We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).

Test techniques for analog circuits characterize the input-output relationship based on coefficients of transfer function, polynomial expansion, wavelet transform, V-transform or Volterra series. However, these coefficients always suffer from errors due to measurement accuracy and noise. This paper presents closed form expressions for an upper bound on the defect level and a lower bound on faul...

Come with us to read a new book that is coming recently. Yeah, this is a new coming book that many people really want to read will you be one of them? Of course, you should be. It will not make you feel so hard to enjoy your life. Even some people think that reading is a hard to do, you must be sure that you can do it. Hard will be felt when you have no ideas about what kind of book to read. Or...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

This paper describes a novel decision procedure for quantifierfree linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g. Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaus...

In poor visibility, paired approaches to airports with closely spaced parallel runways are not permitted, thus halving the arrival rate. With Global Positioning System technology, datalinks and cockpit displays, this could be averted. One important problem is ensuring safety during a blundered approach by one aircraft. This is on-going research. A danger zone around the blunderer is required. I...

This dissertation explores the theory and applications of Exact Geometric Computation (EGC), a general approach to robust geometric computing. The contributions of this thesis are organized into three parts. A fundamental task in EGC is to support exact comparison of algebraic expressions. This leads to the problem of constructive root bounds for algebraic expressions. Such root bounds determin...

Bounds on test sequence length can be used as a testability measure. We give a procedure to compute the upper bound on test sequence length for an arbitrary sequential circuit. We prove that the bound is exact for a certain class of circuits. Three design rules are specified to yield circuits with lower test sequence bounds.

We present reduced basis approximations and associated a posteriori error bounds for nonaffine linear time-varying parabolic partial differential equations. We employ the Empirical Interpolation Method in order to construct “affine” coefficient-function approximations of the “nonaffine” parametrized functions. To this end, we extend previous work on time-invariant functions to time-varying func...