Scalar top study: Detector optimization

A vertex detector concept of the linear collider flavour identification (LCFI) collaboration, which studies pixel detectors for heavy quark flavour identification, has been implemented in simulations for c-quark tagging in scalar top studies. The production and decay of scalar top quarks (stops) is particularly interesting for the development of the vertex detector as only two c-quarks and missing energy (from undetected neutralinos) are produced for light stops. Previous studies investigated the vertex detector design in scenarios with large mass differences between stop and neutralino, corresponding to large visible energy in the detector. In this study we investigate the tagging performance dependence on the vertex detector design in a scenario with small visible energy for the international linear collider (ILC).      

Novel Applications of Millimeter and Submillimeter Wave Gyro-Devices

The possible applications of high-power millimeter (mm) and submillimeter waves from gyro-devices span a wide range of technologies. The plasma physics community has already taken advantage of recent advances in applying high-power micro- and mm-waves generated by gyrotron oscillators in the areas of RF-plasma production, heating, noninductive current drive, plasma stabilization and active plasma diagnostics for magnetic confinement thermonuclear fusion research, such as lower hybrid current drive (8 GHz), electron cyclotron resonance heating (ECRH) (28–170 GHz), electron cyclotron current drive (ECCD), collective Thomson scattering and heat-wave propagation experiments. Other important applications of gyrotrons are electron cyclotron resonance (ECR) discharges for generation of multi-charged ions and soft X-rays, as well as industrial materials processing and plasma chemistry. Submillimeter wave gyrotrons are employed in high-frequency broadband electron paramagnetic resonance (EPR) spectroscopy. Future applications which await the development of novel high-power gyro-amplifiers include high resolution radar ranging and imaging in atmospheric and planetary science as well as deep-space and specialized satellite communications and RF drivers for next-generation high-gradient linear accelerators (supercolliders). The present paper reviews the state-of-the-art and future prospects of these recent applications of gyro-devices.     

Identities between q-hypergeometric and hypergeometric integrals of different dimensions

Given complex numbers m₁,l₁ and nonnegative integers m₂,l₂, such that m₁+m₂=l₁+l₂, for any a,b=0,…,min(m₂,l₂) we define an l₂-dimensional Barnes type q-hypergeometric integral I_a,b(z,μ;m₁,m₂,l₁,l₂) and an l₂-dimensional hypergeometric integral J_a,b(z,μ;m₁,m₂,l₁,l₂). The integrals depend on complex parameters z and μ. We show that I_a,b(z,μ;m₁,m₂,l₁,l₂) equals J_a,b(e^μ,z;l₁,l₂,m₁,m₂) up to an explicit factor, thus establishing an equality of l₂-dimensional q-hypergeometric and m₂-dimensional hypergeometric integrals. The identity is based on the duality for the qKZ and dynamical difference equations.     

Note on the m-step competition numbers of paths and cycles

Since Cohen introduced the competition graph in 1968, the competition graph has been studied widely and many variations of it have been discussed. In 2000, Cho, Kim and Nam defined and studied the m-step competition graph and computed the 2-step competition numbers of paths and cycles. Recently, Ho gave bounds for the m-step competition numbers of paths and cycles. In this paper we continue to study the m-step competition numbers of paths and cycles, partially improve the results of Ho on the upper bounds of the m-step competition numbers of paths and cycles, and show that a conjecture posed by Ho is not true.     

Sample-based polynomial approximation of rational Bézier curves

We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The L_p-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the L_p-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L₁-error criterion are better than those obtained using the L₂-error and L_∞-error criteria.     

Strongly indexable graphs and applications

In 1990, Acharya and Hegde introduced the concept of strongly k-indexable graphs: A (p,q)-graph G=(V,E) is said to be strongly k-indexable if its vertices can be assigned distinct numbers 0,1,2,…,p−1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices form an arithmetic progression k,k+1,k+2,…,k+(q−1). When k=1, a strongly k-indexable graph is simply called a strongly indexable graph. In this paper, we report some results on strongly k-indexable graphs and give an application of strongly k-indexable graphs to plane geometry, viz; construction of polygons of same internal angles and sides of distinct lengths.     

Duplicate form of Carlitz inversions and summation formulae

By applying the duplicate form of Carlitz inversions to three special cases of the q-Saalschütz theorem respectively, we establish three classes of interesting summation formulae.