We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...

 The foreign exchange market (FX market) accounts for 40% of the total volume of the world’s e-commerce by its own. Based on statistics, sometimes up to 90 per cent of the traders lose their total capital in this market just within six months to one year and leave this market. The probability of loss in the FX market can be estimated by probability theory. The present paper intends to demonst...

Consider a word in which the individual symbols are independent integers occurring with probabilities Pi. and let Hn be the height of the suffix tree constructed from the first n suffixes of this word. We show that Hn is asymptotically close to 2 log n/log(lt~pr) in many • respects: the difference is 0 (log log n) in probability, and the ratio tends to one in probability and in the mean.

    In this research in order to frequency analysis of maximum daily rainfall in various climates of Iran the data of 40 synoptic rain gauges collected in 40 years period i.e., 1973 to 2012 were used. These stations are located in various climates of Iran according to De Martonne climatic classification. At first, input of data to HYFA package was performed. The mentioned package includes seven...

Employing profits data of Japanese firms in 2003–2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat’s law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits growth rate is described as a tent-shaped exponential function. Secondly, the val...

in order to evaluate the effects of drought and salinity stresses on growth parameters and essential oil of lemon balm, two experiments with three replications in a randomized complete block design were applied. five levels of salinity including zero, one, two, three and four ds/m of sodium chloride solution, and five drought stress treatments including 50, 62.5, 75, 87.5 and 100% as available ...

LetP be a Poisson process of intensity one in a squareSn of arean. We construct a random geometric graph Gn,k by joining each point of P to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that Gn,k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that Gn,k is connected tends to 1 as n → ∞. They conject...

logistic regression (lr) was used to model urban growth between the years 1987 and 2001 in gorgan city, north east of iran. three groups of variables including economic-social, land use and biophysical variables were used in the modeling practice. using covariance of the independent variables, distance to administrative and sporting centers plus distance to cities were removed. roc (relative op...

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic timescale. The index is modelled using a time transformed squared Bessel process with a log-normal scaling factor for the time transformation. A consistent pricing and hedging framework is established by using the benchmark approach. Here ...