Formula 1 or Grand Prix racing is known for its extensive use of advanced technology, huge monetary investment, and the attention-grabbing looks of its highly aerodynamic, open-wheeled race cars. According to F1 rules, each team must design and build its own car. This typically requires an investment upwards of $1 million for each car and an annual race team budget that can run in the $100s of ...

We present new short proofs for both Stirling’s formula and Stirling’s formula for the Gamma function. Our approach in the …rst case relies upon analysis of Wallis’formula, while the second result follows from the logconvexity property of the Gamma function. The well known formula of Stirling asserts that (1) n! p 2 ne n as n!1; in the sense that the ratio of the two sides tends to 1. This prov...

This article introduces a method for local sensitivity analysis of practical interest. A theorem is given that provides a general and neat manner to obtain all sensitivities of a general nonlinear programming problem (around a local minimum) with respect to any parameter irrespective of it being a right-hand side, objective function or constraint constant. The method is based on the well-known ...

We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decayness of the sinc function. To overcome this drawback, a simple and highly effective method, called the Gaussian regularization of the Shannon series, was proposed in engineering and has...

As the world’s most populous country, with more than 16 million births every year, China has emerged as a large importer of baby formula. China’s relaxation of the one-child policy, which was announced in 2015, is expected to increase the number of births significantly and therefore increase the demand for Chinese and imported baby formula. While information on parent preferences for baby formu...

The aim of this study was to determine the correlation of ultrasonographic estimates of testicular volume with true testicular volume and to compare the accuracy and precision of the three most commonly utilized formulas. A total of 15 patients underwent high-resolution ultrasonography (US) analysis for testicular volume before orchiectomy. Testicular volume was calculated using three common fo...

In this paper, we analyze the multi-transmitting formula (MTF) proposed by Liao et al [19]. From the computed reflection coefficients for the fully discrete MTF boundary conditions, we suggest choices for the artificial wave propagation speed, which are different from Liao’s original choice. Theoretical and numerical studies for various incidence angles demonstrate that the suggested choices ef...

Suppose that U is a locally compact group. It is a fundamental problem to classify the irreducible unitary representations of U. A second basic problem is to decompose the Hilbert space of square integrable functions on U, or on some homogeneous quotient of U, into irreducible U-invariant subspaces. The underlying domain is often attached to a natural Riemannian manifold, and the required decom...