A two-dimensional backward heat problem with statistical discrete data

Abstract We focus on the nonhomogeneous backward heat problem of finding the initial temperature θ = θ ⁢ ( x , y ) = u ⁢ ( x , y , 0 ) {\theta=\theta(x,y)=u(x,y,0)} such that { u t - a ⁢ ( t ) ⁢ ( u x ⁢ x + u y ⁢ y ) = f ⁢ ( x , y , t ) , ( x , y , t ) ∈ Ω × ( 0 , T ) , u ⁢ ( x , y , t ) = 0 , ( x , y ) ∈ ∂ ⁡ Ω × ( 0 , T ) , u ⁢ ( x , y , T ) = h ⁢ ( x , y ) , ( x , y ) ∈ Ω ¯ , \left\{\begin{aligned} \displaystyle u_{t}-a(t)(u_{xx}+u_{yy})&amp;\displaystyle=f% (x,y,t),&amp;\hskip 10.0pt(x,y,t)&amp;\displaystyle\in\Omega\times(0,T),\\ \displaystyle u(x,y,t)&amp;\displaystyle=0,&amp;\hskip 10.0pt(x,y)&amp;\displaystyle\in% \partial\Omega\times(0,T),\\ \displaystyle u(x,y,T)&amp;\displaystyle=h(x,y),&amp;\hskip 10.0pt(x,y)&amp;\displaystyle% \in\overline{\Omega},\end{aligned}\right.\vspace*{-0.5mm} where Ω = ( 0 , π ) × ( 0 , π ) {\Omega=(0,\pi)\times(0,\pi)} . In the problem, the source f = f ⁢ ( x , y , t ) {f=f(x,y,t)} and the final data h = h ⁢ ( x , y ) {h=h(x,y)} are determined through random noise data g i ⁢ j ⁢ ( t ) {g_{ij}(t)} and d i ⁢ j {d_{ij}} satisfying the regression models <jats:disp-formula id="j_jiip-2016-0038_eq_999

Immigration and crime: do Asian immigrants bring more crimes to Australia?

The link between the increased Asian immigration to Australia and crime rates has been subjected to debates in Australian contemporary society. With the concern of Australia being overwhelmed by Asians, some politicians, scholars and the public strongly oppose the increase in Asian immigrants. Most of anti-Asian debates are however based on rather subjective claims that Asian immigrants bring more crimes and social disorders to Australia, and these claims have not been supported by any convincing empirical research. Applying multivariate regression analysis, this paper statistically examines the relationship between Asian population, Asian immigrants and crime rates in six states and two territories of Australia from 1981 to 2004. After controlling for the relevant factors such as the population size, state-specific fixed effects, and a measure of urbanisation, the results are mixed. On the one hand, an increase in Asian immigrants has no effect on crime against persons and crime against properties. On the other hand, an increase in the size of Asian population has a statistically significant effect on crime against persons

Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces

It is proved that if X is an n-dimensional closed covex subset in a linear metric space E, then there is a retraction r: E→X such that ∥x-r(x)∥[?]2(n+1)∥x-X∥ for every x∈E. This fact is applied to study the AR-property in linear metric spaces. We identify a class of Roberts spaces with the AR-property. We also give a direct proof that for every p∈(0.1),Lp is a needle point space

Risk Perceptions of Arsenic in Tap Water and Consumption of Bottled Water

The demand for bottled water has increased rapidly over the past decade, but bottled water is extremely costly compared to tap water. The convenience of bottled water surely matters to consumers, but are others factors at work? This manuscript examines whether purchases of bottled water are associated with the perceived risk of tap water. All of the past studies on bottled water consumption have used simple scale measures of perceived risk that do not correspond to risk measures used by risk analysts. We elicit a probability-based measure of risk and find that as perceived risks rise, expenditures for bottled water rise.Environmental Economics and Policy, Risk and Uncertainty, Q25, Q53, I12,

LC-decomposability and the AR-properly in linear metric spaces

departmental bulletin pape

In-situ physical analysis of cellulose fibre suspensions during enzymatic hydrolysis

In-situ physical analysis of cellulose fibre suspensions during enzymatic hydrolysi

HYDROLOGICAL SURVEY OF THE HUONG RIVER IN 2005

Joint Research on Environmental Science and Technology for the Eart