Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.We give the proofs of the existence and regularity of the solutions in the space C^∞ (t > 0;H^(s+2) (R^n)) ∩ C^0(t ≧ 0;H^s(R^n)); s ∊ R, for the 1-term, 2-term,..., n-term time-fractional equation evaluated from the time fractional equation of distributed order with spatial Laplace operator Δx ..

Spline collocation method for singular perturbation problem

We introduce piecewise interpolating polynomials as an approximation for the driving terms in the numerical solution of the singularly perturbed differential equation. In this way we obtain the difference scheme which is second order accurate in uniform norm. We verify the convergence rate of presented scheme by numerical experiments

A uniformly accurate finite elements method for singular perturbation problems

We consider piecewise polynomial finite elements method for a singular perturbation problem. The finite elements method of Griffiths for a problem with non-constant coefficients was adapted by introducing piecewise polynomial approximation. We generate the tridiagonal difference schemes which are second order accurate in uniform norm

The two forms of fractional relaxation of distributed order

The first-order differential equation of exponential relaxation can be generalized by using either the fractional derivative in the Riemann-Liouville (R-L) sense and in the Caputo (C) sense, both of a single order less than 1. The two forms turn out to be equivalent. When, however we use fractional derivatives of distributed order (between zero and 1), the equivalence is lost, in particular on the asymptotic behaviour of the fundamental solution at small and large times. We give an outline of the theory providing the general form of the solution in terms of an integral of Laplace type over a positive measure depending on the order-distribution. We consider with some detail two cases of fractional relaxation of distributed order: the double-order and the uniformly distributed order discussing the differences between the R-L and C approaches. For all the cases considered we exhibit plots of the solutions for moderate and large times.Comment: 18 pages, 4 figures. International Symposium on Mathematical Methods in Engineering, (MME06), Ankara, Turkey, April 27-29, 200

Quasiasymptotic analysis in Colombeau algebra

AbstractWe consider the main notions of G-quasiasymptotic (G-q.a.) analysis: G-q.a. behavior at zero, G-q.a. expansion at infinity, Sc-asymptotic and boundedness, Sc-expansion at infinity and their applications to the asymptotic behavior of the solution to some types of nonlinear PDEs in Colombeau algebra of generalized functions G

A Centralized Model for Establishing End-to-End Communication Services via Management Agents

This paper presents a centralized approach for establishing end-to-end communication services via management agents. The main proposal is the modular architecture of the third-party based Service Establishment Agent (SEA). The SEA manages inter-provider service negotiation process with per-domain management agents through an appropriate signaling agent. It also receives and interprets end-toend service requests, selects inter-domain paths, performs mapping of service classes among domains on the path, and evaluates conformance of the offered service level with the required one. It allows implementation of different algorithms for the aforementioned functions as well as their selection and combination according to the predefined management policies. Simulation results show that the proposed model significantly outperforms the distributed model in terms of service negotiation times. In the prototype development process, a policy-based solution for mapping of service classes was implemented. The performance evaluation shows that processing requirements for handling multiple service requests are modest, while benefit of the SEA approach is the lack of need to build long-term consensus among providers about technical choices for achieving network interconnection. The SEA architecture is completely independent of the quality of service mechanisms available in particular domains.</p

Spline collocation method for singular perturbation problem

We introduce piecewise interpolating polynomials as an approximation for the driving terms in the numerical solution of the singularly perturbed differential equation. In this way we obtain the difference scheme which is second order accurate in uniform norm. We verify the convergence rate of presented scheme by numerical experiments

Sastav i antimikrobna aktivnost etarskih ulja Salvia fruticosa i Salvia ringens (Lamiaceae)

Background/Aim. Plant essential oils (EOs) can have a significant antibacterial effect especially through additive or synergistic action as antibiotic adjuvants. We investi-gated the composition and activity of EOs of two species of genus Salvia (S) from Greece with the aim to deter-mine their antimicrobial activity as well as the activity in combination with selected antibiotics. Methods. The aerial parts of wild-growing S. fruticosa and S. ringens were subjected to a steam distillation and the obtained EOs were analyzed by gas chromatography and gas chroma-tography/mass spectrometry. The broth-microdilution method was used in order to determine the minimum in-hibitory concentrations (MICs) of EOs on seven strains of bacteria and one yeast. Antimicrobial activity of the combination of EO and antibiotics was investigated by checkerboard method and estimated by calculating frac-tional inhibitory concentration (FIC) of each component and fractional inhibitory concentration index (FICI). Re-sults. Dominant component of S. fruticosa EO was trans-thujone (54.2%) and for S. ringens EO it was α-pinene (28.1%). The MICs of EOs of both species were in the range from 200 μg/mL to > 500 μg/mL. The strongest antimicrobial effect was achieved against Bacillus subtilis and Candida albicans. According to FICI values, EO of S. fruticosa had additive effect with ciprofloxacin against most of bacterial strains but not with amikacin. Conclu-sion. The essential oils of S. ringens and S. fruticosa showed modest antimicrobial activity. However, the es-sential oil of S. fruticosa showed a promising additive ef-fect in combination with ciprofloxacin.Uvod/Cilj. Etarska ulja različitih biljaka mogu imati značajna antibakterijska svojstva, posebno kao adjuvanti antibiotika sa kojima ostvaruju aditivno ili sinergistično dejstvo. Ispitivali smo sastav i aktivnost etarskih ulja dve vrste roda Salvia (S) iz Grčke sa ciljem da odredimo njihovu antimkrobnu aktivnost, kao i dejstvo u kombi-naciji sa odabranim antibioticima. Metode. Nadzemni delovi samoniklih S. fruticosa i S. ringens su destilovani vodenom parom i dobijena etarska ulja su analizirana gasnom hromatografijom i gasnom hromatografijom sa masenom spektrometrijom. Radi određivanja minimalnih inhibitornih koncentracija (MICs) etarskog ulja na sedam sojeva bakterija i na jednoj patogenoj gljivici korišćena je mikrodiluciona metoda. Antimikrobna aktivnost kombi-nacije etarskog ulja i antibiotika ispitana je checkerboard metodom i procenjena je na osnovu frakcione inhibi-torne koncentracije (FIC) svake komponente i indeksa frakcione inhibitorne koncentracije (FICI). Resultati. Dominantna komponenta etarskog ulja S. fruticosa je bio trans-tujon (54,2%), a etarskog ulja S. ringens α-pinen (28,1%). MICs etarskog ulja obe vrste su bile u opsegu od 200 μg/mL do > 500 μg/mL. Najsnažnija anti-mikrobna aktivnost ostvarena je protiv Bacillus subtilis i Candida albicans. Na osnovu FICI vrednosti, etarsko ulje S. fruticosa je sa ciprofloksacinom, ali ne i sa amikacinom imalo aditivni efekat protiv većine bakterijskih sojeva. Zaključak. Etarska ulja S. ringens i S. fruticosa su pokazala skromnu antimikrobnu aktivnost, ali je etarsko ulje S. fru-ticosa u kombinaciji sa ciprofloksacinom ispoljilo značajan aditivni efekat

Work on the digitization of The legacy of Desanka Maksimović

U ovom članku biće reči o radu na digitalizaciji legata Desanke Maksimović, načinu prezentovanja digitalizovane građe, kao i prepisci između Desanke Maksimović i Izeta Sarajlića.In this article there will be talk about the work on the digitization of the legacy of Desanka Maksimović, the way of presenting digitalized material, as well as the correspondence between Desanka Maksimović and Izet Sarajlić