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101.
A graph is 1‐planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge (and any pair of crossing edges cross only once). A non‐1‐planar graph G is minimal if the graph is 1‐planar for every edge e of G. We construct two infinite families of minimal non‐1‐planar graphs and show that for every integer , there are at least nonisomorphic minimal non‐1‐planar graphs of order n. It is also proved that testing 1‐planarity is NP‐complete.  相似文献   
102.
The new procedure for identification of the effective distribution function for determination of the distributed activation energy models, which is based on use the maximum likelihood method (MLM), was established. The five different continuous probability functions (exponential, logistic, normal, gamma, and Weibull probability functions (the extended set of distributions)) were used for searching the best reactivity model for two heterogeneous processes: (a) the isothermal reduction process of nickel oxide under hydrogen atmosphere and (b) the isothermal degradation process of bisphenol‐A polycarbonate (Lexan) under nitrogen atmosphere. The MLM showed that for both processes, the most suitable reactivity model represents the Weibull distribution model. It was concluded that the values of Arrhenius parameters (ln A and Ea), evaluated from the Weibull distribution model, represent the effective kinetic values for both considered processes. This procedure enables identification the suitable distribution model for considered process only from the experimental data (based on the shapes of obtained integral kinetic curves), and this fact represents the advantage of established analysis. The established mathematical procedure, which is based on the MLM, can be applied as the preliminary analysis for evaluating the distribution of activation energies for complex heterogeneous processes. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 27–44, 2009  相似文献   
103.
van Elteren JT  Budic B 《Talanta》2005,66(4):925-930
In an earlier paper (Anal. Chim. Acta 514 (2004) 137) we claimed that the maximal extractability of a metal from soil or sediment for a user-defined extractant, i.e. the chemical availability in that particular extractant, may be biased as a result of inadequate volume to mass (V/m) ratios. Correcting for that artifact using an implementation of the simple linear isotherm model gave good results although we cautioned the general applicability. In this paper we will theoretically derive the limitations of that approach based on the more general assumption that sorption processes are described by a Langmuir isotherm.NIST reference material 8704 was extracted with 1 mol l−1 NaOAc (adjusted to pH 5) to experimentally verify the applicability of the Langmuir isotherm approach and illustrate the deviations obtained for some metals using the linear isotherm approach. Of the seven metals measured (Cr, Co, Ni, Cu, Zn, Cd, and Ba) only for Cr and Cu severe discrepancies between both approaches were found, which could be traced back to non-linear isotherm behaviour. Moreover, the Langmuir isotherm approach showed that the above mentioned extractability artifact is even more serious than earlier assumed applying the linear isotherm approach.  相似文献   
104.
105.
The norm of the operator on (or on any prime C-algebra ) is computed for all and is shown to be equal to the completely bounded norm.

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106.
In this work we investigate the feasibility of two-directional switching of an initially curved or pre-buckled electrostatically actuated microbeams using a single electrode fabricated from the same structural layer. The distributed electrostatic force, which is engendered by the asymmetry of the fringing fields in the deformed state, acts in the direction opposite to the deflection of the beam and can be effectively viewed as a reaction of a nonlinear elastic foundation with stiffness parameterized by the voltage. The reduced order model was built using the Galerkin decomposition with linear undamped modes of a straight beam as base functions and verified using the results of the numerical solution of the differential equation. The electrostatic force was approximated by means of fitting the results of three-dimensional numerical solution of the electrostatic problem. Static stability analysis reveals that the presence of the restoring electrostatic force may result in the suppression of the snap-through instability as well as in the appearance of additional stable configurations associated with higher buckling modes of the beam that are not observed in “mechanically” loaded structures. We show that two-directional switching of a pre-buckled beam between two stable configurations cannot be achieved using quasistatic loading. Furthermore, we show that switching is both associated with the dynamic snap-through mechanism and possible within certain interval of actuation voltages. Using a single-degree-of-freedom (lumped) model, estimation voltage boundaries are obtained. Theoretical results illustrate the feasibility of the suggested operational principle as an efficient mechanism in the arena of non-volatile mechanical memory devices.  相似文献   
107.
This paper establishes a theoretical and computational framework for the development of a novel piezoelectric sensor array for the monitoring of surficial tissue motion that can be used as a basis for the reconstruction of layered viscoelastic skin properties. This is accomplished by the scale reduction of the so-called Multi-channel Analysis of Surface Waves (MASW), a methodology that is successfully used in engineering geophysics for the seismic-wave reconstruction of vertical geological profiles. The utility of the new sensor, containing an array of hair-like PVDF sensors that are sensitive to surficial tissue motion, is enhanced through a systematic solid-fiber interaction analysis that furnishes integral information, cumulative over the length of each fiber, about the attenuation and dispersion of surface waves. On employing such a predictive model as a lynchpin of the full waveform back-analysis used to interpret electric charges generated by the fibers, the methodology allows for an effective reconstruction and viscoelastic characterization of cutaneous and subcutaneous tissue sublayers on a millimeter scale. The performance of the proposed sensor array and data interpretation framework is illustrated through numerical simulations, which point to the feasibility of cost-effective, in vivo mechanical characterization of skin sublayers.  相似文献   
108.
Given a graphic degree sequence D, let χ(D) (respectively ω(D), h(D), and H(D)) denote the maximum value of the chromatic number (respectively, the size of the largest clique, largest clique subdivision, and largest clique minor) taken over all simple graphs whose degree sequence is D. It is proved that χ(D)≤h(D). Moreover, it is shown that a subdivision of a clique of order χ(D) exists where each edge is subdivided at most once and the set of all subdivided edges forms a collection of disjoint stars. This bound is an analogue of the Hajós Conjecture for degree sequences and, in particular, settles a conjecture of Neil Robertson that degree sequences satisfy the bound χ(D) ≤ H(D) (which is related to the Hadwiger Conjecture). It is also proved that χ(D) ≤ 6/5 ω(D)+ 3/5 and that χ(D) ≤ 4/5 ω(D) + 1/5 Δ(D)+1, where Δ(D) denotes the maximum degree in D. The latter inequality is related to a conjecture of Bruce Reed bounding the chromatic number by a convex combination of the clique number and the maximum degree. All derived inequalities are best possible  相似文献   
109.
The A2Mo3O12 family, where A3+ is a large trivalent cation, can show interesting thermal properties such as negative thermal expansion. One member of this family, HfMgMo3O12, where the two A3+ cations have been replaced by Hf4+ and Mg2+, has been shown to have a low positive coefficient of thermal expansion above room temperature. This property makes HfMgMo3O12 an attractive candidate as a component for solid solutions with near-zero thermal expansion. However, its properties below room temperature were unexplored. In this work we report the phase transition from orthorhombic Pnma to monoclinic P21/a at T~175 K with an enthalpy change of 0.27 kJ mol?1. Relaxation calorimetry, from 5 K to 300 K, show only the small anomaly associated with this transition. The thermal conductivity, determined from 2 K to 300 K, was low, but not as low as some other materials exhibiting negative thermal expansion. Analysis of the low-temperature heat capacity indicates the presence of low-energy phonon modes in HfMgMo3O12, consistent with the low thermal conductivity. The upper bound of the Young's modulus, estimated from the effective Debye temperature derived from the low-temperature heat capacity, is 20 GPa, a relatively low value due to the flexibility of the framework structure.  相似文献   
110.
We study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. (2004) [8]: If G is a graph of maximum degree Δ, then G admits a degenerate star coloring using O(Δ3/2) colors. We use this result to prove that every graph of genus g admits a degenerate star coloring with O(g3/5) colors. It is also shown that these results are sharp up to a logarithmic factor.  相似文献   
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