Boneh and Venkatesan have proposed a polynomial time algorithm in a non-uniform model for recovering a ”hidden” element α ∈ IFp, where p is prime, from very short strings of the most significant bits of the residue of αt modulo p for several randomly chosen t ∈ IFp. Here we modify the scheme and amplify the uniformity of distribution of the ‘multipliers’ t and thus extend this result to subgrou...

For any integer m > 1 fix ζm = exp(2πi/m), and let Z ∗ m denote the group of reduced residues modulo m. Let q = pα, a power of a prime p. The hyper-Kloosterman sums of dimension n > 0 are defined for q by R(d, q) = ∑ x1,...,xn∈Z∗ q ζ x1+···+xn+d(x1···xn) q (d ∈ Zq), where x−1 denotes the multiplicative inverse of x modulo q. Salie evaluated R(d, q) in the classical setting n = 1 for even q, and...

Article history: Received 17 December 2014 Received in revised form 1 December 2015 Accepted 3 December 2015 Available online 19 December 2015 The data for the lightflux degradation and chromaticity shift of LED lamps exhibits a considerable amount of scatter due to intrinsic and extrinsic factors. In this study, some degradation models, such as the gamma process model, were reviewed in terms o...

This note is devoted to stabilizing a coupled PDE–ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE–ODE cascadewith an invertible integral transformation,where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, a...

In this paper, we are concerned with the boundary stabilization of two connected strings with middle joint anti-damping for which all eigenvalues of the (control) free system are located on the right complex plane. We first design an explicit state feedback controller to achieve exponential stability for the closedloop system. Consequently, we design the output feedback by using infinite-dimens...

The Camera Augmented Mobile C-arm (CamC) system that augments a regular mobile C-arm by a video camera provides an overlay image of X-ray and video. This technology is expected to reduce radiation exposure during surgery without introducing major changes to the standard surgical workflow. Whereas many experiments were conducted to evaluate the technical characteristics of the CamC system, its c...

The H , control problem for uncertain descriptor systems with time-invariant normbound uncertainty in the state matrix is considered. Necessary and sufficient conditions for robust H, control of descriptor systems by state feedback and dynamic output feedback are derived. The design results are expressed in terms of generalised algebraic Riccati inequalities, which may be considered an extensio...

We consider k-uniform set systems over a universe of size n such that the size of each pairwise intersection of sets lies in one of s residue classes mod q, but k does not lie in any of these s classes. A celebrated theorem of Frankl and Wilson [8] states that any such set system has size at most n s when q is prime. In a remarkable recent paper, Grolmusz [9] constructed set systems of superpol...

This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this important open problem. The paper shows that although many approaches and techniques exist to approach different versions of the problem, no effi...

Expressions are derived for the fluorescence response functions of organic solution systems in which non-radiative energy transfer occurs and obeys either Stern-Volmer or Forster kinetics. Scintillation pulse shapes are evaluated for typical crystals, binary and temary liquid solutions, and binary plastic solutions. The scintillation decay time is inadequate to describe the time characteristics...