Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions between a quadratic residue and its inverse modulo p value formula. to study the asymptotic property of the difference （a prime）, and to give an interesting hybrid mean     

Chemical Speciation of Amphoteric Ions on Semi‐Dry Scrubber Residue and Bag‐House Ash from MSWI

Two series of size‐fractionated combusted residues, a bag‐house ash and a scrubber residue, from a municipal solid waste incinerator (MSWI) were prepared and extracted by means of sequential chemical extraction (SCE) procedures proposed by Tessier. Concentrations of water‐soluble phase, exchangeable phase, carbonated phase, Fe/Mn oxide phase, organic matter phase, and residual phase bound amphoteric metals (Pb and Zn) were obtained, and have been compared with those of single batch extraction of toxic characteristic leaching procedure (TCLP). In each size fraction of baghouse ash or scrubber residue, lead or zinc shows a common phenomena that the TCLP value is always lower than the content of the water‐soluble fraction. For lead, baghouse ash has a significant size‐dependent distribution on the water‐soluble phase to perform a size‐dependent test of lead in the TCLP test. The zinc TCLP data having less size dependence might be due to that neither the baghouse ash nor the scrubber residue has a size‐dependent distribution on the water‐soluble zinc phase.     

A linear minimum mean square error multiuser receiver inRayleigh-fading channels

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system     

The honeycomb network structure of poly[[[μ2‐1,3‐bis(1H‐benzimidazol‐2‐yl)benzene‐κ2N3:N3′](μ2‐terephthalato‐κ2O:O′)zinc(II)] ethanol solvate]

The terephthalate dianion and the bis(imidazolyl)benzene ligand of the title compound, {[Zn(C₈H₄O₄)(C₂₀H₁₄N₄)]·C₂H₆O}_n, each bridges two adjacent zinc centers, resulting in a layer‐type coordination polymer; the zinc center shows tetrahedral coordination. The disordered ethanol solvent molecules occupy the spaces between the layers and are hydrogen bonded to the layers. The two symmetry‐independent dianions lie on different inversion sites.     

The high‐pressure form of cadmium vanadate,CdV2O6

The crystal structure of a new high‐pressure modification of cadmium divanadium hexaoxide, CdV₂O₆, was refined from X‐ray single‐crystal data. It contains zigzag chains of edge‐sharing VO₆ octahedra. Octahedra in adjacent chains share corners and form corrugated layers. Octahedrally coordinated Cd atoms, which lie on twofold axes, are situated between the layers. The columbite‐like structure results in a strong distortion of the CdO₆ octahedra which may be stabilized only at high pressure.     

Synthesis of 5‐Radioiodoarabinosyl Uridine Analog for Probing the HSV‐1 Thymidine Kinase Gene

Tumor cells transduced with herpes simplex virus thymidine kinase gene have been intensively applied to the field of positron emission tomography via imaging of its substrate. As a pilot synthesis approach, a facile preparation of 5‐[¹²⁵I] iodoarabinosyl uridine starting from commercially available uridine is reported herein.     

Cyclic trihydroxamic acid derivatives

In the crystal structures of two cyclic trihydroxamic acid derivatives containing the same substructure unit, viz. 1,3,5‐trihydroxy‐1,3,5‐triazinane‐2,4,6‐trione dihydrate, C₃H₃N₃O₆·2H₂O, (I), and 1,3,5‐benz­yloxy‐1,3,5‐triazinane‐2,4,6‐trione, C₂₄H₂₁N₃O₆, (II), there is no significant difference in the geometric parameters. In (I), there are 11 hydrogen bonds of the O—H⋯O type inter­connecting the mol­ecules in a three‐dimensional network, while in (II) there are only two weak C—H⋯O hydrogen bonds. The results of IR spectroscopic analysis are in good agreement with the crystallographic study.     

A new polymorph of tetraphenyldiboroxane

A new polymorph of tetraphenyldiboroxane [or oxybis(diphenylborane)], C₂₄H₂₀B₂O, (Ia), has been found. It is monoclinic, like the already known form, (Ib), and can be refined in the same space group, namely P2₁/c, or in the equivalent setting P2₁/n. The molecular conformations of the two polymorphs differ in the rotations of two of the phenyl rings about the B—C bonds, leading to markedly different packing patterns and cell dimensions.