Showing papers by "Hungarian Academy of Sciences published in 1983"

Extremal problems in discrete geometry

Abstract: In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erdos, G. Purdy, and G. Dirac. The principal result is that there exists an absolute constantc 1 so that when $$\sqrt n \leqq t \leqq \left( {_2^n } \right)$$ , the number of incidences betweenn points andt lines is less thanc 1 n 2/3 t 2/3. Using this result, it follows immediately that there exists an absolute constantc 2 so that ifk≦√n, then the number of lines containing at leastk points is less thanc 2 n 2/k 3. We then prove that there exists an absolute constantc 3 so that whenevern points are placed in the plane not all on the same line, then there is one point on more thanc 3 n of the lines determined by then points. Finally, we show that there is an absolute constantc 4 so that there are less than exp (c 4 √n) sequences 2≦y 1≦y 2≦...≦y r for which there is a set ofn points and a setl 1,l 2, ...,l t oft lines so thatl j containsy j points.

Sorting in c log n parallel steps

Abstract: We give a sorting network withcn logn comparisons. The algorithm can be performed inc logn parallel steps as well, where in a parallel step we comparen/2 disjoint pairs. In thei-th step of the algorithm we compare the contents of registersR j(i) , andR k(i) , wherej(i), k(i) are absolute constants then change their contents or not according to the result of the comparison.

Effects of drift on the transport of cosmic rays. VI - A three-dimensional model including diffusion

Abstract: The first results are presented from a series of computer simulations of the solar modulation of galactic cosmic rays using a full three-dimensional model which incorporates all known important effects on particle transport, particle drifts, convection with the solar wind, energy loss, and anisotropic diffusion. The model is time-independent in the coordinate frame rotating with the sun, so corotating effects can be studied. Modulation in an interplanetary magnetic field model is considered in which the current sheet separating the northern and southern solar hemispheres is warped and corotating with the sun. The amplitude of the warp is varied to simulate possible solar cycle variation of the magnetic field. Substantial effects due to the warp of the current sheet are found. Comparison of the model results with various data is presented. Among other things, it is shown that the intensity may decrease away from the current sheet for both signs of the magnetic field, as suggested by recent observations, and in contrast with inferences from earlier, more approximate calculations.

On a problem of Oppenheim concerning “factorisatio numerorum”

Abstract: We shall consider graphs (hypergraphs) without loops and multiple edges. Let ℒ be a family of so called prohibited graphs and ex (n, ℒ) denote the maximum number of edges (hyperedges) a graph (hypergraph) onn vertices can have without containing subgraphs from ℒ. A graph (hyper-graph) will be called supersaturated if it has more edges than ex (n, ℒ). IfG hasn vertices and ex (n, ℒ)+k edges (hyperedges), then it always contains prohibited subgraphs. The basic question investigated here is: At least how many copies ofL e ℒ must occur in a graphG n onn vertices with ex (n, ℒ)+k edges (hyperedges)?

Supersaturated graphs and hypergraphs

Abstract: We shall consider graphs (hypergraphs) without loops and multiple edges. Let ℒ be a family of so called prohibited graphs and ex (n, ℒ) denote the maximum number of edges (hyperedges) a graph (hypergraph) onn vertices can have without containing subgraphs from ℒ. A graph (hyper-graph) will be called supersaturated if it has more edges than ex (n, ℒ). IfG hasn vertices and ex (n, ℒ)+k edges (hyperedges), then it always contains prohibited subgraphs. The basic question investigated here is: At least how many copies ofL e ℒ must occur in a graphG n onn vertices with ex (n, ℒ)+k edges (hyperedges)?

On sums and products of integers

Abstract: Let 1 ≦ a 1 <...

Towards a “Chemical” Hamiltonian

Abstract: An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule—a factor completely overlooked in the usual scheme of calculations.

Ion‐induced amorphous and crystalline phase formation in Al/Ni, Al/Pd, and Al/Pt thin films

Abstract: Amorphization by ion beam irradiation of multilayered samples of Al/Pt, Al/Pd, and Al/Ni has been investigated by selected area diffraction and Rutherford backscattering. With a dose of 2×1014 Xe ions/cm2, uniform mixing is achieved in the Al/Pt system and the amorphous phase is produced over a large composition range. In the Al/Pd and Al/Ni systems, amorphous phases or the equilibrium, crystalline phases are formed depending on the composition of the films. The same results were found when the samples were annealed to form crystalline phases before bombardment. For thin films of these fcc metals, only the simplest intermetallics, NiAl and PdAl, (primitive cubic structures with 2 atoms/cell) were formed in crystalline form by ion‐beam irradiation.

Theory of the interaction between electrons and the two-level system in amorphous metals. I. Noncommutative model Hamiltonian and scaling of first order

Abstract: The general form of the interaction between tunneling two-level systems (TLS) and conduction electrons is discussed for metallic glasses. The particular form of the Hamiltonian is given in the case where only a single atom tunnels between two positions. There are two couplings corresponding to the two basic scattering processes: In the first one, the tunneling atom does not change position; the second process is the conduction-electron-assisted tunneling process. The two coupling parameters are estimated. The difference in the angular dependence of these couplings on the directions of the incoming and of the outgoing electrons is responsible for the appearance of logarithmic corrections in the scattering amplitude. Scaling equations are derived for the couplings in terms of changing the bandwidth cutoff. It is shown that the scaling equations lead to especially strong coupling in two conduction-electron scattering channels which are linear combinations of the $s$-, $p$-, and $d$- like spherical wave functions. The Hamiltonian scales to a spin $S=\frac{1}{2}$ antiferromagnetic Kondo Hamiltonian, which indicates the formation of a "bound state," where the motions of the tunneling atom and of the conduction-electron screening cloud around the TLS are strongly correlated; thus the Friedel oscillations follow the tunneling atom. The crossover temperature, below which the correlation becomes especially strong, is determined in the leading logarithmic approximation.

A Method of Including the Effects of Main Flux Path Saturation in the Generalized Equations of A.C. Machines

Abstract: This paper shows how the effects of saturation of the main flux path can be incorporated in the generalized equations of alternating current machines in which the currents are deliberately chosen as the state variables. In the conventional equations linear magnetic conditions are assumed and the forms taken by these equations in various reference frames are well known. When saturation of the main flux path is taken into account, some parameters have to be modified and additional terms introduced; stator (and rotor) self inductances in orthogonal axes are no longer equal. These are the consequence of intersaturation - sometimes called cross-saturation; a phenomenon which has been mentioned in the literature but has not been subjected to general analysis. New forms of generalized equations are derived and their application to the analysis of induction motor starting transients described.

On size Ramsey number of paths, trees, and circuits. I

Abstract: In this paper we shall demonstrate that random graphs satisfy some interesting Ramsey type properties. This paper deals with finite, simple and undirected graphs only. If G and H are graphs, write G → H to mean that if the edges of G are coloured by two colours, then G contains a monochromatic copy of H.

A new generalization of the Erdős-Ko-Rado theorem

Abstract: Let ℱ be a family ofk-subsets of ann-set. Lets be a fixed integer satisfyingk≦s≦3k. Suppose that forF 1,F 2,F 3 ∈ ℱ |F 1 ∪F 2 ∪F 3|≦s impliesF 1 ∩F 2 ∩F 3 ≠ 0. Katona asked what is the maximum cardinality,f(n, k, s) of such a system. The Erdős-Ko-Rado theorem impliesf(n, k, s)= $$\left( {_{k - 1}^{n - 1} } \right)$$ fors=3k andn≧2k. In this paper we show thatf(n, k, s)= $$\left( {_{k - 1}^{n - 1} } \right)$$ holds forn>n 0(k) if and only ifs≧2k. Equality holds only if every member of ℱ contains a fixed element of the underlying set. Further we solve the problem fork=3,s=5,n≧3000. This result sharpens a theorem of Bollobas.

Kinetics of TiSi2 formation by thin Ti films on Si

Abstract: Silicide formation with Ti deposited on single crystal Si and Ti deposited on amorphous Si layers sequentially without breaking the vacuum was investigated using backscattering spectrometry and glancing-angle x-ray diffraction. For Ti deposited on amorphous Si, TiSi2 was formed with a rate proportional to (time)^1/2 and an activation energy of 1.8±0.1 eV. For Ti deposited on single crystal Si, the reaction rate was slower and the silicide layer was nonuniform in thickness. We attribute the difference in behavior to the presences of interfacial impurities in the case where Ti was deposited on single crystal Si.

Hydrogen effects in metal catalysts

Abstract: The interaction of hydrogen with metals is the cause or basis of a host of phenomena ranging from the chemisorption of hydrogen on the surface, its dissolution in the metal, catalytic reactions involving hydrogen as a reactant or as an astoichiometric component, etc., to the formation of metal hydrides. Hydrogen -induced corrosion and hydrogen embrittlement of steel are well known in chemical process industry and metallurgy. Catalytic reactions on metal or metal-oxide catalysts in the presence of hydrogen, often under pressure, are some of the major chemical, petroleum, and petrochemical processes of today, e.g., ammonia, methanol, Fischer-Tropsch, Oxo and other syntheses, hydrogenation of oils and fats, catalytic reforming, hydrode-sulfurization/hydrotreating, hydrocracking, and hydrogenation/ dehydrogenation.

On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry

Abstract: LetS be a set ofn non-collinear points in the Euclidean plane. It will be shown here that for some point ofS the number ofconnecting lines through it exceedsc · n. This gives a partial solution to an old problem of Dirac and Motzkin. We also prove the following conjecture of Erdős: If any straight line contains at mostn−x points ofS, then the number of connecting lines determined byS is greater thanc · x · n.

On determinism versus non-determinism and related problems

Abstract: We show that, for multi-tape Turing machines, non-deterministic linear time is more powerful than deterministic linear time. We also discuss the prospects for extending this result to more general Turing machines.

Cessation of cytokeratin expression in a rat hepatoma cell line lacking differentiated functions.

Abstract: Intermediate-sized filaments (IF) of diameter 7-11 nm occur in the cytoplasm of most cells of vertebrates and their constituent proteins are abundant in most cell types. Expression of IF proteins depends on the route of cell differentiation and five major subclasses of IF proteins have been distinguished: of these, cytokeratins are typical of epithelial cells whereas vimentin occurs in mesenchymally derived cells and some other non-epithelial cells. When epithelial cells are grown in culture this restriction of IF expression is often lost and they begin to synthesize vimentin in addition to cytokeratin, although examples of maintenance of the cell-type-specific expression of only cytokeratin have also been reported. No IFs have been detected in mammalian germ cells or in pre-morula stages of mouse embryogenesis, and the first IF proteins identified in murine blastocysts are cytokeratins of trophectodermal cells. We report here that a dedifferentiated rat hepatoma cell clone, which has become resistant to the action of the glucocorticoid hormone analogue dexamethasone and has lost various liver-specific functions, also stops all synthesis of IF proteins, without obvious consequences for growth and proliferation. The existence of such cells devoid of IF supports the notion that such filaments are not involved in basic cellular functions necessary for growth and proliferation but are related to special functions of the differentiated cell.

Localization of symbiotic mutations in Rhizobium meliloti.

Abstract: A total of 5 Nod- and 57 Fix- symbiotic mutants of Rhizobium meliloti strain 41 have been isolated after either nitrosoguanidine or Tn5 transposition mutagenesis. Chromosomal locations of mutations in 1 Nod- and 11 Fix- derivatives were ascertained by transferring the chromosome (mobilized by plasmid R68.45), in eight fragments, into symbiotically effective recipients and testing the recombinants for symbiotic phenotype. Alternatively, the kanamycin resistance marker of Tn5 was mapped. In five mutants the fix alleles were localized on different chromosomal regions, but six other fix mutations and one nod mutation tested did not map onto the chromosome. It was shown that the chromosome-mobilizing ability (Cma+) of R68.45 was not involved in the mobilization of genes located extrachromosomally. Moreover, Cma- derivatives of R68.45 could mobilize regions of the indigenous plasmid pRme41b but not chromosomal genes. Thus, mobilization of a marker by Cma- R68.45 indicates its extrachromosomal location. With a 32P-labeled DNA fragment carrying Tn5 as a hybridization probe, it was shown that in five extrachromosomally located Tn5-induced fix mutants and one nod mutant Tn5 was localized on plasmid pRme41b. This is in agreement with the genetic mapping data.

Statistical reliability of comparisons based on the citation impact of scientific publications

Abstract: A method for estimating the standard error of mean citation rates per publication is proposed and examplified on journal impact factors. The use of the standard error values in statistical tests is also illustrated.