Showing papers by "University of Science and Technology of China published in 1985"

The complete convergence for partial sums of iid random variables

Abstract: In this paper, by using the equivalence of the a. s. convergence and the convergence in probability for the partial sums of independent random variables, we improved and strengthened a series of Katz and Baums results which are some necessary and sufficient conditions about the complete convergence for the partial sums of iid random variables. On the above basis, we got ideal conditions and results about the complete convergence for the random selected partial sums of lid random variables.

The Difference between Consecutive Primes

Abstract: This paper discusses two problems which relate to the difference between consecu~ve primes. Let p. be the nth prime, and d. = p . + l p . . (1) We want to find a funct ion f(,~) such that d . 0 is a given constant and cl is a number which satisfies ~*((r, T) ~O, (4) provided the funct ion g(x) satisfies g(x) K loglog x fox* every K > 0 and x>fzo(tC). This paper establishes the following theorem and so improves on the above result. Theorem 1. Suppose that the estimate (4) hoZds and the est~mata N (or, T) 0 and q'z>0. For any A > 0 ~e$

Is the periodicity in the distribution of quasar red shifts an evidence of multiply connected universe

Abstract: The periodicity in the distribution of quasar red shifts is interpreted assuming that the cosmological space is a topologically compactified manifold like the three-dimensional torus The present size of such compact space is estimated as the order of 600 Mpc

Distribution of quasars and formation of large-scale structures

Abstract: According to the proposal developed by Fanget al. (1984, referred to as Paper I) on formation of large-scale structure in the Universe, we should expect that: Our various statistical results obtained from quasar distributions are consistent with these predictions. Particularly, the nearest neighbour test for the complete quasar sample given by Savage and Bolton (1979) clearly shows that the distribution ofZ>2 quasars is rather homogeneous while theZ<2 quasars have a tendency to cluster.

Convexity and Variation Diminishing Property of Bernstein Polynomials over Triangles

Abstract: Let Bn(f;P) denote the Bernstein polynomials over triangle T and \({\hat f_n}\) denote the Bezier net associated with Bn(f;P). A certain type of variations of \({\hat f_n}\) is introduced by GOODMAN quite recently. In the present paper the corresponding variation of Bn(f;P) is defined by integration of the absolute value of the Laplacian of BP(f;P) over T. It is shown that the variation of \({\hat f_n}\) is always greater or equal to the variation of Bn(f;P). The equality holds if and only if \({\hat f_n}\) is either convex (or concave) over T. The convexity of \({\hat f_n}\) implies the convexity of Bn(f;P). As an application we receive a simple proof of a theorem due to Chang and Davis.

The problem of existence for the fermion-dyon self-consistent coupling system in aSU2 gauge model

Abstract: A scalar coupling model ofSU2 Higgs and fermion is considered. It is shown that 1) the Julia-Zee dyon's ansatz is not complete. But, if we treat the Julia-Zee dyon as external potential, the closed equations of the radial wave functions of the fermion are obtained. 2) The asymptotic solutions of the fermion's radial wave functions at infinity and near the origin are solved. 3) The necessary condition of the fermion's bound state is qualitatively discussed, which shows that for the dyon case in which the scalar coupling approaches zero, the existence of the fermion's bound states is possible, but for the monopole case in which the scalar coupling approaches zero the fermion's bound states do not exist.

Strong consistency of the kernel estimators of conditional density function

Abstract: Let (X, Y) be a ~ • RS-valued vector. Assume ~hat when X =~ ~ is given, ~her~ exists a conditional density of Y ~o be denoted by f ( y [ z ) , which is a Borel-measurable function of (~, y). Note that we do not assume the existence of a density function of (X, Y). Let (X1, Y~), --., (X., Y.) be i.i.d, samples of (X, Y). Our purpose is to estimate/(~/l~) based on these samples. This is an interesting problem in view of either pure theory or practical applications. Motivated by the idea suggests1 in kernel and NI~ estimations in the theory of nonparametric regression and density estimates, the first author proposes the following two classes of estimators of f (g[~) : 1) Let JE'I(~), K2(v) be density functions on ~Y and R' respectively. Take h ~ h . ~ 0 , and write

Bäcklund transformation of nonlinear evolution equations

Abstract: Using Lax pair and looking for the gauge transformation, we obtain the Backlund transformation in another form (sometimes it is called Darboux transformation) for some nonlinear evolution equations. We shall see that it is more convenient to use this form of Backlund transformation.

Crystallization of amorphous Ge in Ge/Au bilayer films and Ge-Au alloy films

Abstract: The crystallization temperature of amorphous Ge(a-Ge) in a-Ge/polycrystalline Au(p-Au) films is much lower than that in a-Ge/monocrystalline Au(m-Au) films. In order to explain this phenomenon it is suggested that the grain boundary triple points of p-Au films are the favourable nucleation positions. The favourable crystallization regions in a-Ge/p-Au films are related to the agglomeration of p-Au films. The crystallization temperature of Ge-Au alloy films is lower than that of a-Ge/p-Au films when Au content in alloy films is less than 35wt%, and is higher when Au content is more than 35wt%.

The relation of von Kármán equation for elastic large deflection problem and Schrödinger equation for quantum eigenalues problem

Abstract: In this paper the solutions of von Karman for elastic large deflection problem are classified as the several solutions of Schrodinger equation for quantum eigenvalues problem, and we present the transform for elastic large deflection problem from non-linear equation into linear equation. Thus, we create favourable conditions of the adoption of converse scattering method and Backlund transformation. We also discuss the large deflection problem of long and narrow plate. We can study the non-linear transition of elastic thin plate by furnished method from this paper.

Formation of black holes in quantum cosmology

Abstract: The formation of black holes in the quantum cosmology scheme has been discussed by means of calculating the wave function of the universe with a black hole, which is described by a Schwarzschild-de Sitter metric. The average radius of the Schwarzschild black holes formed in the process of the birth of the universe is shown to be about l p 6 H 2 / a 3 , where l p is the Planck length; ∧=3 H 2 is the cosmological constant; a is the radius of the universe when it enters into the classical era.

A forest inventory using LANDSAT imagery in the Mao-shan area of China

Abstract: This paper presents a forest inventory study of the Mao-shan area, a region which is partly representative of the forest types of southern China. In the study, the effectiveness of various feature extraction techniques was investigated, new classification algorithms were developed and supervised classification schemes were implemented and assessed. A scheme involving two-dimensional spectrum decomposition classification, manual editing and Bayes classification is proposed. Its application gives results which show promising potential for forest inventory in southern China using computer processing of LANDSAT imagery.

Profiles of spectral lines of an accretion ring around a Kerr black hole

Abstract: Profiles of spectral lines emitted from an accretion ring around an object with strong gravitational field should be affected by Doppler shift, gravitational redshift, and deflection of light. Taking these effects into account, precise line profile of a Keplerian ring around a Kerr black hole for a distant observer is obtained by solving the kinetic equation of photons.

K-Ar ages and Pb, Sr isotopic characteristics of Cenozoic volcanic rocks in Shandong Province, China

Abstract: 28 samples of Cenozoic volcanic rocks collected from Shandong Province have been dated by K-Ar method. They are mainly Neogene with an age range of 4–19 m. y. The basalts from Linqu and Yishui in west Shandong Province are Miocene and those from Penglai and Qixia in east Shandong Province are Miocene and Pliocene in age. The basalts from Wudi in north Shandong Province are Middle-Early Pleistocene in age. In each area the duration of volcanic eruption was estimated at about 2–3 m. y.

Positron-annihilation study of the structure of pure and hydrogenated amorphous silicon

Abstract: We report measurements of positron annihilation in both pure and hydrogenated amorphous silicon, including lifetime spectra, Doppler-broadening and ACPAR (angular correlation of the positron annihilation radiation). Both the pure (aSi) and the hydrogenated (aSi:H) samples exhibit a lifetime component of about 410 ps which we attribute to small vacancies consisting of about 4 missing atoms. The corresponding defect is analyzed and the concentration is estimated to be of the order of 1017 cm−3. Only aSi:H exhibits a long-lived line with τ > 5 ns, which can represent only the pick-off annihilation of orthopositronium. This is direct evidence for the existence of large microvoids in aSi:H, and is consistent with recent reports of the presence of occluded H2 gas under high pressure in such films. We also measured the Doppler-broadened spectra and angular correlation curves to study the momentum distribution of the e− - p+ pairs in both types of films. Again, only the aSi:H sample showed evidence of positronium formation, consistent with the results of the lifetime spectral analysis.

Amorphous W-Zr Films as Diffusion Barriers Between Al and Si

Abstract: Cosputtered W70Zr30 and W40Zr60 films are investigated as diffusion barriers between Aq and Si. W-Zr alloys of both compositions were determined by x-ray diffraction to crystallize at 900/sup 0/C on A1/sub 2/O/sub 3/ substrates. On Si the W-Zr alloy reacts with the substrate above 700/sup 0/C, forming a uniform, polycrystalline layer of W and Zr silicides. Despite the high crystallization temperatures, an A1 overlayer interacts with W-Zr and the Si substrate at approx. 500/sup 0/C. MeV He-backscattering spectrometry, SEM, and EDAX indicate that this reaction is laterally nonuniform with the formation of deep pits penetrating into the Si substrate. The authors believe this to be a consequence of fractures in the W-Zr layer induced by reaction with A1. Electrical measurements on shallow junction diodes with /W-Zr/Al contacts show that the device junctions were thermally stable after a 30 min annealing at 450/sup 0/C but were all shorted after heat treatments at 500/sup 0/C or above.

Emission line redshift distribution of QSOs

Abstract: This paper is the second one of a series of papers on the redshift distribution of QSOs. In this paper, we shall study the influence of the selection effect in the identification of emission lines on the redshift distribution of QSOs more thoroughly than the previous paper (Zhouet al., 1983). If we assume that the QSO's redshift is cosmological, adopt the standard model, and consider the selection effect due to the redshift identification, the limiting apparent magnitude in the observation and the evolutionary effect of QSOs, we can compute the emission line redshift distribution for the so-called optically selected QSOs discovered by objective prism, grating prism technique alone, the QSOs discovered by positional methods or by colour technique and for whole QSOs, respectively (see Figures 6, 11, 12). The results of computation agree with the observations very well, especially for optically selected QSOs; the computational distribution has almost the same shape with the observational one. For this kind of the QSOs the computational distribution may give the positions and heights of all these observed peaks. The correlation coefficient γ between the calculated and observed distributions is larger than 0.95. It shows that (a) the peaks and dips in the redshift distribution of QSOs are mainly caused by the selection effect in the redshift identification, and (b) the redshift of QSOs is cosmological.

On the influences of large-scale inhomogeneity of sea temperature upon the oceanic waves in the tropical regions——part i : linear theoretical analysis

Abstract: By using a linear oceanic mixed layer model, the influences of the horizontal gradients of sea surface temperature (SST) and the depth variations of the mixed layer upon tropical oceanic waves are investigated. The equatorial Rossby wave will be modified and a kind of slower thermal wave has been revealed under the influences of inhomogeneities of large-scale sea temperature field. An interesting result is that the propagating direction of the thermal wave is opposite to that of the classical Rossby wave. The result also shows that the thermal wave becomes dominant when the meridional gradient of sea temperature in the mixed layer exceeds a critical value. As a first approximation, it seems that both waves obtained by this study may be used to explain the observational facts that the SST anomalies can usually propagate in both directions, that is, eastward and westward, during the El Nino events.

StrongL 1-norm consistency of data based histogram estimates of densities

Abstract: In this paper we investigate the problem of estimating thed-dimensional probability densityf(x),x∈R d from a sample of sizen. The non-parametric estimator is the data based histogramf n (x) as defined in (1). Under suitable conditions, we have proved theL 1-norm consistance of this estimate, that is $$\mathop {\lim }\limits_{n \to \infty } \int_{R^a } {|f(x) - f_n (x)|dx = 0,{\text{ a}}{\text{.s}}{\text{.}}}$$

Planar Metric Inequalities Derived from the Vandermonde Determinant

Abstract: (1985). Planar Metric Inequalities Derived from the Vandermonde Determinant. The American Mathematical Monthly: Vol. 92, No. 7, pp. 495-499.