On the evaluation of the U(3) content of the matrix elements of one- and two-body operators

An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott's basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding Founding errors in the computer codes. The role of dual bases in dealing with nonorthogonal bases is also clarified. © 1992 American Institute of Physics.

O jogo de escopa adaptado para o uso em sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Statistical detection of spurious variations in daily raingauge data caused by changes in observation practices, as applied to records from various parts of the world

In the instrumental records of daily precipitation, we often encounter one or more periods in which values below some threshold were not registered. Such periods, besides lacking small values, also have a large number of dry days. Their cumulative distribution function is shifted to the right in relation to that for other portions of the record having more reliable observations. Such problems are examined in this work, based mostly on the two-sample Kolmogorov–Smirnov (KS) test, where the portion of the series with more number of dry days is compared with the portion with less number of dry days. Another relatively common problem in daily rainfall data is the prevalence of integers either throughout the period of record or in some part of it, likely resulting from truncation during data compilation prior to archiving or by coarse rounding of daily readings by observers. This problem is identified by simple calculation of the proportion of integers in the series, taking the expected proportion as 10%. The above two procedures were applied to the daily rainfall data sets from the European Climate Assessment (ECA), Southeast Asian Climate Assessment (SACA), and Brazilian Water Resources Agency (BRA). Taking the statistic D of the KS test >0.15 and the corresponding p-value <0.001 as the condition to classify a given series as suspicious, the proportions of the ECA, SACA, and BRA series falling into this category are, respectively, 34.5%, 54.3%, and 62.5%. With relation to coarse rounding problem, the proportions of series exceeding twice the 10% reference level are 3%, 60%, and 43% for the ECA, SACA, and BRA data sets, respectively. A simple way to visualize the two problems addressed here is by plotting the time series of daily rainfall for a limited range, for instance, 0–10 mm day−1.

Formalização do conjunto dos números racionais e alguns jogos com frações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lodo de esgoto compostado na produção de tapetes de grama esmeralda e na manutenção de água no solo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ensino e aprendizagem de matemática: o uso de recursos manipulativos em sala de aula

In this work, we understand the importance of the use of manipulative resources for learning mathematics. For both we developed a qualitative phenomenological approach. Performing a case study with nine 7th grade students of the Elementary School, we used the abacus of the integers to examine in what way the use of Abacus contributes to students learning. The choice of material was made according to the focus of research, understanding the signs rule. In the analysis and interpretation of data, highlight lines of students, subject of the research, units of meaning that allow us to say that the material using awakened interest in students Who actively participated in the research and enabled them to understand the rule of signs, to operate with integers enabled them to understand the rule of signs, to operate with integers

Ensino e aprendizagem de matemática: o uso de recursos manipulativos em sala de aula

In this work, we understand the importance of the use of manipulative resources for learning mathematics. For both we developed a qualitative phenomenological approach. Performing a case study with nine 7th grade students of the Elementary School, we used the abacus of the integers to examine in what way the use of Abacus contributes to students learning. The choice of material was made according to the focus of research, understanding the signs rule. In the analysis and interpretation of data, highlight lines of students, subject of the research, units of meaning that allow us to say that the material using awakened interest in students Who actively participated in the research and enabled them to understand the rule of signs, to operate with integers enabled them to understand the rule of signs, to operate with integers

Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Gleichmäßig dünne Basen zweiter Ordnung

Eine Menge B nicht negativer ganzer Zahlen heißt Basis h-ter Ordnung, wenn jede nicht negative ganze Zahl Summe von höchstens h Elementen von B ist. Eine der großen Fragen der additiven Zahlentheorie ist die nach der effektivsten Basis h-ter Ordnung für ein gegebenes h>=2. Im Fokus des Interesses steht dabei der immer noch offene Fall h=2. Bezeichnet B(x) die Anzahl der Elemente b aus B mit 0= af(x), wobei f die Wurzelfunktion bezeichne. Andererseits gibt es Basen B zweiter Ordnung mit B(x) <= cf(x). Daher kann man den Limes superior S(B), den Limes inferior s(B) sowie im Falle der Existenz den Limes d(B) des Quotienten B(x) / f(x) als Dichtefunktionen von Basen zweiter Ordnung betrachten. J. W. S. Cassels konstruierte 1957 eine Basis C zweiter Ordnung mit d(C)=5,196…. G. Hofmeister gab 2001 eine Basis H zweiter Ordnung mit asymptotischer Wurzeldichte d(H)=4,638… an. In der vorliegenden Arbeit wird eine Basis S zweiter Ordnung mit asymptotischer Wurzeldichte d(S)=3,464… konstruiert. Darüber hinaus wird für die von J. W. S. Cassels, für die von G. Hofmeister und für die in dieser Arbeit verwendete Klasse von Basen zweiter Ordnung gezeigt, dass die asymptotische Wurzeldichte innerhalb der jeweiligen Klasse nicht mehr zu verbessern ist. Bisher war die Frage nach möglichen Verbesserungen innerhalb der jeweiligen Konstruktionsprinzipien offen geblieben.

q-Hook length formulas for colored labeled forests

The major index has been deeply studied from the early 1900s and recently has been generalized in different directions, such as the case of labeled forests and colored permutations. In this thesis we define new types of labelings for forests in which the labels are colored integers. We extend the definition of the flag-major index for these labelings and we present an analogue of well known major index hook length formulas. Finally, this study (which has just apparently a simple combinatoric nature) allows us to show a notion of duality for two particular families of groups obtained from the product G(r,n)×G(r,m).

Parallel algorithm for solving integer linear programs

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for solving ILPs. We discuss a serial algorithm using a breadth-first branch-and-bound search to check the feasible solution space, and then extend it into a parallel algorithm using a client-server model. In the parallel mode, the search may not be truly breadth-first, depending on the solution time for each node in the solution tree. Our search takes advantage of pruning, often resulting in super-linear improvements in solution time. Finally, we present results from sample ILPs, describe a few modifications to enhance the algorithm and improve solution time, and offer suggestions for future work.

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Phase transition in the countdown problem

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.