2. Articole
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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 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, NicolaeItem PROIECTAREA SISTEMULUI EXPERT PENTRU DIAGNOSTICAREA TULBURĂRILOR PSIHICE ŞI DE COMPORTAMENT LA EPILEPSIELEPTICI(CEP USM, 2013-09-26) Popov, AlexandruItem ASUPRA π-T-QUASIGRUPURILOR(CEP USM, 2013-09-26) Ceban, DinaItem JOCURI CELEBRE REPETATE(CEP USM, 2013-09-26) Lozan, VictoriaItem INTERIORUL UNEI ELIPSE DETERMINAT LA COMPUTER(CEP USM, 2013-09-26) Zabolotnîi, Pavel; Solovei, LiliaItem REZOLVAREA PROBLEMELOR DECIZIONALE MONOCRITERIALE ÎN CONDIŢII DE INCERTITUDINE CU AJUTORUL MS EXCEL(CEP USM, 2013-09-26) Beldiga (Vasilache), Maria; Căpăţână, Gheorghe