Characteristic Elements of Unimodular -lattices

Characteristic elements have been useful in the classification of unimodular lattices over the integers. This article gives an explicit formula for characteristic elements of a lattice in terms of a basis for the lattice and the dual of that basis.     

Operational characteristics of dual gain single cavity Nd:YVO4 laser

Operational characteristics of a dual gain single cavity Nd:YVO₄ laser have been investigated. With semiconductor diode laser pump power of 2 W, 800 mW output was obtained with a slope efficiency of 49%. Further, by changing the relative orientation of the two crystals the polarization characteristics of the output could be varied. In particular by keeping the two Nd:YVO₄ crystals with their c-axes orthogonal to each other and adjusting the gain of the crystals so that both operate at approximately the same power level, completely unpolarized beams could be obtained.     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

（张泽银）（王建忠）ＯＮＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＤＵＡＬＳＯＦＷＡＶＥＬＥＴＦＲＡＭＥＳ￥ＺｈａｎｇＺｅｙｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕｂａｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００６２，Ｃｈｉｎａ...     

On an Isomorphism Problem of Some Dual Hyperovals in PG(2d + 1, q) with q even

Let q = 2^l with l≥ 1 and d ≥ 2. We prove that any automorphism of the d-dimensional dual hyperoval over GF(q), constructed in [3] for any (d + 1)-dimensional GF(q)-vector subspace V in GF(qⁿ) with n≥ d + 1 and for any generator σ of the Galois group of GF(qⁿ) over GF(q), always fixes the special member X(∞). Moreover, we prove that, in case V = GF(q^d+1), two dual hyperovals and in PG(2d + 1,q), where σ and τ are generators of the Galois group of GF(q^d+1) over GF(q), are isomorphic if and only if (1) σ = τ or (2) σ τ = id. Therefore, we have proved that, even in the case q > 2, there exist non isomorphic d-dimensional dual hyperovals in PG(2d + 1,q) for d ≥ 3.     

Dual effects of ultrasound on fabrication of anodic aluminum oxide

Ultrasound has been proven to enhance the mass transfer process and impact the fabrication of anodic aluminum oxide (AAO). However, the different effects of ultrasound propagating in different media make the specific target and process of ultrasound in AAO remain unclear, and the effects of ultrasound on AAO reported in previous studies are contradictory. These uncertainties have greatly limited the application of ultrasonic-assisted anodization (UAA) in practice. In this study, the bubble desorption and mass transfer enhancement effects were decoupled based on an anodizing system with focused ultrasound, such that the dual effects of ultrasound on different targets were distinguished. The results showed that ultrasound has the dual effects on AAO fabrication. Specifically, ultrasound focused on the anode has a nanopore-expansion effect on AAO, leading to a 12.24 % improvement in fabrication efficiency. This was attributed to the promotion of interfacial ion migration through ultrasonic-induced high-frequency vibrational bubble desorption. However, AAO nanopores were observed to shrink when ultrasound was focused on the electrolyte, accompanied by a 25.85 % reduction in fabrication efficiency. The effects of ultrasound on mass transfer through jet cavitation appeared to be the reason for this phenomenon. This study resolved the paradoxical phenomena of UAA in previous studies and is expected to guide AAO application in electrochemistry and surface treatments.     

An Interface Crack for a Functionally Graded Strip Sandwiched Between Two Homogeneous Layers of Finite Thickness

In this paper, the behavior of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness subjected to an uniform tension is resolved using a somewhat different approach, named the Schmidt method. The Fourier transform technique is applied and a mixed boundary value problem is reduced to two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surface. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effects of the crack length, the thickness of the material layer and the materials constants upon the stress intensity factor of the cracks. It can be obtained that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.     

Enantiomeric separation of 1,3‐dimethylamylamine by capillary electrophoresis with indirect UV detection using a dual‐selector system

The CE method employing an indirect UV detection for the enantioseparation of 1,3‐dimethylamylamine (DMAA), widely used in various preworkout and dietary supplements labeled as a constituent of geranium extract has been developed. The dual‐selector system consisting of negatively charged sulfated α‐CD (1.1% w/v) and sulfated β‐CD (0.2% w/v) in 5 mM phosphate/Tris buffer (pH 3.0) containing the addition of 10 mM benzyltriethylammonium chloride (BTEAC) as the chromophoric additive was used for the enantiomeric separation of DMAA stereoisomers with the LODs in the range of 7.82–9.24 μg/mL. The method was partly validated and applied for the determination of the stereoisomeric composition of DMAA in commercial dietary supplements to verify the potential natural origin of DMAA.     

Double-ion imprinted polymer @magnetic nanoparticles modified screen printed carbon electrode for simultaneous analysis of cerium and gadolinium ions

A typical, reproducible, and rugged screen printed carbon electrode, modified with dual-ion imprinted beads, was fabricated employing the “surface grafting from” approach. For this, the acyl chloride functionalized magnetic nanoparticles were first immobilized and chemically attached with a typical functional monomer (but-2-enedioic acid bis-[(2-amino-ethyl)-amide]) on the electrode surface. This was subsequently subjected to the thermal polymerization in the presence of template ions (Ce(IV) and Gd(III)), cross-linker (ethylene glycol dimethacrylate), initiator (AIBN), and multiwalled carbon nanotubes. The modified sensor was used for the simultaneous analysis of both template ions in aqueous, blood serum, and waste-water samples, using differential pulse anodic stripping voltammetry which revealed two oxidation peaks for respective templates with resolution as much as 950 mV, without any cross reactivity, interferences and false-positives. The detection limits realized by the proposed sensor, under optimized conditions, were found to be as low as 0.07 ng mL⁻¹ for Ce(IV) and 0.19 ng mL⁻¹ for Gd(III) (S/N = 3) that could eventually be helpful for lanthanide estimation at stringent levels.     

Dual gold nanoparticle lateflow immunoassay for sensitive detection of Escherichia coli O157:H7

Two patterns of signal amplification lateral flow immunoassay (LFIA), which used anti-mouse secondary antibody-linked gold nanoparticle (AuNP) for dual AuNP-LFIA were developed. Escherichia coli O157:H7 was selected as the model analyte. In the signal amplification direct LFIA method, anti-mouse secondary antibody-linked AuNP (anti-mouse-Ab-AuNP) was mixed with sample solution in an ELISA well, after which it was added to LFIA, which already contained anti-E. coli O157:H7 monoclonal antibody-AuNP (anti-E. coli O157:H7-mAb-AuNP) dispersed in the conjugate pad. Polyclonal antibody was the test line, and anti-mouse secondary antibody was the control line in nitrocellulose (NC) membrane. In the signal amplification indirect LFIA method, anti-mouse-Ab-AuNP was mixed with sample solution and anti-E. coli O157:H7-mAb-AuNP complex in ELISA well, creating a dual AuNP complex. This complex was added to LFIA, which had a polyclonal antibody as the test line and secondary antibody as the control line in NC membrane. The detection sensitivity of both LFIAs improved 100-fold and reached 1.14 × 10³ CFU mL⁻¹. The 28 nm and 45 nm AuNPs were demonstrated to be the optimal dual AuNP pairs. Signal amplification LFIA was perfectly applied to the detection of milk samples with E. coli O157:H7 via naked eye observation.