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

The Influence of Factors on the Demand for Performance Auditing in the Public Sector

Performance audits (PA) are becoming essential in supreme audit institutions (SAIs). This study aims to explain why developing countries need to expand the function of PA and to explore and measure the impact of each factor on the need to develop PA in Vietnam. The research combines qualitative (group discussion) and quantitative methods by surveying 157 state auditors of the State Audit of Vietnam (SAV). Data is processed through SmartPLS 4.0.8.5 to verify the measurement and linear structure models. The results of the statistical analysis also show that all three factors have an impact on the development of PA, including (i) the degree of public governance reform, (ii) the accountability of SAV, and (iii) occupational influence. Besides, the model test results show that, from the perspective of SAV, the need to improve performance is higher than accountability. Public governance reform factors, external support, and SAI accountability contribute to enhancing the value of PA. The findings of this study complement the audit theory on three fronts: (i) PA will become more important when pursuing the goal of increasing accountability rather than improving performance; (ii) PA continues to evolve to adapt to social changes; and (iii) additional empirical evidence demonstrating that countries with low levels of transparency and accountability and inconsistent legal systems have higher audit “demand” but low supply of PA. This study proposes a PA development model to: (i) forecast the ability and level of the development audit of each SAI; and (ii) contribute to enhancing the value of PA using the PA topic selection tool. In addition, the developed scale is tested to ensure its reliability and validity. So this scale can be used to survey the needs, feasibility, and expected value that each audit subject brings before and after implementation. Doi: 10.28991/ESJ-2024-08-01-07 Full Text: PD

Temperature Effects on the Plasmon Modes of Double-layer Graphene

We calculate the dynamical dielectric function of doped double-layer graphene (DLG), made of two parallel graphene monolayers with carrier densities $n_1, n_2$, respectively, and a separation interlayer of $d$ at finite temperature. The results are used to find the dispersion of plasmon modes. We study the temperature effects on the DLG plasmon modes in the case of symmetric system $(n_1=n_2)$, asymmetric system $(n_1\neq n_2)$ and no free carriers in the second layer $(n_2=0)$. We show that the effect of temperature on the plasmon dispersion is significant and can not be ignored in investigating graphene properties

ESP Students’ Perceptions of the Role of Community Language Learning on Learning Motivation: A Case at a College of Medicine and Pharmacy in the Mekong Delta

Community language learning (CLL) is a language teaching method in which students work together to develop what aspects of a language they would like to learn. It is based on the Counselling-approach in which the teacher acts as a counselor and the learner as a client. CLL techniques are believed to help learners alleviate anxiety, threat and the personal and language problems a person encounters in using the language. The research entitled: “An Investigation into ESP Students’ Perceptions of the Role of Community Language Learning on Learning Motivation: A study in a college of medicine and pharmacy in the Mekong Delta” was conducted to find out ESP students’ perception of the role of CLL on their learning motivation. It was conducted with the participation of 144 ESP students from a College in Can Tho city using the questionnaire. The result shows that ESP students’ perception of the role of CLL on their learning motivation was quite high although the level of perceptions on their interest was not high

Newton polytope of good symmetric polynomials

We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.Comment: 10 pages, 3 figure