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About 2,979 papers for “Transcendental function”

Rational and transcendental Lyapunov function generation

N.K. Bose · IEEE Transactions on Automatic Control · 1970

In this correspondence, feasibility of generation of rational Lyapunov functions (LF) from any given Lyapunov function, and any RL, RC, or LC immittance function is shown. Extensions of these general results are made. Some methods of generating transcendental Lyapunov functions are also mentioned.

Cited by 0

A design of transcendental function accelerator

Minte Song, Nan Liu, Zhanqiang Ru et al. · 2023

The calculation of transcendental functions is a common step in industrial control algorithms. Taking up a large number of CPU cycles, the transcendental function calculation by software compresses the computing resources of real-time control algorithms. As the complexity of industrial control system increases, hardware accelerators have become one of the strategies to solve this contradiction. In this paper, we designed a multi-thread, high-performance, configurable hardware accelerator for transcendental functions, which is based on the iterative calculation. It supports the calculations of sine cosine, arc-tangent, modulus, exponent and logarithm. The accelerator uses the standard cell library of SMIC 40nm Eflash platform for synthesis, achieving a frequency of 200MHz and a synthesis area of 176,840um<sup>2</sup>.

Cited by 0

A transcendental function invariant of virtual knots

Zhiyun Cheng · Journal of the Mathematical Society of Japan · 2017

In this work we introduce a new invariant of virtual knots. We show that this transcendental function invariant generalizes several polynomial invariants of virtual knots, such as the writhe polynomial [3], the affine index polynomial [19] and the zero polynomial [14]. Several applications of this new invariant are discussed.

Cited by 16

Transcendental function analogue computation with magnetic cores

D. H. Schaefer, R. L. Van Allen · Transactions of the American Institute of Electrical Engineers Part I Communication and Electronics · 1956

SQUARE loop magnetic cores used in conjunction with switching transistors can be made to perform a great number of arithmetical operations. Previous papers have shown how these elements can be used to obtain 4-quadrant multiplication1 and division2. This paper presents a basic circuit and shows how this circuitry can be utilized to obtain various sorts of computations. Specifically, experimental data are presented showing results obtained with the use of the circuit to obtain an output voltage proportional to the square root and other fractional powers of an input voltage, the arc sine of an input voltage, the sine of an input voltage and the product of two voltages. These are only a few of the possible outputs which are theoretically attainable.

Cited by 2

Structurally Similar Sets of Transcendental Entire Function

Bishnu Hari Subedi · Journal of Advanced College of Engineering and Management · 2018

In complex dynamics, the complex plane is partitioned into invariant subsets. In classical sense, these subsets are of course Fatou set and Julia set.&#x0D; Rest of the abstract available with the full text

Cited by 0Open access

On residually transcendental valued function fields of conics

Sudesh K. Khanduja · Glasgow Mathematical Journal · 1996

Let K/Ko be a finitely generated field extension of transcendence degree 1. Let u 0 be a valuation of K o and v a valuation of K extending v 0 such that the residue field of v is a transcendental extension ofthe residue field k 0 of v o / such a prolongation v will be called a residually transcendental prolongation of v 0 . Byan element with the uniqueness property for (K, v)/(K 0 , v 0 ) (or more briefly for v/v 0 ) we mean an element / of K having u-valuation 0 which satisfies (i) the image of t under the canonicalhomomorphism from the valuation ring of v onto the residue field of v (henceforth referred to as the v -residue ot t ) is transcendental over k o ; that is v coincides with the Gaussian valuation on the subfield K 0 (t) defined by (ii) v is the only valuation of K (up to equivalence) extending the valuation .

Cited by 1Open access

The Wt transcendental function and quantum-mechanical applications

V. E. Markushin, L. Feld, Andreas Schreiber · 2002

We discuss the function wt(x) defined via the implicit equation wt(x)*tan[wt(x)]=x which appears in certain quantum mechanical and field theoretic applications. We investigate its analytic structure, develop series expansions for both small and large x, and provide various techniques for its numerical evaluation in the complex plane.

Cited by 2

The W_t Transcendental Function and Quantum Mechanical Applications

V. E. Markushin, L. Feld, Andreas Schreiber · DORA PSI (Paul Scherrer Institute) · 2001

We discuss the function wt(x) defined via the implicit equation wt(x)*tan[wt(x)]=x which appears in certain quantum mechanical and field theoretic applications. We investigate its analytic structure, develop series expansions for both small and large x, and provide various techniques for its numerical evaluation in the complex plane.

Cited by 5Open access

Some transcendental functions over function fields with positive characteristic

Jia-Yan Yao · Comptes Rendus Mathématique · 2002

In this work we shall define two families of functions over function fields with positive characteristic and show that such a function is transcendental if and only if its generating sequence is not ultimately zero. As a result, the Carlitz exponential and the Carlitz logarithm are transcendental functions. Our proof is elementary in the sense that we only use a theorem due to H. Sharif and C. Woodcock, and to T. Harase which generalizes the theorem of Christol about automatic sequences.

Cited by 7