The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution

In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot B$ in (0,T) \times \bR^d, with vanishing initial conditions, driven by a Gaussian noise $\dot B$ which is fractional in time, with Hurst index $H \in (1/2,1)$, and colored in space, with spatial covariance given by a function $f$. Our main result gives the necessary and sufficient condition on $H$ for the existence of the process solution. When $f$ is the Riesz kernel of order $\alpha \in (0,d)$ this condition is $H>(d-\alpha)/4$, which is a relaxation of the condition $H>d/4$ encountered when the noise $\dot B$ is white in space. When $f$ is the Bessel kernel or the heat kernel, the condition remains $H>d/4$

Retail store design and environment as branding support in the services marketing

The services are intangibles, therefore their quality is difficult to be evaluated by the client and building a strong brand image is a challenging task. The services are distributed using diverse channels such as: company retail stores, dealers, franchise. The service companies are interested in the environment of the location, not only to increase sells but also in order to boost the image of the company. The excitement that a retail store induces to a client can modify the perception of the brand. The client values more a brand that distributes its services in a luxury, high-tech retail environment than a discount store. In this paper we intended to investigate the techniques that a service company is using to enhance the brand image in a retail location. For this purpose, the various aspects of the retail store design and environment were analyzed in connection with the customer-based brand equity model. This original association will offer the services companies’ new perspectives on how to leverage brand image.retail environment, brand architecture, point of sale marketing

Photoresist patterned thick-film piezoelectric elements on silicon

A fundamental limitation of screen printing is the achievable alignment accuracy and resolution. This paper presents details of a thick-resist process that improves both of these factors. The technique involves exposing/developing a thick resist to form the desired pattern and then filling the features with thick film material using a doctor blading process. Registration accuracy comparable with standard photolithographic processes has been achieved resulting in minimum feature sizes of <50 ?m and a film thickness of 100 ?m. Piezoelectric elements have been successfully poled on a platinised silicon wafer with a measured d 33 value of 60 pCN?1

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that when odd number of subbands are occupied the system realizes non-trivial topological state supporting Majorana modes localized at the ends. We study the topological quantum phase transition in this system and analytically calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows to have higher carrier density in the nanowire and as such multisubband nanowires are better-suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that in the limit of strong interband mixing there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.Comment: 4 pages, 3 figures, expanded version includes new results; accepted for publication in PR