scholarly journals Formal Chaos Existing Conditions on a Transmission Line Circuit with a Piecewise Linear Resistor

2021 ◽  
Vol 11 (20) ◽  
pp. 9672
Author(s):  
Kazuya Ozawa ◽  
Kaito Isogai ◽  
Hideo Nakano ◽  
Hideaki Okazaki
Keyword(s):  
Transmission Line ◽  
Piecewise Linear ◽  
Sufficient Conditions ◽  
Voltage Source ◽  
One Dimensional ◽  
In Series ◽  
Load Resistor ◽  
Dc Bias ◽  
Definition Of ◽  
Bifurcation Behavior

By using one-dimensional (1-D) map methods, some lossless transmission line circuits with a short at one side terminal have been actively studied. Bifurcation results or chaotic states in the circuits have been reported. On the other hand, many weak or strong definitions such that a 1-D map is mathematically chaotic are still being studied. In such definitions, the definition of formal chaos is well known as being the most traditional and most definite. However, formal chaos existences have not been rigorously proven in such circuits. In this paper, a general lossless transmission circuit is considered first with a dc bias voltage source in series with a load resistor at one side terminal and with a three-segment piecewise linear resistor at another side terminal. Secondly, the method for deriving a 1-D map describing the behavior of the circuit is summarized. Thirdly, to provide a basis of chaotic application for the 1-D map, the mathematical definition of formal chaos and the sufficient conditions of the existence of formal chaos are discussed. Furthermore, by using Maple, formal chaos existences and bifurcation behavior of 1-D maps are presented. By using the Lyapunov exponent, the observability of formal chaos in such bifurcation processes is outlined. Finally, the principal results and the future works are summarized.

scholarly journals ON SOME QUALITATIVE PROPERTIES OF THE OPERATOR OF FRACTIONAL DIFFERENTIATION IN KIPRIYANOV SENSE

2017 ◽  
Vol 23 (2) ◽  
pp. 32-43
Author(s):  
M. V. Kukushkin
Keyword(s):  
Fractional Calculus ◽  
Fractional Integral ◽  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Fractional Differentiation ◽  
Qualitative Properties ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Integral Equality ◽  
Definition Of

In this paper we investigated the qualitative properties of the operator of fractional differentiation in Kipriyanov sense. Based on the concept of multidimensional generalization of operator of fractional differentiation in Marchaud sense we have adapted earlier known techniques of proof theorems of one-dimensional theory of fractional calculus for the operator of fractional differentiation in Kipriyanov sense. Along with the previously known definition of the fractional derivative in the direction we used a new definition of multidimensional fractional integral in the direction of allowing you to expand the domain of definition of formally adjoint operator. A number of theorems that have analogs in one-dimensional theory of fractional calculus is proved. In particular the sufficient conditions of representability of a fractional integral in the direction are received. Integral equality the result of which is the construction of the formal adjoint operator defined on the set of functions representable by the fractional integral in direction is proved.

Necessary and Sufficient Conditions for the Occurrence of Bisecting Bifurcations in the General 2D Piecewise-Linear Mapping

2017 ◽  
Vol 27 (05) ◽  
pp. 1750079
Author(s):  
Hannachi Fareh ◽  
Zeraoulia Elhadj
Keyword(s):  
Periodic Orbits ◽  
Piecewise Linear ◽  
Sufficient Conditions ◽  
Linear Mapping ◽  
Necessary And Sufficient Conditions ◽  
Stable Periodic ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Infinite Set

In this work, we focus on the conditions for the occurrence of a special type of bifurcations in the general 2D piecewise-linear mapping called bisecting bifurcations. This kind of bifurcation is mediated by an infinite set of neutrally stable periodic orbits, i.e. cycles with multiplier unity. We used the definition of the rank of both coefficient and augmented matrices based on minors to find the necessary and sufficient conditions in which the bisecting bifurcation occurs.

A Philosophical Analysis To Uncover The Meaning And Terminology Of Person In Indonesian Criminal Law Context

2017 ◽  
Vol 1 (1) ◽  
pp. 56
Author(s):  
Nani Mulyati ◽  
Topo Santoso ◽  
Elwi Danil
Keyword(s):  
Criminal Law ◽  
Sufficient Conditions ◽  
Criminal Code ◽  
Legal Person ◽  
Philosophical Approach ◽  
Legal Personality ◽  
Legal Subject ◽  
Long Time ◽  
Definition Of ◽  
Broad Meaning

The definition of person and non-person always change through legal history. Long time ago, law did not recognize the personality of slaves. Recently, it accepted non-human legal subject as legitimate person before the law. This article examines sufficient conditions for being person in the eye of law according to its particular purposes, and then, analyses the meaning of legal person in criminal law. In order to do that, scientific methodology that is adopted in this research is doctrinal legal research combined with philosophical approach. Some theories regarding person and legal person were analysed, and then the concept of person was associated with the accepted definition of legal person that is adopted in the latest Indonesian drafted criminal code. From the study that has been done, can be construed that person in criminal law concerned with norm adressat of the rule, as the author of the acts or omissions, and not merely the holder of rights. It has to be someone or something with the ability to think rationally and the ability to be responsible for the choices he/she made. Drafted penal code embraces human and corporation as its norm adressat. Corporation defined with broad meaning of collectives. Consequently, it will include not only entities with legal personality, but also associations without legal personality. Furthermore, it may also hold all kind of collective namely states, states bodies, political parties, state’s corporation, be criminally liable.

KANTHAL 70

Alloy Digest ◽  
1981 ◽  
Vol 30 (9) ◽  
Keyword(s):  
Operating Temperature ◽  
Heat Treating ◽  
Positive Temperature Coefficient ◽  
Pure Nickel ◽  
Voltage Source ◽  
Voltage Regulator ◽  
Positive Temperature ◽  
Automotive Applications ◽  
Resistance Thermometers ◽  
In Series

Abstract KANTHAL 70 alloy was designed to provide a high positive temperature coefficient to electrical resistance comparable with that of pure nickel; however, it has much higher electrical resistivity than pure nickel. This makes it useful as a voltage regulator when placed in series with another electrical device across a fluctuating voltage source. Kanthal 70 has a maximum recommended operating temperature of 600 C and is used widely in resistance thermometers and in various appliance and automotive applications. This datasheet provides information on composition, physical properties, and tensile properties. It also includes information on corrosion resistance as well as forming, heat treating, and joining. Filing Code: Ni-270. Producer or source: The Kanthal Corporation.

scholarly journals Flyback Converter for Solid-State Lighting Applications with Partial Energy Processing

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 60
Author(s):  
Mario Ponce-Silva ◽  
Daniel Salazar-Pérez ◽  
Oscar Miguel Rodríguez-Benítez ◽  
Luis Gerardo Vela-Valdés ◽  
Abraham Claudio-Sánchez ◽  
...  
Keyword(s):  
Solid State ◽  
Power Supply ◽  
Design Methodology ◽  
Low Frequency ◽  
Solid State Lighting ◽  
Voltage Source ◽  
Flyback Converter ◽  
Partial Energy ◽  
In Series ◽  
Energy Processing

The main contribution of this paper is to show a new AC/DC converter based on the rearrangement of the flyback converter. The proposed circuit only manages part of the energy and the rest is delivered directly from the source to the load. Therefore, with the new topology, the efficiency is increased, and the stress of the components is reduced. The rearrangement consist of the secondary of the flyback is placed in parallel with the load, and this arrangement is connected in series with the primary side and the rectified voltage source. The re-arranged flyback is only a reductive topology and with no magnetic isolation. It was studied as a power supply for LEDs. A low frequency averaged analysis (LFAA) was used to determine the behavior of the proposed circuit and an equivalent circuit much easier to analyze was obtained. To validate the theoretical analysis, a design methodology was developed for the re-arranged flyback converter. The designed circuit was implemented in a 10 W prototype. Experimental results showed that the converter has a THDi = 21.7% and a PF = 0.9686.

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

scholarly journals Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 730
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Initial Time ◽  
Lipschitz Stability ◽  
Comparison Results ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Definition Of

In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

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