Asymptotics for Two-dimensional Atoms

We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2) when $Z\to \infty$ and $N/Z\to \lambda$, where E^{\TF}(\lambda) is given by a Thomas-Fermi type variational problem and $c^{\rm H}\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\to \infty$, which is contrary to the expected behavior of three-dimensional atoms.Comment: Revised version to appear in Ann. Henri Poincar\'

Amino-functionalized CoFe2O4 magnetic nanoparticles as an efficient heterogeneous catalyst for benzaldehyde cyanosilylation

Diaminosilane-functionalized cobalt spinel ferrite (CoFe2O4) magnetic nanoparticles were synthesized and used as an efficient heterogeneous base catalyst for the cyanosilylation reaction benzaldehyde with trimethylsilyl cyanide. The magnetic nanoparticle catalyst was characterized by X-ray powder diffraction (XRD), transmission electron microscope (TEM), thermogravimetric analysis (TGA), fourier transform infrared (FT-IR), nitrogen physisorption measurements. Quantitative conversion (99%) was achieved under mild conditions. Recovery of catalyst was facilely achieved by magnetic decantation. The supported catalyst could be reused without significant degradation in catalytic activity

BUILDING DATABASE IN BALANCING KNITTED GARMENT LINES SOFTWARE IN INDUSTRY

The garment industry is one of the key industries contributing to the economic growth of Vietnam. Industry 4.0 has significantly altered the operational procedures of conventional enterprises. The implementation of technological, digital, and artificial intelligence applications has increased the global efficacy of corporate governance. To successfully assimilate into the regional and global economies, Vietnamese businesses must enhance their management capabilities and maximize both the quantity and quality of their products. In order to achieve this objective, the authors have conducted research to develop a database of sewing line balancing implemented in Assembly Line Balancing software for two common knitted products, namely Polo- Shirts, and T-Shirts. School of Textile-Leather and Fashion, Hanoi University of Science and Technology (HUST) methods compared and evaluated this result of sewing line balancing of 2 Polo-Shirt and T-Shirt products according to the manual, software, and actual calculation method at 3 enterprises: Star Fashion Company Ltd., Regent Garment Factory Ltd., and Hanoi General Textile Garment Joint Stock Company (Hanosimex). Since then, we have completed the sewing line balancing database for Polo-Shirt and T-Shirt products to row sewing lines for cases in which the path of semi-finished products is both straight and zigzag. The findings of this study can be applied to group conjugation lines and suspended lines transporting semifinished goods. The database has been constructed meticulously and standardized to ensure the diversity, richness, and universality of all product technology structure options applicable to garment companies. The database is utilized in the Assembly Line Balancing software developed by the research team; this is an application-oriented research product that will transfer technology to garment enterprises producing knitwear, assisting them in overcoming current challenges. Reasonable production line layout contributes to optimizing existing production conditions, increasing labor productivity and the efficiency of production organization, and laying the groundwork for the application of digital technology

Determine the source term of a two-dimensional heat equation

Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.Comment: 18 page

On the effective quasi-bosonic Hamiltonian of the electron gas: collective excitations and plasmon modes

We consider an effective quasi-bosonic Hamiltonian of the electron gas which emerges naturally from the random phase approximation and describes the collective excitations of the gas. By a rigorous argument, we explain how the plasmon modes can be interpreted as a special class of approximate eigenstates of this model