When Does a Polynomial Over a Finite Field Permute the Elements of the Field?

We present a class of indecomposable polynomials of non prime-power degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field. The associated geometric monodromy groups are the simple ...

on quadratic bent functions in polynomial forms

In this correspondence, we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields. The results improve some previous work. Moreover, we solve a problem left by Yu and Gong in 2006.

A discrete square global grid system based on the parallels plane projection

Knowledge Innovation Project of Chinese Academy of Sciences [KZCX3-SW-347]; National Science Fund for Distinguished Young Scholar [40225004]

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Lanthanide-hinged calixarene bicapsules: Discrete hexanuclear Ln(III)/phenanthroline/p-sulfonatocalix[4]arene oligomers (Ln = Gd, Tb)

The dumbbell-like calixarene bicapsule in two novel Ln(III)-C4AS compounds was found to be a hexanuclear Ln(III)/phenanthroline/p-sulfonatocalix[4]arene oligomer. The magnetic and luminescent properties of these compounds were examined.

Assembly of 'discrete' (H2O)(16) water clusters within a supramolecular compound of calixarene

A 'discrete' (H2O)(16) cluster, featuring four basic cyclic nine-membered rings and a twelve-membered ring, illustrates a new mode of supramolecular association of water molecules.

Observation of Slow Magnetic Relaxation in Discrete Dysprosium Cubane

A discrete dysprosium cubane has been prepared and structurally characterized Slow relaxation of magnetization in this complex is observed, which may stimulate further investigations into the dynamics of magnetization in lanthanide clusters with different topologies.

The first discrete mixed-valence hexadecavanadate host shell cluster anions: hydrothermal synthesis, structure and characterization of [V16O38(Cl)](8-)

A new compound, [NH4](2)[Zn(phen)(3)](2)[Zn(phen)(2)(H2O)(2)][V16O38(Cl)] (.) 5H(2)O (1), was synthesized in the hydrothermal condition. The "naked" [V16O38(Cl)](8-) is the first observation with host shell structure in polyoxovanadate chemistry.

LEAST-SQUARES POLYNOMIAL SMOOTHING FOR INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTRA

The use of least-squres polynomial smoothing in ICP-AES is discussed and a method of points insertion into spectral scanning intervals is proposed in the present paper. Optimal FWHM/SR ratio can be obtained, and distortion of smoothed spectra can be avoided by use of the recommended method.