After spatial discretization to the fractional diffusion equation by the shifted Grünwald formula, it leads to a system of ordinary differential equations, where the resulting coefficient matrix possesses the Toeplitz-like structure. An exponential quadrature rule is employed to solve such a system of ordinary differential equations. The convergence by the proposed method is theoretically studi...

We give a short new proof of large N duality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold. Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the DonaldsonThomas, and the Chern-Simons invariants as different characterizations of the same holomorphic function. For the resolve...

A new real-time interferometer based on diffraction phenomena is discussed. It consists of a point-diffraction interferometer fabricated on a transmission grating. The real-time data-analysis capability is achieved by simultaneously introducing a phase shift (piston) on the three separate channels of diffracted interferograms. Mathematical analysis and preliminary observational results are incl...

We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman’s mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion o...

Delayed mixing is a problem of theoretical interest and practical importance, e.g., in speech processing, bio-medical signal analysis and nancial data modelling. Most previous analyses have been based on models with integer shifts, i.e., shifts by a number of samples, and have often been carried out using time-domain representation. Here, we explore the fact that a shift in the time domain corr...

It is well known that the Riemann Zeta function ζ ( p ) = ∑∞n=1 1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑∞ n=1 1/ ( 4n2−α2)p . In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form repre...

We prove an explicit formula for infinitely many convergents of Hurwitzian continued fractions that repeat several copies of the same constant and elements of one arithmetic progression, in a quasi-periodic fashion. The proof involves combinatorics and formal Laurent series. Using very little analysis we can express their limits in terms of (modified) Bessel functions and Fibonacci polynomials....

We propose a simple strategy to generate multiple interleavers. As suggested in literature, using user-distinct interleavers is an effective means to separate multiple users, if applied in addition to user-specific spreading codes in code division multiple access (CDMA). In this paper we particularly focus on interleave division multiple access (IDMA), which has a close relation to CDMA, but us...

Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and diverse problems ranging from congestive to partitioning problems. In particular, every standard combinatorial optimization problem has its shifted counterpart, ...