In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to starting value and analyze relevant statistical magnitudes. We focus our attention on monotonous continuous-time walks with constant drift: increases between events, either by effect of jumps, or action deterministic drift. As result all these combined factors interesting properties emerge, like existence|for any drift strength|of stationary transition probability density...

In this paper we consider a particular version of the random walk with restarts: reset events which suddenly bring system to starting value. We analyze its relevant statistical properties, like transition probability, and show how an equilibrium state appears. Formulas for first-passage time, high-water marks, other extreme statistics are also derived; counting problems naturally associated system. Finally indicate feasible generalizations useful interpreting different physical effects.

We propose a stochastic epidemiological model for simplicial complex networks by means of differential equation (SDE) that extends the mean field approach social contagion model. show that, under appropriate conditions, if basic reproductive number is smaller than one, then disease dies out with probability one; otherwise solution SDE oscillates infinitely often around point which can be explicitly computed. perform numerical experiments illustrate theoretical results. In addition, we carry...

A method to obtain a new class of discrete eigenfunctions and associated real, nonsingular, decaying, ``reflectionless'' potentials the time dependent Schr\"odinger equation is presented. Using inverse scattering transform, related solutions Kadomtsev-Petviashvili are found. The have poles order $m$, $m>1$ in complex plane also characterized by an index, or ``charge,'' which obtained as constraint theory.

The initial‐boundary‐value problem for the Kadomtsev‐Petviashvili equation in infinite space is considered. When formulated as an evolution equation, found that a symmetric integral appropriate choice nonlocal term; namely, . If one simply chooses , then number of constraints on initial data physical are required, first being conserved quantities calculated, and it shown they must be suitably regularized from those have been used when imposed.

The operation of photovoltaic (PV) tweezers, using the evanescent light-induced PV fields to trap and pattern nano- micro-meter particles on a LiNbO(3) crystal surface, is discussed. case periodic light addressed in detail, including role particle shape modulation index pattern. use single Gaussian beam also considered. Illustrative experiments for two situations are presented. performance such tweezers comparison best established optical forces, Differential features between trapping...

We derive a class of localized solutions 2+1 nonlinear Schrödinger (NLS) equation and study their dynamical properties. The ensuing dynamics these configurations is superposition uniform, “center mass” motion slower, individual motion; as result, nontrivial scattering between humps may occur. Spectrally, correspond to the discrete spectrum certain associated operator, comprised higher‐order meromorphic eigenfunctions.

The singular manifold method is used to generate lump solutions of a generalized integrable nonlinear Schrödinger equation in 2 + 1 dimensions. We present several essentially different types solutions. connection between this and the Ablowitz–Villarroel scheme also analysed.

The appearance of light intensity thresholds for catastrophic optical damage in LiNbO3 is satisfactorily explained by using a photorefractive model based on the Fe(2+)?Fe(3+) and NbLi(4+)?NbLi(5+) defect pairs. Model simulations amplification gain as function present sharp threshold behavior. A similar behavior shown saturating refractive index change. In agreement with experiments, predicted appear shifted towards higher intensities (up to 10(4) factor) when Nb(Li) concentration decreased...

The longstanding problem of the physical interpretation one-dimensional quantum damped oscillator is analysed here from viewpoint group theory. It shown how to transform system into a with variable frequency. However, main features final are rather those simple stationary 'renormalised' constant mechanical cannot be at all interpreted as 'dissipative' has been claimed by some authors.

Photorefractive optical damage of single beams in LiNbO(3) crystals is analyzed within a framework two photoactive centres (Fe(2+)/Fe(3+) and Nb(Li) (4+)/Nb(Li) (5+)). It compares model simulations significant experimental measurements waveguides. A good agreement found the performed comparisons: photovoltaic currents, refractive index changes and, especially relevant, degraded beam-profiles. The progress wavefront has been simulated by implementing finite-difference beam-propagating method...

We consider the Cauchy problem for Kadomstev–Petviashvili II (KPII) equation with generic data that do not decay along a line. The linearization is in terms of spectral properties heat operator decaying 'time independent' potential. A bounded Green's function this constructed and its main are determined. solution KPII obtained via linear integral equations.

The point and contact Lie groups for the damped harmonic oscillator are found several realisations of SL(3,R) group analysed. non-critical critical cases studied separately a sort limiting procedure is defined, which leaves algebra structure unchanged. Some physical applications these results also pointed out.

Candida auris es una levadura multi-resistente emergente con rápida diseminación mundial. Desde el primer reporte 2009, varios aislados a través de los cinco continentes han sido identificados como agentes infecciones asociadas la atención en salud. Brotes independientes y simultáneos por C. se vuelto prioridad para comunidad hospitalaria científica. Además, errores identificación perfiles multi-resistencia, raramente observados otras especies Candida, resultan difícil erradicación fallas...

We consider propagation of optical pulses under the interplay dispersion and Kerr non-linearity in fibres with impurities distributed at random uniformly on fibre. By using a model based non-linear Schrodinger equation we clarify how such inhomogeneities affect different aspects as number solitons present intensity signal. also obtain mean distance for signal to dissipate given level.

The initial value problem for the Kadomstev–Petviashvili II (KPII) equation is considered with given data that are nondecaying along a line. associated direct and inverse scattering of two‐dimensional heat constructed. formulated in terms bounded Green's function. decomposed into line from decaying portion potential. solution KPII then obtained via coupled linear integral equations.

The discrete spectrum of first order systems in the plane and localized solutions Davey--Stewartson II equation are studied via inverse scattering transform. Localized nonsingular algebraically decaying potentials found which correspond to a whose related eigenfunctions have, general, multiple poles associated kernels with dimension $\ge 2$. There is an index, or winding number, used classify these potentials. With suitable assumptions mass corresponding solution be proportional index.