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.
The paper can be understood as a completion of the $q$-Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear $q$-difference equations. The $q$-Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice $q^{\mathbb {N}_0}:=\{q^k\colon k\in \mathbb {N}_0\}$ with $q>1$. In addition to recalling the existing concepts of $q$-regular variation and $q$-rapid variation we introduce $q$-regularly bounded functions and prove many related properties. The $q$-Karamata theory is then applied to describe (in an exhaustive way) the asymptotic behavior as $t\to \infty $ of solutions to the $q$-difference equation $D_q^2y(t)+p(t)y(qt)=0$, where $p\colon \smash {q^{\mathbb {N}_0}}\to \mathbb {R}$. We also present the existing and some new criteria of Kneser type which are related to our subject. A comparison of our results with their continuous counterparts is made. It reveals interesting differences between the continuous case and the $q$-case and validates the fact that $q$-calculus is a natural setting for the Karamata like theory and provides a powerful tool in qualitative theory of dynamic 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.
The possible formation of a new stellar generation may be seen in the bright rimmed dark clouds that surround the giant HII region IC 1396. A well.defined ring of IRAS point sources is projected near the ionisation front indicated by the bright rims. We sugest that some of these sources are young stellar objects, and the majority represents density enhancements in the shocked neutral gas layer preceding the ionisation front which might eventually become stars.
The main trends in spontaneous regeneration were studied in old-fields in the Transylvanian Lowland (Câmpia Transilvaniei) over a period of 40 years using the chronosequence method. Succession proceeds to grassland, because the establishment of woody vegetation is hindered by grazing and mowing of the old- fields and by the scarcity of woodlands in the vicinity. Community properties and population-level changes were recorded at different stages of succession and compared with semi-natural grassland in the surrounding landscape. Due to favourable soil conditions and temperate climate, vegetation cover develops quickly after the fields are abandoned. Annuals dominated only in the first year. After two years the fast growing clonal grass, Elymus repens, became dominant. After approximately 12 years, Elymus was replaced by Festuca rupicola, which is more resistant to stress and disturbance. In the later stages of succession various species, some typical of surrounding grassland, attained high cover values. A steady increase in species diversity, measured by the Shannon index, and richness was recorded at both the field (1.0–2.5 ha) and plot (4 × 4 m) scales. Species richness increased rapidly in early and middle stages and stabilized after the 14th year. Specific features of the succession in the old-fields in the Transylvanian Lowland can be attributed to the continued grazing and mowing of the fields after they are abandoned. This increases species richness because it arrests succession at a stage when species diversity is high. The management directs regeneration towards secondary grassland rather than species poor woodland.
We assessed vegetation changes on acidic sandy soils in permanent plots to follow secondary succession after cessation of intensive goose breeding in E Hungary. We also aimed to estimate the time required for vegetation regeneration and indicate differences in secondary succession patterns at different altitudes in sand dunes. Two sites in the low and two in the high parts of the dunes were chosen and sampled for twelve years. The initial stages are characterized by ruderal communities dominated by nitrophilous annual weeds. Ruderal vegetation was soon replaced by nutrient-poor communities dominated by short-lived pioneer dicotyledonous plants and grasses. In the last few years of the study, coinciding with a rainy period, the low sites were dominated by the perennial grasses, Poa angustifolia, P. pratensis and Cynodon dactylon. In contrast, in the high sites a less dense cover of perennials developed. The influence of initial composition on vegetation development decreased with time and the influence of altitude increased during succession. The altitude of the site had a significant effect on regeneration. Species richness and Shannon diversity of the high sites increased during vegetation development and that of the lowsites decreased. Most annuals persisted in the high sites but became extinct in the low sites. The mean species turnover rate, irrespective of altitude, decreased during the study.
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