Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

Spatial variability of air pollution in the vicinity of a permanent monitoring station in central Paris

The strong spatial and temporal variability of traffic-related air pollution detected at roadside locations in a number of European cities has raised the question of how representative the site and time period of air quality measurements actually can be. To address this question, a 7-month sampling campaign was carried out on a major road axis (Avenue Leclerc) leading to a very busy intersection (Place Basch) in central Paris, covering the surroundings of a permanent air quality monitoring station. This station has recorded the highest CO and NOx concentrations during recent years in the region of Paris. Diffusive BTX samplers as well as a mobile monitoring unit equipped with real-time CO, NOx and O3 analysers and meteorological instruments were used to reveal the small-scale pollution gradients and their temporal trends near the permanent monitoring station. The diffusive measurements provided 7-day averages of benzene, toluene, xylene and other hydrocarbons at different heights above the ground and distances from the kerb covering summer and winter periods. Relevant traffic and meteorological data were also obtained on an hourly basis. Furthermore, three semiempirical dispersion models (STREET-SRI, OSPM and AEOLIUS) were tested for an asymmetric canyon location in Av. Leclerc. The analysis of this comprehensive data set has helped to assess the representativeness of air quality monitoring information.

The practical implications of using standardized estimation equations in calculating the prevalence of chronic kidney disease

Background. Kidney Disease Outcomes Quality Initiative (KDOQI) chronic kidney disease (CKD) guidelines have focused on the utility of using the modified four-variable MDRD equation (now traceable by isotope dilution mass spectrometry IDMS) in calculating estimated glomerular filtration rates (eGFRs). This study assesses the practical implications of eGFR correction equations on the range of creatinine assays currently used in the UK and further investigates the effect of these equations on the calculated prevalence of CKD in one UK region Methods. Using simulation, a range of creatinine data (30–300 µmol/l) was generated for male and female patients aged 20–100 years. The maximum differences between the IDMS and MDRD equations for all 14 UK laboratory techniques for serum creatinine measurement were explored with an average of individual eGFRs calculated according to MDRD and IDMS 30 ml/min/1.73 m2. Observed data for 93,870 patients yielded a first MDRD eGFR 3 months later of which 47 093 (71%) continued to have an eGFR

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.