相关论文: Comment on "Phase Transition-Like Behavior in a Lo…
We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category…
The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite…
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
Single-ended circuit topologies, and a theorem for the development thereof, are presented with which one may realize constant-resistance (or reflectionless) filters, having ideally zero reflection coefficient at all frequencies and from all…
We present an analytic study of a periodic Josephson array with long-range interactions in a transverse magnetic field. We find that this system exhibits a first-order transition into a phase characterized by an extensive number of states…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
We describe a new notation for finite transformations. This attractor-cycle notation extends the orbit-cycle notation for permutations and builds upon existing transformation notations. How the basins of attraction of a finite…
We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…
Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of…
We show that if the sum of the resistances of an electrical network $N$ is finite, then there is a unique electrical current in $N$ provided we do not allow, in a sense, any flow to escape to infinity.
Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its…
The total impedance of a ladder-shape network consisting of inductors and capacitors does not converge to a certain value when the steps of the network increased. In this paper, we analyze this effect in frequency domain. We find that in…
Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions.…
The Bessel filters are optimized to collect competent transient response due to a linear phase in the passband. In other words, during the filtering process, there will be comparatively impoverished frequency response with lower amplitude…
Modifications of the authors' previously-published, generalized, lumped-element, reflectionless filter topologies are presented which remove the original constraints on the relative values of its prototype parameters. Thus, any transfer…
A recent physics challenge shows a circuit, where a voltmeter is connected in series. Indeed, real voltmeters have finite input resistance, therefore one may think that they can be used as resistors. In addition, voltmeters measure the…
This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of $\it{negative}$ resistance. Such active elements are necessary…
Guided by classical concepts, we define the notion of \emph{ends} of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points…