Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding

Dental Treatment Approach in Cantho University of Medicine and Pharmacy of Vietnam

The traditional morphological concept to dental care has shown many drawbacks and is not appropriate in many cases. To counteract these shortcomings, a problem-solving approach has been introduced in dental curriculum of Cantho University of Medicine and Pharmacy (CTUMP), Vietnam. This approach should be reflected in dental practice in CTUMP. Objective: To investigate the problem-solving approach to dental care of CTUMP by patterns of tooth extraction, and tooth rehabilitation. Methods: Cross-sectional data on DMF, dental treatments planned, dental treatments delivered from 1549 dental records of patients aged ≥18 of CTUMP were analyzed. Results: The majority of patients were aged 18-29 (929, 60%), classified as professional and skilled workers (1112 subjects, 72%), lived in urban areas (1156 subjects, 75%), and women (932, 60%). The number of teeth eventually receiving dental treatment was lower than the number of teeth indicated for the treatment. On average, each patient had 2 teeth receiving treatment. Tooth restoration was the most common treatment (1390, 70%). Molars were the most treated teeth (842, 43%). Molars showed statistically significant higher chance for restoration and extraction than premolars and anterior teeth (Wilcoxon-signed-ranks test p ≤ 0.017). No statistically significance was found in tooth replacement between premolar and molar regions. The dental treatments aimed to preserve all teeth regardless of dental regions. Tooth replacement may tend to be morphologically based rather than functionally as most prostheses restored the complete dental arch. Conclusions: The approach to dental care in CTUMP tends to be morphologically conservative.DOI: 10.14693/jdi.v22i1.37

On the reduced density matrix for a chain of free electrons

The properties of the reduced density matrix describing an interval of N sites in an infinite chain of free electrons are investigated. A commuting operator is found for arbitrary filling and also for open chains. For a half filled periodic chain it is used to determine the eigenfunctions for the dominant eigenvalues analytically in the continuum limit. Relations to the critical six-vertex model are discussed.Comment: 8 pages, small changes, Equ.(24) corrected, final versio

Some theoretical results on semiconductor spherical quantum dots

We use an improved version of the standard effective mass approximation model to describe quantum effects in nanometric semiconductor Quantum Dots (QDs). This allows analytic computation of relevant quantities to a very large extent. We obtain, as a function of the QD radius, in precise domains of validity, the QD excitonic ground state energy and its Stark and Lamb shifts. Finally, the Purcell effect in QDs is shown to lead to potential QD-LASER emitting in the range of visible light

Kosterlitz-Thouless transition in three-state mixed Potts ferro-antiferromagnets

We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix are used, on infinite strips of width $L$ sites, $4 \leq L \leq 14$. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz-Thouless) phase is present, whose upper limit is, in our best estimate, $T_c=0.29 \pm 0.01$. From analysis of the (extremely anisotropic) nature of excitations below $T_c$, we argue that the critical phase extends all the way down to T=0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for $T>T_c$, as $\xi (T) =a_\xi \exp [ b_\xi (T-T_c)^{-\sigma}]$, $\sigma \simeq 1/2$, we attempt finite-size scaling plots of our finite-width correlation lengths. Our best results are for $T_c=0.50 \pm 0.01$. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.Comment: 11 pages, 6 .eps figures, LaTeX with IoP macros, to be published in J Phys

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure