Continuity Argument Research Articles

Stability analysis for semi-linear stochastic differential equation with piecewise continuous arguments

In this paper, the exponential stability in mean square of the exponential Euler method for semi-linear stochastic differential equation with piecewise continuous arguments is obtained. Firstly, the exponential Euler scheme of the equation is given. Secondly, under Lipschitz condition, sufficient conditions of exponential stability to the exact solution are achieved in mean square. Furthermore, it is proved that exponential Euler method preserves exponential stability of the exact solution without any restriction on the step-size. Finally, an example is provided to illustrate our theories.

Large sample autocovariance matrices of linear processes with heavy tails

We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time. Assuming that the dimension increases with the sample size, we provide theory for the eigenvectors of the sample autocovariance matrices and find explicit approximations of a simple structure, whose finite sample quality is illustrated for simulated data. We also obtain the limits of the normalized eigenvalues of functions of the sample autocovariance matrices in terms of cluster Poisson point processes. In turn, we derive the distributional limits of the largest eigenvalues and functionals acting on them. In our proofs, we use large deviation techniques for heavy-tailed processes, point process techniques motivated by extreme value theory, and related continuous mapping arguments.

Optimal time decay of the compressible Navier–Stokes equations for a reacting mixture

In this paper, we are concerned with the large-time behavior of solutions to the Cauchy problem on the compressible Navier–Stokes equations for ideal reacting gases. The asymptotic stability of the constant equilibrium state with strictly positive constant density, temperature and the vanishing velocity, mass fraction of the reactant is established under suitable small initial perturbation in . Precisely, we show the convergence of the density, velocity and temperature towards the corresponding equilibrium state with the optimal rate in L 2-norm as well as the convergence of the mass fraction to the equilibrium state with the optimal rate in L 2-norm. Furthermore, the optimal decay rates for the spatial-derivatives of the solution are also obtained. The proof is based on the time-weighted energy estimate and continuation argument.

Global well-posedness of solutions for the epitaxy thin film growth model

In this paper, we consider the global well-posedness of solutions for the initial-boundary value problems of the epitaxy growth model. We first construct the local smooth solution, then by combining some a priori estimates, continuity argument, the local smooth solutions are extended step by step to all t > 0, provided that the initial datums sufficiently small and the smooth nonlinear functions satisfy certain local growth conditions.

Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs

We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system and then applying the Leray–Schauder fixed point theorem. We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so-called global controllability).

Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

Uniform a priori estimates for solutions of higher critical order fractional equations

In this paper, we establish uniform a priori estimates for positive solutions to higher critical order fractional Lame-Emden equations for all large exponents by adopting a new idea of using the combination of Green’s representations with suitable cut-off functions. We obtain two key ingredients needed in the estimates. One is the monotonicity of solutions in the inward normal direction near the boundary by using the method of moving planes in a local way, and the other is the integration by parts formula for higher order fractional operators. Both of them will become useful tools in the analysis of higher order fractional equations. It is well-known that, with such a priori estimate, one will be able to obtain the existence of solutions via topological degree or continuation arguments.

Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

In this paper, we consider the equivalence of the pth moment exponential stability for stochastic differential equations (SDEs), stochastic differential equations with piecewise continuous arguments (SDEPCAs) and the corresponding Euler-Maruyama methods EMSDEs and EMSDEPCAs. We show that if one of the SDEPCAs, SDEs, EMSDEs and EMSDEPCAs is pth moment exponentially stable, then any of them is pth moment exponentially stable for a sufficiently small step size h and τ under the global Lipschitz assumption on the drift and diffusion coefficients.

On Fast Jerk–, Acceleration– and Velocity–Restricted Motion Functions for Online Trajectory Generation

Finding fast motion functions to get from an initial state (distance, velocity, acceleration) to a final one has been of interest for decades. For a solution to be practically relevant, restrictions on jerk, acceleration and velocity have to be taken into account. Such solutions use optimization algorithms or try to directly construct a motion function allowing online trajectory generation. In this contribution, we follow the latter strategy and present an approach which first deals with the situation where initial and final accelerations are 0, and then relates the general case as much as possible to this situation. This leads to a classification with just four major cases. A continuity argument guarantees full coverage of all situations which is not the case or is not clear for other available algorithms. We present several examples that show the variety of different situations and, thus, the complexity of the task. We also describe an implementation in MATLAB® and results from a huge number of test runs regarding accuracy and efficiency, thus demonstrating that the algorithm is suitable for online trajectory generation.

Continuity in Morality and Law

Abstract According to an influential and intuitively appealing argument (the Continuity Argument), (1) morality is usually continuous, namely, a gradual change in one morally significant factor triggers a gradual change in another; (2) the law should usually track morality; (3) therefore, the law should often be continuous. This argument is illustrated by cases such as the following example: since the moral difference between a defensive action that is reasonable and one that is just short of being reasonable is small, the law should not impose a severe punishment when the action is almost reasonable and no punishment at all when the action is reasonable (as positive law sometimes does). In this Article, I consider two doubts regarding this argument. First, the premise that morality is continuous in such cases is incompatible with the common view that the moral status of actions is not continuous since there is an important difference between actions that are permissible and actions that are wrong— even if this difference is due to a difference that is very small, such as the one between an action whose consequences are the best and an action whose consequences are just slightly less good. This view extends also to the overall moral status of agents given the common assumption that it depends on the moral status of their actions. This is an important challenge that the Continuity Argument should confront. However, I argue that the best account of morality is more scalar than the common view in these respects. Therefore, I conclude that the first premise of the Continuity Argument is correct in this regard, although it is based on a minority view. The second doubt concerns the scope of the second premise: since there are reasons both in favor and against legal continuity, and the applicability and force of these reasons depend not only on various moral propositions but also on contingent non-moral facts, we often lack the evidence to determine the degree to which the law, at a certain place and time, should be continuous, and specifically that it should often be continuous.

The Pulse of Non-Democracy?

The article continues the discussion of Grigory Yudin’s book Public Opinion. The review considers Yudin’s arguments on the “plebiscitarian bias” in opinion-poll technology, on the linkages between opinion-polls, Rousseauist tradition and the “plebiscitarian model”, and on Gallup’s, Schumpeter’s, and Weber’s contributions to plebiscitarism. In the context of the proposed conceptual model, controversial issues in the interpretation of Weber’s and Schumpeter’s ideas, as well as an estimation of the Russian political regime in the 2010s are debated. Models of plebescitarism (including their principles and criteria) as proposed by Yudin, and by Urbinati in Democracy Disfigured are compared. The article highlights the differences between Gallup and Schumpeter, as well as between Schumpeter and Weber, in their insights into democracy and public opinion. The reviewer pays attention to the relationship between the classical doctrine of representative democracy by Schumpeter and the bourgeois public sphere by Habermas, and between public debates and the quantification of public opinion. We examine the argument about the continuity between public-opinion polls and the big projects of Modernity, such as representative democracy, public sphere, and biopolitics. Continuity argument is proposed as an alternative to Yudin’s hypothesis about the radical reinvention of ‘democracy’ and ‘public opinion’ during the inter-war period of the 20th century. Yudin’s insights on the social and political onthology of opinion-polls are preliminary, and are reconstructed for further discussion.

The Moderating Role of Religious Satisfaction on Purchasing Over-The-Counter Medicines in Malaysia: An Islamic Perspective

Medications can be found in different formulations and ingested in different ways. OTC medications are used to cure, avoid or alleviate disease and to promote the well-being of people. There is continuous argument building up by taking a possibly Halal medication among the growing Muslim consumers around the world. Therefore, the focus of this study drawn from Maqasid al-Shariah approach for medicine usage and its significance in Islam. A sample of 308 Muslim consumers of pharmacies was being surveyed from the metropolitan territory of Kuala Lumpur and Selangor states in Malaysia. The Exploratory Factor Analysis and Confirmatory Factor Analysis techniques have been used to analyse the data. The outcome revealed that customers’ religious satisfaction significantly moderates the purchasing of OTC medicines. The purpose of self-medication comes from the consumer’s decision-making. Hence, the self-medication phenomenon is critical to understand, and it should be subjected to strict control for the betterment of the Ummah.

Factores asociados a la violencia contra los adolescentes dentro del hogar en el Perú

Background: Adolescence responds to a period of maturity and adjustment to the adult world; therefore, it is influenced by the social and family context, as well as by the previous stages of development. The objective of the present investigation was to determine the factors associated with violence against adolescents at home in Peru. Methods. A secondary analysis of the National Survey of Social Relations 2015 was carried out. The sample was of 1491 adolescents between 12 to 17 years old. Raw (PR) and adjusted (PRa) prevalence ratios using Poisson regression with robust variance were estimated. Results. It was found that adolescent women (PRa: 1.4; 95% CI: 1.17-1.68) and adolescents who live in homes where there are continuous fights or arguments between parents or adults who live there (PRa: 2.75; 95% CI: 2.11-3.57) have a higher risk of violence. Conclusions. Women and adolescents who live in families where there are continuous arguments between parents or adults have a high risk of domestic violence.

African pathway to achieve inclusive growth: COMESA case study

Purpose The relationship between economic growth performance and achieving inclusive growth, especially concerning poverty rate, is a subject of continuous argument in economic literature. Although some argue that this relationship is deterministic, i.e. achieving economic growth will definitely reduce poverty and enhance inclusive growth, others believe that the relationship between growth and poverty is conditional, depends mainly on the status of income distribution in this country, i.e. if the growth is combined with a significant improve in distribution then it will reduce poverty. Design/methodology/approach Africa is a clear example of the nexus between economic growth and poverty reduction. Although many African countries manage to achieve relatively high growth rates, hit two digits in some cases, during the last decades, poverty still widely spread in those countries. Of the 30 poorest countries in the world, 24 are African countries. And about 50% of African people still live under the poverty line. Common Market for Eastern and Southern Africa (COMESA), which could be considered as one of the fastest growing regions in Africa, is not an exception; although the region achieves relatively high growth rates, poverty and inequality are still among the region’s main development challenges. Findings This paper found that the economic growth rate achieved in COMESA countries could not be considered as inclusive growth as it does not combine with adequate enhancement in inclusiveness indicators. And that the structural characteristics of those countries economy and its inelasticity are the main reasons behind this inefficiency. Originality/value In this context, this paper aims to evaluate the effectiveness of economic growth achieved in COMESA countries in achieving inclusive growth and to identify the main factors affecting this relationship by using two steps data envelopment analysis. Although this method is originally developed to evaluate the relative economic efficiencies, the main contribution of this paper is the adaptation of data envelopment analysis to evaluate the efficiency of economic growth achieved in COMESA countries in enhancing inclusive growth dimensions such as poverty rate, inequality, unemployment, education, health, and then to identify in its second step the main indicators that could be used to explain the variation in efficiency scores.

On well-posedness and large time behavior for smectic-A liquid crystals equations in $$\mathbb {R}^3$$

The main purpose of this manuscript is to study the well-posedness and decay estimates for strong solutions to the Cauchy problem of 3D smectic-A liquid crystals equations. First, applying Banach fixed point theorem, we prove the local existence and uniqueness of strong solutions. Then, by establishing some nontrivial estimates with energy method and a standard continuity argument, we prove that there exists a unique global strong solution provided that the initial data are sufficiently small. Moreover, we also establish the suitable negative Sobolev norm estimates and obtain the optimal decay rates of the higher-order spatial derivatives of the strong solutions.

Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments

This paper deals with numerical solutions of nonlinear stiff stochastic differential equations with jump-diffusion and piecewise continuous arguments. By combining compensated split-step methods and balanced methods, a class of compensated split-step balanced (CSSB) methods are suggested for solving the equations. Based on the one-sided Lipschitz condition and local Lipschitz condition, a strong convergence criterion of CSSB methods is derived. It is proved under some suitable conditions that the numerical solutions produced by CSSB methods can preserve the mean-square exponential stability of the corresponding analytical solutions. Several numerical examples are presented to illustrate the obtained theoretical results and the effectiveness of CSSB methods. Moreover, in order to show the computational advantage of CSSB methods, we also give a numerical comparison with the adapted split-step backward Euler methods with or without compensation and tamed explicit methods.

A novel decision probability transformation method based on belief interval

In Dempster–Shafer evidence theory, the basic probability assignment (BPA) can effectively represent and process uncertain information. How to transform the BPA of uncertain information into a decision probability remains a problem to be solved. In the light of this issue, we develop a novel decision probability transformation method to realize the transition from the belief decision to the probability decision in the framework of Dempster–Shafer evidence theory. The newly proposed method considers the transformation of BPA with multi-subset focal elements from the perspective of the belief interval, and applies the continuous interval argument ordered weighted average operator to quantify the data information contained in the belief interval for each singleton. Afterward, we present an approach to calculate the support degree of the singleton based on quantitative data information. According to the support degree of the singleton, the BPA of multi-subset focal elements is allocated reasonably. Furthermore, we introduce the concepts of probabilistic information content in this paper, which is utilized to evaluate the performance of the decision probability transformation method. Eventually, a few numerical examples and a practical application are given to demonstrate the rationality and accuracy of our proposed method.

Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments

Delay-differential-algebraic equations have been widely used to model some important phenomena in science and engineering. Since, in general, such equations do not admit a closed-form solution, it is necessary to solve them numerically by introducing suitable integrators. The present paper extends the class of block boundary value methods (BBVMs) to approximate the solutions of nonlinear delay-differential equations with algebraic constraint and piecewise continuous arguments. Under the classical Lipschitz conditions, convergence and stability criteria of the extended BBVMs are derived. Moreover, a couple of numerical examples are provided to illustrate computational effectiveness and accuracy of the methods.

Decay rate of global solutions to three dimensional generalized MHD system

We investigate the initial value problem for the three dimensional generalized incompressible MHD system. Analyticity of global solutions was proved by energy method in the Fourier space and continuous argument. Then decay rate of global small solutions in the function space $ \mathcal {X}^{1-2\alpha}\bigcap \mathcal {X}^{1-2\beta} $ follows by constructing time weighted energy inequality.

Nazi Criminology: Continuity and Radicalisation

Contrary to the ‘rupture thesis’ favoured in Anglo-American academic discourse, Nazi criminal law did not emerge from a vacuum; nor did it disappear after 1945. The article explains and defends this ‘continuity thesis’. In fact, Nazi criminal law adopted earlier authoritarian tendencies of German criminal law and exacerbated them (the ‘radicalisation thesis’). It is for this reason that Nazi criminal law should not lightly be dismissed as ‘non-law’, thus omitting any further engagement with it. The article will show that the same continuity and radicalisation arguments can be made, mutatis mutandis, for German Nazi criminology, which ultimately became a legitimating science (‘Legitimationswissenschaft’) for Nazi criminal justice policy. The argument is developed in four stages. First, an account is given of the racist and criminal-biologistic foundations of National Socialist criminology, including their continuity both with the past and into the future. This is followed by an explanation of the influence of criminal anthropology (particularly that of Lombroso) on the ‘scientification’ of criminology (the ‘Kraepelin and Aschaffenburg paradigms’). Third, the National Socialist radicalisation of criminology on the basis of the criminal-biological utopia of the ‘blood-based’ Volksgemeinschaft is described. Thus, Nazi criminology derived its strength from and built upon biological theories of crime, which in turn laid the foundations of the deadly Nazi criminal justice policy. The discipline became a science that legitimated National Socialism, contrary to Wetzell's thesis of a somewhat dissident ‘mainstream criminology’. With regard to disturbing developments in current German politics, all this will make clear that the approach of the (German) ‘New Right’ to criminal justice is not novel at all but is derived from the ideologically infused theories and policies of Nazi criminologists during the 1930s.