Correction: Pareto Optimization or Cascaded Weighted Sum:  A Comparison of Concepts. Algorithms 2014, 7, 166–185

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.

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Evaluation of Different Weighted-Sum-of-Gray-Gases Formulations to Estimate the Planck-Mean Absorption Coefficient for CO2-H2O Mixtures

10.26678/abcm.cobem2019.cob2019-1297 ◽

2019 ◽

Author(s):

Guilherme Fraga ◽

Francis França ◽

Pedro Coelho

Keyword(s):

Absorption Coefficient ◽

Weighted Sum

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COMPUTATION OF A LAMINAR DIFFUSION ETHYLENE/AIR FLAME CONSIDERING SOOT FORMATION AND THE WEIGHTED-SUM-OF-GRAY-GASES MODEL

10.26678/abcm.encit2018.cit18-0250 ◽

2018 ◽

Author(s):

Luís Gustavo Pires Rodrigues ◽

Francis França ◽

Fernando Pereira ◽

PAULO PAGOT

Keyword(s):

Soot Formation ◽

Weighted Sum ◽

Laminar Diffusion

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Penerapan Weighted Sum Model (WSM) Dalam Penentuan Peserta Jaminan Kesehatan Masyarakat

Jurasik (Jurnal Riset Sistem Informasi dan Teknik Informatika) ◽

10.30645/jurasik.v2i1.17 ◽

2017 ◽

Vol 2 (1) ◽

pp. 40

Author(s):

Mesran Mesran ◽

Suginam Suginam ◽

Surya Darma Nasution ◽

Andsyah Putera Utama Siahaan

Keyword(s):

Low Income ◽

Poverty Line ◽

Weighted Sum ◽

Government Programs ◽

Head Of Household ◽

Treatment Services ◽

The People ◽

Community Health Insurance ◽

The Government ◽

Simple Additive Weighting

Community Health Insurance is one of the government programs for the people of Indonesia in obtaining treatment services at Puskesmas. The program is very helpful for people who are low income and live below the poverty line. Indicators for the government in providing this service consists of 10 (ten) criteria that are House Ownership Status, Floor Area per Household Member, Type of Floor of House, Type of Wall House, Lighting House Used, Fuel Used, Frequency Of Eating In A Day, Ability Buy meat/chicken/milk in a week, Employment of head of household, Education of head of household. In the application, of course, has constraints in deciding who the participants who get the Jamkesmas service. With the application of one of Multi-Criteria Decision Making (MCDM) able to overcome obstacles faced by government. Some methods of MCDM such as Simple Additive Weighting(SAW), Weighted Product(WP), Weighted Sum Model(WSM) can solve this problem. By applying the WSM is relatively easy and fast, is believed to be able to get the best results.

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