On the position-dependent mass Schrödinger equation for Mie-type potentials

The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

SmartUAV’sDelivery System using Fingerprint Authentication

In general, it is not possible to complete the delivery of the package competently because the main challenge is insufficient smart technology to identify the user for a package authentication. Therefore, fingerprint authentication is one of the intelligent authentication ideas of the package used as one solution to the above reference problem. The model should be properly prepared with regard to behavioral design in order to incorporate the UAV transport system in cities. The drone activity preparation and fingerprint authentication model for providing solutions is suggested in this regard. In terms of the computing time of the UAV and the optimality difference, the experimental results indicate a feasible solution and provide an efficient solution model.

Analysis on Cost-Benefit of Rainwater Storage Facility through Water Balance Analysis

The installation of rainwater storage facilities is mandatory for public buildings over a certain size. However, the standards for determining the capacity of rainwater storage facilities vary by ministries and agencies. Even within the same institution, various unifying standards are often applied. In addition, rainwater storage facilities generally have a low B/C (Benefit-Cost ratio), which is negatively evaluated in terms of economy. Therefore, this study sought to improve the existing non-standard capacity reference problem for rainwater storage facilities and to suggest more efficient capacity determination measures. To this end, the study proposed a plan for calculating the benefits and determining the capacity of the reservoir through the analysis of the water balance in order to take into account the utility of the rainwater reservoir in terms of actual use. The empirical analysis was conducted on rainwater storage facilities in the Korea Land and Housing Institute, and the water balance analysis was conducted based on the actual rainfall data of 2019 by Daejeon Metropolitan City. Among the factors to evaluate the benefit and cost of rainwater storage facilities were the reduction of rainwater runoff, reduction of heat waves, reduction of fine dust, and use of landscaping water. In addition, the benefit analysis was conducted by the reservoir capacity and collection area, and the guide for determining the optimum capacity of the rainwater reservoir was presented accordingly.

Analysis of Students' Critical Thinking Skills in Solving Mathematics Problems on Pythagoras

This study aims to describe the critical thinking skills in solving math problems. The approach used in this research is qualitative research with descriptive research type. The research subjects were 32 students. The six interview subjects were divided into three levels of critical thinking, namely 2 high categories, 2 medium categories and 2 low categories. Data collection procedures are tests of critical thinking skills and interviews. Research data analysis refers to indicators of critical thinking, namely: interpreting, analyzing, evaluating and inferring. Student achievement on each indicator includes: 1) Percentage of students' ability to interpret the completion of the test questions by 65.5%; 2) The percentage of students' ability to analyze the completion of the test questions by 39.1%; 3) The percentage of students' ability to evaluate is 66.6%; and 4) Percentage of students' ability to infer by 40%. The ability of students to interpret a problem solving is good. Students have been able to write out what is known and asked in the problem correctly, but there are students who are less thorough and incomplete in writing the unit of distance. The ability of students to analyze problem solving is quite low. Students do not provide information on drawing illustrations. The ability of students in evaluating problem solving is good. Students are able to do the calculations correctly in accordance with the rubric of assessment. The ability of students to reference problem solving is low. Students are not used to writing the final conclusions of the answers obtained.

PREPARING FOR MATHEMATICAL COMPETITIONS: A PROBLEM SERIES ON METRIC RATIOS IN A QUADRANGLE

Solving of competitive problems by pupils and students is a good foundation and preparation for future practical and scientific activities, as mastering the methods of solving competitive problems requires them to work hard, actively and focused, as well as develops their creativity and raises level of interest in mathematics. The article reveals the mathematical aspects of preparing students to solve competitive problems on the example of one geometric problem (the ratio between the areas of triangles formed by the intersection of diagonals of a convex quadrilateral), which is the basis of many competitive problems in geometry; the problem is solved using the facts of elementary mathematics, available to students of the eighth form of secondary school; an analysis of the range of competitive problems of various mathematical competitions, for which the considered reference problem is a key subtask in the solution. An author's competitive problem for high school students has been created, which allows integrating a purely theoretical-numerical problem into the geometric shell with the study of simplicity of elements, divisibility of a product by a prime number, mutual simplicity of elements, with the need to find solutions of Diophantine equations in natural numbers. The article combines a problem series of a large number of different competitive geometric problems around one reference problem, presents the methodological aspects of preparing students to solve competitive problems on the example of this problem; attention is paid to checking the correctness of the obtained results, which avoids erroneous solutions; the tasks which urge to find and realize ways of their fulfillment are analyzed; examples of different tasks in terms of age capabilities of researchers are selected; the problems of competitions of regional levels with geometric and theoretical-numerical filling are considered; the competitive task on the given subject is created. Further research will be aimed at creating a broader series of tasks for the considered reference problem, including problems with integration into related competitive topics. The article emphasizes the problem content and structuring according to the age capabilities of students on the research topic.

Younan-Veletsos retaining wall: The exact solution

The assessment of forces exerted on walls by the backfill is a recurrent problem in Geotechnical Engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Veletsos and Younan becomes pertinent when considering pressure increments on underground structures triggered by seismic events. These scholars furnished the first satisfactory engineering solution corresponding to a simple configuration, which has become a milestone in the field. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain, hence it comes in terms of inverse Fourier transforms, which in turn are verified against finite-element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed.

Medical Concept Representation Learning from Multi-source Data

Representing words as low dimensional vectors is very useful in many natural language processing tasks. This idea has been extended to medical domain where medical codes listed in medical claims are represented as vectors to facilitate exploratory analysis and predictive modeling. However, depending on a type of a medical provider, medical claims can use medical codes from different ontologies or from a combination of ontologies, which complicates learning of the representations. To be able to properly utilize such multi-source medical claim data, we propose an approach that represents medical codes from different ontologies in the same vector space. We first modify the Pointwise Mutual Information (PMI) measure of similarity between the codes. We then develop a new negative sampling method for word2vec model that implicitly factorizes the modified PMI matrix. The new approach was evaluated on the code cross-reference problem, which aims at identifying similar codes across different ontologies. In our experiments, we evaluated cross-referencing between ICD-9 and CPT medical code ontologies. Our results indicate that vector representations of codes learned by the proposed approach provide superior cross-referencing when compared to several existing approaches.

The Substantive/Procedural Distinction: Law's Solution to the Problem ofJus Cogensin a World of Sovereign States

This Article uses social systems theory to examine the increased reliance on a distinction between substantive and procedural international law to resolve cases involving a conflict betweenjus cogensand state immunity. This presents the problem of an evolutionary relationship between international law and the complex differentiation of world society. International law is shown to be structurally related to the segmentary differentiation of states that underwrites modern society's functional differentiation. At the same time, it is shown to be structurally related to the increasing formulation of global norms that result from advanced functional differentiation. The Article then turns to examining the substantive/procedural law distinction as a solution to this dual functional reference problem. The distinction is shown to not only maintain the autopoiesis of law under these difficult conditions, but to also secure law's continued functional relevance in globalized society. This functionalist perspective is used to expose differences in the self-description and operation of international law, to point out how law has been blind to its own coding, and to highlight opportunities for programming law to respond in a more constructive manner to the challenges of globalization.