Edge irregular total labellings for graphs of linear size

As an edge variant of the well-known irregularity strength of a graph G=(V,E) we investigate edge irregular total labellings, i.e. functions f:V∪E→{1,2,…,k} such that f(u)+f(uv)+f(v)≠f(u^′)+f(u^′v^′)+f(v^′) for every pair of different edges uv,u^′v^′∈E. The smallest possible k is the total edge irregularity strength of G. Confirming a conjecture by Ivan?o and Jendrol’ for a large class of graphs we prove that the natural lower bound is tight for every graph of order n, size m and maximum degree Δ with m>111000Δ. This also implies that the probability that a random graph from G(n,p(n)) satisfies the Ivan?o-Jendrol’ Conjecture tends to 1 as n→∞ for all functions p∈[0,1]^N. Furthermore, we prove that is an upper bound for every graph G of order n and size m≥3 whose edges are not all incident to a single vertex.     

Total outer-connected domination numbers of trees

Let G=(V,E) be a graph without an isolated vertex. A set DV(G) is a total dominating set if D is dominating, and the induced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total dominating set of G. A set DV(G) is a total outer-connected dominating set if D is total dominating, and the induced subgraph G[V(G)−D] is a connected graph. The total outer-connected domination number of G is the minimum cardinality of a total outer-connected dominating set of G. We characterize trees with equal total domination and total outer-connected domination numbers. We give a lower bound for the total outer-connected domination number of trees and we characterize the extremal trees.     

On total domination vertex critical graphs of high connectivity

A graph is called γ-critical if the removal of any vertex from the graph decreases the domination number, while a graph with no isolated vertex is γ_t-critical if the removal of any vertex that is not adjacent to a vertex of degree 1 decreases the total domination number. A γ_t-critical graph that has total domination number k, is called k-γ_t-critical. In this paper, we introduce a class of k-γ_t-critical graphs of high connectivity for each integer k≥3. In particular, we provide a partial answer to the question “Which graphs are γ-critical and γ_t-critical or one but not the other?” posed in a recent work [W. Goddard, T.W. Haynes, M.A. Henning, L.C. van der Merwe, The diameter of total domination vertex critical graphs, Discrete Math. 286 (2004) 255-261].     

Convergence of a fixed point iteration method for the OSV model

In image processing, image denoising and texture extraction are important problems in which many new methods recently have been developed. One of the most important models is the OSV model [S. Osher, A. Solé, L. Vese, Image decomposition and restoration using total variation minimization and the H^-1 norm, Multiscale Model. Simul. A SIAM Interdisciplinary J. 1(3) (2003) 349-370] which is constructed by the total variation and H^-1 norm. This paper proves the existence of the minimizer of the functional from the OSV model and analyzes the convergence of an iterative method for solving the problems. Our iteration method is constructed by a fixed point iteration on the fourth order partial differential equation from the computation of the associated Euler-Lagrange equation, and the limit of our iterations satisfies the minimizer of the functional from the OSV model. In numerical experiments, we compare the numerical results of our works with those of the ROF model [L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D 60 (1992) 259-268].     

带马氏切换的马氏过程的指数收敛速度

设 (X(t), Z(t))是以[0,∞) ×{1, 2,…, n₀} 为状态空间的强马氏过程, 其第一分量 X(t) 依赖于第二分量 Z(t), 而第二分量 Z(t) 是一个马氏链. 应用耦合方法, 估计了(X(t), Z(t)) 的转移概率依全变差范数收敛于其不变概率测度的指数收敛速度.     

Electrochromic devices based on copolymers of 3-Trimethoxysilanylpropyl-N-aniline-2,5-Dimethoxyaniline

Electrochemical copolymerization of 3-trimethoxysilanyl-propyl-N-aniline (TMSPA) with 2,5-dimethoxyaniline (DMA) was performed in 1 M HCl aqueous solution for different feed ratios of TMSPA using cyclic voltammetry. The deposition rate of TMSPA–DMA copolymer is higher than that of PTMSPA but lower than that of PDMA. (TMSPA-co-DMA) film was deposited using electrochemical polymerization as conducting film on indium tin oxide (ITO) electrode and used as an electrode in an electrochromic device. Poly(3,4-ethylenedioxythiophene):poly(4-styrenesulfonate) (PEDOT:PSS) was spin-coated on ITO as the other electrode. Carboxyl-terminated- butadiene-acrylonitrile (CTBN) blended with LiClO₄ was used as solid polymer electrolyte. A total solid electrochromic device was assembled as follows: ITO|P(TMSPA-co-DMA)LiClO₄-CTBNPEDOT:PSS|ITO. The columbic efficiency of the devices reached to 104% for P(TMSPA-co-DMA) film with TMSPA feed ratio of 0.25. The optical contrast (ΔT, %) of the single electrode and the device were determined by UV–vis spectroelectrochemical studies. The stability of ΔT was improved during color switching from +1.5 to −1.5 V (vs. PEDOT) for this device. The device was pale yellow at −1.5 V and blue at +1.5 V.     

Determination of nitrogen in hydrolyzed protein formulations by continuous vapour phase FTIR

An on-line system with vapour generation (VG) and Fourier transform infrared (FTIR) spectrometric detection has been developed for the determination of free ammonium and organic nitrogen in agrochemical formulations containing hydrolyzed proteins. Commercial samples were digested, in batch mode, with sulphuric acid and the obtained solution was alkalinized on-line to transform the NH₄⁺ to NH₃ that was continuously monitored by FTIR. Free ammonium was determined in the same system after simple dilution of undigested samples with water. Different gas phase separators were assayed in order to introduce gaseous NH₃ into a home made IR gas cell of 10 cm pathlength, where the corresponding FTIR spectra were acquired by accumulating 10 scans per spectrum. The 967.0 cm⁻¹ band was used for the quantification of ammonia. The figures of merit of the proposed method involve a linear range up to 100 mg L⁻¹, a limit of detection (3σ) of 1.4 mg L⁻¹ of N, a limit of quantification (10σ) of 4.8 mg L⁻¹ of N, a precision (R.S.D.) of 3.0% for 10 replicate determinations of a 10.0 mg L⁻¹ of N and a sample measurement frequency of 60 h⁻¹. The method was successfully applied to the determination of free ammonium and total N in commercial amino acid formulations and results compare well with those obtained by the Kjeldhal method.     

Application of the total evaporation technique to chromium isotope ratio measurement by thermal ionization mass spectrometry

The total evaporation technique of thermal ionization mass spectrometry was applied to the isotopic analysis of chromium. High measurement reproducibility of the chromium isotope ratios was verified (2 S.E. < 0.05% (⁵³Cr/⁵²Cr)), while a clear mass fractionation effect was observed by using conventional measurement technique. The chromium isotope ratios analyzed by the total evaporation method were not affected by the sample amount on the rhenium filament (50-500 ng Cr). The isotopic analysis under the coexistence of zinc was also performed, and its effect to the chromium isotope ratios was confirmed.     

Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements

Nowadays, little technology exists that can monitor various water sources quickly and at a reasonable cost. The ultra-sensitive, fully automated and robust biosensor River Analyser (RIANA) is capable of detecting multiple organic targets rapidly and simultaneously at a heterogeneous assay format (solid phase: bulk optical glass transducers). Commercialization of such a biosensor requires the availability of commercial high-affinity recognition elements (e.g. antibodies) and suitable commercial haptens (modified target molecules) for surface chemistry. Therfore, testosterone was chosen as model analyte, which is also a task of common analytical methods like gas chromatography-mass spectrometry (GC-MS), because they have to struggle with detecting sub-nanogram per liter levels in environmental samples. The reflectometric interference spectroscopy (RIfS) was used to characterize the commercially available immunochemistry resulting in a high-affinity constant of 2.6 ± 0.3 × 10⁹ mol⁻¹ for the unlabeled antibody. After the labeling procedure, necessary for the TIRF-based biosensor, a mean affinity constant of 1.2 × 10⁹ mol⁻¹ was calculated out of RIfS (1.4 ± 0.4 × 10⁹ mol⁻¹) and TIRF (1.0 ± 0.3 × 10⁹ mol⁻¹) measurements.Thereafter, the TIRF-based biosensor setup was used to determine the steroidal hormone testosterone at real world samples without sample pre-treatment or sample pre-concentration. Results are shown for rapid and ultra-sensitive analyses of testosterone in aqueous samples with at a remarkable limit of detection (LOD) of 0.2 ng L⁻¹. All real world samples, even those containing testosterone in the sub-nanogram per liter range (e.g. 0.9 ng L⁻¹), could be determined with recovery rates between 70 and 120%. Therefore, the sensor system is perfectly suited to serve as a low-cost system for surveillance and early warning in environmental analysis in addition to the common analytical methods. For the first time, commercially available immunochemistry was fully characterized using a label-free detection method (RIfS) and successfully incorporated into a TIRF-based biosensor setup (RIANA) for reliable sub-nanogram per liter detection of testosterone in aqueous environmental samples.     

First synthesis of a steroid containing an unstable 19-nor-androsta-1,5-dien-3-one system

Mechanisms involved in the maintenance of human pregnancy and initiation of labour are poorly defined. A novel steroid hormone named estradienolone (ED), and having an unusual 19-nor-androsta-1,5-dien-3-one system, was previously reported. However, ED is scarcely available from urine, placenta and blood of pregnant women. For this reason, we have synthesized ED in order to verify its proposed structure. Although a 1,5-dien-3-one system had already been described for a C19-steroid (androstane) nucleus (no possible aromatization), the synthesis of the 19-nor-analogue is a major challenge because this system is very sensitive to aromatization. We now describe the successful construction and characterization of this unstable system. Starting from nortestosterone, the synthesis of 17β-hydroxy-19-nor-androsta-1,5-dien-3-one (1) is based on a protection of the 5,6-double bond, the introduction of the second 1,2-double bond, the careful recovery of the exo double bond and a final regioselective oxidation or reduction.