Transformation Theorem Research Articles

Source Transformation Theorem Revisited

It is known that a parallel combination of a current source and a resistance can be replaced by a series combination of a voltage source and a resistance and vice versa according to the source transformation theorem. Thus, the source transformation gives only one current to voltage or voltage to current equivalent circuit In this short paper, we show that there is a large number of current to voltage, voltage to current, current to current and voltage to voltage source transformations possible under certain given terminal condition. This result is not given in the text books.

Source Transformation Theorem Revisited

It is known that a parallel combination of a current source and a resistance can be replaced by a series combination of a voltage source and a resistance and vice versa according to the source transformation theorem. Thus, the source transformation gives only one current to voltage or voltage to current equivalent circuit. In this short paper, we show that there is a large number of current to voltage, voltage to current, current to current and voltage to voltage source transformations possible under certain given terminal condition. This result is not given in the text books.

Transformation and reduction formulae for double q‐Clausen hypergeometric series

AbstractBy means of the Sears transformations, we establish eight general transformation theorems on bivariate basic hypergeometric series. Several transformation, reduction and summation formulae on the double q‐Clausen hypergeometric series are derived as consequences. Copyright © 2007 John Wiley & Sons, Ltd.

CONVOLUTION THEOREM OF THE COMPLEX FRACTIONAL FOURIER TRANSFORMATION DERIVED BY TRANSFORMATION OF ENTANGLED STATES

Based on our previous paper [H.-Y. Fan and H.-L. Lu, Int. J. Mod. Phys.19, 799 (2005)] and the two mutually-conjugate entangled state representations, we derive the convolution theorem of complex fractional Fourier transformation in the context of quantum mechanics. This approach seems convenient and neat.

Vortices, circumfluence, symmetry groups, and Darboux transformations of the(2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, and oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1) -dimensional EE is obtained via a simple direct method which is thus utilized to find exact analytical vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1) -dimensional EE can be obtained for an arbitrary spectral parameter from the general symmetry group theorem. Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.

Mixing Limit Theorems for Ergodic Transformations

We show that distributional and weak functional limit theorems for ergodic processes often hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the setup of ergodic sums, renewal-theoretic variables, and hitting times for ergodic measure preserving transformations.

Solution generating theorems for perfect fluid spheres

The first static spherically symmetric perfect fluid solution with constant density was found by Schwarzschild in 1918. Generically, perfect fluid spheres are interesting because they are first approximations to any attempt at building a realistic model for a general relativistic star. Over the past 90 years a confusing tangle of specific perfect fluid spheres has been discovered, with most of these examples seemingly independent from each other. To bring some order to this collection, we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres. In addition, we develop new ‘‘solution generating’’ theorems for the TOV, whereby any given solution can be ‘‘deformed’’ to a new solution. Because these TOV-based theorems work directly in terms of the pressure profile and density profile it is relatively easy to impose regularity conditions at the centre of the fluid sphere.

Symmetry group and non-propagating solitons in the (2 + 1)-dimensional sine-Gordon equation

Starting from the compact version of the (2 + 1)-dimensional sine-Gordon equation, the symmetry group and then the Lie symmetries and the related algebra can be obtained via a simple combination of a gauge transformation of the spectral function and the transformations of the space time variables. Thereout, applying the group transformation theorem on a two-straight-line soliton solution, one can derive two types of meaningful non-propagating dromion lattice excitations.

High efficient ECG compression based on reversible round-off non-recursive 1-D discrete periodized wavelet transform

Error propagation and word-length-growth are two intrinsic effects influencing the performance of wavelet-based ECG data compression methods. To overcome these influences, a non-recursive 1-D discrete periodized wavelet transform (1-D NRDPWT) and a reversible round-off linear transformation (RROLT) theorem are developed. The 1-D NRDPWT can resist truncation error propagation in decomposition processes. By suppressing the word- length-growth effect, RROLT theorem enables the 1-D NRDPWT process to obtain reversible octave coefficients with minimum dynamic range (MDR). A non-linear quantization algorithm with high compression ratio (CR) is also developed. This algorithm supplies high and low octave coefficients with small and large decimal quantization scales, respectively. Evaluation is based on the percentage root-mean-square difference (PRD) performance measure, the maximum amplitude error (MAE), and visual inspection of the reconstructed signals. By using the MIT-BIH arrhythmia database, the experimental results show that this new approach can obtain a superior compression performance, particularly in high CR situations.

Bäcklund Transformations, Solitary Waves, Conoid Waves and Bessel Waves of the (2+1)-Dimensional Euler equation

Some simple special Backlund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation.

Special Bäcklund transformations and nonlinear superpositions for the non-integrable ϕ4 field model

Some special Bäcklund transformation (BT) theorems and a particular nonlinear superposition theorem are established to find exact solutions for a non-integrable model, the (N+1)-dimensional ϕ4 scalar field. Some new types of exact solutions such as the conoid periodic–periodic interaction waves and the periodic–solitary wave interaction solutions are explicitly given. The interaction solutions possess abundant structures, thanks to the intrusion of some arbitrary functions in the expressions of the special solutions.

Tauberian-type theorems with application to the Stieltjes transformation

In the first part, we define the spaceL'(r)and the modified Stieltjes transformation introduced by Lavoine and Misra (1979) and Marichev (1983), respectively. In the second part of the paper, we extend Tauberian-type theorems for the distributional Stieltjes transformations to the distributional modified Stieltjes transformations.

A T1 theorem for integral transformations with operator-valued kernel

We consider generalized Calderón-Zygmund operators whose kernel K(x, y) takes values in ℒ(X) (continuous linear operators on the Banach space X) and satisfies variants of the classical standard estimates involving R-boundedness, which has recently become a crucial notion in connection with operator-valued singular integrals. Boundedness criteria in the spirit of the T1 theorem of David and Journé are proved for such operators on the Bôchner spaces Lp(ℝn, X), where 1 < p < ∞ and X is a UMD-space. For some results, X is also required to have Pisier's property (α).

K-quasi-additive fuzzy integrals of set-valued mappings*

Abstract We first define the quasi-addition and quasi-multiplication operations by introducing the inductive operator, and then, in the K-quasi additive fuzzy measure space, we establish the K-quasi-additive fuzzy integral of a generally measurable set-valued mapping. Applying the integral transformation theorem, some basic properties of the K-quasi-additive fuzzy integrals with respect to this kind of set-valued mapping are studied. Finally, the generalized monotone convergence theorems of this kind of fuzzy integrals are obtained. Supported by National Natural Science Foundation of China (Grant No. 70571056)

Generating perfect fluid spheres in general relativity

Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.

Abstract abstract reduction

We propose novel algebraic proof techniques for rewrite systems. Church–Rosser theorems and further fundamental statements that do not mention termination are proved in Kleene algebra. Certain reduction and transformation theorems for termination that depend on abstract commutation, cooperation or simulation properties are proved in an extension with infinite iteration. Benefits of the algebraic approach are simple concise calculational proofs by equational reasoning, connection with automata-based decision procedures and a natural formal semantics for rewriting diagrams. It is therefore especially suited for mechanization and automation.

Transformations of Border Strips and Schur Function Determinants

We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions for a given skew shape. Outside decompositions are introduced by Hamel and Goulden and are used to give an identity for the skew Schur function that unifies the determinantal expressions for the skew Schur functions including the Jacobi-Trudi determinant, its dual, the Giambelli determinant and the rim ribbon determinant due to Lascoux and Pragacz. Using cutting strips, one obtains a formula for the number of outside decompositions of a given skew shape. Moreover, one can define the basic transformations which we call the twist transformation among cutting strips, and derive a transformation theorem for the determinantal formula of Hamel and Goulden. The special case of the transformation theorem for the Giambelli identity and the rim ribbon identity was obtained by Lascoux and Pragacz. Our transformation theorem also applies to the supersymmetric skew Schur function.

Modeling of extremal fuzzy dynamic systems. Part I. Extended extremal fuzzy measures

The basic properties of extended extremal fuzzy measure are considered and several variants of their representation are given. In considering extremal fuzzy measures, several transformation theorems are proved for extended lower and upper Sugeno integrals. Extended extremal conditional fuzzy measures are defined. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed.

A generalized coincidence point index

The paper is devoted to build for some pairs of continuous single-valued maps a coincidence point index. The class of pairs (f, g) satisfies the condition that f induces an epimorphism of the Cech homology groups with compact supports and coefficients in the field of rational numbers Q. Using this concept one defines for a class of multi-valued mappings a fixed point degree. The main theorem states that if the general coincidence point index is different from {0}, then the pair (f, g) admits at least a coincidence point. The results may be considered as a generalization of the above Eilenberg-Montgomery theorems [12], they include also, known fixed-point and coincidence-point theorems for single-valued maps and multi-valued transformations.

Scattering by an Infinite Circular Dielectric Cylinder Coating Eccentrically an Elliptic Dielectric Cylinder

Scattering of a plane electromagnetic wave by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric one, is under consideration. Both E and H polarizations are treated for normal incidence. The electromagnetic field is expressed in terms of both circular and elliptical-cylindrical wave functions. Using proper transformation theorems between the field expressions in different coordinate systems, for the satisfaction of the boundary conditions, we obtain two infinite sets of linear nonhomogeneous equations for the expansion coefficients of the field. In case of small values of h=k/sub 2/c/2, where c is the interfocal distance of the elliptic cylinder and k/sub 2/ the wavenumber of the dielectric coating, the former sets of equations provide, by truncation, semianalytical expressions of the form S(h)=S(0)[1+gh/sup 2/+O(h/sup 4/)] for the scattered field and the various scattering cross sections. The coefficients g are independent of h. Graphical results for the scattering cross sections are given for various values of the parameters.