1,440 research outputs found
A study of adult education in the Jewish Community centers of Greater Boston
Thesis (M.S.)--Boston Universit
Quaternionic differential operators
Motivated by a quaternionic formulation of quantum mechanics, we discuss
quaternionic and complex linear differential equations. We touch only a few
aspects of the mathematical theory, namely the resolution of the second order
differential equations with constant coefficients. We overcome the problems
coming out from the loss of the fundamental theorem of the algebra for
quaternions and propose a practical method to solve quaternionic and complex
linear second order differential equations with constant coefficients. The
resolution of the complex linear Schrodinger equation, in presence of
quaternionic potentials, represents an interesting application of the
mathematical material discussed in this paper.Comment: 25 pages, AMS-Te
Reviving the Victory Garden: The Military Benefits of Sustainable Farming
The article of record as published may be found at https://warontherocks.com/2022/01/reviving-the-victory-garden-the-military-benefits-of-sustainable-farming
Delay Time in Quaternionic Quantum Mechanics
In looking for quaternionic violations of quantum mechanics, we discuss the
delay time for pure quaternionic potentials. The study shows in which energy
region it is possible to amplify the difference between quaternionic and
complex quantum mechanics.Comment: 9 pages, 5 figure
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena
We introduce an approximation scheme to perform an analytic study of the
oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian
wave packets, we show that the oscillation is bounded by a time-dependent
vanishing function which characterizes the slippage between the mass-eigenstate
wave packets. We also demonstrate that the wave packet spreading represents a
secondary effect which plays a significant role only in the non-relativistic
limit. In our analysis, we note the presence of a new time-dependent phase and
calculate how this additional term modifies the oscillating character of the
flavor conversion formula. Finally, by considering Box and Sine wave packets we
study how the choice of different functions to describe the particle
localization changes the oscillation probability.Comment: 16 pages, 7 figures, AMS-Te
Potential Scattering in Dirac Field Theory
We develop the potential scattering of a spinor within the context of
perturbation field theory. As an application, we reproduce, up to second order
in the potential, the diffusion results for a potential barrier of quantum
mechanics. An immediate consequence is a simple generalization to arbitrary
potential forms, a feature not possible in quantum mechanics.Comment: 7 page
Self-consistent field predictions for quenched spherical biocompatible triblock copolymer micelles
We have used the Scheutjens-Fleer self-consistent field (SF-SCF) method to
predict the self-assembly of triblock copolymers with a solvophilic middle
block and sufficiently long solvophobic outer blocks. We model copolymers
consisting of polyethylene oxide (PEO) as solvophilic block and
poly(lactic-co-glycolic) acid (PLGA) or poly({\ko}-caprolactone) (PCL) as
solvophobic block. These copolymers form structurally quenched spherical
micelles provided the solvophilic block is long enough. Predictions are
calibrated on experimental data for micelles composed of PCL-PEO-PCL and
PLGA-PEO-PLGA triblock copolymers prepared via the nanoprecipitation method. We
establish effective interaction parameters that enable us to predict various
micelle properties such as the hydrodynamic size, the aggregation number and
the loading capacity of the micelles for hydrophobic species that are
consistent with experimental finding.Comment: accepted for publication in Soft Matte
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