A new model is presented for a step-index fiber in the form of an equivalent slab guiding structure. This model simplifies the analysis of fiber directional couplers and coupler half-blocks with dielectric and metallic superstrates. Simple empirical formulas to obtain the model parameters are also given. The use of this model is illustrated with some numerical examples.

Experimental excitation functions of isotopes produced in reactions p + natSi are compared with the results nuclear reaction program TALYS 1.95 and semi-empirical cross section formulas. We consider 7 (28Mg, 26Al, 24,22Na, 18F 10,7Be) at bombarding energies 20-144 MeV. They predictions code 1.95, formulas Silberberg-Tsao (code yieldx) SPACS. Comparisons previously published ALICE made. The pred...

To explain several stylized facts concerning catastrophe-linked securities premium spread, we propose an intertemporal equilibrium model by allowing agents to act in a robust control framework against model misspecification with respect to rare events. We have presented closed-form pricing formulas in some special cases and tested the model using empirical data and simulation. © 2011 Elsevier B...

We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑

This paper considers the birth of algebraic proof by looking at the works of Cardano, Viète, Harriot and Pell. The transition from geometric to algebraic proof was mediated by appeals to the Eudoxan theory of proportions in book V of Euclid. The crucial notational innovation was the development of brackets. By the middle of the seventeenth century, geometric proof was unsustainable as the sole ...

We show that, for a finite set A of real numbers, the size of the set A + A A + A = { a + b c + d : a, b, c, d ∈ A, c + d 6= 0 } is bounded from below by ∣∣∣∣A + A A + A ∣∣∣∣ |A|2+1/4 |A/A|1/8 log |A| . This improves a result of Roche-Newton (2016).

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...

Semantical expansion aims at boosting minimisation heuristics for Boolean formulas. It provides an easy way of deciding whether or not a given minterm, resp. clause, can be added safely to a formula in DNF, resp. CNF. We suggest to use incremental and complete SAT solvers and instances of UNSAT for these decisions, and report on some preliminary empirical results.

Background: Many techniques in molecular biology depend on the oligonucleotide melting temperature (Tm), and several formulas have been developed to estimate Tm. Nearest-neighbor (N-N) models provide the highest accuracy for Tm prediction, but it is not clear how to adjust these models for the effects of reagents commonly used in PCR, such as Mg, deoxynucleotide triphosphates (dNTPs), and dimet...