We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying [K1,W ] = 1 always leads to Kontsevich type models, in the case of [K1,W ] = W the corresponding KP τ -functions are represented as more sophisticated matrix integrals.

A. Bigdelou, L. Schwarz, N. Navab. “An Adaptive Solution for Intra-operative Gesture-based Human-Machine Interaction.“ International ACM Conference on Intelligent User Interfaces (IUI), Lissabon, Portugal, February 2012 L. Schwarz, A. Bigdelou, N. Navab “Learning Gestures for Customizable Human-Computer Interaction in the Operating Room.“ Medical Image Computing and Computer Assisted Intervent...

The direct and inverse spectral problems are solved for a wide subclass of the class of Schwarz matrices. A connection between Schwarz matrices and the so-called generalized Hurwitz polynomials is found. The known results due to H. Wall and O. Holtz are briefly reviewed and obtained as particular cases.

In this work we design new interface transmission conditions for a domain decomposition Schwarz algorithm for the Euler equations in 2 dimensions. These new interface conditions are designed to improve the convergence properties of the Schwarz algorithm. These conditions depend on a few parameters and they generalize the classical ones. Numerical results illustrate the effectiveness of the new ...

Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g, we have the Cauchy-Schwarz inequality: 0.1 THEOREM (Cauchy-Schwarz inequality). Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g such that

A classical action for open superstring field theory has been proposed which does not suffer from contact term problems. After generalizing this action to include the non-GSO projected states of the Neveu-Schwarz string, the pure tachyon contribution to the tachyon potential is explicitly computed. The potential has a minimum of V = −

Lower bounds for the condition numbers of the preconditioned systems are obtained for two-level additive Schwarz preconditioners for both second order and fourth order problems. They show that the known upper bounds are sharp in the case of a small overlap.

Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M -matrix. The case of inexact local solvers is also covered. These bounds are analogous to those that exist using A-norms when the matrix A is symmetric positive definite. A new theorem concerningP -regular splittings is present...

We prove a \general shrinking lemma" that resembles the Schwarz{Pick{ Ahlfors Lemma and its generalizations, but diiers in applying to maps of a nite disk into a disk, rather than requiring the domain of the map to be complete. The conclusion is that distances to the origin are all shrunk, and by a limiting procedure we can recover the original Ahlfors Lemma, that all distances are shrunk. The ...

We develop a new class of overlapping Schwarz type algorithms for solving scalar convectiondi usion equations discretized by nite element or nite di erence methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The order...