The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous case

Consider the Navier-Stokes flow past a rotating obstacle with a general time-dependent angular velocity and a time-dependent outflow condition at infinity -- sometimes called an Oseen condition. By a suitable change of coordinates the problem is transformed to an non-autonomous problem with unbounded drift terms on a fixed exterior domain $\Omega\subset \R^d$. It is shown that the solution to the linearized problem is governed by a strongly continuous evolution system $\{T_\Omega(t,s)\}_{t\geq s\geq0}$ on $L^p_\sigma(\Omega)$ for $1<p<\infty$. Moreover, $L^p$-$L^q$ smoothing properties and gradient estimates of $T_\Omega(t,s)$, $0\leq s \leq t$, are obtained. These results are the key ingredients to show local in time existence of mild solutions to the full nonlinear problem for $p\geq d$ and initial value in $L^p_\sigma(\Omega)$.Comment: 25 page

Kernel estimates for Schr\"odinger type operators with unbounded diffusion and potential terms

We prove that the heat kernel associated to the Schr\"odinger type operator $A:=(1+|x|^\alpha)\Delta-|x|^\beta$ satisfies the estimate $$k(t,x,y)\leq c_1e^{\lambda_0t}e^{c_2t^{-b}}\frac{(|x||y|)^{-\frac{N-1}{2}-\frac{\beta-\alpha}{4}}}{1+|y|^\alpha} e^{-\frac{2}{\beta-\alpha+2}|x|^{\frac{\beta-\alpha+2}{2}}} e^{-\frac{2}{\beta-\alpha+2}|y|^{\frac{\beta-\alpha+2}{2}}}$$ for $t>0,|x|,|y|\ge 1$, where $c_1,c_2$ are positive constants and $b=\frac{\beta-\alpha+2}{\beta+\alpha-2}$ provided that $N>2,\,\alpha\geq 2$ and $\beta>\alpha-2$. We also obtain an estimate of the eigenfunctions of $A$

RANCANG BANGUN SISTEM INFORMASI AKUTANSI DENGAN STUDY KASUS DI PT. RIGEN NET TRAVEL

Dalam kegiatan pengolahan data laporan keuangan di zaman sekarang ini masih banyak yang menggunakan cara manual. Sekarang ini tuntunan untuk menggunakan teknologi computer sangatlah wajar karena zaman sudah canggih. Banyaknyadqta laporan yang ada membuat pegawai kerepotan dalam merapikan setiap data yang ada. Mempermudah hal tersebut d butuhkan sebuah aplikasi yang dapat mendukung proses tersebut. Data laporan keuangan yang ada d PT. RIGEN NET TRAVEL CUKUP BANYAK. Dengan demikian data yang cukup banyak tersebut perlu ditata dan d kelompokkan sesuai dengankriteria yang ada dengan menggunakan sebuah aplikasi sistem informasi akuntansi yang menggunakan framework codeigniter dengan menggunakan metode Model View Controller (MVC). Dengan adanya aplikasi di harapkan dapat membantu pihak travel untuk dapat mengelola datanya dengan baik. Aplikasi ini merupakan sarana untuk mempermudah prose pengolaha data laporan keuangan di dalam perusahaan travel yang melipputi p[enjualan tiket, laporan keuangan, kas perusahaan, beban yang ditanggung perusahaan secara komputerisasi dan aplikasi ini secara offline. Supaya tidak menggunakkan system manual lagi dalam merekapitulasi dat

A multispecies birth-death-immigration process and its diffusion approximation

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The dynamics on each ray evolves according to a one-dimensional linear birth-death process with immigration. We investigate the transient and asymptotic behavior of the process via its probability generating function. The stationary distribution, when existing, is a zero-modified negative binomial distribution. We also study a diffusive approximation of the process, which involves a diffusion process with linear drift and infinitesimal variance on each ray. It possesses a gamma-type transient density admitting a stationary limit. As a byproduct of our study, we obtain a closed form of the number of permutations with a fixed number of components, and a new series form of the polylogarithm function expressed in terms of the Gauss hypergeometric function.Comment: 26 pages, 7 figure