Quasi-kernels and quasi-sinks in infinite graphs

Given a directed graph G=(V,E) an independent set A⊂V is called quasi-kernel (quasi-sink) iff for each point v there is a path of length at most 2 from some point of A to v (from v to some point of A). Every finite directed graph has a quasi-kernel. The plain generalization for infinite graphs fails, even for tournaments. We study the following conjecture: for any digraph G=(V,E) there is a a partition (V₀,V₁) of the vertex set such that the induced subgraph G[V₀] has a quasi-kernel and the induced subgraph G[V₁] has a quasi-sink.     

How To Split Antichains In Infinite Posets*

A maximal antichain A of poset P splits if and only if there is a set B ⊂ A such that for each p ∈ P either b ≤ p for some b ∈ B or p ≤ c for some c ∈ A\B. The poset P is cut-free if and only if there are no x < y < z in P such that [x,z]_P = [x,y]_P ∪ [y,z]_P . By [1] every maximal antichain in a finite cut-free poset splits. Although this statement for infinite posets fails (see [2])) we prove here that if a maximal antichain in a cut-free poset “resembles” to a finite set then it splits. We also show that a version of this theorem is just equivalent to Axiom of Choice. We also investigate possible strengthening of the statements that “A does not split” and we could find a maximal strengthening. * This work was supported, in part, by Hungarian NSF, under contract Nos. T37846, T34702, T37758, AT 048 826, NK 62321. The second author was also supported by Bolyai Grant.     

The Interaction of the Supersonic Plasma-Jet with the Substrate in the RF Plasma-Chemical Reactor

Although the plasma-chemical processes and properties of the deposited thin film can strongly depend on the interaction of the supersonic plasma jet channel with the substrate, up to now the study of this phenomenon has not yet been done. We decided to study this interaction by means of CCD camera. The presented results indicate that the light intensity recorded close to the substrate can be used as a measure of the intensity of plasma-chemical deposition processes on the substrate surface.     

Backscatter from a limestone seafloor at 2-3.5 kHz: measurements and modeling

Physics-based interface scattering models for the seafloor [H.-H. Essen, J. Acoust. Soc. Am. 95, 1299-1310 (1994); Gragg et al., ibid. 110, 2878-2901 (2001)] exhibit features in their predicted grazing angle dependence. These features have a strong dependence on the assumed composition and roughness of the bottom. Verifying such predictions requires data that cover a wide range of grazing angles and involve minimal sub-bottom penetration. Such measurements were performed in the frequency band 2-3.5 kHz over an exposed limestone bottom off the Carolina coast during the second Littoral Warfare Advanced Development Focused Technology Experiment of 1996 (LWAD FTE 96-2). Direct-path bottom scattering strengths were obtained in shallow water (198-310 m deep) for grazing angles from 8 degrees to 75 degrees using data fusion from multiple experimental geometries coupled with careful signal processing. The processing included corrections for the surface-reflected path, other multipaths, and characteristics of the reverberation decay observed over the pulse duration at higher grazing angles. The resulting frequency and grazing-angle dependences exhibit trends consistent with theoretical predictions, and geoacoustic parameters obtained by inversion are consistent with values expected for limestone.     

Über 3,3,6,9,9-Pentamethyl-2,10-diaza-bicyclo-[4.4.0]-1-decen und einige seiner Derivate. Über synthetische Methoden. 13. Mitteilung

3,3,6,9,9-Pentamethyl-2,10-diaza-bicyclo[4.4.0]-1-decen and some of its derivatives A simple synthesis for the bicyclic amidine 1 (Scheme 3) is described. This base and the salts which were prepared from it show solubility characteristics which make the amidine a potentially useful reagent for salt formation of carboxylic acids and related proton complexes of bidentate ligands. Among the derivatives made from 1 are the sterically strongly hindered N-alkylated amidines 11 , 12 and 14 (Scheme 5), as well as the stable crystalline N¹-oxidoamidine-N²-oxyl radical 2 (Scheme 6). The ability of the latter to serve as a paramagnetic chelating ligand for metal ions is illustrated by the preparation of a corresponding nickel(II) complex. The radical is also a source for the α-nitronyl-nitrosonium cation 4 which shows in its reactivity towards conjugated dienes and olefines some of the expected resemblance to singlet oxygen.     

Essentially disjoint families, conflict free colorings and Shelah’s revised GCH

Using Shelah’s revised GCH theorem we prove that if μ<? _ω ≦λ are cardinals, then every μ-almost disjoint family ${\mathcal{A}}\subset {[\lambda]}^{\beth_{\omega}}$ is essentially disjoint, i.e. for each ${A\in {\mathcal{A}}}$ there is a set F(A)∈[A]^<|A| such that the family $\{{A\setminus F(A)}: {A\in {\mathcal{A}}}\}$ is disjoint. We also show that if μ≦κ≦λ are cardinals, κ≧ω, and

• every μ-almost disjoint family ${\mathcal{A}}\subset {[\lambda]}^{{\kappa}}$ is essentially disjoint,

then

• every μ-almost disjoint family ${\mathcal {B}}\subset {[\lambda]}^{\geqq {\kappa}}$ has a conflict-free coloring with κ colors, i.e. there is a coloring f:λ→κ such that for all ${B\in {\mathcal{B}}}$ there is a color ξ<κ such that |{β∈B:f(β)=ξ}|=1.

Putting together these results we obtain that if μ<? _ω ≦λ, then every μ-almost disjoint family ${{\mathcal{B}}\subset {[\lambda]}^{\geqq \beth_{\omega}}}$ has a conflict-free coloring with ? _ω colors. To yield the above mentioned results we also need to prove a certain compactness theorem concerning singular cardinals.     

Transient vibration of thin viscoelastic orthotropic plates

This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flu¨gge and Timoshenko-Mindlin.The linear model,a general standard viscoelastic body,of the rheologic properties of a viscoelastic material was applied.The time and coordinate curves of the basic quantities displacement,rotation,velocity,stress and deformation are compared.The results obtained by an approximate analytic method are compared with numerical results for 3D plate generated by FEM application and with experimental investigation.     

Superatomic Boolean algebras constructed from strongly unbounded functions

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ^{++ +} ≤ λ, κ^<κ = κ and 2^κ = κ⁺, and η is an ordinal with κ⁺ ≤ η < κ⁺⁺ and cf(η) = κ⁺. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal BUsing Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ^{++ +} ≤ λ, κ^<κ = κ and 2^κ = κ⁺, and η is an ordinal with κ⁺ ≤ η < κ⁺⁺ and cf(η) = κ⁺. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal B$ such that $\mathrm{ht}(\mathcal B) = \eta + 1$, $\mathrm{wd}_{\alpha }(\mathcal B) = \kappa$ for every α < η and $\mathrm{wd}_{\eta }(\mathcal B) = \lambda$(i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉_η^??〈λ〉). Especially, $\langle {\omega }\rangle _{{\omega }_1}{}^{\smallfrown } \langle {\omega }_3\rangle$ and $\langle {\omega }_1\rangle _{{\omega }_2}{}^{\smallfrown } \langle {\omega }_4\rangle$ can be cardinal sequences of superatomic Boolean algebras.