Electrodynamics in accelerated frames revisited

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.Comment: 17 pages, no figure

Balayage of Fourier Transforms and the Theory of Frames

Every separable Hilbert space has an orthogonal basis. This allows every element in the Hilbert space to be expressed as an infinite linear combination of the basis elements. The structure of a basis can be too rigid in some situations. Frames gives us greater flexibility than bases. A frame in Hilbert space is a spanning set with the reconstruction property. A frame must satisfy both an upper frame bound and a lower frame bound. The requirement of an upper bound is rather modest. Most of the mathematical difficulty lies in showing the lower bound exists. We examine the theory of Beurling on Balayage of Fourier transforms and the role of spectral synthesis in this theory. Beurling showed that if the condition of Balayage holds, then the lower frame bound for a Fourier frame exists under suitable hypothesis. We extend this theory to obtain lower bound inequalities for other types of frames. We prove that lower bounds exist for generalized Fourier frames and two types of semi-discrete Gabor frames

A BGK relaxation model for polyatomic gas mixtures

We present a BGK approximation of a kinetic Boltzmann model for a mixture of polyatomic gases, in which non-translational degrees of freedom of each gas are represented by means of a set of discrete internal energy levels. We also deal with situations, in which even chemical reactions implying transfer of mass may occur. The consistency of the proposed BGK model is proved in both inert and reactive frames, and numerical simulations in space homogeneous settings are presented

Simplifying the Formal Verification of Safety Requirements in Zone Controllers through Problem Frames and Constraints based Projection

Formal methods have been applied widely to verifying the safety requirements of Communication-Based Train Control (CBTC) systems, while the problem situations could be much simplified. In industrial practices of CBTC systems, however, huge complexity arises, which renders those methods nearly impossible to apply. In this paper, we aim to reduce the state space of formal verification problems in Zone Controller, a sub-system of a typical CBTC. We achieve the simplification goal by reducing the total number of device variables. To do this, two projection methods are proposed based on Problem Frames and constraints, respectively. The Problem Frames based method decomposes the system according to sub-properties through functional decomposition, whilst the constraints based projection method removes redundant variables. Our industrial case study demonstrates the feasibility though an evaluation, confirming that these two methods are effective in reducing the state spaces of complex verification problems in this application domain

An exploration of relative frame potential

A frame for a vector space is a set of vectors which behaves in some ways like a basis for the vector space while having a more flexible structure that allows for frames to be constructed to fit a variety of application situations, such as in signal processing. The frame potential function, developed in 2001, takes a frame as input and returns its “frame potential value”. This value reveals important information about the properties of the input frame. In this paper, we adapt the frame potential function to create a “relative frame potential function”, which takes one frame as input with respect to another frame. We analyze the behavior of this function to determine what information the relative frame potential value can reveal about the relationship between the two frames.Honors CollegeThesis (B.?

Generalized Task-Parameterized Skill Learning

Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new situations, a task-parameterized Gaussian mixture model (TP-GMM) has been recently developed. This model has achieved reliable performance in areas such as human-robot collaboration and dual-arm manipulation. However, the crucial task frames and associated parameters in this learning framework are often set by the human teacher, which renders three problems that have not been addressed yet: (i) task frames are treated equally, without considering their individual importance, (ii) task parameters are defined without taking into account additional task constraints, such as robot joint limits and motion smoothness, and (iii) a fixed number of task frames are pre-defined regardless of whether some of them may be redundant or even irrelevant for the task at hand. In this paper, we generalize the task-parameterized learning by addressing the aforementioned problems. Moreover, we provide a novel learning perspective which allows the robot to refine and adapt previously learned skills in a low dimensional space. Several examples are studied in both simulated and real robotic systems, showing the applicability of our approach

Discourses, Conventions, and Critique - Perspectives of the Institutionalist Approach of the Economics of Convention

The institutionalist approach of economics of conventions (EC) was developed in France in the last decades and recombines pragmatist and structuralist concepts. In EC, conventions are not regarded as institutions, but are conceived as interpretative frames how to interpret the meaning of institutions and situations, and how to handle institutions in situations of coordination. The difference between institutions and conventions offers space for “critical movements” and can implement a tension as well as an infrastructure for critique. The article introduces main concepts of EC, which could be applied to the analysis of social critique. In fact, the pragmatist analysis of critical moments and practices of justification was one of the birth moments of EC and EC has developed strategies to analyze and explain social change. The article presents some newer reflections of EC on power and dispositive. Furthermore, the article relates the Foucaultian notions of discourse and power to EC’s analysis of critique and social change. Finally, a current strand of EC research is discussed, which is the study and cri-tique of neoliberalism and the role of the state

A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized