Consider a root system of type BC1 on the real line R with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an L-space on R to a L-space of C-valued functions on R with the Harish-Chandra measure |c(λ)|dλ. By introducing a weight function of the form cosh(t) tanh t on R we find an orthogonal basis for the L-space on R consisting of even and odd func...

In this paper, we study the general question of how characteristics of functional equations innuence whether or not they are robust. We isolate examples of properties which are necessary for the functional equations to be robust. On the other hand, we show other properties which are suucient for robustness. We then study a general class of functional equations, which are of the form 8x;y Ff(x ?...

Let H be the Hill operator and let G n = (A ? n ; A + n) and M n ; n 1; be the corresponding gaps and the eeective masses for the Hill operator. Denote by F(E) the Lyapunov function for the Hill operator. Let n 2 A ? n ; A + n ] be such that F 0 (n) = 0 and h n 0 be the solution of the equation cosh h n = (?1) n F(n): We prove some identities for the eeective masses M n : Then we nd "second ord...

We consider the Willmore boundary value problem for surfaces of revolution over the interval [−1, 1] where, as Dirichlet boundary conditions, any symmetric set of position α and angle tanβ may be prescribed. Energy minimising solutions uα,β have been previously constructed and for fixed β ∈ R, the limit limαց0 uα,β(x) = √ 1 − x has been proved locally uniformly in (−1, 1), irrespective of the b...

In this paper, we propose a novel independent components (ICs) arrangement strategy to cooperate with the independent component analysis (ICA) method used for ECG beat classification. The ICs calculated with a regular ICA algorithm are re-arranged according to the L2 norms of the rows of the de-mixing matrix. The validity of this ICs arrangement strategy is discussed mathematically and testifie...

Single crystal epitaxial films of CoSi2 were grown by MBE on various (111)Si single crystal substrates, whose surfaces were purposely tilted towards the < 1IO >, direction by small angles 4>, t, 0° :54>, :5 4°, measured between the surface normal and the < 111 >. direction of Si. The actual offset angle, 4>,, was determined by back Laue reflection method. The average perpendicular strain of the...

We study the enhancement of tunneling through a potential barrier $V(x)$ by time-dependent electric field with special emphasis on pulse-shaped vector potentials such as $A_x(t)=A_0/\cosh^2(\omega t)$. In addition to known effects pre-acceleration and deformation already present in adiabatic regime, well energy mixing analogy Franz-Keldysh effect non-adiabatic (impulse) pulse $A_x(t)$ can enhan...

0. Introduction In [1], gravitational anomaly cancellation formulas are derived from direct computations. In particular, in dimension 12, the Alvarez-Gaumé and Witten ‘‘miraculous cancellation’’ formula can be written as {L(TX, ∇TX )}(12) = {8A(TX, ∇TX )ch(TCX, ∇TCX )}(12) − 32{A(TX, ∇TX )}(12), (0.1) where X is a twelve-dimensional Riemannian manifold, ∇TX is the associated Levi-Civita conn...

Traditional speech enhancement algorithms consider speech detection and estimation process independently. The simultaneous detection and estimation approach (SDA) combines both detection and estimation processes to reduce the effects due to missed detection. SDA is based on an estimator which minimizes bayesian risk with the aid of minimum mean square error (MMSE) estimator. The MMSE estimator ...