Lubell proved this by observing that the left-hand side is a probability: it is simply the probability that a maximal chain, chosen uniformly at random, intersects A. The LYM inequality implies that an antichain in P([n]) has size at most ( n bn/2c ) , the size of the ‘middle layer’ in P([n]). (This can also be proved by partitioning P([n]) into ( n bn/2c ) disjoint chains.) Bollobás’ Inequalit...

measurement of soil saturated hydraulic conductivity, ks, is normally affected by flow patterns such as macro pore; however, most current techniques do  not differentiate flow types, causing major problems in describing water and chemical flows within the soil matrix. this study compares eight models for scaling ks and predicted matrix and macro pore ks, using a database composed of 50 datasets...

let $l$ be a lattice in $zz^n$ of dimension $m$. we prove that there exist integer constants $d$ and $m$ which are basis-independent such that the total degree of any graver element of $l$ is not greater than $m(n-m+1)md$. the case $m=1$ occurs precisely when $l$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. as a corollary, we show t...

The Heart of Mersey cardiovascular disease prevention programme in the UK Launched in 2003, following a visit to Finland, the Heart of Mersey (HoM) cardiovascular disease (CVD) prevention programme aims to improve the health of the local population through structural changes at regional, national and European level.(1) Based on the evidence (ie raised blood cholesterol and blood pressure, and t...

protection of water resources from contamination and detection of the contaminants and their treatments are among the essential issues in the management of water resources. in this work, the time-lapse electrical resistivity tomography (ert) surveys were conducted along 7 longitudinal lines in the downstream of the latian dam in jajrood (iran), in order to detect the contamination resulting fro...

abstract saturated water content is one of the important parameters which its measurement is necessary in estimation of soil water retention and unsaturated hydraulic conductivity curves. in several researches, saturated water content is assumed to be equal to soil total porosity. in some others, its value is estimated by pedotransfer functions using readily available parameters, such as bulk d...

mathematical simulation of flow toward drains is an important and indispensable stage in drainage design and management. many related models have been developed, but most of them simulate the saturated flow toward drains without a due consideration of the unsaturated zone. in this study, the two dimensional differential equation governing saturated and unsaturated flow in porous media is numeri...

abstract the temperature of water entering the soil or variation in soil temperature has a direct impact on soil hydraulic conductivity via the effect on water viscosity. in this research, the time variability of soil saturated hydraulic conductivity (ks) was studied. the relation between soil temperature and fluid viscosity with hydraulic conductivity were also studied. the necessary experimen...