Solution to the Bethe-Faddeev equation within the continuous version of the hole-line expansion

2006 ◽  
Vol 73 (3) ◽  
Author(s):  
R. Sartor
Keyword(s):  
Faddeev Equation ◽  
Continuous Version

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

scholarly journals Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4418
Author(s):  
Alejandra Paz-Rodríguez ◽  
Juan Felipe Castro-Ordoñez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Search Algorithm ◽  
Peak Load ◽  
Distribution Networks ◽  
Energy Losses ◽  
Continuous Version ◽  
Continuous Section ◽  
Daily Energy ◽  
Discrete Part

This paper deals with the optimal siting and sizing problem of photovoltaic (PV) generators in electrical distribution networks considering daily load and generation profiles. It proposes the discrete-continuous version of the vortex search algorithm (DCVSA) to locate and size the PV sources where the discrete part of the codification defines the nodes. Renewable generators are installed in these nodes, and the continuous section determines their optimal sizes. In addition, through the successive approximation power flow method, the objective function of the optimization model is obtained. This objective function is related to the minimization of the daily energy losses. This method allows determining the power losses in each period for each renewable generation input provided by the DCVSA (i.e., location and sizing of the PV sources). Numerical validations in the IEEE 33- and IEEE 69-bus systems demonstrate that: (i) the proposed DCVSA finds the optimal global solution for both test feeders when the location and size of the PV generators are explored, considering the peak load scenario. (ii) In the case of the daily operative scenario, the total reduction of energy losses for both test feeders are 23.3643% and 24.3863%, respectively; and (iii) the DCVSA presents a better numerical performance regarding the objective function value when compared with the BONMIN solver in the GAMS software, which demonstrates the effectiveness and robustness of the proposed master-slave optimization algorithm.

GEOMETRIC ALGORITHMS FOR THE CONSTRAINED 1-D K-MEANS CLUSTERING PROBLEMS AND IMRT APPLICATIONS

2009 ◽  
Vol 20 (02) ◽  
pp. 361-377
Author(s):  
DANNY Z. CHEN ◽  
MARK A. HEALY ◽  
CHAO WANG ◽  
BIN XU
Keyword(s):  
Radiation Therapy ◽  
Treatment Planning ◽  
Intensity Modulated Radiation Therapy ◽  
Geometric Algorithms ◽  
Maximum Difference ◽  
Continuous Version ◽  
Heuristic Approaches ◽  
Clustering Problem ◽  
Intensity Modulated ◽  
Clustering Problems

In this paper, we present efficient geometric algorithms for the discrete constrained 1-D K-means clustering problem and extend our solutions to the continuous version of the problem. One key clustering constraint we consider is that the maximum difference in each cluster cannot be larger than a given threshold. These constrained 1-D K-means clustering problems appear in various applications, especially in intensity-modulated radiation therapy (IMRT). Our algorithms improve the efficiency and accuracy of the heuristic approaches used in clinical IMRT treatment planning.

A Continuous Version of Newton's Method

1997 ◽  
Vol 28 (5) ◽  
pp. 348 ◽  
Author(s):  
Steven M. Hetzler
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Continuous Version

Solution of the relativistic three quark Faddeev equation in the Nambu-Jona-Lasinio (NJL) model

1993 ◽  
Vol 318 (1) ◽  
pp. 26-31 ◽  
Author(s):  
Noriyoshi Ishii ◽  
Wolfgang Bentz ◽  
Koichi Yazaki
Keyword(s):  
Faddeev Equation ◽  
Njl Model

scholarly journals Proton tensor charges from a Poincaré-covariant Faddeev equation

2018 ◽  
Vol 98 (5) ◽  
Author(s):  
Qing-Wu Wang ◽  
Si-Xue Qin ◽  
Craig D. Roberts ◽  
Sebastian M. Schmidt
Keyword(s):  
Faddeev Equation

scholarly journals Specializing Word Embeddings (for Parsing) by Information Bottleneck (Extended Abstract)

2020 ◽  
Author(s):  
Xiang Lisa Li ◽  
Jason Eisner
Keyword(s):  
Dimensionality Reduction ◽  
Semantic Information ◽  
State Of The Art ◽  
Word Embedding ◽  
Discrete Version ◽  
Word Embeddings ◽  
Continuous Version ◽  
Continuous Vector ◽  
Information Bottleneck ◽  
Art Performance

Pre-trained word embeddings like ELMo and BERT contain rich syntactic and semantic information, resulting in state-of-the-art performance on various tasks. We propose a very fast variational information bottleneck (VIB) method to nonlinearly compress these embeddings, keeping only the information that helps a discriminative parser. We compress each word embedding to either a discrete tag or a continuous vector. In the discrete version, our automatically compressed tags form an alternative tag set: we show experimentally that our tags capture most of the information in traditional POS tag annotations, but our tag sequences can be parsed more accurately at the same level of tag granularity. In the continuous version, we show experimentally that moderately compressing the word embeddings by our method yields a more accurate parser in 8 of 9 languages, unlike simple dimensionality reduction.

scholarly journals A Continuous Analogue of Lattice Path Enumeration

10.37236/8788 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Quang-Nhat Le ◽  
Sinai Robins ◽  
Christophe Vignat ◽  
Tanay Wakhare
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lattice Paths ◽  
Lattice Path ◽  
Continuous Version ◽  
Continuous Analog ◽  
Continuous Analogue ◽  
Lattice Path Enumeration ◽  
Multinomial Coefficients ◽  
General Method

Following the work of Cano and Díaz, we consider a continuous analog of lattice path enumeration. This process allows us to define a continuous version of many discrete objects that count certain types of lattice paths. As an example of this process, we define continuous versions of binomial and multinomial coefficients, and describe some identities and partial differential equations that they satisfy. Finally, as an important byproduct of these continuous analogs, we illustrate a general method to recover discrete combinatorial quantities from their continuous analogs, via an application of the Khovanski-Puklikov discretizing Todd operators.  

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