Strongly polynomial-time approximation for a class of bicriteria problems

Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm.     

Color-critical graphs have logarithmic circumference

A graph G is k-critical if every proper subgraph of G is (k−1)-colorable, but the graph G itself is not. We prove that every k-critical graph on n vertices has a cycle of length at least , improving a bound of Alon, Krivelevich and Seymour from 2000. Examples of Gallai from 1963 show that the bound cannot be improved to exceed . We thus settle the problem of bounding the minimal circumference of k-critical graphs, raised by Dirac in 1952 and Kelly and Kelly in 1954.     

Experimental studies on the ring opening polymerization of p-dioxanone using an Al(OPr)3-monosaccharide initiator system

The ring opening polymerization (ROP) of p-dioxanone using a protected monosaccharide (1,2;3,4-di-O-isopropylidene-α-d-galactopyranose)/Al(OⁱPr)₃ initiator system to yield polydioxanone with a protected monosaccharide end-group is described. The products were synthesized at 60-100 °C and characterized by ¹H and ¹³C NMR, and MALDI-TOF mass spectrometry. Besides the desired polydioxanone functionalised with a monosaccharide end-group, also polydioxanone with an OⁱPr end-group was formed (20-30%). Systematic studies showed that the polymer yield is a function of the reaction temperature and the reaction time, with higher temperatures (100 °C) leading to lower yields. The average chain length of the polymers is between 7 and 58 repeating units and may be tuned by the monomer to monosaccharide ratio (at constant Al(OⁱPr)₃ intake). A statistical model has been developed that successfully describes the experimentally observed relation between the average chain length of the functionalized polymer and reaction parameters.     

Electrical conductivity and chemical diffusion coefficient measurements in single crystalline nickel oxide at high temperatures

Electrical conductivity measurements on nickel oxide have been performed at high temperatures (1273 K<T< 1673 K) and in partial pressures of oxygen ranging from Po₂ = 1.89 × 10^?4 atm to Po₂ = 1 atm. The $\text{po}{}_2{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$ dependence of the conductivity decreases from about $\text{1}\text{4}$ for Po₂ = 1 atm to smaller values for lower partial pressures of oxygen. The activation enthalpy for conduction increases for decreasing oxygen partial pressures (from 22.5 kcal mol^?1 at Po₂ = 1 atm to 26.0 kcal mol^?1 for Po₂ = 1.89 × 10^?4 atm). This behaviour can be explained by the simultaneous presence of singly and doubly ionized nickel vacancies, with different energies of formation.Furthermore, chemical diffusion coefficient measurements have been performed in the same temperature range, using the conductivity technique, and leading to the result:

$\text{D}\text{?}\text{= 0.244 exp (?}\text{36,600}\text{RT}\text{) cm}{}^2\text{s}{}^{\mathrm{?1}}$

.     

The Local Limit of the Uniform Spanning Tree on Dense Graphs

Let G be a connected graph in which almost all vertices have linear degrees and let \(\mathcal {T}\) be a uniform spanning tree of G. For any fixed rooted tree F of height r we compute the asymptotic density of vertices v for which the r-ball around v in \(\mathcal {T}\) is isomorphic to F. We deduce from this that if \(\{G_n\}\) is a sequence of such graphs converging to a graphon W, then the uniform spanning tree of \(G_n\) locally converges to a multi-type branching process defined in terms of W. As an application, we prove that in a graph with linear minimum degree, with high probability, the density of leaves in a uniform spanning tree is at least \(e^{-1}-\mathsf {o}(1)\), the density of vertices of degree 2 is at most \(e^{-1}+\mathsf {o}(1)\) and the density of vertices of degree \(k\geqslant 3\) is at most \({(k-2)^{k-2} \over (k-1)! e^{k-2}} + \mathsf {o}(1)\). These bounds are sharp.     

Influence of the temperature on the heat of formation of nickel monoxide at high temperature

In order to see whether the heat of formation ΔH⁰ of the insulating transition metal monoxides shows any change at high temperatures, this property has been accurately measured for NiO by the electrochemical method in the temperature range 743–1323 K. The results show that ΔH⁰ changes from ? 56.10 kcal mol^?1 to ? 55.66 ± 0.08 kcal mol^?1 as the temperature is increased through 913 K. The significance of the heat of formation is discussed from the viewpoint of electronic structure of this compound.     

Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are uniquely defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue is introduced, and the ergodic theory is used to define a growth rate. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the average growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of roads with a junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions.     

Mean-Field Conditions for Percolation on Finite Graphs

Let {G _n } be a sequence of finite transitive graphs with vertex degree d = d(n) and |G _n | = n. Denote by p ^t (v, v) the return probability after t steps of the non-backtracking random walk on G _n . We show that if p ^t (v, v) has quasi-random properties, then critical bond-percolation on G _n behaves as it would on a random graph. More precisely, if $\mathop {\rm {lim\, sup\,}} \limits_{n} n^{1/3} \sum\limits_{t = 1}^{n^{1/3}} {t{\bf p}^t(v,v) < \infty ,}$ then the size of the largest component in p-bond-percolation with ${p =\frac{1+O(n^{-1/3})}{d-1}}Let {G _n } be a sequence of finite transitive graphs with vertex degree d = d(n) and |G _n | = n. Denote by p ^t (v, v) the return probability after t steps of the non-backtracking random walk on G _n . We show that if p ^t (v, v) has quasi-random properties, then critical bond-percolation on G _n behaves as it would on a random graph. More precisely, if

lim sup  n n1/3 ?t = 1n1/3 tpt(v,v) < ￥,\mathop {\rm {lim\, sup\,}} \limits_{n} n^{1/3} \sum\limits_{t = 1}^{n^{1/3}} {t{\bf p}^t(v,v) < \infty ,}      20. Une approche polynomiale du théorème de Faltings      Bakir Farhi 《Comptes Rendus Mathematique》2005,340(2):103-106 We present here an elementary proof of a quantitatively improved version of the Mordell's Conjecture which is now Faltings's Theorem. For the count of the ‘large points’ of $C(K)$ (see below for the notations) we use Vojta's method which was simplified by Bombieri and then by T. de Diego, G. Rémond. To count the points of small heights of $C(K)$, we use a result of S. David and P. Philippon, allowing to us estimate the number of points of small height of the bigger set $C(\overline{K})\cap J(K)$. To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).      [首页] « 上一页 [1] 2 [3] [4] [5] [6] [7] [8] [9] [10] [11] 下一页 » 末  页»

Une approche polynomiale du théorème de Faltings

We present here an elementary proof of a quantitatively improved version of the Mordell's Conjecture which is now Faltings's Theorem. For the count of the ‘large points’ of $C(K)$ (see below for the notations) we use Vojta's method which was simplified by Bombieri and then by T. de Diego, G. Rémond. To count the points of small heights of $C(K)$, we use a result of S. David and P. Philippon, allowing to us estimate the number of points of small height of the bigger set $C(\overline{K})\cap J(K)$. To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).