Continuity Argument Research Articles

Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

Emergent behaviors of relativistic flocks with adaptive coupling laws

In this paper, we investigate the emergent behaviors of the relativistic Cucker–Smale (RCS) model equipped with adaptive couplings. To do this, we first divide adaptive couplings into two types, Hebbian or anti-Hebbian. For the Hebbian case, we demonstrate the asymptotic flocking of the RCS model in two ways based on the Lyapunov functional approach and continuous argument. Meanwhile, for the anti-Hebbian case, depending on the regularity of the adaptive law at the origin, we prove the various emergent behaviors such as the slow velocity alignment or the group formation.

Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization

AbstractIn this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise constant vector fields as well as a discrete integration-by-parts formula between the Crouzeix–Raviart and the Raviart–Thomas element, all convex duality relations are transferred to a discrete level, making the explicit a posteriori error representation –initially based on continuous arguments only– practicable from a numerical point of view. In addition, we provide a generalized Marini formula that determines a discrete primal solution in terms of a given discrete dual solution. We benchmark all these concepts via the Rudin–Osher–Fatemi model. This leads to an adaptive algorithm that yields a (quasi-optimal) linear convergence rate.

A Conceptualist Reading of the Continuity Argument

In this paper I analyze the non-conceptualist continuity argument to show that it implies an implausible conception of perceptual experience in animals that are supposed to lack concepts. In order to do this, I show the limitations and implicit premises in the traditional formulations of the argument, and the additional premises needed to use it as an objection against conceptualism. Then, I review studies in cognitive neuroscience, ethology, comparative psychology, developmental psychology, and philosophical considerations to show that the argument implies a conception of animal experience that is at odds with our scientific theories and even with the motivations for adopting non-conceptualism. I conclude that, if we wish to defend the continuity between adult human’s and other animal’s experiences, we should do it by attributing concepts to the latter.

Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are given by the far field patterns u∞(xˆ,k) for all observation directions xˆ in some neighborhood of a fixed direction xˆ0 and for all wave numbers k belonging to a finite interval (0,K). In this paper, we discuss the increasing stability with respect to the width of the wavenumber interval K>1. In three dimensions we establish stability estimates of the L2-norm and H−1-norm of the source function from the far field data. The ill-posedness of the inverse source problem turns out to be of Hölder type while increasing the wavenumber band K. We also discuss an analytic continuation argument of the far-field data with respect to the wavenumbers at a fixed direction.

Coaches Behaviour Towards Motivational Climate and Performance Satisfaction of College Volleyball Players in Guangdong China

Coaches plays a significant role on how an athlete behave, perform and act. Each coach utilizes different method and approach in coaching which describe their coaching behaviour. Coaching behavior represents the personal characteristics and attitudes of the coaches. The impact of coaching behaviour has been an extensive topic of study in sports psychology where continuous arguments on how coaching behaviour affects motivational climate and performance of the athletes. Therefore, the researcher in this study deemed to bridge the knowledge gap through identifying the impact of coaching behaviour, motivational climate and performance satisfaction of the climate and performance satisfaction of college volleyball players in Guangdong, China. In conducting the study, the researcher employed descriptive correlational design. Two hundred collegiate volleyball players in selected universities in Guangdong, Chine were selected through stratified simple random sampling technique as respondents of the study. Validated self-made questionnaire was used as the main instrument of the study in describing coaching behaviour of the team coaches in terms of action, belief and attitude, motivational climate in terms of task/mastery and ego-oriented climate and performance satisfaction in terms of individual, team and coach’s performance. The data was analyzed through the use of Pearson r. The result of the study revealed that there is a significant relationship between the coaching and the motivational climate within the team as perceived by the respondents. Furthermore, coaching behaviour is significantly related to performance satisfaction in terms of individual, team and coach’s performance. Finally, the study formulated a proposed program of action to better enhance the coaching behaviour of the volleyball team coaches.

Stability equivalence between regime‐switching jump diffusion delayed systems and corresponding systems with piecewise continuous arguments and application to discrete‐time feedback control

AbstractIn this paper, we mainly study the equivalence of exponential stability for regime‐switching jump diffusion delayed systems (RSJDDSs) and RSJDDSs with piecewise continuous arguments (RSJDDSs‐PCA). Our results show that if one of the RSJDDS and the RSJDDS‐PCA is th moment exponentially stable, then another system is also th moment exponentially stable when time delay and segment step size have a common upper bound, while both equations are almost surely exponentially stable, and we also provided a method to calculate this upper bound. In addition, as an application of the stability equivalence theorem, we design discrete‐time state and mode observations feedback control to stabilize unstable RSJDDSs and investigate that controllers of the drift, diffusion, and jump terms are all able to play a stabilizing effect on the controlled system.

The Palestinian Curriculum and European Foreign Aid: The Challenges to Preserve National Content

The continuous and controversial arguments about any relationship between foreign aid and the national content of the learned curricula in new and emerging entities in post-conflict areas in general, and in the Palestinian case in particular, have been a source of apprehension for many educators, stakeholders, educational experts, and even school children’s parents. This study aims at investigating the challenges to preserve authentic national and historical content in the light of receiving European foreign aid, taking Palestine as a case. The researcher adopted a mixed-methods approach to achieve the study’s goals. The national content of the school textbooks of the lower basic stage was analysed as a purposive sample of the Palestinian national curriculum. Moreover, semi-structured interviews were conducted with a) curriculum professionals and policymakers from the Ministry of Education to find out the direct impact of European aid on the national content of the Palestinian curriculum, and b) with Palestinian teachers to investigate their attitudes towards the adequacy and efficiency of the national and historical content of the Palestinian curriculum. The results of the content analysis present many national themes and values, yet with diverse dominance and distribution. The semi-structured interviews revealed the continuous pressure on the Ministry of Education to change the content of Palestinian curricula, and its impact on the national content. As for the teachers’ interviews, the results demonstrate that Palestinian teachers do not have positive perspectives on the national and historical content and look forwards to fundamental improvements in the national and historical curriculum.

Short Essay on Difference Equations with Continuous Argument

Short Essay on Difference Equations with Continuous Argument

Comparison between four different suture configurations for rotator cuff repair: a biomechanical animal study.

The arthroscopic repair of a massive rotator cuff tear could be surgically challenging. There is a continuous argument regarding the best surgical technique and suture configuration used to treat massive rotator cuff tears. The purpose of this study was to assess the in vitro strength of the new double Mason-Allen suture and compare it to the commonly used other suture configurations. Twenty-five fresh sheep shoulders were randomly divided into five equal groups. Each group had their infraspinatus tendons cut and repaired with one of five suture configurations (simple, horizontal mattress, Mason-Allen, modified Mason-Allen, and double Mason-Allen) using Arthrex® 1.3mm suture tape. The specimens were fixed to the test apparatus through their scapulae and hung with the repair tape to Sartorius® precision balance with sequential load increments till failure. The load to failure was measured for each of the five suture configurations. Study data found the double Mason-Allen configuration to have the highest mean load to failure 423.30±23.05 (Newtons), followed by modified Mason-Allen, Mason-Allen, horizontal mattress, and simple suture respectively. The double Mason-Allen repair configuration has the highest load to failure compared to the other known suture configuration to repair rotator cuff tears.

Strong convergence of explicit numerical schemes for stochastic differential equations with piecewise continuous arguments

Strong convergence of explicit numerical schemes for stochastic differential equations with piecewise continuous arguments

Convergence and stability of modified partially truncated Euler-Maruyama method for stochastic differential equations with piecewise continuous arguments

ABSTRACT This paper constructs a modified partially truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift and diffusion coefficients grow superlinearly. We divide the coefficients of SDEPCAs into global Lipschitz continuous and superlinearly growing parts. Our method only truncates the superlinear terms of the coefficients to overcome the potential explosions caused by the nonlinearities of the coefficients. The strong convergence theory of this method is established and the 1/2 convergence rate is presented. Furthermore, an explicit scheme is developed to preserve the mean square exponential stability of the underlying SDEPCAs. Several numerical experiments are offered to illustrate the theoretical results.

Collective behavior for the delayed Cucker-Smale system in a harmonic potential field

We consider a time varying delayed Cucker-Smale system in a harmonic potential field and analyze its long time collective behavior. Under appropriate assumptions on the initial data, we show the asymptotic collective behavior when the time varying delay is uniformly bounded by a sufficiently small constant. Our strategies are based on the Lyapunov functional approach, forward-backward estimate and the continuity argument. Finally, some numerical tests are performed to illustrate the theoretical result.

Well‐posedness and decay for 3D non‐isothermal Navier–Stokes–Allen–Cahn system in ℝ3

In this paper, we investigate the local existence, global existence and time decay estimates for the nonisentropic Navier–Stokes–Allen–Cahn system in . This system describes the flow of a two‐phase immiscible heat‐conducting viscous incompressible mixture. In order to overcome the difficulties caused by the derivatives of double‐well potential and the nonlinear terms, we rewrite the Cahn–Hilliard part of the system as a new equivalent equation with “good” linear principle parts. Then, on the basis of the higher order norm estimates of solutions and the mollifier technique, we obtain the local well‐posedness of strong solutions. Moreover, by using pure energy method and standard continuity argument together with negative Sobolev norm estimates, one proves the global well‐posedness and time decay estimates provided that the initial data are sufficiently small.

Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments

Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments

Convergence and stability of an explicit method for nonlinear stochastic differential equations with piecewise continuous arguments

This paper constructs a new explicit method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift coefficients grow superlinearly and the diffusion coefficients have at most linear growth. We show that this method converges strongly with the convergence rate 1/2 to the exact solutions of SDEPCAs over the finite time interval and demonstrate it can inherit the mean square exponential stability of the underlying SDEPCAs. Several numerical experiments are carried out to support our findings.

Three Kinds of Arguments for Panpsychism

Panpsychism may be roughly defined as a view that at least some of the properties constituting the fundamental level of reality are mental or proto-mental. Despite its long history, it has been revived in recent discussions as a solution to the problems raised by the mind, especially to the so-called hard problem of consciousness. Contemporary panpsychism differs significantly from incarnations known from the history of philosophy mainly due to the fact that the former is often combined with so-called Russellian monism. According to Russellian monism, the intrinsic properties of physical things remain unknown. This encourages panpsychists to argue that those properties are in fact mental. In my paper, I examine the three most common arguments for panpsychism: the Continuity Argument, the Hegelian Argument, and the Agnostic Argument. I take a closer look at each of them to assess their advantages and weaknesses. As I point out, the way in which one argues implies the version of panpsychism one adopts. This turns out to be especially important with regard to the Hegelian Argument and the Agnostic Argument. Both can be combined with Russellian monism, resulting in Russellian panpsychism. However, I claim that the philosophical consequences of these arguments are different, so it is legitimate to distinguish two kinds of Russellian panpsychism. In conclusion, I hold that there are reasons to prefer panpsychism based on the Agnostic Argument, which is more promising, as it responds to some general problems of panpsychism.

CONVERGENCE AND STABILITY OF GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS OF ADVANCED TYPE

This paper deals with the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments of advanced type. First of all, we obtain the expression of analytic solution by the method of separation variable, then the sufficient conditions for stability are obtained. Semidiscrete and fully discrete schemes are derived by Galerkin finite element method, and their convergence are both analyzed in L2-norm. Moreover, the stability of the two schemes are investigated. The semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are derived under which the analytic solution is asymptotically stable. Finally, some numerical experiments are presented to illustrate the theoretical results.

Emergence, Continuity, and Scientific Realism

Scientific realism postulates that science aims for truth in both the domains of the observable and the unobservable, and is capable of achieving this aim, at least approximately. From the realist perspective our current scientific theories are on the right path to their aim, encapsulating a significant degree of theoretical truth. A key argument supporting this viewpoint is the continuity observed between successive scientific theories, interpreted as the preservation of truth. However, we contend that this continuity argument is problematic in significant cases. Features of older theoretical schemes frequently do not persist in subsequent theories but emerge as limiting cases with restricted applicability domains and fine-grained structures that differ from what the older theories deemed possible. The alterations accompanying theory replacement are often more drastic than what is assumed by realist intuition, justifying skepticism about continuity serving as an indicator of theoretical truth preservation. We propose an argument wherein continuity is instead viewed as a consequence of empirical success preservation.

Satiation in Fisher Markets and Approximation of Nash Social Welfare

We study linear Fisher markets with satiation. In these markets, sellers have earning limits, and buyers have utility limits. Beyond applications in economics, they arise in the context of maximizing Nash social welfare when allocating indivisible items to agents. In contrast to markets with either earning or utility limits, markets with both limits have not been studied before. They turn out to have fundamentally different properties. In general, the existence of competitive equilibria is not guaranteed. We identify a natural property of markets (termed money clearing) that implies existence. We show that the set of equilibria is not always convex, answering a question posed in the literature. We design an FPTAS to compute an approximate equilibrium and prove that the problem of computing an exact equilibrium lies in the complexity class continuous local search ([Formula: see text]; i.e., the intersection of polynomial local search ([Formula: see text]) and polynomial parity arguments on directed graphs ([Formula: see text])). For a constant number of buyers or goods, we give a polynomial-time algorithm to compute an exact equilibrium. We show how (approximate) equilibria can be rounded and provide the first constant-factor approximation algorithm (with a factor of 2.404) for maximizing Nash social welfare when agents have capped linear (also known as budget-additive) valuations. Finally, we significantly improve the approximation hardness for additive valuations to [Formula: see text]. Funding: J. Garg was supported by the National Science Foundation [Grant CCF-1942321 (CAREER)]. M. Hoefer was supported by Deutsche Forschungsgemeinschaft [Grants Ho 3831/5-1, Ho 3831/6-1, and Ho 3831/7-1].