the uniform and integral norms the least possible constant K is found. The estimates are obtained by linear approximation methods. Bibliography: 13 titles.

Using the Sociological Imagination to Teach about Academic Integrity

The sociological imagination is a useful tool for teaching about plagiarism and academic integrity, and, in turn, academic integrity is a good case to help students learn about the sociological imagination. We present an exercise in which the class discusses reasons for and consequences of dishonest academic behavior and then examines a series of scenarios using the sociological imagination. Students and instructors consider whether each scenario is a violation of academic integrity norms and how it can be viewed as both personal and public. We demonstrate that this kind of discussion helps students learn about academic integrity and how to think of violations (including causes and a range of outcomes) sociologically. In other words, we encourage students to think of academic dishonesty (both causes and consequences) not just as “personal troubles” but also as “public issues.”

Regulations Initiatives in France for the Interoperability of Communicating Medical Devices

Telemedicine has introduced new challenges in health delivery with the introduction of advanced information communication technologies in home care medicine. To meet the high standard of quality in health service delivery, the data flow of medical data must be maintained, which implies harmonization and standardization frameworks within the field of the communicating medical devices. Those medical devices must be certified to prove their effectiveness and compliance with the requirements on health and safety of patients, before to be brought into service or used. But there is no requirement concerning the interoperability of these communicating medical devices. A group of French experts have anticipated the need in developing projects to define communication medical device in the home and by taking part in standardization projects on the interoperability of data and systems in health. They first identified the standardization rules at European and national level and confirmed that most guides and directives are well available. They based their study on three specialties, commonly using medical devices and telemedicine and covering various use cases. Then, they defined a methodology following the IHE International and Continua Alliance approach in order to define the integration profile. Eventually, they defined a generic workflow and an inventory of the integration profiles, norms and standards that can support this generic workflow.

Approximation of polygonal fuzzy neural networks in sense of Choquet integral norms

Approximation capabilities are important and primary properties of neural networks and fuzzy neural networks (FNNs). Neural networks have been successfully applied in many fields since they can work as approximators in nature. Many scholars research FNNs’ approximation abilities for continuous fuzzy functions. It is concluded that FNNs can work as approximators for continuous fuzzy functions if the fuzzy functions satisfy some specified conditions. However, the problem whether FNNs can work as approximators for discontinuous fuzzy functions is not solved completely until now. In this work, we focus on the approximation of polygonal FNN for discontinuous fuzzy functions in sense of Choquet integral norms. We first introduce the Choquet integral norms in sub-additive fuzzy measure. Then the universal approximation of polygonal FNNs for fuzzy valued functions in sense of Choquet integral norms is analyzed in this paper. It is proved that the polygonal FNNs can work as approximators for fuzzy valued functions in the sense of Choquet integral norms with respect to sub-additive fuzzy measure.

Customer perception and response to ethical norms in legal services marketing

The study here examines the relationship between ethical marketing norms, relationship quality (RQ), and commitment in the context of legal services. Through a survey of customers of legal services providers in Malaysia, data were collected. Results from a standard analysis of data show that the four dimensions of ethical marketing norms contribute significantly and explain a significant amount of variance in RQ and commitment. The results further show that three dimensions of ethical norms namely price and distribution norm, information and contract norm, and general honesty and integrity norm are significantly associated with relationship quality and commitment. Product and promotion norm has no significant relationship with relationship quality and commitment. RQ plays a mediating role in the relationship between marketing norms and commitment. The study reveals that the same three dimensions of marketing norms predict both RQ and commitment, and are useful for effective legal services marketing. These findings lead to research, managerial, contextual and policy implications that conclude the paper.

Optimal weak type estimates for dyadic-like maximal operators

We provide sharp weak estimates for the distribution function of Mwhen onwe impose L 1 , L q and L p;1 restrictions. Here M is the dyadic maximal operator associated to a tree T on a non-atomic probability measure space. As a consequence we produce that the inequality jjMTjjp;1 • jjjjjjp;1 is sharp allowing every possible value for the L 1 and the L q norm for a fixed q such that 1 < q < p, where jjj ¢ jjjp;1 is the integral norm on and jj ¢ jjp;1 the usual quasi norm on L p;1 .

Optimal Replication of Random Claims by Ordinary Integrals with Applications In Finance

By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential equation. We found that the solution of this replication problem exists and is not unique. This leads to a new optimal control problem: find a replicating process that is minimal in an integral norm. We found an explicit solution of this problem. Possible applications to portfolio selection problems and to bond pricing models are suggested.

The Implementation of Social Capital Component Amoung High schools in city of Izeh

The aim of this research was measure of proving social capital components at the high schools Izeh city. Method of research was a descriptive and statistical community was including all of the teachers of high school course in Izeh city which were 452 people. The bulk of statistical sample using Karjis and Morgan table was obtained 207 people but returned questionnaires were 191 questionnaires. The method of classical random sampling was proportional to the statistical community of female and male teachers. The tools of measuring were a social capital questionnaire including 35 items based on SCAT model. Contextual reliability using Kandal coefficient 0.65 was obtained and reliability of the questionnaire was obtained by Alpha coefficient of Cronbach 0.83. To analyze data, the statistical methods of one_ variable t and multivariable variance analysis were used. The results were indicated in point of view of teachers, trust, cooperation, commitment, reciprocal relations, attitudes, integration, social norms components were proved in the high schools of Izeh city and this finding was significant as statistical aspect. Results showed that in the view of teachers trust, cooperation, commitment, reciprocal relations, attitudes, integration, and social norms of social capital proved in high schools of Izehcounty and this finding was significant statistically

Optimal replication of random vectors by ordinary integrals

We consider a problem of replication of random vectors by ordinary integrals in the setting when an underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral at a fixed terminal time matches this variable. The optimal process has to be minimal in an integral norm.

On improved estimates for parabolic equations with double degeneracy

We obtain improved pointwise estimates for solutions to nonlinear parabolic equations with double degeneracy. These estimates differ from the classical estimates known for the linear case in that the supremum of the modulus of a solution is estimated by the sum of two powers of the integral norm of the solution.

Ground state solutions for quasilinear stationary Schrödinger equations with critical growth

We establish the existence of ground state solution for quasilinear Schrodinger equations involving critical growth. The method used here is minimizing the gradient integral norm in a manifold defined by integrals involving the primitive of the nonlinearity function.

East Asians' Social Heterogeneity: Differences in Norms Among Chinese, Japanese, and Korean Negotiators

This paper shows that the assumption, widely accepted in the culture and negotiation literature, that East Asian cultures are homogeneous in their value for preserving social relationships is an oversimplification. We propose that there will be differences in negotiation norms among managers from China, Japan, and Korea because the focus of social relations – individual versus group – and the emotional versus instrumental nature of those relations varies systematically among these three cultures. Web survey data from managers from the three countries showed, as predicted, that Japanese managers were most likely to endorse distributive tactic norms; Chinese managers were least likely to endorse integrative tactic norms; and Korean managers were most likely to endorse norms for self-interest.