The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension.Both of the reductions are incorporated into one algorithm.As an applicati...The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension.Both of the reductions are incorporated into one algorithm.As an application,the authors present an additive decomposition in rationally hyperexponential towers.The decomposition yields an alternative algorithm for computing elementary integrals over such towers.The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of MAPLE and MATHEMATICA.展开更多
Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm...Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.展开更多
Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener nois...Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener noise,including the stochastic p-Laplace equation,the stochastic porous medium equation and the stochastic fast-diffusion equation.We also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative SPDEs.These SPDEs can be stochastic systems driven by heavy-tailedα-stable process.展开更多
基金supported by the National Key Research and Development Projects under Grant Nos.2020YFA0712300 and 2023YFA1009401the National Natural Science Foundation of China under Grant Nos.12271511,11688101,12201065 and 11971029+1 种基金CAS Project for Young Scientists in Basic Research under Grant No.YSBR-034the CAS Fund of the Youth Innovation Promotion Association under Grant No.Y2022001。
文摘The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension.Both of the reductions are incorporated into one algorithm.As an application,the authors present an additive decomposition in rationally hyperexponential towers.The decomposition yields an alternative algorithm for computing elementary integrals over such towers.The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of MAPLE and MATHEMATICA.
基金The research is supported in part by the 973 project of China(2004CB31830).
文摘Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.
基金supported by National Natural Science Foundation of China(Grant Nos.11431014 and 11671076)supported by University of Macao Multi-Year Research Grant(Grant No.MYRG2016-00025-FST)Science and Technology Development Fund,Macao SAR(Grant Nos.025/2016/A1,030/2016/A1 and 038/2017/A1)the Faculty of Science and Technology,University of Macao,for financial support and hospitality。
文摘Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener noise,including the stochastic p-Laplace equation,the stochastic porous medium equation and the stochastic fast-diffusion equation.We also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative SPDEs.These SPDEs can be stochastic systems driven by heavy-tailedα-stable process.
