An analytical solution to the optimal power flow

This letter presents an approach for a geometrical solution of an optimal power flow (OPF) problem for a two-bus system (slack and PV busses). The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

WZW-like action for heterotic string field theory

We complete the construction of the Neveu-Schwarz sector of heterotic string field theory begun in [9] by giving a closed-form expression for the action and gauge transformations. Just as the Wess-Zumino-Witten (WZW) action for open superstring field theory can be constructed from pure-gauge fields in bosonic open string field theory, our heterotic string field theory action is constructed from pure-gauge fields in bosonic closed string field theory. The construction involves a simple alternative form of the WZW action which is consistent with the algebraic structures of closed string field theory. © SISSA/ISAS 2004.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via, the employment of an algebraic condition n·A = 0 in the Lagrangian density, where Aμ is the gauge field (Abelian or non-Abelian) and nμ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition (n·A) (∂·A) = 0 with n·A = 0 = ∂·A. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous nonlocal singularities of the type (k·n)-α where α = 1, 2. These singularities must be conveniently treated, and by convenient we mean not only mathemathically well-defined but physically sound and meaningful as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.

Geração de modelos digitais de superfície por meio de plataformas computacionais com estrutura vetorial e raster

Geographic Information Systems (GIS) integrate the technologies related to Geoprocessing, with the ability to manipulate georeferenced information through data storage, management and analysis. One of the GIS applications is the generation of Digital Elevation Models (DEM) as a result of rebuilding the elevation of a region using computation tools and artificial representation. This paper presents the DEM created from a point base in two computational frameworks with different structures (vector and raster), comparing the contour lines generated from these models with the original contour lines from analog cartographic base. It was observed that one of the generated models presented some discrepancies related to real space for both GIS structures. However, using constrained Delaunay's triangulation in raster GIS a digital elevation model was generated with contour lines quite close to the original ones, with satisfactory results. A 3-D terrain representation was also created offering a very useful tool for analysis.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Evaluating residues and integrals through negative dimensional integration method (NDIM)

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

Fontes de distorções da rede geodésica Brasileira

The Brazilian Geodetic Network started to be established in the early 40's, employing classical surveying methods, such as triangulation and trilateration. With the introduction of satellite positioning systems, such as TRANSIT and GPS, that network was densified. That data was adjusted by employing a variety of methods, yielding distortions in the network that need to be understood. In this work, we analyze and interpret study cases in an attempt to understand the distortions in the Brazilian network. For each case, we performed the network adjustment employing the GHOST software suite. The results show that the distortion is least sensitive to the removal of invar baselines in the classical network. The network would be more affected by the inexistence of Laplace stations and Doppler control points, with differences up to 4.5 m.

A 2-D delaunay refinement algorithm using an initial prerefinement from the boundary mesh

An improvement to the quality bidimensional Delaunay mesh generation algorithm, which combines the mesh refinement algorithms strategy of Ruppert and Shewchuk is proposed in this research. The developed technique uses diametral lenses criterion, introduced by L. P. Chew, with the purpose of eliminating the extremely obtuse triangles in the boundary mesh. This method splits the boundary segment and obtains an initial prerefinement, and thus reducing the number of necessary iterations to generate a high quality sequential triangulation. Moreover, it decreases the intensity of the communication and synchronization between subdomains in parallel mesh refinement. © 2008 IEEE.

Potential scenarios for Internet use in the mathematics classroom

Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation of tools. This kind of research led to the theoretical perspective presented in this paper: knowledge is constructed by collectives of humans-with-media. In this paper, I will discuss how media have shaped the notions of problem and knowledge, and a parallel will be developed between the way that software has brought new possibilities to mathematics education and the changes that the Internet may bring to mathematics education. This paper is, therefore, a discussion about the future of mathematics education. Potential scenarios for the future of mathematics education, if the Internet becomes accepted in the classroom, will be discussed. © FIZ Karlsruhe 2009.

Optimal clone identifier based on dynamic rules and process algebra

The rule creation to clone selection in different projects is a hard task to perform by using traditional implementations to control all the processes of the system. The use of an algebraic language is an alternative approach to manage all of system flow in a flexible way. In order to increase the power of versatility and consistency in defining the rules for optimal clone selection, this paper presents the software OCI 2 in which uses process algebra in the flow behavior of the system. OCI 2, controlled by an algebraic approach was applied in the rules elaboration for clone selection containing unique genes in the partial genome of the bacterium Bradyrhizobium elkanii Semia 587 and in the whole genome of the bacterium Xanthomonas axonopodis pv. citri. Copyright© (2009) by the International Society for Research in Science and Technology.

SIG - SPRING aplicado na determinação da capacidade de uso das terras da microbacia do Ribeirão Pouso Alegre - Jaú (SP)

A população mundial vem sofrendo, cada vez mais, as conseqüências das agressões efetuadas pelo homem ao meio ambiente, principalmente quanto à ocupação e uso inadequado das terras, o que ocasiona empobrecimento e depauperamento do solo, influenciando na qualidade e disponibilidade de água, levando à destruição das reservas florestais. Assim, é necessária a implantação de políticas públicas, que contemplem o desenvolvimento econômico, urbano, rural e social de uma região, preservando os recursos naturais para futuras gerações. A bacia em estudo está localizada entre as coordenadas UTM 764942; 7546214 e 741816; 7534759, com uma área de 14699,7ha. Este trabalho visou definir as classes de capacidade de uso de terra da microbacia do Ribeirão Pouso Alegre - Jaú (SP) através do Sistema de Informações Geográficas - SPRING. A carta de capacidade de uso da terra foi elaborada a partir do cruzamento das cartas clinográfica e de solo, que foram elaboradas pelo SIG Spring, e o cruzamento de dados foi feito através do LEGAL - Linguagem Espacial para Geoprocessamento Algébrico. Os resultados mostraram que a microbacia é constituída essencialmente pelas classes II e III e o SIG-SPRING permitiu através dos seus módulos discriminarem e quantificar as áreas das classes de terras, declive e capacidade de uso da terra rapidamente.

Variabilidade espacial de atributos químicos do solo cultivado com café arábica (Coffea arabica L.) sob diferentes manejos

The objective of this work was to assess the spatial variability of the chemical attributes of two coffee areas, managed in conventional and organic crop systems, and to calculate the percent of variation between them. In each area, a 40-point-mesh was sampled at 0-0.10 m and 0.10-0.20 m layers, within the crown projection, for pH, SB, K, P, Ca and Mg analysis. The data were analyzed through descriptive statistics and geostatistics. From the soil chemical attributes map, the percent of variation between the systems' chemical attributes was determined by GIS algebraic operations. The results show that the soil chemical attributes present a spatial dependence in both systems and layers. Analysis of the soil chemical attributes showed less spatial variability in the organic system, in relation to the conventional, indicating homogeneous zones for different fertilizer applications. The percent of variation of the chemical attributes in the conventional system, in relation to the organic, at 0-0.10 m and 0.10-0.20m layers are 54.80% and 35.61%, respectively.