Lia Margolin | Marymount Manhattan College (original) (raw)
Papers by Lia Margolin
Success and failure in math and science performance are greatly determined by students' attit... more Success and failure in math and science performance are greatly determined by students' attitudes towards the subject matter. A multidimensional survey, including motivation, usefulness, self-confidence, and enjoyment subscales was developed and administered in two New York City Private High schools. Student attitudes were examined and compared by sex, age, and number of mathematics and science courses taken. Majority of study participants regardless of their age, sex, and level of coursework found mathematics and science courses challenging and not enjoyable. Few students demonstrated understanding of the benefits of acquiring mathematical and scientific skills and expressed desire to pursue careers in science, mathematics, and related fields. The Spearman's rank-order correlation coefficient was calculated to identify the strength and direction of relationship between student attitudes toward science and mathematics and possible career choices in these fields. Chi-Square a...
Microscopic Theory of the Structure and Decay of Four Particle Hypernuclei R. Jibuti, N.Krupennik... more Microscopic Theory of the Structure and Decay of Four Particle Hypernuclei R. Jibuti, N.Krupennikova, L. Sarkisyan-Margolin, Sh.Tsiklauri Abstract. The principle information about hyperon-nucleon interaction is obtained by investigation of the structure and decays of light hypernuclei. Therefore, development of the microscopic, model independent mathematical approach to the study of the structure and decays of light hyperniclei is important [1-6]. Gibson and Lehman [7] performed exact four-body calculuatioins of the He binding energy difference using Faddeev’s integral equation method. However, making cetain approximations were necessary in order to solve obtained eighteen coupled Faddeev-Yakubovsky equations. The hyperspherical function (HF) method in coordinate spece was applied to the investigation of hyper-triton [8]. Microscopic approach to the study of the structure and mesonic decays of four-body hypernucleus with the use of the HF method in momentum space was developed in [3...
Few-Body Systems, 1988
ABSTRACT The problem of symmetrization of four-body hyperspherical functions is discussed. A cons... more ABSTRACT The problem of symmetrization of four-body hyperspherical functions is discussed. A construction scheme is given for the symmetrized hyperspherical asis in the (3+1)-configuration. The transformation between hyperspherical functions corresponding to the (2+2)- and (3+1)-configurations is considered.
Abstract. The binding energy and the structure of superheavy hydrogen-Λ are studied within the me... more Abstract. The binding energy and the structure of superheavy hydrogen-Λ are studied within the method of hyperspherical harmonics. The 6ΛH hypernucleus is considered as a six body system consisting of particle and five nucleons. 1.
arXiv: Mathematical Physics, 2007
A new mathematical model for the description of three electron quantum dots in 2D space is create... more A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is solved by the use of the Hyperspherical Function Method (HFM) It is shown that the HFM allows us to separate the center of mass movement and solve Schrodinger Equation with the use of the logarithmic potential of electron-electron interactions. Ground state energy levels as function of the magnetic field frequency is obtained.
arXiv: Nuclear Theory, 2006
The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relat... more The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relation method of determination of transformation coefficients for arbitrary N-values is demonstrated.
ABSTRACT Available from http://www.aps.org/meet/DNP03/baps/abs/S660008.html
PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON MESON-NUCLEON PHYSICS AND THE STRUCTURE OF THE NUCLEON
Investigating few-body systems with identical particles in a hyperspherical basis yields the prob... more Investigating few-body systems with identical particles in a hyperspherical basis yields the problem of obtaining symmetrized hyperspherical functions from functions with arbitrary quantum numbers. This article solves the problem of hyperspherical basis symmetrization for four-, five-, and six-body systems using Parentage Scheme of Symmetrization. Parentage coefficients and transformation coefficients corresponding to the [4], [31], [22], [211], representations of S groups with specific quantum numbers are obtained, and relationship between parentage coefficients and transformation coefficients between different sets of Jacobi coordinates for six-body systems are derived. Young operators, acting on N = 4, 5, 6 body hyperspherical functions symmetrized with respect to (N-1) particles, are derived. The symmetrized N = 4, 5, 6 body hyperspherical functions are obtained with different values of quantum numbers. The connection between the transformation coefficients for the identical particle systems and the parentage coefficients is demonstrated and the corresponding formulas are introduced.
Journal of Physics: Conference Series, 2012
This paper consider possibility that three proton may bind uniform magnetic field. The purpose of... more This paper consider possibility that three proton may bind uniform magnetic field. The purpose of this article is to use of the hyperspherical function method for investigation confined three protons. It is apparent that one requires magnetic fields order 10^12 T for the Coulomb repulsion to be modest enough to be treated as a correction. Such magnetic fields are believed to be found in nature -- on the surface of magnetars. This novel class of quantum bound states is the focus of the present paper.
Few-body Systems, 2008
Three electrons confined by a parabolic well in a two-dimensional quantum dot and interacting via... more Three electrons confined by a parabolic well in a two-dimensional quantum dot and interacting via a logarithmic potential in a magnetic field are treated in the framework of the hyperspherical functions (HF) method by expanding the wave function in terms of the three-body symmetrized HF and the hyperradial functions of noninteracting trapped electrons. The binding energies and pair correlation function are calculated.
Epj Web of Conferences, 2014
The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary... more The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary for the description of the structural characteristics and decay reactions of the hypernuclear and nuclear systems with arbitrary amount of particles, is applied to the solution of five-body problem in hypernuclear physics. Hypernucleus ݁ܪ ఒ ହ as a system of four nucleons and one hyperon is investigated by the use of the Hyperspherical Function Method in momentum space. The dependence of the structure characteristics and wave functions on the types of nucleon-nucleon and hyperon-nucleon interaction potentials is studied. Mean square ߣ − ܪ ଷ and ߙ − ߣ distances and the binding energies for the ݁ܪ ସ and ݁ܪ ఒ ହ are obtained.
A new mathematical model for the description of three electron quantum dots in 2D space is create... more A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is solved by the use of the Hyperspherical Function Method (HFM) It is shown that the HFM allows us to separate the center of mass movement and solve Schrodinger Equation with the use of the logarithmic potential of electron-electron interactions. Ground state energy levels as function of the magnetic field frequency is obtained.
EPJ Web of Conferences, 2014
EPJ Web of Conferences, 2014
Success and failure in math and science performance are greatly determined by students' attit... more Success and failure in math and science performance are greatly determined by students' attitudes towards the subject matter. A multidimensional survey, including motivation, usefulness, self-confidence, and enjoyment subscales was developed and administered in two New York City Private High schools. Student attitudes were examined and compared by sex, age, and number of mathematics and science courses taken. Majority of study participants regardless of their age, sex, and level of coursework found mathematics and science courses challenging and not enjoyable. Few students demonstrated understanding of the benefits of acquiring mathematical and scientific skills and expressed desire to pursue careers in science, mathematics, and related fields. The Spearman's rank-order correlation coefficient was calculated to identify the strength and direction of relationship between student attitudes toward science and mathematics and possible career choices in these fields. Chi-Square a...
Microscopic Theory of the Structure and Decay of Four Particle Hypernuclei R. Jibuti, N.Krupennik... more Microscopic Theory of the Structure and Decay of Four Particle Hypernuclei R. Jibuti, N.Krupennikova, L. Sarkisyan-Margolin, Sh.Tsiklauri Abstract. The principle information about hyperon-nucleon interaction is obtained by investigation of the structure and decays of light hypernuclei. Therefore, development of the microscopic, model independent mathematical approach to the study of the structure and decays of light hyperniclei is important [1-6]. Gibson and Lehman [7] performed exact four-body calculuatioins of the He binding energy difference using Faddeev’s integral equation method. However, making cetain approximations were necessary in order to solve obtained eighteen coupled Faddeev-Yakubovsky equations. The hyperspherical function (HF) method in coordinate spece was applied to the investigation of hyper-triton [8]. Microscopic approach to the study of the structure and mesonic decays of four-body hypernucleus with the use of the HF method in momentum space was developed in [3...
Few-Body Systems, 1988
ABSTRACT The problem of symmetrization of four-body hyperspherical functions is discussed. A cons... more ABSTRACT The problem of symmetrization of four-body hyperspherical functions is discussed. A construction scheme is given for the symmetrized hyperspherical asis in the (3+1)-configuration. The transformation between hyperspherical functions corresponding to the (2+2)- and (3+1)-configurations is considered.
Abstract. The binding energy and the structure of superheavy hydrogen-Λ are studied within the me... more Abstract. The binding energy and the structure of superheavy hydrogen-Λ are studied within the method of hyperspherical harmonics. The 6ΛH hypernucleus is considered as a six body system consisting of particle and five nucleons. 1.
arXiv: Mathematical Physics, 2007
A new mathematical model for the description of three electron quantum dots in 2D space is create... more A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is solved by the use of the Hyperspherical Function Method (HFM) It is shown that the HFM allows us to separate the center of mass movement and solve Schrodinger Equation with the use of the logarithmic potential of electron-electron interactions. Ground state energy levels as function of the magnetic field frequency is obtained.
arXiv: Nuclear Theory, 2006
The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relat... more The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relation method of determination of transformation coefficients for arbitrary N-values is demonstrated.
ABSTRACT Available from http://www.aps.org/meet/DNP03/baps/abs/S660008.html
PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON MESON-NUCLEON PHYSICS AND THE STRUCTURE OF THE NUCLEON
Investigating few-body systems with identical particles in a hyperspherical basis yields the prob... more Investigating few-body systems with identical particles in a hyperspherical basis yields the problem of obtaining symmetrized hyperspherical functions from functions with arbitrary quantum numbers. This article solves the problem of hyperspherical basis symmetrization for four-, five-, and six-body systems using Parentage Scheme of Symmetrization. Parentage coefficients and transformation coefficients corresponding to the [4], [31], [22], [211], representations of S groups with specific quantum numbers are obtained, and relationship between parentage coefficients and transformation coefficients between different sets of Jacobi coordinates for six-body systems are derived. Young operators, acting on N = 4, 5, 6 body hyperspherical functions symmetrized with respect to (N-1) particles, are derived. The symmetrized N = 4, 5, 6 body hyperspherical functions are obtained with different values of quantum numbers. The connection between the transformation coefficients for the identical particle systems and the parentage coefficients is demonstrated and the corresponding formulas are introduced.
Journal of Physics: Conference Series, 2012
This paper consider possibility that three proton may bind uniform magnetic field. The purpose of... more This paper consider possibility that three proton may bind uniform magnetic field. The purpose of this article is to use of the hyperspherical function method for investigation confined three protons. It is apparent that one requires magnetic fields order 10^12 T for the Coulomb repulsion to be modest enough to be treated as a correction. Such magnetic fields are believed to be found in nature -- on the surface of magnetars. This novel class of quantum bound states is the focus of the present paper.
Few-body Systems, 2008
Three electrons confined by a parabolic well in a two-dimensional quantum dot and interacting via... more Three electrons confined by a parabolic well in a two-dimensional quantum dot and interacting via a logarithmic potential in a magnetic field are treated in the framework of the hyperspherical functions (HF) method by expanding the wave function in terms of the three-body symmetrized HF and the hyperradial functions of noninteracting trapped electrons. The binding energies and pair correlation function are calculated.
Epj Web of Conferences, 2014
The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary... more The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary for the description of the structural characteristics and decay reactions of the hypernuclear and nuclear systems with arbitrary amount of particles, is applied to the solution of five-body problem in hypernuclear physics. Hypernucleus ݁ܪ ఒ ହ as a system of four nucleons and one hyperon is investigated by the use of the Hyperspherical Function Method in momentum space. The dependence of the structure characteristics and wave functions on the types of nucleon-nucleon and hyperon-nucleon interaction potentials is studied. Mean square ߣ − ܪ ଷ and ߙ − ߣ distances and the binding energies for the ݁ܪ ସ and ݁ܪ ఒ ହ are obtained.
A new mathematical model for the description of three electron quantum dots in 2D space is create... more A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is solved by the use of the Hyperspherical Function Method (HFM) It is shown that the HFM allows us to separate the center of mass movement and solve Schrodinger Equation with the use of the logarithmic potential of electron-electron interactions. Ground state energy levels as function of the magnetic field frequency is obtained.
EPJ Web of Conferences, 2014
EPJ Web of Conferences, 2014
The effect of Collaborative Project Based Learning (CPBL) on student performance and motivation i... more The effect of Collaborative Project Based Learning (CPBL) on student performance and motivation in undergraduate mathematical modeling classes is investigated. The inquiry based collaborative learning strategies that incorporate The American Museum of Natural History as a Learning Laboratory and the STELLA Systems Thinking software are introduced.
The Parentage Scheme of Summarization to the N-body symmetrized basis construction [1], necessary... more The Parentage Scheme of Summarization to the N-body symmetrized basis
construction [1], necessary for the description of the structural characteristics and decay
reactions of the hypernuclear and nuclear systems with arbitrary amount of particles, is
applied to the solution of five-body problem in hypernuclear physics. Hypernucleus
as a system of four nucleons and one hyperon is investigated by the use of the
Hyperspherical Function Method in momentum space. The dependence of the structure
characteristics and wave functions on the types of nucleon-nucleon and hyperon-nucleon
interaction potentials is studied. Mean square − and − distances and the
binding energies for the
and
are obtained.
Success and failure in math and science performance are greatly determined by students’ attitudes... more Success and failure in math and science performance are greatly determined by students’
attitudes towards the subject matter. A multidimensional survey, including motivation,
usefulness, self-confidence, and enjoyment subscales was developed and administered in two
New York City Private High schools. Student attitudes were examined and compared by sex,
age, and number of mathematics and science courses taken. Majority of study participants
regardless of their age, sex, and level of coursework found mathematics and science courses
challenging and not enjoyable. Few students demonstrated understanding of the benefits of
acquiring mathematical and scientific skills and expressed desire to pursue careers in science,
mathematics, and related fields. The Spearman's rank-order correlation coefficient was
calculated to identify the strength and direction of relationship between student attitudes toward
science and mathematics and possible career choices in these fields. Chi-Square and Kruskal-
Wallis nonparametric tests were performed to compare student attitudes by gender, age, and
number of math and science courses taken.