Let Z be a positive hermitian Jordan triple system and B be any connected component of its regular set. A general framework for studying Hardy spaces and associated Toeplitz operators over B is developed. As application , the full spectrum of all Hardy-Toeplitz C-algebras is constructed for the example Z = Sym(2; C), leading to a complete C-structure theory, described in terms of the facial bou...

We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind, which turns out to be the hypergeometric function. To match the experimental findings of the statistical behavior, we regard the substructure as a grand canonical ensemble and find its fugacity value. We also suggest a hierarchical picture based on t...

In arXiv:0709.0483 Günther and Samsonov outline a “generalization” of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be “capable to produce effects beyond those of standard Hermitian quantum mechanics.” We give a simple physical interpretation of Hermiticity and discuss in detail the shortcomings of the above-mentioned composi...

In this paper we generalize the shift radix systems to finite dimensional Hermitian vector spaces. Here the integer lattice is replaced by the direct sum of imaginary quadratic Euclidean domains. We prove in two cases that the set of one dimensional Euclidean shift radix systems with finiteness property is contained in a circle of radius 0.99 around the origin. Thus their structure is much simp...

Let M be a compact complex manifold of complex dimension two with a smooth Kahler metric and D a smooth divisor on M. If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E' = E|M\D compatible with the parabolic structure, and whose curvature is square integrable. MIRAMARE TRIESTE January 2000

We call a positive definite even Hermitian lattice even universal if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields Q( √ −m) for all m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermitian lattices. And we apply our r...

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q( √ −m) for all m. For each imaginary quadratic field Q( √ −m), we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that t...

Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A1.