Search results for "Hyperbolic function"

Space‐vector state dynamic model of SynRM considering self‐ and cross‐saturation and related parameter identification

2020

This study proposes a state formulation of the space-vector dynamic model of the Synchronous Reluctance Motor (SynRM) considering both saturation and cross-saturation effects. The proposed model adopts the stator currents as state variables and has been theoretically developed in both the rotor and stator reference frames. The proposed magnetic model is based on a flux versus current approach and relies on the knowledge of 11 parameters. Starting from the definition of a suitable co-energy variation function, new flux versus current functions have been initially developed, based on the hyperbolic functions and, consequently, the static and dynamic inductance versus current functions have be…

Turán type inequalities for generalized inverse trigonometric functions

2013

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.

Painlevé analysis and exact solutions for the coupled Burgers system

2006

We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.

A Polynomial Approach to the Piecewise Hyperbolic Method

2003

In this paper, a local (third-order accurate) shock capturing method for hyperbolic conservation laws is presented. The method has been made with the same idea as the PHM method, but with a simpler reconstruction. A comparison with the classic high order methods is discussed.

A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator

1998

Abstract Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.

Boundary Behavior of Harmonic Functions on Gromov Hyperbolic Manifolds

2013

Substitution–dilution method to correct the matrix effect in multi-element quantitative analysis by X-ray fluorescence

2001

Abstract A mathematical model based on the dilution–addition method (DAM) for multi-elemental analysis using an X-ray fluorescence technique is proposed. The conditions for sample preparation do not require both the unknown and standard samples to be similar in composition and mineralogy, and the unknown sample is replaced quantitatively by the standard sample, hence the denomination substitution–dilution method (SDM). This method makes it possible to correct the matrix effect in multi-elemental quantitative analysis by X-ray fluorescence for each analyte. The proposed model presents hyperbolic behaviour of the experimental data when the X-ray fluorescence intensities are represented versus…

Description of the retention behaviour of solutes in micellar liquid chromatography with organic modifiers: Comparison of two methods

1995

Two methods for the description of the retention behaviour of solutes in micellar liquid chromatography are compared. One of them divides the parameter space into triangular subspaces, fitting a different equation in each subspace. The second method makes use of a unique equation, valid in the whole parameter space. In both cases, equations of the type log k=f (μ, ϕ), and 1/k=f (μ, ϕ), (μ and ϕ are the concentration of surfactant and alcohol, respectively), were used to describe the retention. The use of the hyperbolic function, 1/k=c0+c1μ+c3μϕ, to describe the whole parameter space yielded the best prediction. When a small portion of the parameter space was modelled, a simpler hyperbolic f…

Annihilation Operators for Exponential Spaces in Subdivision

2022

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.

Functional inequalities for generalized inverse trigonometric and hyperbolic functions

2014

Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.