DECOMPOSITION METHOD IN COMPARISON WITH NUMERICAL SOLUTIONS OF BURGERS EQUATION

This paper presents a solution of the one-dimension Burgers equation using Decomposition Method and compares this solution to the analytic solution [Cole] and solutions obtained with other numerical methods. Even though decomposition method is a non-numerical method, it can be adapted for solving nonlinear differential equations. The advantage of this methodology is that it leads to an analytical continuous approximated solution that is very rapidly convergent [2,7,8]. This method does not take any help of linearization or any other simplifications for handling the non-linear terms. Since the decomposition parameter, in general, is not a perturbation parameter, it follows that the non-linearities in the operator equation can be handled easily, and accurate solution may be obtained for any physical problem

Directed Graphs representing isomorphism classes of C-Hypergroupoids

We investigate the relation of directed graphs and hyperstructures by virtue of the graph hyperoperation. A new class of graphs arises in this way representing isomorphism classes of C-hypergroupoids and we present the 17 such graphs that correspond to the 73 C-hypergroupoids associated with binary relations on three element sets. As it is shown they constitute an upper semilattice with respect tograph inclusion

Fuzzy graphs: Algebraic structure and syntactic recognition

© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved

Global burden of peripheral artery disease and its risk factors, 1990–2019 : a systematic analysis for the Global Burden of Disease Study 2019

peripheral artery disease were modelled using the Global Burden of Disease, Injuries, and Risk Factors Study (GBD) 2019 database. Prevalence, disability-adjusted life years (DALYs), and mortality estimates of peripheral artery disease were extracted from GBD 2019. Total DALYs and age-standardised DALY rate of peripheral artery disease attributed to modifiable risk factors were also assessed. Findings In 2019, the number of people aged 40 years and older with peripheral artery disease was 113 million (95% uncertainty interval [UI] 99·2–128·4), with a global prevalence of 1·52% (95% UI 1·33–1·72), of which 42·6% was in countries with low to middle Socio-demographic Index (SDI). The global prevalence of peripheral artery disease was higher in older people, (14·91% [12·41–17·87] in those aged 80–84 years), and was generally higher in females than in males. Globally, the total number of DALYs attributable to modifiable risk factors in 2019 accounted for 69·4% (64·2–74·3) of total peripheral artery disease DALYs. The prevalence of peripheral artery disease was highest in countries with high SDI and lowest in countries with low SDI, whereas DALY and mortality rates showed U-shaped curves, with the highest burden in the high and low SDI quintiles. Interpretation The total number of people with peripheral artery disease has increased globally from 1990 to 2019. Despite the lower prevalence of peripheral artery disease in males and low-income countries, these groups showed similar DALY rates to females and higher-income countries, highlighting disproportionate burden in these groups. Modifiable risk factors were responsible for around 70% of the global peripheral artery disease burden. Public measures could mitigate the burden of peripheral artery disease by modifying risk factors

DECOMPOSITION METHOD IN COMPARISON WITH NUMERICAL SOLUTIONS OF BURGERS EQUATION

This paper presents a solution of the one-dimension Burgers equation using Decomposition Method and compares this solution to the analytic solution [Cole] and solutions obtained with other numerical methods. Even though decomposition method is a non-numerical method, it can be adapted for solving nonlinear differential equations. The advantage of this methodology is that it leads to an analytical continuous approximated solution that is very rapidly convergent [2,7,8]. This method does not take any help of linearization or any other simplifications for handling the non-linear terms. Since the decomposition parameter, in general, is not a perturbation parameter, it follows that the non-linearities in the operator equation can be handled easily, and accurate solution may be obtained for any physical problem

A Hybrid Soft Computing Approach Producing Robust Forest Fire Risk Indices

Part 4: Environmental AI Modeling (ENAIM)International audienceForest fires are one of the major natural disaster problems of the Mediterranean countries. Their prevention - effective fighting and especially the local prediction of the forest fire risk, requires the rational determination of the related factors and the development of a flexible system incorporating an intelligent inference mechanism. This is an enduring goal of the scientific community. This paper proposes an Intelligent Soft Computing Multivariable Analysis system (ISOCOMA) to determine effective wild fire risk indices. More specifically it involves a Takagi-Sugeno-Kang rule based fuzzy inference approach, that produces partial risk indices (PRI) per factor and per subject category. These PRI are unified by employing fuzzy conjunction T-Norms in order to develop pairs of risk indices (PARI). Through Chi Squared hypothesis testing, plus classification of the PARI and forest fire burned areas (in three classes) it was determined which PARI are closely related to the actual burned areas. Actually we have managed to determine which pairs of risk indices are able to determine the actual burned area for each case under study. Wild fire data related to specific features of each area in Greece were considered. The Soft computing approach proposed herein, was applied for the cases of Chania, and Ilia areas in Southern Greece and for Kefalonia island in the Ionian Sea, for the temporal period 1984–2004