A number of algorithms have been developed for three-dimensional (3D) deconvolution of fluorescence microscopical images. These algorithms use a mathematical-physics model for the process of image formation and try estimate the specimen function, i.e. the distribution of fluorescent dye in the specimen. To keep the algorithms tractable and computational load practical, the algorithms rely on si...

The accuracy of the JWKB method for determining the survival factor defined for dissociative electron attachment (DEA) processes is examined for a range of electronic resonance lifetimes within the local complex potential approximation. The author concludes that the accuracy is inadequate for molecules with properties commonly found for shape resonance induced DEA. More accurate methods using t...

A well-developed phase modulation method is utilized to design a nanogroove grating for a desired diffraction process, which gives rise to the conversion of a surface plasmon wave to an Airy-like radiation beam. Experiments and simulations revealed the unique characteristics of the generated Airy-like beam, such as nonspreading, self-bending, and self-healing. Our result confirms the validation...

The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generaliz...

Closed form solutions are obtained for a Fokker-Planck model for cell growth as a function of maturation velocity and degree of maturation. For reproduction rules where daughter cells inherit their parent's maturation velocity the complete solution is derived in terms of Airy functions. For more complicated reproduction rules partial results are obtained. Emphasis is given to the relationship o...

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm deter...

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determin...

Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the spatio-temporal field structure when observed in reference frames moving at relativistic speeds. For such an observer, it is predicted that the associated Lor...

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.