Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

The urban ecological environment is the material basis and condition for human beings to engage in social and economic activities and the supporting system for the formation and sustainable development of cities. With the acceleration of urbanization and industrialization, urban living environments and economic development have become the focus of people’s attention. This leads to the necessity of studying how to improve the quality of the urban living environment and promote the harmonious coexistence of population, natural environment, and social economy. Traditional methods focus on multiple regression models to evaluate the urban environmental and economic harmony, but this method does not consider the weight of each index, resulting in poor accuracy of the evaluation results. This paper proposes a discrete mathematical model to design the evaluation index and evaluation system of urban environmental and economic coordination. It calculates the weight of each index; carrying capacity of the urban environment, the value of each environmental factor, and the comprehensive value of the environment is determined. The static evaluation and dynamic evaluation are used to evaluate the coordination of the urban environmental economy. The experimental results show that the designed evaluation method of urban environmental economic coordination has high accuracy and effectively improves the reliability and evaluation time.

/pdf/evaluation-of-urban-environmental-and-economic-coordination-373e62f71x.pdf

Evaluation of Urban Environmental and Economic Coordination Based on Discrete Mathematical Model

http://perso.ens-lyon.fr/michael.rao/publi/kab.pdf

On some generalizations of abelian power avoidability

Avoidability of circular formulas

A vertex colouring of a graph $G$ is "nonrepetitive" if $G$ contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively 3-colourable. This paper surveys results about nonrepetitive colourings of graphs. The goal is to give a unified and comprehensive presentation of the major results and proof methods, as well as to highlight numerous open problems.

/pdf/nonrepetitive-graph-colouring-3ysaw9pnw2.pdf

Nonrepetitive graph colouring.

We propose a new proof technique that aims to be applied to the same problems as the Lovasz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve upper-bounds relating different non-repetitive numbers to the maximal degree of a graph. It seems that there should be other interesting applications to the presented approach. In terms of upper-bound our approach seems to be as strong as entropy-compression, but the proofs are more elementary and shorter. The application we provide in this paper are upper bounds for graphs of maximal degree at most $\Delta$: a minor improvement on the upper-bound of the non-repetitive number, a $4.25\Delta +o(\Delta)$ upper-bound on the weak total non-repetitive number and a $ \Delta^2+\frac{3}{2^\frac{1}{3}}\Delta^{\frac{5}{3}}+ o(\Delta^{\frac{5}{3}})$ upper-bound on the total non-repetitive number of graphs. This last result implies the same upper-bound for the non-repetitive index of graphs, which improves the best known bound.

/pdf/another-approach-to-non-repetitive-colorings-of-graphs-of-3l84bya7j7.pdf

Another approach to non-repetitive colorings of graphs of bounded degree

We study the avoidability of long $k$-abelian-squares and $k$-abelian-cubes on binary and ternary alphabets. For $k=1$, these are Makela's questions. We show that one cannot avoid abelian-cubes of abelian period at least $2$ in infinite binary words, and therefore answering negatively one question from Makela. Then we show that one can avoid $3$-abelian-squares of period at least $3$ in infinite binary words and $2$-abelian-squares of period at least 2 in infinite ternary words. Finally we study the minimum number of distinct $k$-abelian-squares that must appear in an infinite binary word.

Avoidability of long $k$-abelian repetitions

We propose a new proof technique that aims to be applied to the same problems as the Lovasz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve upper-bounds relating different non-repetitive numbers to the maximal degree of a graph. It seems that there should be other interesting applications to the presented approach. 
In terms of upper-bound our approach seems to be as strong as entropy-compression, but the proofs are more elementary and shorter. The application we provide in this paper are upper bounds for graphs of maximal degree at most $\Delta$: a minor improvement on the upper-bound of the non-repetitive number, a $4.25\Delta +o(\Delta)$ upper-bound on the weak total non-repetitive number and a $ \Delta^2+\frac{3}{2^\frac{1}{3}}\Delta^{\frac{5}{3}}+ o(\Delta^{\frac{5}{3}})$ upper-bound on the total non-repetitive number of graphs. This last result implies the same upper-bound for the non-repetitive index of graphs, which improves the best known bound.

A long standing question asks whether $\mathbb{Z}$ is uniformly 2-repetitive, that is, whether or not there is an infinite sequence over a finite subset of $\mathbb{Z}$ avoiding two consecutive blo...

Avoiding Two Consecutive Blocks of Same Size and Same Sum over $\mathbb{Z}^2$

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We consider the patterns such that at most two variables appear at least twice, or equivalently, the formulas with at most two variables. For each such formula, we determine whether it is $2$-avoidable, and if it is $2$-avoidable, we determine whether it is avoided by exponentially many binary words.

Matthieu Rosenfeld

Papers

Another approach to non-repetitive colorings of graphs of bounded degree

Avoidability of long $k$-abelian repetitions

Another approach to non-repetitive colorings of graphs of bounded degree

Avoiding Two Consecutive Blocks of Same Size and Same Sum over $\mathbb{Z}^2$

Avoidability of formulas with two variables