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1.
Electrochemical Behaviour and Rapid Determination of L‐Dopa at Electrochemically Pretreated Screen Printed Carbon Electrode 下载免费PDF全文
Andreea Alexandra Rabinca Mihaela Buleandra Adriana Balan Ioan Stamatin Anton Alexandru Ciucu 《Electroanalysis》2015,27(10):2275-2279
A simple and rapid voltammetric method based on a disposable electrochemically pretreated screen‐printed carbon electrode is proposed for the determination of L ‐dopa. Under optimum differential pulse voltammetry conditions a limit of detection of 3.6×10?7 M for L ‐dopa was obtained. The method was successfully applied to the determination of L ‐dopa in a commercial pharmaceutical formulation. 相似文献
2.
Let ℓ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let H{\mathcal{H}} be the half plane to the left of ℓ. We consider lozenge tilings of H{\mathcal{H}} that have a triangular gap of side-length two and in which ℓ is a free boundary — i.e., tiles are allowed to protrude out half-way across ℓ. We prove that the correlation function of this gap near the free boundary has asymptotics
\frac14pr{\frac{1}{4\pi r}}, r → ∞, where r is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric
charge near a conductor can be obtained by the method of images. 相似文献
3.
Mihai Ciucu 《Journal of Algebraic Combinatorics》2003,17(3):335-375
In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin.
1 (1992), 111–132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present an approach that allows proving them in a unified way. We use this approach to prove a conjecture of James Propp stating that the number of tilings of the so-called Aztec dungeon regions is a power (or twice a power) of 13. We also prove a conjecture of Matt Blum stating that the number of perfect matchings of a certain family of subgraphs of the square lattice is a power of 3 or twice a power of 3. In addition we obtain multi-parameter generalizations of previously known results, and new multi-parameter exact enumeration results. We obtain in particular a simple combinatorial proof of Bo-Yin Yang's multivariate generalization of fortresses, a result whose previously known proof was quite complicated, amounting to evaluation of the Kasteleyn matrix by explicit row reduction. We also include a new multivariate exact enumeration of Aztec diamonds, in the spirit of Stanley's multivariate version. 相似文献
4.
Mihai Ciucu 《Discrete Mathematics》2007,307(15):1957-1960
The even Aztec diamond ADn is known to have precisely four times more spanning trees than the odd Aztec diamond ODn—this was conjectured by Stanley and first proved by Knuth. We present a short combinatorial proof of this fact in the case of odd n. Our proof works also for the more general case of odd-by-odd Aztec rectangles. 相似文献
5.
A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G. 相似文献
6.
Mihai Ciucu 《Journal of Algebraic Combinatorics》1999,9(3):281-293
Motivated by the close relationship between the number of perfect matchings of the Aztec diamond graph introduced in [5] and the free energy of the square-ice model, we consider a higher dimensional analog of this phenomenon. For d 1, we construct d-uniform hypergraphs which generalize the Aztec diamonds and we consider a companion d-dimensional statistical model (called the 2d + 2-vertex model) whose free energy is given by the logarithm of the number of perfect matchings of our hypergraphs. We prove that the limit defining the free energy per site of the 2d + 2-vertex model exists and we obtain bounds for it. As a consequence, we obtain an especially good asymptotical approximation for the number of matchings of our hypergraphs. 相似文献
7.
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9.
Mihai Ciucu 《Journal of Algebraic Combinatorics》2008,27(4):493-538
We say that two graphs are similar if their adjacency matrices are similar matrices. We show that the square grid G
n
of order n is similar to the disjoint union of two copies of the quartered Aztec diamond QAD
n−1 of order n−1 with the path P
n
(2) on n vertices having edge weights equal to 2. Our proof is based on an explicit change of basis in the vector space on which the
adjacency matrix acts. The arguments verifying that this change of basis works are combinatorial. It follows in particular
that the characteristic polynomials of the above graphs satisfy the equality P(G
n
)=P(P
n
(2))[P(QAD
n−1)]2. On the one hand, this provides a combinatorial explanation for the “squarishness” of the characteristic polynomial of the
square grid—i.e., that it is a perfect square, up to a factor of relatively small degree. On the other hand, as formulas for
the characteristic polynomials of the path and the square grid are well known, our equality determines the characteristic
polynomial of the quartered Aztec diamond. In turn, the latter allows computing the number of spanning trees of quartered
Aztec diamonds.
We present and analyze three more families of graphs that share the above described “linear squarishness” property of square
grids: odd Aztec diamonds, mixed Aztec diamonds, and Aztec pillowcases—graphs obtained from two copies of an Aztec diamond
by identifying the corresponding vertices on their convex hulls.
We apply the above results to enumerate all the symmetry classes of spanning trees of the even Aztec diamonds, and all the
symmetry classes not involving rotations of the spanning trees of odd and mixed Aztec diamonds. We also enumerate all but
the base case of the symmetry classes of perfect matchings of odd square grids with the central vertex removed. In addition,
we obtain a product formula for the number of spanning trees of Aztec pillowcases.
Research supported in part by NSF grant DMS-0500616. 相似文献
10.
Ana-Maria Iordache Rodica Cristescu Eugenia Fagadar-Cosma Andrei C. Popescu Anton A. Ciucu Stefan M. Iordache Adriana Balan Cornelia Nichita Ioan Stamatin Douglas B. Chrisey 《Comptes Rendus Chimie》2018,21(3-4):270-276
This study reports on deposition of asymmetrical substituted meso-phenyl porphyrin, 5-(4-carboxyphenyl)-10,15,20-triphenylporphyrin (CPTPP) thin films by matrix-assisted pulsed laser evaporation (MAPLE) on screen-printed electrodes, aiming for histamine detection. Raman spectrometry confirmed that CPTPP chemical structure was preserved in MAPLE-deposited thin films at 200 mJ/cm2 laser fluence. Atomic force microscopy topography revealed that MAPLE-deposited thin films have a better coverage on the working electrode made of carbon compared to the ones obtained by dropcasting. Cyclic voltammetry demonstrated that CPTPP is an appropriate mediator for histamine detection in trichloroacetic acid solution. We proved that MAPLE serves as a soft technique in fabrication of porphyrin thin films and patterns. 相似文献