In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both the Sturm-Liouville theory and the formal treatment yield the same Green functions. We shall also show how the analyticity of the Green functions as function...

The study of finite projective planes involves planar functions, namely, functions f : Fq → Fq such that, for each a ∈ F ∗ q , the function c 7→ f(c + a) − f(c) is a bijection on Fq. Planar functions are also used in the construction of DES-like cryptosystems, where they are called perfect nonlinear functions. We determine all planar functions on Fq of the form c 7→ c , under the assumption tha...

Classical plasticity and damagemodels for porous quasi-brittle media usually suffer from mathematical defects such as non-convergence and nonuniqueness. Yield or damage functions for porous quasi-brittle media often have yield functions with contours so distorted that following those contours to the yield surface in a return algorithm can take the solution to a false elastic domain. A steepest-...

in order to study of nitrogen effect on critical period of weed control in sunflower (helianthus annuus l.) in birjand region, a split plot experiment based on randomized complete block design was conducted with 24 treatments and 3 replications in research farm of college of agriculture of birjand university in 2010. the main factor was three levels of nitrogen (0, 100 and 200 kg.ha-1) and the ...

in this paper, we introduce and characterize fuzzy wea-kly $e$-closed functions in fuzzy topological spaces and the relationship between these mappings and some properties of them are investigated.

Angle dependent yield functions for different Neutron Monitor types are calculated using a simulation of cosmic ray air showers combined with a detection efficiency simulation for different secondary particle species. Results are shown for IGY and NM64 configurations using the standard 10BF3 detectors and the new He detectors to be used in the Spaceship Earth Project (Bieber and Evenson, 1995)....

The class of Functional Signal plus Noise (FSN) models is introduced that provides a new, general method for modelling and forecasting time series of economic functions. The underlying, continuous economic function (or ‘signal’) is a natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates (or ‘y-values’) at the knots of the spline. The na...

Yield functions and plastic potentials are expressed in terms of the invariants of the stress tensor for polycrystalline metals and other isotropic materials. The plastic volume change data of Richmond is used to evaluate the embedded materials properties for some bcc metals and one polymer. A general form for the plastic potential is found that is intended to represent and cover a wide range o...

Although the concept of utility is fundamental to many economic theories, up to now a generally accepted method determining a subject’s utility function is not available. We investigated two methods that are used in economic sciences for describing utility functions by using response-locked event-related potentials in order to assess their neural underpinnings. For defining the certainty equiva...