References of "Mathonet, Pierre"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 8 of 8 1 Reducibility of n-ary semigroups: from quasitriviality towards idempotencyCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc et alin Beiträge zur Algebra und Geometrie (in press)Let $X$ be a nonempty set. Denote by $\mathcal{F}^n_k$ the class of associative operations $F\colon X^n\to X$ satisfying the condition $F(x_1,\ldots,x_n)\in\{x_1,\ldots,x_n\}$ whenever at least $k$ of the ... [more ▼]Let $X$ be a nonempty set. Denote by $\mathcal{F}^n_k$ the class of associative operations $F\colon X^n\to X$ satisfying the condition $F(x_1,\ldots,x_n)\in\{x_1,\ldots,x_n\}$ whenever at least $k$ of the elements $x_1,\ldots,x_n$ are equal to each other. The elements of $\mathcal{F}^n_1$ are said to be quasitrivial and those of $\mathcal{F}^n_n$ are said to be idempotent. We show that $\mathcal{F}^n_1=\cdots =\mathcal{F}^n_{n-2}\subseteq\mathcal{F}^n_{n-1}\subseteq\mathcal{F}^n_n$ and we give conditions on the set $X$ for the last inclusions to be strict. The class $\mathcal{F}^n_1$ was recently characterized by Couceiro and Devillet \cite{CouDev}, who showed that its elements are reducible to binary associative operations. However, some elements of $\mathcal{F}^n_n$ are not reducible. In this paper, we characterize the class $\mathcal{F}^n_{n-1}\setminus\mathcal{F}^n_1$ and show that its elements are reducible. We give a full description of the corresponding reductions and show how each of them is built from a quasitrivial semigroup and an Abelian group whose exponent divides $n-1$. [less ▲]Detailed reference viewed: 142 (20 UL) Decomposition schemes for symmetric n-ary bandsDevillet, Jimmy ; Mathonet, PierreScientific Conference (2020, August 27)We extend the classical (strong) semilattice decomposition scheme of certain classes of semigroups to the class of idempotent symmetric n-ary semigroups (i.e. symmetric n-ary bands) where n \geq 2 is an ... [more ▼]We extend the classical (strong) semilattice decomposition scheme of certain classes of semigroups to the class of idempotent symmetric n-ary semigroups (i.e. symmetric n-ary bands) where n \geq 2 is an integer. More precisely, we show that these semigroups are exactly the strong n-ary semilattices of n-ary extensions of Abelian groups whose exponents divide n-1. We then use this main result to obtain necessary and sufficient conditions for a symmetric n-ary band to be reducible to a semigroup. [less ▲]Detailed reference viewed: 74 (2 UL) On the structure of symmetric $n$-ary bandsDevillet, Jimmy ; Mathonet, PierreE-print/Working paper (2020)We study the class of symmetric $n$-ary bands. These are $n$-ary semigroups $(X,F)$ such that $F$ is invariant under the action of permutations and idempotent, i.e., satisfies $F(x,\ldots,x)=x$ for all $x ... [more ▼]We study the class of symmetric$n$-ary bands. These are$n$-ary semigroups$(X,F)$such that$F$is invariant under the action of permutations and idempotent, i.e., satisfies$F(x,\ldots,x)=x$for all$x\in X$. We first provide a structure theorem for these symmetric$n$-ary bands that extends the classical (strong) semilattice decomposition of certain classes of bands. We introduce the concept of strong$n$-ary semilattice of$n$-ary semigroups and we show that the symmetric$n$-ary bands are exactly the strong$n$-ary semilattices of$n$-ary extensions of Abelian groups whose exponents divide$n-1$. Finally, we use the structure theorem to obtain necessary and sufficient conditions for a symmetric$n$-ary band to be reducible to a semigroup. [less ▲]Detailed reference viewed: 48 (5 UL) Joint signature of two or more systems with applications to multistate systems made up of two-state componentsMarichal, Jean-Luc ; Mathonet, Pierre; Navarro, Jorge et alin European Journal of Operational Research (2017), 263(2), 559-570The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the ... [more ▼]The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the k-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order n whose (k,l)-entry is the probability that the k-th failure causes the first system to fail and the l-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In the first part of this paper we provide an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. We also provide and discuss a necessary and sufficient condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. In the second part of this paper we show how our results can be efficiently applied to the investigation of the reliability and signature of multistate systems made up of two-state components. The key observation is that the structure function of such a multistate system can always be additively decomposed into a sum of classical structure functions. Considering a multistate system then reduces to considering simultaneously several two-state systems. [less ▲]Detailed reference viewed: 183 (20 UL) A classification of polynomial functions satisfying the Jacobi identity over integral domainsMarichal, Jean-Luc ; Mathonet, Pierrein Aequationes Mathematicae (2017), 91(4), 601-618The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of ... [more ▼]The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that satisfy the Jacobi identity over infinite integral domains. Although this description depends on the characteristic of the domain, it turns out that all these polynomials are of degree at most one in each indeterminate. [less ▲]Detailed reference viewed: 181 (13 UL) Probability signatures of multistate systems made up of two-state componentsMarichal, Jean-Luc ; Mathonet, Pierre; Jorge, Navarro et alScientific Conference (2017, July)The structure signature of a system made up of$n$components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the$n$-tuple whose$k$-th coordinate is the probability ... [more ▼]The structure signature of a system made up of$n$components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the$n$-tuple whose$k$-th coordinate is the probability that the$k$-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order$n$whose$(k,l)$-entry is the probability that the$k$-th failure causes the first system to fail and the$l$-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In this talk we will show an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. Then we will discuss a condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. Finally we will show how these results can be applied to the investigation of the reliability and signature of multistate systems made up of two-state components. [less ▲]Detailed reference viewed: 74 (3 UL) A classification of barycentrically associative polynomial functionsMarichal, Jean-Luc ; Mathonet, Pierre; Tomaschek, Jörgin Aequationes Mathematicae (2015), 89(5), 1281-1291We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.Detailed reference viewed: 157 (17 UL) On modular decompositions of system signaturesMarichal, Jean-Luc ; Mathonet, Pierre; Spizzichino, Fabioin Journal of Multivariate Analysis (2015), 134Considering a semicoherent system made up of$n$components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the$n$-tuple whose$k$-th coordinate is the probability that ... [more ▼]Considering a semicoherent system made up of$n$components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the$n$-tuple whose$k$-th coordinate is the probability that the$k$-th component failure causes the system to fail. This$n$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the$n\$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results. [less ▲]Detailed reference viewed: 141 (10 UL) 1