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This work presents Retail-GPT, an open-source RAG-based chatbot designed to enhance user engagement in retail e-commerce by guiding users through product recommendations and assisting with cart operations. The system is cross-platform and adaptable to various e-commerce domains, avoiding reliance on specific chat applications or commercial activities. Retail-GPT engages in human-like conversations, interprets user demands, checks product availability, and manages cart operations, aiming to serve as a virtual sales agent and test the viability of such assistants across different retail businesses., Comment: 5 pages, 4 figures

This paper presents inferences for the discrete Bilal (DB) distribution introduced by Altun et al. (2020). We consider parameter estimation for DB distribution in the presence of randomly right-censored data.We use maximum likelihood and Bayesian methods for the estimation of the model parameters. We also consider the inclusion of a cure fraction in the model. The usefulness of the proposed model was illustrated with three examples considering real datasets. These applications suggested that the model based on DB distribution performs at least as good as some other traditional discrete models as the DsFx-I, discrete Lindley, discrete Rayleigh, and discrete Burr- Hatke distributions. R codes are provided in an appendix at the end of the paper so that reader can carry out their own analysis., Comment: 20 pages, 10 figures

Boron and Silicon site occupancies of the T2 phase in the Cr-Si-B system were investigated experimentally and by first-principles electronic-structure calculations within the scope of the Density Functional Theory (DFT). A sample with nominal composition Cr$_{0.625}$B$_{0.175}$Si$_{0.2}$ was arc-melted under argon, encapsulated in a quartz-tube and heat-treated at 1400{\deg}C for 96 hours. It was then analyzed using Scanning Electron Microscopy (SEM) and X-Ray Diffractometry (XRD) with synchrotron radiation. An excellent agreement was obtained between experiments and theoretical calculations, revealing that Si occupies preferably the $4a$ sublattice of the structure due to the presence of weak B bonds, making the site preferences a key factor for its stabilization. The results of this work provide important information to support a better description of this phase in alloys with Si and B, since T2 phases are known to occur in many important Transition Metal-Si-B ternary systems, such as Nb/Mo/W/Ta/V-Si-B.

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique one-parameter family of periodic orbits, scrolls, invariant cylinders foliated by orbits which can be periodic or no.

Our start point is a 3D piecewise smooth vector field defined in two zones and presenting a shared fold curve for the two smooth vector fields considered. Moreover, these smooth vector fields are symmetric relative to the fold curve, giving raise to a continuum of nested topological cylinders such that each orthogonal section of these cylinders is filled by centers. First we prove that the normal form considered represents a whole class of piecewise smooth vector fields. After we perturb the initial model in order to obtain exactly $\mathcal{L}$ invariant planes containing centers. A second perturbation of the initial model also is considered in order to obtain exactly $k$ isolated cylinders filled by periodic orbits. Finally, joining the two previous bifurcations we are able to exhibit a model, preserving the symmetry relative to the fold curve, and having exactly $k.\mathcal{L}$ limit cycles., Comment: research paper