The authors consider the boundary value problem with a two-parameter nonhomogeneous multi-point boundary condition u ′′ + g(t)f(t, u) = 0, t ∈ (0, 1), u(0) = αu(ξ) + λ, u(1) = βu(η) + µ. Criteria for the existence of nontrivial solutions of the problem are established. The nonlinear term f(t, x) may take negative values and may be unbounded from below. Conditions are determined by the relationship between the behavior of f(t, x)/x for x near 0 and ±∞, and the smallest positive characteristic value of an associated linear integral operator. The analysis mainly relies on topological degree theory. This work complements some recent results in the literature. The results are illustrated with examples.
The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.
We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in (0, T ) is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in (0,∞) (boundedness and stabilization as t → ∞) are shown.
Death and funerary customs belong to the stable and conservative elements in a society. They are very slow to change and can remain almost identical for hundreds, even thousands of years, varying only with fundamental changes in the social sphere and culture. In the case of ancient Israel, changes to long-established death and funerary customs often occurred when new foreign influences were incorporated and transformed in accordance with indigenous traditions and norms. Even when a new theory within the death "ideology" appeared, it did not necessarily dictate a change in mortuary behavior towards the dead. Actually, we cannot always find a causal relationship between a doctrine or particular religious attitude and the corresponding burial practice. For nearly two millennia Jews practiced the full body treatment, including manipulation during the secondary burial, while at the same time regarding corpse handling as unclean and polluting.
A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid port is not a sufficient condition to admit an ideal secret sharing scheme. In this work we present a linear secret sharing scheme construction for ports of matroids of rank 3 in which the size of each share is at most nn times the size of the secret. Using the previously known secret sharing constructions, the size of each share was O(n2/logn) the size of the secret. Our construction is extended to ports of matroids of any rank k≥2, obtaining secret sharing schemes in which the size of each share is at most nk-2 times the size of the secret. This work is complemented by presenting lower bounds: There exist matroid ports that require (Fq,ℓ)-linear secret schemes with total information ratio Ω(2n/2/ℓn3/4logq)., Oriol Farràs., and Obsahuje bibliografické odkazy
The paper describes a new approach for treatment security issues in reconfigurable grids used for computing or communication, in particular, in the semantic web environment. The proposed strategy combines a convenient mathematical model, efficient combinatorial algorithms which are robust with respect to changes in the grid structure, and an efficient implementation. The mathematical model uses properties of weighted hypergraphs. Model flexibility enables to describe basic security relations between the nodes such that these relations are preserved under frequent changes in connections of the hypergraph nodes. The algorithms support construction of a grid with embedded security concepts on a given set of nodes. The proposed implementation makes use of the techniques developed for time and space-critical applications in numerical linear algebra. Our combination of the mentioned combined building blocks is targeted to the emerging field of the semantic web, where the security seems to be very important. Nevertheless, the ideas can be generalized to other concepts describable by weighted hypergraphs. The paper concentrates on explaining the model and the algorithms for the chosen application. The consistency of the proposed ideas for security management in the changing grid was verified in a couple of tests with our pilot implementation SECGRID.
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details of the segmentation curve. The purpose of the article is to indicate how the algorithm parameters are set up and to show how the algorithm behaves when applied to the particular class of medical data. In detail we describe the algorithm parameters influencing the segmentation procedure. The left ventricle volume estimated by the segmentation of scanned slices is evaluated through the cardiac cycle. Consequently, the ejection fraction is evaluated. The described approach allows the user to process cardiac cine MR images in an automated way and represents, therefore, an alternative to other commonly used methods. Based on the physical and mathematical background, the presented algorithm exhibits the stable behavior in the segmentation of MRI test data, it is computationally efficient and allows the user to perform various implementation improvements.
Kovy a jejich slitiny jsou jedním ze základních konstrukčních materiálů používaných v technické praxi. Přestpže jsou jejich vlastnosti dostatečně známé, stále hrozí, že u kovových konstrukcí nebo jiejich součástí dojde k náhlému kolapsu v důsledku mezikrystalového křehkého lomu, který je způsoben postupnou změnou chemického složení oblastí mezi jednotlivými krystaly. Této problematice se po léta věnuje řada odborníků včetně českých specialistů. Článek pojednává o vztahu mezi chemií mezikrystalových oblastí - hranic zrn - a jejich soudružností a o tom, jakou stopu v této oblasti zanechali čeští vědci., Metals and their alloys belong to the basic construction materials used in technology and building. Although their properties are very well-known, there is always a danger that a sudden collapse occurs in metallic constructions, or in their parts, as a result of intergranular embrittlement. Such an embrittlement may be caused by a progressive change in chemical composition in the regions between individual crystals, i.e. grain boundaries. Many specialists, including Czechs, are engaged in finding a solution for this issue. This article deals with the relationship between the chemistry of grain boundaries and their cohesion, and demonstrates the footprint bequeathed by Czech scientists., Pavel Lejček, Mojmír Šob, Václav Paidar., and Obsahuje seznam literatury
This article is concerned with seismicity in the region of West Bohemia - Vogtland after the Nový Kostel swarm of 2000. Seismicity during the period 2001 - 2006 is weak, though with several clusters of earthquakes; although these do not meet the criteria for a seismic swarm, their groupi ng in time and spacing along a line give an impression of tectonic disturbances and their behaviour in a period between swarms., Vladimír Nehybka and Radka Tilšarová., and Obsahuje bibliografické odkazy