Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item MACHINE GUESSING, PIGEON SUPERSTITION AND TRUST IN AI(CEP USM, 2020) Alvarado, RamónIn this paper I argue that the predictive prowess of artificial intelligence methods, such as machine learning, is not sufficient as an epistemic warrant for us to allocate trust in them. This is because of two reasons: 1) they are opaque in ways that other methodology is not and 2) they fail in ways that other methodology does not. In order to motivate my analysis, I compare the prowess of some machine learning methodology in image recognition to the ability for pattern identification by some animals, such as pigeons, and suggest that while useful in certain practical circumstances, their success does not constitute the kinds of epistemic warrants that we should aim for in more epistemically demanding contexts such as science, medicine, and/or policy-making.Item MEDITATIONS ABOUT THE MYSTIC OF MATHEMATICAL LANGUAGE(CEP USM, 2020) Pagliacci, Mario G.R.Mathematics is the science of measurement of greatness and form. It is fundamental for trying to understand, describe and explain phenomena, especially when they are chaotic and complex. Mathematical language is not true or false for itself. It is neutral in respect of truth or falsity of the described phenomena. However, it can give a distorted representation of reality when it is utilized in not correct way, by doing conceptual forcing or large approximations. Quantitative language can suggest in inexpert minds that anything is expressed in quantitative statement is more credible than qualitative one. The mystic conception that mathematical language is synonym of truth is confuted.Item ON RECURSIVELY DIFFERENTIABLE QUASIGROUPS(2015) Larionova-Cojocaru, IngaIf ( ),Q ⋅ is a binary groupoid then will denote its recursive derivative of order s by „ s ⋅ ”, hence 0 1 2 1 , , , ( ) ( ), s s s x y x y x y y xy x y x y x y − − ⋅ = ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ ⋅K for every , .x y Q∈ If the recursive derivatives „ s ⋅ ”, s=1,2,…,k, of a binary quasigroup ( ),Q ⋅ are quasigroup operations, then ( ),Q ⋅ is called recursively k- differentiable. The notions of recursive derivatives and recursively differentiable quasigroups raised in the algebraic coding theory [1]. Recursively differentiable binary quasigroups in particular groups, are studied in the present paper. Proposition 1. If a quasigroup ( ),Q ⋅ , with the left unit, is recursively 1- differentiable then the mapping 2 x x→ is a bijection. Proposition 2. A diassociative loop ( ),Q ⋅ is recursively 1-differentiable if and only if the mapping 2 x x→ is a bijection. Corollary 1. A Moufang loop ( ),Q ⋅ , in particular a group, is recursively 1- differentiable if and only if the mapping 2 x x→ is a bijection on Q . Corollary 2. Finite groups of even order are not recursively 1-differentiable.Item SUBGRAFURILE B-STABILE ÎN ORIENTAREA TRANZITIVĂ A GRAFURILOR(2015) Grigoriu, NicolaeSe formulează rezultate noi ce țin de studierea problemei orientării tranzitive a grafurilor neorientate. Amintim că un graf 𝐺𝐺⃗ = 𝑋𝑋; 𝑈𝑈 este tranzitiv orientat dacă pentru oricare trei vârfuri 𝑥𝑥, 𝑦𝑦, 𝑧𝑧 ∈ 𝑋𝑋 este satisfăcută relația de tranzitivitate: [𝑥𝑥, 𝑦𝑦] ∈ 𝑈𝑈 & [𝑦𝑦, 𝑧𝑧] ∈ 𝑈𝑈 ⇒ [𝑥𝑥, 𝑧𝑧] ∈ 𝑈𝑈 [3]. Graful neorientat 𝐺𝐺 = (𝑋𝑋; 𝑈𝑈) este tranzitiv orientabil dacă atribuind o anumită orientare muchiilor sale obținem un graf tranzitiv orientat. Un subgraf determinat de o mulțime de vârfuri 𝐴𝐴, se va numi subgraf stabil dacă pentru orice vârf 𝑥𝑥 ∈ 𝑋𝑋 ∖ 𝐴𝐴 se verifică una din relațiile: [𝑥𝑥, 𝑦𝑦] ∈ 𝑈𝑈𝐺𝐺 sau [𝑦𝑦, 𝑥𝑥] ∉ 𝑈𝑈𝐺𝐺, unde ∀𝑦𝑦 ∈ 𝐴𝐴.[1], [3] Definiția 1.[2] Subgraful stabil 𝐹𝐹 se numește subgraf B-stabil dacă pentru orice subgraf stabil 𝑀𝑀 din 𝐺𝐺 = (𝑋𝑋; 𝑈𝑈) are loc una din relațiile: 𝐹𝐹 ⊆ 𝑀𝑀 ∨ 𝐹𝐹 ∩ 𝑀𝑀 = ∅ Reieșind din definiția subgrafului B-stabil rezultă, că dacă 𝐺𝐺 nu conține subgraf stabil atunci acesta nu conține nici subgraf B-stabil. Lema 1. Dacă graful 𝐺𝐺 conține subgraf stabil, atunci 𝐺𝐺 conține și subgraf B- stabil. Teorema 1. Subgraful 𝐹𝐹 al grafului tranzitiv orientabil 𝐺𝐺 este B-stabil dacă și numai dacă orientarea tranzitivă 𝐹𝐹⃗ se construiește în mod independent de orientarea tranzitivă a întregului graf 𝐺𝐺.Item ON INTELLIGENT SOFTWARE TOOLS IN SOLVING OF INTEGRAL EQUATIONS OF SECOND KIND(2015) Carmocanu, Gheorghe; Căpăţână, Gheorghe; Seiciuc, Eleonora; Seiciuc, VladislavThe Intelligent Support System for approximate solving of the Fredholm and Volterra integral equations of the second kind are developed. Some components for Computing Modules of the Intelligent Support System for solving of regular integral equations of second kind with spline-collocations, splinequadratures and degenerated kernel methods are proposed.Item TEHNOLOGII INFORMAŢIONALE DE COMUNICARE: ÎNDRUMAR PENTRU LUCRĂRI DE LABORATOR(CEP USM, 2020) Calmîş, Elena; Braguţa, Galina; Buzatu, Radu; Leonte, Stanislav; Ţurcanu, CălinSetul de lucrări de laborator acoperă integral competenţele şi obiectivele generale prevăzute în curriculumul disciplinei TIC, elaborat în cadrul Departamentului Matematică, Facultatea de Matematică şi Informatică (USM) şi destinată studenţilor anului I, Ciclul I Licenţă, ai facultăţilor de Drept, Istorie şi Filosofie, Psihologie şi Ştiinţe ale Educaţiei, Litere, precum şi tuturor celor care doresc să se iniţieze în utilizarea TIC.Item NUMERICAL SIMULATION OF NONLINEAR PROCESSES IN SEMICONDUCTOR DEVICES WITH THE APPLICATION OF THE NEWTON’S METHOD FOR LINEARIZATION(2020) Sprincean, GalinaThis article relates to the use of Newton’s method and Scharfetter– Gummel scheme, to linearize and discretize the equations, for numerical modeling of nonlinear processes in semiconductor devices. The mathematical model of the problem represents a system of nonlinear differential equations, in the unknowns ϕ–electrostatic potential, n, p–the concentrations of electrons and holes, respectively. The problem is further complicated by the fact that the boundary conditions are of two types: the Dirichlet conditions and the Neumman conditions, which act on different portions of the boundary. The subproblems that were solved in this paper: linearization of nonlinear differential equations, using Newton’s method; discretization of equations, using Scharfetter–Gummel scheme. The obtained systems have five diagonal and nonsymmetrical matrices. The numerical method of Bi–Conjugate Gradients was used to solve the systems.Item ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF MONOTONE DIFFERENTIAL EQUATIONS WITH A STRICT MONOTONE FIRST INTEGRAL(2020) Ceban, DavidThe paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.Item CONVERGENCE ESTIMATES FOR SOME ABSTRACT LINEAR SECOND ORDER DIFFERENTIAL EQUATIONS WITH TWO SMALL PARAMETERS(IOS Press, 2016) Perjan, Andrei; Rusu, GalinaIn a real Hilbert space H we consider the following singularly perturbed Cauchy problem (Equation presented) where u0, u1 ∈ H, f : [0, T ] → H and ϵ, δ are two small parameters. We study the behavior of the solutions uϵδ to the problem (Pϵδ) in two different cases: (i) when ϵ → 0 and δ ≥ δ0 > 0; (ii) when ϵ → 0 and δ → 0. We obtain a priori estimates of the solutions to the perturbed problem, which are uniform with respect to the parameters, and a relationship between the solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior with respect to the parameters in the neighborhood of t = 0. We describe the boundary layer and the boundary layer function in both cases.Item THE DEVELOPMENT LANGUAGE KNOWLEDGE FOR DEVELOPMENT SPEECH RECOGNITION APPLICATION(CEP USM, 2013-09-26) Objelean, Nicolae