We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of ∗-semigroups from the point of view of generation of ∗-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifie...

An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real symmetric matrices with a bounded number of different eigenvalues is investigated. These results are applied to the study of sum of squares presentations of...

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . . This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution. Mathemati...

In-beam spectroscopy of drip line nuclei at intermediate energies is discussed from the aspects of the inverse kinematics and the selectivities of secondary reactions. As an example of the invariant mass spectroscopy, a study of the isobaric analog state of the dripline nucleus 14Be excited by the (p,n) reaction is presented. For the next phase of γ-ray spectroscopy, a new array consisting of s...

This paper provides a new analytical robust stability checking method of fractionalorder linear time invariant interval uncertain system. This paper continues the authors’ previous work [4] where matrix perturbation theory was used. For the new robust stability checking, Lyapunov inequality is utilized for finding the maximum eigenvalue of a Hermitian matrix. Through numerical examples, the use...

Forcing theorems based on topological features of invariant sets have played a fundamental role in dynamics and differential equations. This talk focuses on the recent work of Vandervorst, Van den Berg, and the author using braids to construct a forcing theory for scalar parabolic PDEs, second-order Lagrangian ODEs, and one-dimensional lattice dynamics. Mathematics Subject Classification (2000)...

We consider numerical computation of Taylor expansions of invariant manifolds around equilibria of maps and flows. These are obtained by writing the corresponding functional equation in a number of points, setting up a nonlinear system of equations and solving that using a simplified Newton’s method. This approach will avoid symbolic or explicit numerical differentiation. The linear algebra iss...

A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...

Two recent measurements of beauty production in deep inelastic ep scattering with the ZEUS detector are presented. In the first analysis, beauty production was identified using muons associated to a jet. In the second measurement, beauty content was extracted using the decay length significance and invariant mass of secondary vertices. Measured differential cross sections were compared to theor...

In this article, we prove coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in complete quasi-metric spaces without the mixed g-monotone property, using the concept of invariant condition, together with transitivity with a Qfunction q. We also provide illustrative examples in support of our new results. 2206 Sachin V. Bedre, S. M. Khairnar and B. S. ...