This work presents an analytical study of the structure of steady Marangoni-driven singularities in the context of chemical-reaction driven tip-streaming, which identifies the conditions when such singularities are observable. As motivated by experimental observations of the conical symmetry of the problem, one can construct self-similar solutions of the Stokes equations, which are singular at ...

In many fields of physics and chemistry, explicit analytical solutions of the fundamental dynamical equations are much valuable for a general understanding of phenomena, e. g. the role played by physical parameters. Two typical examples in quantum mechanics are the exact solutions of the Schrödinger equation (SE) for a hydrogen atom (Coulombic) and for a harmonic oscillator [1 – 3]. The Mie-typ...

A higher order nonlinear Schrödinger equation (NLSE) with thirdand fourth-order dispersions, cubic-quintic nonlinearities, self steepening, and self-frequency shift effects is considered. This model describes the propagation of femtosecond light pulses in optical fibers. It is to be noted that soliton pulses are used as the information carriers (elementary "bits") to transmit digital signals ov...

We study the inverse fluorescent source problem for optical molecular imaging. In particular, we recover key properties of a fluorescent source inside a halfspace composed of a uniform absorbing and scattering medium from angularly resolved measurements at the boundary plane. We use the radiative transport equation to model the multiple scattering of light in tissues. Using Green’s function, gi...

Previously, we deened innnite dimensional exact lters as nonlinear lters which can be conveniently reduced without approximation to a single convo-lution (plus a simple transformation and substitution). We showed that such problems do exist and the observation process can be far more general than those for exact nite dimensional lters like the Kalman and Benes lters. Moreover, our innnite dimen...

The two-dimensional case occupies a special position in the theory of critical phenomena due to exact results provided by lattice solutions and, directly continuum, infinite-dimensional character conformal algebra. However, some sectors theory, and most notably criticality systems with quenched disorder short range interactions, have appeared out reach methods lacked insight coming from analyti...

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of p...

By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components. The decomposition series analytic solution of the problem is quickly obtained by observing the existence ...

One of the remaining methodological challenges of agricultural LCAs is the inclusion of crop rotation effects. They are caused by changes in physical, chemical and biological properties of the agricultural land over time (e.g. soil structure, presence and availability of nutrients, phytosanitary conditions) and cannot be easily measured. LCA studies, focusing on only one vegetation period, have...

We consider the special class of semidefinite linear programs (IV P ) maximize traceCX subject to L A(X) U, where C,X,L, U are symmetric matrices, A is a (onto) linear operator, and denotes the Löwner (positive semidefinite) partial order. We present explicit representations for the general primal and dual optimal solutions. This extends the results for standard linear programming that appeared...