Institute of Mathematics AS CR, v. v. i.
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A generalization of the mean-square derivative for fuzzy stochastic processes and some properties
Get PDFsummary:The purpose of this paper is to generalize and develop a mean-square calculus for fuzzy stochastic processes and study their differentiability and integrability properties. Some results for second-order fuzzy stochastic processes are presented
Up to the Clouds
No full textsummary:Článek se věnuje životním a profesním cestám bratří Wrightových, které ušli bok po boku do okamžiku prvního vzletu jimi zkonstruovaného letadla. V krátkosti shrnuje i jejich následující osudy
Vanishing viscosity of one-dimensional isentropic Navier-Stokes equations with density dependent viscous coefficient
No full textsummary:We study the vanishing viscosity of isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of shock wave. Given a shock wave to the corresponding Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the shock wave as the viscosity tends to zero. The proof is given by an elementary energy method
On the Kirchhoff index of hypergraphs
No full textsummary:Let be a connected -uniform hypergraph on vertices and hyperedges. K. Feng, W. Li (1996) introduced an adjacency matrix for hypergraphs. We consider the corresponding Laplacian matrix. We extend the concept of the Kirchhoff index to connected hypergraphs. We compute the Kirchhoff index for uniform complete, uniform complete bipartite, hypertriangle, and uniform Fano plane. A hypergraph is the Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. In the process, three different classes of hypergraphs with Laplacian integral are provided. We show that the Kirchhoff index of any connected -uniform hypergraph is at least and the equality holds if and only if is a -uniform complete hypergraph. We also obtain some bounds for the Kirchhoff index in terms of hypergraph invariants such as the number of vertices, number of hyperedges, and first Zagreb index
Optimality conditions for an interval-valued vector problem
No full textsummary:The present article considers a nonsmooth interval-valued vector optimization problem with inequality constraints. We first figure out Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions for the interval-valued problem designed in the paper under quasidifferentiable -convexity in connection with compact convex sets. Subsequently, sufficient optimality conditions are extrapolated under aforesaid quasidifferentiability supported by a suitable numerical example
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle
No full textsummary:We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov's flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way at the junction to cover a wider variety of scenarios in the analysis. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers' preferences. We prove that the explicit Euler or SSP DG scheme with limiters satisfies a maximum principle on general networks. Numerical experiments demonstrate the obtained results
A robust hybrid observer for estimating states, reaction rates, and an external input disturbance for a continuous bioreactor
Get PDFsummary:The controlling and monitoring of bioprocesses very often requires the estimation of certain biological concentrations that are difficult to measure, usually assuming some structure of the reaction rates which might be barely known. Although many algorithms have been designed to estimate these reaction rates, they are not robust against input disturbances and cannot be updated to treat them. This paper addresses the problem of estimating unmeasurable states, reaction rates, and input disturbance by applying a hybrid observer in a continuous bioreactor. The proposed algorithm uses an extended super-twisting algorithm coupled with an adaptive observer to exponentially estimate the reaction rates and input disturbance provided the persistent excitation condition is fulfilled. Later, an asymptotic observer estimates the unmeasurable states with the previous estimations. The hybrid observer is tested through simulations in a continuous sulfate-reducing bioprocess. Finally, the advantage of estimating the external disturbance is highlighted through its use in a disturbance rejection control to counteract its undesirable effect
Maximal non--Mori subrings of a ring
No full textsummary:Let be the set of all commutative rings with unity whose nilradical is a divided prime ideal. The concept of maximal non--Mori subrings of a ring is introduced to generalize the concept of maximal non-Mori subrings of domain. A proper subring of a ring is called a maximal non--Mori subring if is not a -Mori ring but each subring of properly containing is a -Mori ring
Filtrations by cosupports via tensor actions
No full textsummary:Suppose is a rigidly-compactly generated tensor triangulated category and is a compactly generated triangulated category on which acts, in the sense of Stevenson. We prove that if is Noetherian and is stable, then each object in has a unique functorial tower, filtered by Balmer-Favi cosupports. This is an analogy of Stevenson's work on filtrations by Balmer-Favi supports