Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Countable Fréchetα 1-spaces may be first countable

It is shown to be consistent that countable, Fréchet, ₁-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of length ₂.The research of both authors is partially supported by NSERC     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

A theoretical analysis of modulation noise and dc erased noise in magnetic recording

The modulation noise and the special case, dc erased noise in magnetic recording are discussed theoretically, taking account of two main causes at the same stage, i.e. the magnetic properties such as the inhomogeneous distribution of the particles on the tape, and the mechanical properties such as the head-to-tape space variations arising from the tape surface roughness. We derive the signal as well as the noise power spectrum of the induced voltage at the read head. This is done by generalizing the theory of the signal behaviour. The theoretical result turned out to agree quite well with the experimental one. The modulation noise power spectrum can be interpreted to consist of two parts, i.e. the steep peak due to the mechanical causes near the recorded signal wavenumber and the broad peak due to magnetic causes.Nomenclature A(k) variable defined by(Km_av L _g L _d)² - d head-to-tape spacing [m] - d _av average value ofd [m] - d variance ofd [m] - D variable defined by (8) - e(t) induced voltage at the read head [V] - g gap length [m] - H the Karlqvist head field excited by a current uniti [A/m] - i a curren unit [A] - j –1 - k=¦k¦ wavenumber [m^–1] - k _c wavenumber of recorded signal [m^–1] - K constant which includes the number of turn of head, the read head efficiency and the permeability ₀[Vs/Am] - l _d correlation length of the variationd [m] - l _m correlation length of the variationm [m] - L _d (k) spacing loss defined by exp(–kd_av) - L _g (k) gap loss defined by sin(gk/2)/(gk/2) - M magnetization of the tape [A/m] - M variable defined by (8) - m amplitude of the magnetization of the signal pattern [A/m] - m _av average value ofm [A/m] - m variance ofd [A/m] - P(k) power spectrum [V²/Hz] - P _dc(k) noise power spectrum [V²/Hz] - S signal pattern of the tape - v relative velocity between the head and the tape [m/s] - x _t =(x _t ,y_t) coordinate on the tape - (x ₀,y₀) coordinate fixed on the read head - (x ₁,y₁) coordinate defined by (10) - tape thickness [m] - _d random phase variable defined by (8) - _m random phase variable defined by (8) - _O permeability [Vs/Am] - read-head detected flux [Wb]     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.     

An Encryption Algorithm for Region of Interest in Medical DICOM Based on One-Dimensional eλ-cos-cot Map

Today, with the rapid development of the Internet, improving image security becomes more and more important. To improve image encryption efficiency, a novel region of interest (ROI) encryption algorithm based on a chaotic system was proposed. First, a new 1D eλ-cos-cot (1D-ECC) with better chaotic performance than the traditional chaotic system is proposed. Second, the chaotic system is used to generate a plaintext-relate keystream based on the label information of a medical image DICOM (Digital Imaging and Communications in Medicine) file, the medical image is segmented using an adaptive threshold, and the segmented region of interest is encrypted. The encryption process is divided into two stages: scrambling and diffusion. In the scrambling stage, helical scanning and index scrambling are combined to scramble. In the diffusion stage, two-dimensional bi-directional diffusion is adopted, that is, the image is bi-directionally diffused row by column to make image security better. The algorithm offers good encryption speed and security performance, according to simulation results and security analysis.     

Unusual Reactivities of ortho-Hydroxy-β-nitrostyrene

Nitrostyrene derivatives are widely used in organic syntheses as a substrate for Michael addition, photoisomerization and cycloaddition. In contrast, ortho-hydroxy derivatives exhibit unusual behaviors in these reactions. Conjugate addition proceeded upon treatment of the ortho-hydroxy-β-nitrostyrene with an amine; however, subsequent C–C bond cleavage readily occurred to afford the corresponding imine. Moreover, conversion of the trans-isomer to a cis-isomer did not occur efficiently, even when UV light was irradiated. We studied these unusual behaviors of β-nitrostyrene, focusing on the role of the ortho-hydroxy group.