Search results for " 05"
showing 10 items of 51 documents
Total and fractional total colourings of circulant graphs
2008
International audience; In this paper, the total chromatic number and the fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.
Preparation of fouling resistant and highly perm-selective novel PSf/GO-vanillin nanofiltration membrane for efficient water purification
2022
International audience; To meet the rising global demand for water, it is necessary to develop membranes capable of efficiently purifying contaminated water sources. Herein, we report a series of novel polysulfone (PSf)/GO-vanillin nanofiltration membranes highly permeable, selective, and fouling resistant. The membranes are composed of two-dimensional (2D) graphite oxide (GO) layers embedded with vanillin as porogen and PSf as the base polymer. There is a growing interest in addressing the synergistic effect of GO and vanillin on improving the permeability and antifouling characteristics of membranes. Various spectroscopic and microscopic techniques were used to perform detailed physicoche…
Mahonian STAT on rearrangement class of words
2017
In 2000, Babson and Steingr\'{i}msson generalized the notion of permutation patterns to the so-called vincular patterns, and they showed that many Mahonian statistics can be expressed as sums of vincular pattern occurrence statistics. STAT is one of such Mahonian statistics discoverd by them. In 2016, Kitaev and the third author introduced a words analogue of STAT and proved a joint equidistribution result involving two sextuple statistics on the whole set of words with fixed length and alphabet. Moreover, their computer experiments hinted at a finer involution on $R(w)$, the rearrangement class of a given word $w$. We construct such an involution in this paper, which yields a comparable jo…
Pattern statistics in faro words and permutations
2021
We study the distribution and the popularity of some patterns in $k$-ary faro words, i.e. words over the alphabet $\{1, 2, \ldots, k\}$ obtained by interlacing the letters of two nondecreasing words of lengths differing by at most one. We present a bijection between these words and dispersed Dyck paths (i.e. Motzkin paths with all level steps on the $x$-axis) with a given number of peaks. We show how the bijection maps statistics of consecutive patterns of faro words into linear combinations of other pattern statistics on paths. Then, we deduce enumerative results by providing multivariate generating functions for the distribution and the popularity of patterns of length at most three. Fina…
The infinite dihedral group
2022
We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.
LAMN in a class of parametric models for null recurrent diffusion
2017
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A finite number of other parameters, of secondary importance, introduces additional flexibility for the modelization of the drift, and does not perturb the null recurrent behaviour. Under time-continuous observation we obtain local asymptotic mixed normality (LAMN), state a local asymptotic minimax bound, and specify asymptotically optimal estimators.
Relaxation of the order-parameter statistics and dynamical confinement
2020
We study the relaxation of the local ferromagnetic order in the quantum Ising chain in a slant field with both longitudinal and transverse components. After preparing the system in a fully polarised state, we analyse the time evolution of the entire probability distribution function (PDF) of the magnetisation within a block of $\ell$ spins. We first analyse the effect of confinement on the gaussification of the PDF for large $\ell$, showing that the melting of initial order is suppressed when the longitudinal field is aligned to initial magnetisation while it is sped up when it is in the opposite direction. Then we study the thermalisation dynamics. In the paramagnetic region, the PDF quick…
Strong chromatic index of products of graphs
2007
Graphs and Algorithms
Circular law for sparse random regular digraphs
2020
Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…
Radio Labelings of Distance Graphs
2013
A radio $k$-labeling of a connected graph $G$ is an assignment $c$ of non negative integers to the vertices of $G$ such that $$|c(x) - c(y)| \geq k+1 - d(x,y),$$ for any two vertices $x$ and $y$, $x\ne y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio labelings of distance graphs, i.e., graphs with the set $\Z$ of integers as vertex set and in which two distinct vertices $i, j \in \Z$ are adjacent if and only if $|i - j| \in D$.