Functions In Cn Research Articles

Interpolating multiplicity varieties in C n

A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for weighted spaces of entire functions in Cn.

The Cantorian structure of the background magnetic field and high temperature superconductors

One builds the solution of GL equation in terms of the elliptic cn function of complex argument. The real part of the complex action, S=ℏ ln cn (u) , corresponds to the potential of a vortex lattice, and from here, through the elliptic function degeneration, to the vortex streets. Considering the vortex streets fixed on vacuum by a background magnetic field through pinning, from equating the current density to zero one determines the field structure: the mean value will be roughly equal to B C 2 , and its flux will be fractional. The fractional flux will be associated to quasi-particles obeying the ‘anyonic’ statistics. At low temperatures and high external magnetic field, the structure of background field will be of Cantorian type.

CN algorithm and long-lasting changes in reported magnitudes: the case of Italy

SUMMARY Prediction methods based on seismic precursors, and hence assuming that catalogues contain the necessary information to predict earthquakes, are sometimes criticised for their sensitivity to the unavoidable catalogue errors and possible undeclared variations in the evaluation of reported magnitudes. We consider a real example and we discuss the eVect, on CN predictions, of a long-lasting underestimation of the reported magnitudes. Starting approximately in 1988, the CN functions in Central Italy evidence an anomalous behaviour, not associated with TIPs, that indicates an unusual absence of moderate events. To investigate this phenomenon, the magnitudes given in the catalogue used, which since 1980 is defined by the ING bulletins, are compared to the magnitudes reported by the global catalogue NEIC (National Earthquake Information Centre, USGS, USA) and by the regional LDG bulletins issued at the Laboratoire de Detection et de Geophysique, Bruyeres-le-Chatel, France. The comparison is performed between the ING bulletins and the NEIC catalogue, considering the local, M L , and duration, M d , magnitudes, first within the Central region, and then extended to the whole Italian territory. To check the consistency of the conclusions drawn from ING and NEIC data, the comparison of local magnitudes is extended to a third data set, the LDG bulletins. The diVerences between duration magnitudes M d that are reported by ING and NEIC since 1983 appear quite constant with time. Starting in 1987, an average underestimation of about 0.5 can be attributed to M L reported by ING for the Central region; this diVerence decreases to about 0.2 when the whole Italian territory is considered. The anomalous behaviour of the CN functions disappears if a magnitude correction of +0.5 is applied to M L reported in the ING bulletins. However, such a simple magnitude shift cannot restore the real features of the seismic flow, and ING bulletins are not suitable for CN algorithm application.

On Power Series of Algebraic and Rational Functions in Cn

On Power Series of Algebraic and Rational Functions in Cn

Deposition mechanisms and properties of oxygenated carbon nitride films from rf discharges of acetylene, nitrogen, oxygen and argon mixtures

Oxygen-containing carbon nitride films were deposited in rf discharges of C 2H 2, N 2, O 2 and Ar mixtures. Actinometric optical emission spectroscopy was used to determine relative concentrations of the species H, O, CH, CN and CO in the discharge as a function of the proportion of oxygen in the feed, using Ar as an actinometer. The Ar emission intensity decreases as the proportion of O 2 in the feed increases, indicating that O 2 has a `cooling effect' on the discharge. The variations in the concentrations of CH and CN species, two possible precursors of film formation, showed different behaviors. The concentration of CH increases monotonically as the proportion of O 2 in the feed is increased, but the concentration of CN shows a maximum at an oxygen to acetylene ratio of about 0.15, which coincides with the maximum film deposition rate. This strongly suggests that the CN species is the main precursor of film formation. Infrared reflection spectroscopy revealed the presence of CN, CH, NH and CO functionalities in the deposited films. The presence of such species and their relationship to deposition via gas-phase and surface reactions are outlined. The optical properties of the films were investigated using transmission and reflection ultraviolet–visible spectroscopy. At increasing proportions of oxygen in the gas feed, the refractive index decreases while the optical gap increases. Free radicals were investigated using electron paramagnetic resonance. Unpaired spin concentrations of the order of 10 20 cm −3 were measured in the films a short time after deposition. These large spin concentrations are common in films prepared by plasma-enhanced chemical-vapor deposition (PECVD) but decrease at relatively high rates with time. Possible mechanisms accounting for the high spin concentrations and for the disappearance of the free radicals are discussed.

The uniqueness problem and meromorphic solutions of partial differential equations

A general uniqueness theorem is proved for meromorphic functions in Cn which share three distinct small functions with their linear partial differential polynomials. As a consequence, a necessary and sufficient condition in terms of shared values for a meromorphic function to be a solution of a linear partial differential equation of constant coefficients is obtained.

Application of the CN Intermediate-term Earthquake Prediction Algorithm to the Area of the Southern External Dinarides

—The paper presents the results of application of the CN algorithm to the area of the Southern External Dinarides. Two cases are considered—one for the knowledge gained throughout the considered period of time (1936–1996), and the other when learning ceased in 1986. In the first case 8 out of 9 strong earthquakes could have been predicted, three false alarms are declared (covering 7% of the total time considered) and TIPs occupy 32% of the total time. There is no clear relation between the TIPs duration and the size of the related earthquake. The second case (when the CN functions are defined on the basis of a shorter learning period) produces even slightly better results: only two false alarms are declared. In both cases current alarm exists in the region. All attempts to reduce the area of the regional polygon resulted in poorer prediction results.

Level sets of a typical 𝐶ⁿ function

We determine the level set structure of a typical C n C^n function.

Density functional theory investigation of physical properties of the OCCN radical and the cation

Structural and thermodynamic properties for the OCCN radical and its cation were estimated with hybrid, gradient-corrected and local density functional theory methods by using three various Gaussian type basis sets. It was estimated that the radical structure should be a zig-zag structure, which corresponds to the sp 2 hybridization of the carbonyl carbon, while the OCCN cation is linear. The radical ionization potential should be between 8.7 and 9.1 eV with the enthalpy of formation at approximately 51 kcal/mol. It was computed in the infrared spectra that there were two strong absorptions at 1863 and 2080 cm −1 for the CO and the CN functionalities and they should be observable for the OCCN radical.

Disjoint unions of complex affine subspaces interpolating for Ap

Let X be a discrete variety of ℂn. Berenstein and Li [Berenstein, C.A. and Li, B.Q.: Interpolating varieties for weighted spaces of entire functions in ℂn. Publicacions. Malemàtiqucs 38 (1994), 157–173] obtained a necessary and sufficient analytic condition for X to be interpolating for Ap. In this paper, we extend it to the case when X is a disjoint union of complex affine subspaces of ℂn. As a corollary, we solve an open problem posed by Berenstein and Taylor [Berenstein, C.A. and Taylor, B. A.: On the geometry of interpolating varieties. In: Seminaire Lelong-Skoda (1980/1981). (ed. by P. Lelong and H. Skoda), pp. 1–25. Lecture Notes in Math. 919. Springer-Verlag, New York–Berlin–Heidelberg 1982] on the interpolation, when the subvariety under consideration is a disjoint union of complex affine subspaces.

Carleman approximation on products of riemann surfaces

In [19] Scheinberg generalized a celebrated theorem of Carleman by showing that a continous function on R n can be approximated with arbitrary speed by entire ffunctions of n complex variables. Alexander showed in [1] that an unbounded smooth curve in C n is such a set of Carleman approximation. Frih and Gauthier in [8] studied Carleman approximation by entire functions in Cn on products of curves in C n, n1+…+n>k =n. In the present paper, we show that a product set in a product of Riemann surfaces is a Carleman set if and only of each projection is a Carleman set, thus generalizing the results of [18] and [19].

Growth properties of plurisubharmonic functions related to Fourier-Laplace transforms

The purpose of the paper is to study the behavior at infinity of Fourier-Laplace transforms of distributions or more generally plurisubharmonic functions u in Cn with bounds of the form $$u(\zeta ) \leqslant C + A|\zeta |, \zeta \in C^n , \int_{R^n } {u^ + (\xi )(1 + |\xi |)^{ - n - 1} d\xi< \infty .} $$ The set L∞(u) of limits of Ttu = u(t·)/t as t → +∞ is a compact T invariant subset of the set PH of plurisubharmonic functions in Cn with v(ξ) ≤H(Im ξ), ξ ∈ Cn, and equality on CRn. Here H is a supporting function associated with u, and T is chain recurrent on L∞(u). The behavior of functions in PH at CRn is studied in detail, which leads to conditions on a set M ⊂PH which guarantee that M = L∞(u) for some u as above. One can then choose u = log ¦ F ¦ where F is the Fourier-Laplace transform of a distribution with compact support.

The Time of Diffusion and Infinite Conductivity of High-Tc Superconductors

In the composite fermion approach, extending in complex space the elliptic cn function (which is the perturbative solution of the Ginzburg-Landau equation in the strong coupling limit), we estimate the diffusion time of the superconductor charge carriers and we find that it diverges for particular values of the coherence length. We believe this mechanism may account for the infinite conductivity of high-temperature superconductors.

Cell-Specific Calcineurin Inhibition by a Modified Cyclosporin

The immunosuppressive drug cyclosporin A (CsA) is widely used to suppress graft rejection following transplantation in humans. Its cellular effects are mediated by a complex of CsA and its intracellular, soluble receptor cyclophilin (Cyp).1 The Cyp-CsA complex is a specific inhibitor of the protein phosphatase calcineurin (Cn).2 Consequently, CsA has also been used to illuminate the cellular functions of Cn. For example, its use revealed that, in T cells, Cn mediates the nuclear translocation and activation of NFAT,3 a transcription factor essential for T cell activation. As a therapeutic agent, CsA has several undesirable side effects including hypertension, CNS toxicity, and nephrotoxicity. These side effects result from CsAmediated inhibition of Cn in cells outside the immune system.4 We now report the synthesis of R-cyclopentylsarcosine11CsA (CsA*), a rationally modified CsA that does not bind to Cyp and consequently does not inhibit Cn in cells. We also describe a modified Cyp with compensatory mutations in its CsA-binding pocket (F113G, C115M, S99T; Cyp*) that promote high affinity complexation with CsA*. The resulting Cyp*CsA* complex presents a composite surface that binds Cn with high affinity. As a result, Cn inhibition by CsA* is restored in cells expressing Cyp*. These results provide a method to control the inhibition of Cn spatially and temporally in animals by targeting the expression of Cyp* to specific cells and tissues. Modifying receptors or ligands by adding even a few atoms can abolish their binding, often changing the function of the molecules involved. When these loss-of-interaction substituents are introduced into proteins by mutation5 and small molecules by synthesis,6 information about the cellular function of interacting molecules can be obtained. To achieve our goal of cellspecific Cn inhibition, it was essential that the modified receptor-ligand complex have a composite surface suited for Cn binding, since altered Cyp-CsA complexes can be envisioned that will no longer bind Cn (lower right schematic in Figure 1). We designed a variant of CsA having two additional methylenes (CH2) attached to the two methyl groups of the MeVal11 side chain, resulting in the cyclopentyl side chain of CsA*. The crystal structure of the CypA-CsA complex7 shows residue 11 of CsA directly contacting Cyp, binding in a deep hydrophobic pocket in the active site of Cyp (Figure 2A). The additional atoms were expected to reduce the binding of CsA* to Cyp significantly, presumably through steric interactions

Molecular characterization of the cinnabar region of Drosophila melanogaster: identification of the cinnabar transcription unit.

Early studies of eye pigmentation in Drosophila melanogaster provided compelling evidence that the cinnabar (cn) gene encodes the enzyme kynurenine 3-monooxygenase (EC 1.14.13.9). Here we report the cloning of approximately 60 kb of DNA encompassing the cn gene by chromosome walking in the 43E6-F1 region of chromosome 2. An indication of the position of cn within the cloned region was obtained by molecular analysis of mutants: 9 spontaneous cn mutants were found to have either DNA insertions or deletions within a 5 kb region. In addition, a 7.8 kb restriction fragment encompassing the region altered in the mutants was observed to induce transient cn function when microinjected into cn- embryos. The cn transcription unit was identified by Northern blotting and sequence analysis of cDNA and genomic clones from this region. The predicted cn protein contains several sequence motifs common to aromatic monooxygenases and is consistent with the assignment of cn as encoding the structural gene for kynurenine 3-monooxygenase.

Comparison of certain 𝐻^{∞}-domains of holomorphy

We study open sets defined by certain global plurisubharmonic functions in C N {\mathbb {C}^N} . We examine how the fact that the connected components of the sets are H ∞ {H^\infty } -domains of holomorphy is related to the structure of the set of discontinuity points of the global defining functions and to polynomial convexity.

X-ray Photoelectron Spectroscopy Study of Argon Plasma-Treated Fluoropolymers

Films of poly(tetrafluoroethylene) (PTFE) and of a tetrafluoroethylene-perfluoroalkyl vinyl ether (approximately 49:1) copolymer (PFA) were exposed to a radio-frequency argon plasma and then examined by X-ray photoelectron spectroscopy (XPS). The use of fluoropolymer films nearly free of surface hydrocarbon contamination as well as the use of a monochromatized X-ray source for XPS removed two factors contributing to conflicting reports on the effect of exposure time on the fluorine-to-carbon (F/C) and oxygen-to-carbon (O/C) ratios for several Ar-plasma-treated fluoropolymers. Contrary to literature indications, a common pattern was found for PTFE and PFA: a moderate decrease in F/C ratio (from 1.99 to 1.40, and from 1.97 to 1.57, respectively), together with a moderate increase in O/C ratio (from negligible to about 0.10, and from 0.012 to about O.10, respectively) at very short exposures, after which the F/C ratios remained essentially constant on prolonged exposures, while the O/C ratios for PTFE and PFA leveled off at 0.11 and 0.15, respectively. The XPS C(sub 1s), spectra for these polymers exposed to the Ar plasma for 20 min were similar and presented, besides a prominent peak at 292.0 eV (CF2,) and a minor peak at 294.0 or 294.1 eV (CF3), a composite band of four curve-resolved peaks (approximately 285-290 eV) representing various CH, CC, CO, CN, and CF functionalities.

Synthesis of [amine(tert-butylisonitrile) dihydroboron(III)] cations via the antimony pentachloride complexes of amine-dihydrocyanoboranes. A new route to amine-carboxyboranes

The reaction of the cyanoborane complexes L·BH 2CN [where L = R 3N (R = Me, Et, Pr, Bu); quinuclidine (Q) and Ph 3P] with SbCl 5 in CCl 4 afforded 1:1 complexes. Coordination of antimony to the nitrogen atom of the cyano groupp was clearly implied by the 35–42 cm −1 shift of the ν CN cyano resonances towards the higher wave-numbers. The L·BH 2CN·SbCl 5 complexes, carrying a bridge-head CN function, readily transformed with Bu t Cl into the [BH 2(L)CNBu t ]SbCl 6 tert-butylnitrilium salts with high crystallization ability. In the case of L = R 3N and Q substituents partial chlorination of the BH bond accompanied the formation of the nitrilium salt. The relatively weak coordination of the Bu t NC ligand in the above antimony complexes was indicated by the 2282–2292 cm −1 values observed for ν CN, unexpectedly high for isonitrile complexes, as well as by the exchange reactions with strong donors (i.e. Me 2SO, Q, DMAP), giving rise to the liberation of the Bu t NC. The synthetic utility of related complexes was shown by the highly efficient transformation of [BH 2(L)CNBu t ]SbCl 6 into Me·BH 2C(O)NHBu t in an alkaline medium, whose acid hydrolysis furnishes Me 3N·BH 2COOH, a well-known and important compound in boron chemistry with high yield. Preparation of this substance with the presented new process, via the tert-butylnitrilium salt, is much more efficient than by means of the previously reported procedures employing the ethylnitrilium salt. The proposed structures of the new compounds L·BH 2CN·SbCl 5, [BH 2(L)CNBu t ]SbCl 6 and Me 3·BH 2C(O)NHBu t were derived from IR, 1H and 11B NMR spectral data.

Synthesis of μ‐Cyano(2,3‐naphthalocyaninato)iron(III) and Comparison to μ‐Cyano(phthalocyaninato)iron(III)

AbstractPotassium dicyano(2,3‐naphthalocyaninato)ferrate(III), K[2,3‐NcFe(CN)2] (2), reacts in water with elimination of KCN to form μ‐cyano(2,3‐naphthalocyaninato)iron(III), [2,3‐NcFe(CN)]n (4a). Dichloro(2,3‐naphthalocyaninato)iron(III), 2,3‐NcFeCl2 (3), reacts with KCN to yield also [2,3‐NcFe(CN)]n (4b). Both compounds 4a and 4b show similar IR spectra with a typical blue‐shifted CN valence frequency caused by a bridging function of CN‐. Compounds 4a and 4b also show almost identical 57Fe‐Mössbauer spectra which, however, might be interpreted with a Fe(+II) oxidation state of the iron. The measured magnetic moment of 4 however clearly proves the expected oxidation state +III of the iron in [2,3‐NcFe(CN)]n (4). Compounds 4a and 4b both exhibit good semiconducting properties (σRT ∼ 10–3 S/cm) without additional external oxidative doping. The property is quite similar to that of the known μ‐cyano(phthalocyaninato)iron [PcFe(CN)]n (σRT ∼ 10‐2 S/cm).

Analysis of nonlinear TE waves in a three‐layer slab waveguide with self‐focusing nonlinear film and substrate layers

AbstractThe analysis of propagation characteristics of TE waveguiding in linear/self‐focusing nonlinear/self‐focusing nonlinear, three‐layer slab waveguide with a symmetric linear dielectric distribution is presented. In this analysis, the electric field inside the film is expressed in terms of Jacobi's cn function with a constant amplitude, and the equation to determine the transverse wavenumber inside the film is derived by considering the relation between this amplitude and the electric field on both sides of the film.By introducing the maximum optical power density divided by the dielectric constant difference between the film and the substrate as a measure for nonlinearity, this equation contains only three parameters (nonlinearity parameter, normalized thickness and relative nonlinear coefficient difference).By changing the values of these parameters and restricting the numerical calculation for TEo modes, the number of TEo modes with its peaks in the substrate or in the film or at the boundary between the film and the substrate is examined. These results are illustrated in a plane in which we take the normalized thickness along the vertical axis and nonlinearity parameter along the horizontal axis.Moreover, it is shown that for the waveguide with nonlinear coefficient of the substrate greater than the film, there is a possibility of existence of TEo mode for which the values of the normalized guide index and the change of the electric field profile are discontinuous for the change of the nonlinearity parameter.