Quantum MDS codes with new length and large minimum distance

According to the well-known CSS construction, constructing quantum MDS codes are extensively investigated via Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes. In this paper, given two Hermitian self-orthogonal GRS codes $GR{S}_{k_1}(A,{\mathit{v}}_A)$ and $GR{S}_{k_2}(B,{\mathit{v}}_B)$, we propose a sufficient condition to ensure that $GR{S}_k(A\cup B,{\mathit{v}}_{A\cup B})$ is still a Hermitian self-orthogonal code. Consequently, we first present a new general construction of infinitely families of quantum MDS codes from known ones. Moreover, applying the trace function and norm function over finite fields, we give another two new constructions of quantum MDS codes with flexible parameters. It turns out that the forms of the lengths of our quantum MDS codes are quite different from previous known results in the literature. Meanwhile, the minimum distances of all the q-ary quantum MDS codes are bigger than $q/2+1$.     

原子吸收光谱法测定人体毛发中的微量元素锌、铁和钙

经混合酸消解样品后,直接用火焰原子吸收光谱法测定人体毛发的锌、铁和钙3种微量元素的含量。该法简便,快速,精密度高,相对标准偏差(RSD)≤1.96%,回收率在95%—100%之间,结果准确可靠。     

A note on a generalization of the Luo's uncertainty relation

We give the trace inequalities as a generalization of the uncertainty relation improved by S. Luo. These inequalities are refinements of the trace inequality conjectured by Furuichi et al.     

A Highly Sensitive Method for Determination of Monobutyltin in Aqueous Media by Stripping Voltammetry at a Renewable Silver Amalgam Annular Band Electrode

An adsorptive stripping voltammetric (AdSV) procedure for the determination of monobutyltin in aqueous media at a silver liquid amalgam film‐modified silver solid amalgam annular band electrode (AgLAF? AgSAE) is described. Determination of monobutyltin proceeds in two steps. At the beginning monobutyltin ions (BuSn³⁺) are accumulated from 0.1 M NH₄NO₃ and 10 % ethanol solution at a potential of ?0.2 V, than the BuSn⁰ film is preconcentrated at the working electrode surface at a potential of ?0.7 V. After this step the DP AdSV voltammogram is recorded. The analytical parameters and the procedure of the electrode regeneration and activation were optimized. The calibration curve of monobutyltin in the range 0.02–0.30 mg L^?1 is linear (r=0.9973). The detection limit for 5 s of preconcentration, calculated as 3σ of the blank was equal to 0.004 mg L^?1, repeatability of the peak current was 1.8 % (n=5). Repeatability and sensitivity of monobutyltin determination depends strongly on the analyzed solution properties, measurement conditions and the working electrode quality. The proposed procedure was tested by means of monobutyltin determination in tap waters.     

Determination of rare earth, major and trace elements in authigenic fraction of Andaman Sea (Northeastern Indian Ocean) sediments by Inductively Coupled Plasma-Mass Spectrometry

Downcore variation of rare earth elements (REEs) in the authigenic Fe-Mn oxides of a sediment core (covering a record of last ∼ 40 kyr) from the Andaman Sea, a part of the Indian Ocean shows distinctive positive Ce and Eu anomalies. These positive Ce anomalies (Ce* = 1.1 ∼ 1.8) are ascribed to be due to oxidation of deep sea sediments. The large positive Eu anomalies (i.e., Eu* >1.8 to 3.2) occur within a time span near the glacial/interglacial transition (∼ 7000-14,000 yr BP) which could be due to the past hydrothermal activity or to the effects arising from sea level changes. During glacial times, the Andaman Sea was almost completely isolated due to low sea level, leading to a reduction in sediment supply from the Ayeyarwady River. The variations of metal abundances (i.e., Ca, Al, Mn, and Fe) in the authigenic fraction provided independent information to evaluate the water column physicochemical changes during the glacial/interglacial transition period. The studied sediment core records changes in riverine inputs and reflects depositional changes related to sea level fluctuations and climatic events over the past 40 kyr in the Andaman Sea.     

A trace representation of binary Jacobi sequences

We determine the trace function representation, or equivalently, the Fourier spectral sequences of binary Jacobi sequences of period pq, where p and q are two distinct odd primes. This includes the twin-prime sequences of period p(p+2) whenever both p and p+2 are primes, corresponding to cyclic Hadamard difference sets.     

Trace-Like Invariant for Representations of Nilpotent Liftings of Quantum Planes

We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module.     

Three-way principal component analysis of chemical data from Lake Como watershed

A large data set obtained by a one-year monthly determination of ions (F⁻, Cl⁻, Br⁻, NO₃⁻, NO₂⁻, PO₄³⁻, SO₄²⁻, Na⁺, K⁺, Ca²⁺, Mg²⁺, NH₄⁺) and trace metals of environmental concern (Ni, Co, Mn, Fe) from the tributaries of Lake Como (Lombardy, Northern Italy) was treated by three-way Principal Component Analysis. The results showed that the chemical features of the investigated rivers are mainly related to the lithology of the watershed. Some cases of contamination were evidenced and rationalized on the basis of anthropic pollution or on the basis of the geochemical features of the territory. The method here proposed allows an easy and quick interpretation of the chemical data by means of graphical devices. The information extracted by the three-way models would be very useful to regional agencies in developing a strategy to manage water resources in the whole basin of Lake Como.     

Microfabricated disposable lab-on-a-chip sensors with integrated bismuth microelectrode arrays for voltammetric determination of trace metals

This work reports the fabrication of disposable three-electrode cells with integrated metal-film electrodes. The devices were fabricated by a multi-step micro-fabrication approach combining sputtering for the deposition of metals and the dielectric material (SiO₂) on the surface of a silicon wafer and photolithography for the definition of the geometry of the sensors. The working electrode was a microelectrode array consisting of bismuth microdisks while the reference and counter electrode strips were made of Ag and Pt, respectively. The utility of these devices was tested for the trace determination of Pb(II) and Cd(II) by anodic stripping voltammetry and Ni(II) by adsorptive stripping voltammetry. The detection of these trace metals was carried out in unstirred and undeoxygenated solutions exhibiting sub-μg L⁻¹ limits of detection and enhanced analytical characteristics compared to conventional bismuth-film electrodes.