On some interval methods for algebraic,exponential and trigonometric polynomials

New inclusion methods for the simultaneous determination of the zeros of algebraic, exponential and trigonometric polynomials are presented. These methods are realized in real interval arithmetic and do not use any derivatives. Using Weierstrass' correction some modified methods with the increased convergence rate are constructed. Convergence analysis and numerical example are included.     

An approach to emulating separable graphs

A technique foremulating multicomputer interconnection networks that are based onseparable graphs (graphs having bounded degree and sublinear multicolor recursive bisectors) is presented. Efficient emulations among interconnection networks are necessary for porting programs designed for one network to another.Emulations are formalized asgraph embeddings, where the nodes (processors) of theguest graph (emulated network) are assigned to nodes of thehost graph (emulator), while the edges (communication links) of the guest are routed via paths in the host. The communication slowdown in an emulation depens on thedilation (length of the longest routing path) and thecongestion (number of paths that contend for a host edge) of the embedding. Theexpansion of the embedding (the ratio of the sizes of the host to guest) determines the inefficiency of processor utilization. Cell trees are introduced as interconnection networks whose special communication properties enable them to serve as intermediate devices in these emulations. Nodes in cell trees are organized into equinumerous parts calledcells; the cells are labeled by nodes of a complete binary tree. Communication in cell trees is restricted to two specific and distinct primitives:cell communication is confined within cells, whiletransfer communication occurs between adjacent cells. Rather than solved directly, the emulation problem for the original guest-host pair is decomposed into two independent parts: emulating the guest by the cell tree, and emulating the cell tree by the host.In emulations of separable graphs by cell trees, the node assignment that ensures small dilation is derived from the separator-based decomposition of guest graphs. The congestion-free edge routing is achieved by coordinatingglobal andlocal phases, which are based on two characteristic cell-tree communication primitives.The technique is instantiated by emulating cell trees on specific host graphs. Withshuffle-like hypercube-derivative networks as hosts new constant-expansion emulations are obtained that have both dilation and congestion logarithmic in the size of the multicolor bisector of guest graphs. These emulations are the first such to have optimal (up to constants)congestion; they provide the firstoptimal algorithm for emulating arbitrary separable graphs on shuffle-like networks. The application of the technique tohypercubes as hosts also produces optimal emulations that differ from those previously known by having smaller expansion constants.This research was supported in part by NSF Grants CCR-88-12567 and CCR-90-13184, and by the University of Massachusetts Graduate School Fellowship for the academic year 1991-92. A preliminary version of this paper was presented at the 3rd ACM Symposium on Parallel Algorithms and Architectures, July 22–24, 1991, in Hilton Head, South Carolina, USA.     

Scientometric analysis of the research activities of chemists from the “Rugjer Bošković” Institute (Yugoslavia), 1976–1985

The research activity of chemists from the Rugjer Bokovi Institute (RBI, Zagreb, Yugoslavia) was analyzed for the period 1976–1985, covering 2018 research years of scientific work, and 1149 SCI registered papers (0.57 publications per research year). At the average, one paper was published by 3.05 scientists. The papers were published in 235 different journals, most frequently is the nationalCroatica Chemica Acta (171 papers). The publications were divided into two groups: for the periods 1976–1980 and 1981–1985, and for each paper citations were collected in the respective time period. An average publication had 2.58 citations. Chemical papers from the second period had 2.73 citations per paper, which is 85% of the expected value, and this was considerably more than for Yugoslav papers (66%) in general. The papers were classified according to the subfields used in theJournal Citation Reports, and the results compared with the data published bySchubert, Glänzel andBraun. The distribution of citations was also analyzed.     

Frequency dependence of the spin-fluctuation spectrum in Pd: Calculations within the finite bandwidth model

The frequency dependence of the electron-paramagnon spectrumP() in Pd is calculated within the finite bandwidth model. It is found that for an almost full band, the magnitude, the range, and the position of the peak frequency inP() are dramatically reduced compared to their values in the usual paramagnon theory. Also, we find that the frequency dependence of the spin-fluctuation contribution to the electron self-energy is strongly affected by a close proximity of the Fermi level to the top of the band. We speculate that an unusually large value of the Coulomb pseudopotential is probably partially responsible for the absence of superconductivity in Pd.     

Observation of higher order NMR larmor lines by SQUID in solids at low magnetic field

We describe an apparatus allowing the observation of the NMR static longitudinal component of nuclear magnetizationM _z by a SQUID at low magnetic fields and atT=4.2 K in Plexiglas, Teflon, and CaF₂. The higher order NMR Larmor lines at 2f ₀, 3f ₀, and 4f ₀, wheref ₀ is the Larmor frequency of the allowed NMR line, were measured. These lines correspond to a flip of two, three, and four spins, respectively, by one photon. The amplitudes of 2f ₀ and 3f ₀ lines and their field dependences show that the common assertion that the forbidden lines at 2f ₀ and 3f ₀ appear in the same order of perturbation theory and that their intensity decreases with static magnetic fieldB ₀ asB ₀ ^–2 is wrong. In fact, the third Larmor line 3f ₀ appears at higher order than the second Larmor line 2f ₀ and its intensity decreases asB ₀ ^–4 . This is also shown by a theoretical calculation of its intensity. For the first time the NMR SQUID technique allowed the detection of the 4f ₀ line, corresponding to the simultaneous flip of four spins by one photon.     

Formation of oxide phases in the system Fe2O3−Gd2O3

The formation of oxide phases in the system (1 -x) Fe₂O₃ +xGd₂O₃ was investigated for 0 x 1. On the basis of XRD measurements the distribution of oxide phases, -Fe₂O₃, Gd₃Fe₅O₁₂, GdFeO₃ and Gd₂O₃ was determined, as a function ofx. No solid solutions were observed with certainty even at the very ends of the concentration range. This was also confirmed by⁵⁷Fe Mössbauer spectroscopy. New accurate crystallographic data for Gd₃Fe₅O₁₂ are given. The formation of oxide phases in the system Fe₂O₃- Gd₂O₃ is compared with the data for analogous system Fe₂O₃-Eu₂O₃.     

Qualitative analysis of motion properties of semistate models of large-scale systems

This paper studies the behavior of motions of large-scale (LS) semistate systems (SSS) governed byP _i (t)x _i =M _i (t,x _i )x _i +f _i (t)+h _i (t, x), i=1,2,...,s, =(x ₁ ^T x ₂ ^T x _s ^T )^T, where matricesP _i (t) are singular. Using Lyapunov's approach and the tools for LS system analysis, a variant of attractivity and ultimate boundedness of appropriate time-variable sets are investigated. The results are based on a specific choice of the aggregate functions. It is assumed that the reduction of equations to a normal form of lower order is inconvenient. The aggregation-decomposition approach used in this paper reduces the dimensionality of an aggregate matrix of the system to the number of its systems. Motion properties of LS systems are deduced from the properties of its isolated subsystems, the character of interconnections, and the conditions imposed on the system aggregate matrix. Sufficient algebraic conditions for the above-mentioned motion properties are developed.     

Magnetic pinning in inhomogeneous type II superconductors

The magnetic structure of a vortex in the presence of an anisotropic inhomogeneity distribution is calculated within the London model. The anisotropic supercurrent pattern consists of closed current loops, superimposed on a backflow pattern. The nonvanishing current density at the vortex core gives rise to an intrinsic Lorentz force identical with the pinning force resulting from the spatial variation of the vortex self-energy.     

DC and ac Josephson effects observed in high-temperature superconductor YBaCuO

We report the observation of the dc and ac Josephson effect and quasiparticle tunnelling in the high-temperature superconductor YBaCuO. The observation is made at 4.2 K. These effects were observed in a junction made by a niobium tip pressed against a high-T _c sample of YBaCuO ceramic. We observed a clean dc Josephson effect with a critical currentI _c 2 A and the ac effect with Shapiro steps corresponding toV=(hf/2e)n. The nature of the junction is not clear; however, we suggest that all observed effects can be explained by assuming a singlet pairing state in the ceramic. We have also observed a very peculiar noise behavior along theV-I characteristic.