Supersymmetry of a Nonstationary Pauli Equation

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated.Comment: 12 pages, Late

Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.Comment: 17 pages, latex, no figure

Topologies generated by discrete subspaces

A topological space X is called discretely generated if for every subset A X we have A = {D : D A and D is a discrete subspace of X}. We say that X is weakly discretely generated if A X and A A implies D A for some discrete D A. It is established that sequential spaces, monotonically normal spaces and compact countably tight spaces are discretely generated. We also prove taht every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely generated space is metrizable

Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields

We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.Comment: 14 page

Features of Nickel-Cadmium Batteries Recycling

The issue of operated-off alkaline nickel-cadmium batteries recycling is currently relevant due to a number of aspects: economic, environmental and social. It is most acute across the national corporation JSC Russian Railways. The article deals with some technological features of operated-off alkaline nickel-cadmium batteries recycling with valuable components being extracted (from the example of nickel-cadmium storage batteries of JSC ”RZD” rolling equipment). The results of leaching in Trilon B synthetic oxides solution, the presence of which is possible in the raw material being processed, are presented in the study. Based on the study of leaching processes of CdO, NiO, FeO, Femet and Fe2O3 in Trilon B solution, the dependence of complexing on the pH of the solution was revealed. The experimental site of the hydrometallurgical processing of the research center (OCGP IC) in the GMO KhMC PJSC ”Uralelectromed” was selected as the testing one for the technology proposed. As a raw material for the tests, a lot of negative lamellae packed in alkaline storage batteries of two different types were used. They were obtained as a result of preliminary drying and cutting at OOO Kursk factory ”Accumulator”. The particle size is 90% - 0.1 mm. The results obtained during the research allowed the author to formulate a hypothesis about the practical use of Trilon B for the processing of operated-off alkaline nickel-cadmium batteries with the extraction of valuable components having greater economic, environmental and social benefits compared to methods based on pyro metallurgy. Keywords: nickel-cadmium batteries, recycling, Trilon B, Russian Railways, hydrometallurgica

The prospect of developing national standards in the field of additive technologies

Аддитивные технологии – это новое направление изготовления различных деталей. В настоящее время все изделия изготавливаются по специальным техническим заданиям заказчиков, т.к. в России пока нет стандартов на данную продукцию. Успешное развитие и применение аддитивных технологий предполагает создание нормативной базы, позволяющей обеспечить качество изделийAdditive technologies are a new direction in the manufacture of various parts. Currently, all products are manufactured according to special technical orders of customers, because in Russia there are no standards for this product. Successful development and application of additive technologies presuppose the creation of a regulatory framework that will ensure the quality of product

Deformed Heisenberg algebra and minimal length

A one-dimensional deformed Heisenberg algebra $[X,P]=if(P)$ is studied. We answer the question: For what function of deformation $f(P)$ there exists a nonzero minimal uncertainty in position (minimal length). We also find an explicit expression for the minimal length in the case of arbitrary function of deformation.Comment: to be published in JP

Mathematical simulation of package delivery optimization using a combination of carriers

A variety of goods and services in the contemporary world requires permanent improvement of services e-commerce platform performance. Modern society is so deeply integrated with mail deliveries, purchasing of goods and services online, that makes competition between service and good providers a key selection factor. As long as logistic, timely, and cost-effective delivery plays important part authors decided to analyze possible ways of improvements in the current field, especially for regions distantly located from popular distribution centers. Considering both: fast and lazy delivery the factor of costs is playing an important role for each end-user. Given work proposes a simulation that analyses the current cost of delivery for e-commerce orders in the context of delivery by the Supplier Fleet, World-Wide delivery service fleet, and possible vendor drop-ship and checks of the alternative ways can be used to minimize the costs. The main object of investigation is focused around mid and small businesses living far from big distribution centers (except edge cases like lighthouses, edge rocks with very limited accessibility) but actively using e-commerce solutions for daily activities fulfillment. Authors analyzed and proposed a solution for the problem of cost optimization for packages delivery for long-distance deliveries using a combination of paths delivered by supplier fleets, worldwide and local carriers. Data models and Add-ons of contemporary Enterprise Resource Planning systems were used, and additional development is proposed in the perspective of the flow selection change. The experiment is based on data sources of the United States companies using a wide range of carriers for delivery services and uses the data sources of the real companies; however, it applies repetitive simulations to analyze variances in obtained solutions

General approach to potentials with two known levels

We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $\xi (x)$ and one parameter $\Delta E=E_{2}$-$E_{1}$. We show how the quantum numbers of both levels depend on properties of the function $\xi (x)$. Our approach does not need resorting to the technique of supersymmetric (SUSY) quantum mechanics but automatically generates both the potential and superpotential.Comment: 14 pages, REVTeX 3.0. In v.2 misprints and inaccuracies in presentation corrected, discussion of 3-dim. case added. In v.3 misprint in eq. 41, several typos and inaccuracies in English corrected. To be published in J. of Phys. A: Math. Ge