For positive integers m and r, one can easily show there exist integers N such that for every map ∆ : {1, 2, · · · , N} → {1, 2, · · · , r} there exist 2m integers x1 < · · · < xm < y1 < · · · < ym which satisfy: 1. ∆(x1) = · · · = ∆(xm), 2. ∆(y1) = · · · = ∆(ym), 3. 2(xm − x1) ≤ ym − x1. In this paper we investigate the minimal such integer, which we call g(m,r). We prove that g(m, 2) = 5(m − ...

The purpose of this report is to provide a perspective on future accelerator projects, and to identify the R&D activities necessary to prepare for these projects. The report summarizes the conclusions of accelerator studies made during the 2001 Snowmass Summer Study on the Future of Particle Physics. In doing so, it serves as a summary of the opinions on accelerator R&D expressed by the scienti...

We prove that product and sum types are de nable in polymorphic PCF with call-by-name evaluation strategy. This establishes polymorphic PCF and its extensions can be conservatively extended by product and sum types and recursive types.

We investigate a fast optimization method for determining the minimizer of the negative Poisson likelihood function for the global analysis of fluorescence lifetime microscopy. Using the alternating optimization strategy, we iteratively solve a non-convex optimization problem to estimate the lifetime parameters and a convex optimization problem to estimate the concentration parameters. We effec...

Using cocommutativity of the Hopf algebra of symmetric functions, certain skew Schur functions are proved to be equal. Some of these skew Schur function identities are new.

In this equation, n represents the number of Figures of Merit (FoMs) that are to be combined, xi represents the output of the scoring function for the ith FoM and wi represents the weight of importance assigned to the ith FoM. The Product Tradeoff Function is commonly used for example in computing cost to benefit ratios and in doing risk analyses. Unfortunately, the published equation on page 1...

We present a collocation method to obtain the approximate solution of Troesch's problem which arises in the confinement of a plasma column by radiation pressure and applied physics. By using the Christov rational functions and collocation points, this method transforms Troesch's problem into a system of nonlinear algebraic equations. The rate of convergence is shown to be exponential. The numer...

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

Let S be a many sorted signature. A gate of S is an element of the operation symbols of S. Let A be a set and let f be a function. One can check that A 7−→ f is function yielding. Let f , g be non-empty functions. Observe that f +·g is non-empty. Let A, B be sets, let f be a many sorted set indexed by A, and let g be a many sorted set indexed by B. Then f +·g is a many sorted set indexed by A∪B...

Advances in technology equip tra c domain with instruments to gather and analyze data for safe and fuele cient traveling. This article elaborates on the e↵ects from taxi drivers route selection on fuel e ciency. We fuse real driving behavior data from taxi cabs, weather, and digital map information for fuel consumption prediction. That way we compare actually driven trips and their quickest and...