C cosh(zs) (sin z − sin x)n+1 dz, y = sinn+1 x ∮ C cosh(zs) (cos z − cos x)n+1 dz, s2 = −λ, and their associated second-order ordinary differential equationswhich are not studied are given. Complete solution is given by calculating residues for n = 1. The eigenvalues and eigenfunctions along with certain boundary conditions are explored for the first contour integral. The contour integral y(x) ...

A new method (the sinh–sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and...

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finitevolume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, sim...

Abstract: Sinh-domain CMOS filters have favorable properties, such as a wide dynamic range at low supply voltage, compactness, linearity, and low power consumption. These properties are becoming increasingly important for biomedical applications that require extremely low-power dissipation and neuromorphic circuits that attempt to reproduce the biophysics of biological neurons and synapses. In ...

This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a combination of the double-exponential...

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator Φ 13 at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the " staircase " phenomenon discovered by Al. Zamolodchikov, we...

Using the recently obtained exact results for the expectation values of operators in the sineand sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B493, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B406, 83 (1997)] we calculate the specific heat of the corresponding classical models. We show that the temperature dependence of t...

Let F be a distribution inD′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ s sinh−1x r does no...

The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the twoparameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. ...

in this work, we successfully construct the new exact traveling wave solutions ofthe generalized sinh–gordon equation by new application of the homogeneousbalance method. the idea introduced in this paper can be applied to othernonlinear evolution equations.