共查询到20条相似文献,搜索用时 62 毫秒
1.
mRNA degradation plays an important role in gene regulation. However, a defect in mRNA decay is expected to result in an increase in mRNA levels. In this paper, we will first establish a model of mRNA regulation by two pathways denoted by $5''\rightarrow 3''$ and $3''\rightarrow 5''$ for short, where there are two degradation rates $\delta_1$, $\delta_2$ on $5''\rightarrow3''$ pathway and the degradation rate on $3''\rightarrow 5''$ pathway is $\delta_3$. The advantage of this model is that it captures fundamental biochemical reactions in the gene expression process in eukaryotic cells. Then we obtain several basic principles on the monotonicity of the mean level of newly accumulated mRNAs. It is proved that (1) the newly mean level is strictly increasing in $p$ and $\kp$, but is strictly decreasing in $\gm$, where $p, \kp$ and $ \gm$ are the initial activation frequency, the activation rate, and the inactivation rate, respectively; (2) the newly mean level is strictly decreasing in both $\delta_2$ and $\delta_3$, remarkably, is strictly increasing in $\delta_1$ when $\delta_2<\delta_3$ and decreasing when $\delta_2>\delta_3$ and; (3) the newly mean level is strictly increasing in time $t$ when $p<\kp/(\kp+\gm)$. These conclusions not only provide a better understanding on gene expression dynamics but also would be helpful to design reasonable gene expression modules. 相似文献
2.
Assume that we want to recover $f : \Omega \to {\bf C}$ in the
$L_r$-quasi-norm ($0 < r \le \infty$) by a linear sampling method
$$
S_n f = \sum_{j=1}^n f(x^j) h_j ,
$$
where $h_j \in L_r(\Omega )$ and $x^j \in \Omega$
and $\Omega \subset {\bf R}^d$ is an arbitrary bounded Lipschitz domain.
We assume that $f$ is from the unit ball of
a Besov space $B^s_{pq} (\Omega)$ or of a
Triebel--Lizorkin space $F^s_{pq} (\Omega)$ with
parameters such that the space is compactly embedded
into $C(\overline{\Omega})$. We prove that the optimal rate
of convergence of linear sampling methods is
$$
n^{ -{s}/{d} + ({1}/{p}-{1}/{r})_+} ,
$$
nonlinear methods do not yield a better rate.
To prove this we use a result from Wendland (2001) as well
as results concerning the spaces $B^s_{pq} (\Omega) $ and $F^s_{pq}(\Omega)$.
Actually, it is another aim of this paper to complement the
existing literature about the function spaces $B^s_{pq} (\Omega)$ and $F^s_{pq}
(\Omega)$ for bounded Lipschitz domains $\Omega \subset {\bf R}^d$.
In this sense, the paper is also a continuation of a paper by Triebel (2002). 相似文献
3.
Global dynamics in a multi-group epidemic model for disease with latency spreading and nonlinear transmission rate 下载免费PDF全文
In this paper, we investigate a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate. Under biologically motivated assumptions, we show that the global dynamics are completely determined by the basic production number $R_0$. The disease-free equilibrium is globally asymptotically stable if $R_0\leq1$, and there exists a unique endemic equilibrium which is globally asymptotically stable if $R_0>1$. The proofs of the main results exploit the persistence theory in dynamical system and a graph-theoretical approach to the method of Lyapunov functionals. A simpler case that assumes an identical natural death rate for all groups and a gamma distribution for exposed distribution is also considered. In addition, two numerical examples are showed to illustrate the results. 相似文献
4.
5.
本文在Banach空间$B$是$p$可光滑($1
相似文献
6.
ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS 总被引:2,自引:0,他引:2
A useful reduction is presented to determine the finiteness of △-good module category F(△)of a quasi-heredltary algebra. As an application of the reduction, the f(△)-finitenetess of quasi-hereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(△)-finite M-twisted double incidence algebras is given in case the posets are linearly ordered. 相似文献
7.
Multidimensional stability of planar waves for delayed reaction-diffusion equation with nonlocal diffusion 下载免费PDF全文
In this paper, we consider the multidimensional stability of planar waves for a class of nonlocal dispersal equation in $n$--dimensional space with time delay. We prove that all noncritical planar waves are exponentially stable in $L^{\infty}(\RR^n )$ in the form of $\ee^{-\mu_{\tau} t}$ for some constant $\mu_{\tau} =\mu(\tau)>0$( $\tau >0$ is the time delay) by using comparison principle and Fourier transform. It is also realized that, the effect of time delay essentially causes the decay rate of the solution slowly down. While, for the critical planar waves, we prove that they are asymptotically stable by establishing some estimates in weighted $L^1(\RR^n)$ space and $H^k(\RR^n) (k \geq [\frac{n+1}{2}])$ space. 相似文献
8.
ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS 总被引:2,自引:0,他引:2
ONΔ┐GOODMODULECATEGORIESOFQUASI┐HEREDITARYALGEBRAS**DENGBANGMING*XICHANGCHANG*ManuscriptreceivedJune12,1995.RevisedMay3,1996.... 相似文献
9.
Bart De Bruyn 《Journal of Geometry》2003,78(1-2):50-58
We provide purely geometrical proofs for the uniqueness of the near
hexagon with parameters $(s,t,T_2)=(2, 5, \{1, 2\})$. As a by-product we
find a new construction for the near hexagon. Generalizing this new
construction, we obtain an infinite class $\mathcal{C}$ of incidence
structures.In [4] it will be proved that all members of
$\mathcal{C}$ are near polygons. 相似文献
10.
Yanan Zhao Xiaoying Zhang Donal O''Regan 《Journal of Applied Analysis & Computation》2019,9(6):2096-2110
We discuss the dynamic of a stochastic Susceptible-Infectious-Recovered-Susceptible (SIRS) epidemic model with nonlinear incidence rate.The crucial threshold $\tilde{R}_0$ is identified and this will determine the extinction and persistence of the epidemic when the noise is small. We also discuss the asymptotic behavior of the stochastic model around the endemic equilibrium of the corresponding deterministic system. When the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it dies out. Finally, these results are illustrated by computer simulations. 相似文献
11.
In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate (1 + t)^-u, provided that the initial data decay with the rate (1 + x)^-(l+u) (resp. (1 - x)^-(1+u)) as x tends to +∞ (resp. -∞), where u is a positive constant. 相似文献
12.
We consider the operator ${\cal A}$ formally defined by ${\cal
A}u(x)=\alpha(x)\Delta u(x)$
for any $x$ in a sufficiently smooth bounded open set
$\Om\subset\R^N$ ($N\ge 1$), where $\alpha\in C(\ov\Omega)$ is a
continuous nonnegative function vanishing only on $\partial\Omega$,
and such that $1/\alpha$ is integrable in $\Omega$.
We prove that the realization $A_p$ of ${\cal A}$, equipped with
suitable nonlinear boundary conditions is an m-dissipative operator in
suitably weighted $L^p(\Omega)$-spaces in the
case where either $(p,N)\in (1,+\infty)\times\{1\}$ or
$(p,N)=\{2\}\times\N$. Moreover, we prove that $A_p$ is a densely
defined closed operator.
We consider nonlinear boundary conditions of the following type: in the one
dimensional case we take $\Omega=(0,1)$ and we assume that
$u(j)=(-1)^j\beta_j(u(j))$ ($j=0,1$), $\beta_0$ and $\beta_1$ being
nondecreasing continuous functions in $\R$ such that
$\beta_0(0)=\beta_1(0)=0$; in the $N$-dimensional setting we
assume that
$(D_{\nu}u)_{|\partial\Omega}=-\beta(u_{|\partial\Omega})$, $\beta$
being a nondecreasing Lipschitz continuous function in $\R$ such that
$\beta(0)=0$. Here $\nu$ denotes the unit outward normal to
$\partial\Om$. 相似文献
13.
Steven E. Golowich 《Annales Henri Poincare》2003,4(3):413-438
The Greens function for the nearest-neighbor self-avoiding walk on a
hypercubic lattice in d > 2 dimensions is constructed and shown to be analytic for
values of the killing rate $ a \in \textbf{C} $ satisfying
$ \vert a \vert > \epsilon, \vert \textrm{arg}\,\, a \vert $ \lt; $ 3\pi/4 - b $
with $ \epsilon > 0 $ and 0 \lt; b \lt; $ \pi/4 $.
We restrict $ \vert a \vert > \epsilon > 0 $ in order to use the killing rate as an
infrared cutoff, which allows us to construct Greens function using a single scale
cluster expansion. The presence of non-real killing introduces complications that
we resolve through the use of an appropriate choice of decoupling scheme and a
subsidiary expansion. Our methods can be used to control a single momemtum slice
in a phase-space expansion.
Communicated by Vincent Rivasseau
submitted 3/12/02, accepted: 24/02/03 相似文献
14.
Traveling waves of a nonlocal diffusion SIRS epidemic model with a class of nonlinear incidence rates and time delay 下载免费PDF全文
Weifang Yan 《Journal of Applied Analysis & Computation》2019,9(2):452-474
In this paper, we study the traveling waves of a delayed SIRS epidemic model with nonlocal diffusion and a class of nonlinear incidence rates. When the basic reproduction ratio $\mathscr{R}_0>1$, by using the Schauder''s fixed point theorem associated with upper-lower solutions, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of traveling wave solutions connecting the disease-free steady state and the endemic steady state. When $\mathscr{R}_0<1$, the nonexistence of traveling waves is obtained by the comparison principle. 相似文献
15.
本文研究了在样本$(X_1,Y_1),(X_2,Y_2),\ldots,(X_n,Y_n)$ 为取值于$R^{d}\times R^{1}$的同分布的$\alpha$混合序列时,回归函数改良分割估计的强相合性和收敛速度. 相似文献
16.
F. den Hollander F.R. Nardi E. Olivieri E. Scoppola 《Probability Theory and Related Fields》2003,125(2):153-194
The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas
with Kawasaki dynamics at low temperature and low density.
Let $\Lambda\subseteq{\mathbb Z}^3$ be a large finite box. Particles perform simple exclusion on $\Lambda$, but when they
occupy neighboring sites they feel a binding energy $-U<0$ that slows down their dissociation. Along each bond touching the
boundary of $\Lambda$ from the outside, particles are created with rate $\rho=e^{-\Delta\beta}$ and are annihilated with rate
1, where $\beta$ is the inverse temperature and $\D>0$ is an activity parameter. Thus, the boundary of $\Lambda$ plays the
role of an infinite gas reservoir with density $\rho$.
We consider the regime where $\Delta\in (U,3U)$ and the initial configuration is such that $\Lambda$ is empty. For large $\beta$,
the system wants to fill $\Lambda$ but is slow in doing so. We investigate how the transition from empty to full takes place
under the dynamics. In particular, we identify the size and shape of the critical droplet\/ and the time of its creation in the limit as $\beta\to\infty$.
Received: 23 February 2002 / Revised version: 24 June 2002 / Published online: 24 October 2002
Mathematics Subject Classification (2000): 60K35, 82B43, 82C43, 82C80
Key words or phrases: Lattice gas – Kawasaki dynamics – Metastability – Critical droplet – Large deviations – Discrete isoperimetric inequalities 相似文献
17.
Let $G_p$ be the $p$-series field. In this paper we prove the a.e. convergence $\sigma_n f\to f$ $(n\to \infty)$ for an integrable function $f\in L^1(G_p)$, where $\sigma_nf$ is the $n$th $(C,1)$ mean of $f$ with respect to the character system in the Kaczmarz rearrangement. We define the maximal operator $\sigma^* $ by $\sigma^*f := \sup_n|\sigma_nf|$. We prove that $\sigma^*$ is of type $(q,q)$ for all $1
相似文献
18.
In this paper, we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time. A novel regularization method, which we call the exponential Tikhonov regularization method with a parameter $\gamma$, is proposed to solve the inverse source problem, and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules. When $\gamma$ is less than or equal to zero, the optimal convergence rate can be achieved and it is independent of the value of $\gamma$. However, when $\gamma$ is greater than zero, the optimal convergence rate depends on the value of $\gamma$ which is related to the regularity of the unknown source. Finally, numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method. 相似文献
19.
In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β: Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ. 相似文献
20.
Let G be a group and πe(G) the set of element orders of G.Let k∈πe(G) and m k be the number of elements of order k in G.Letτe(G)={mk|k∈πe(G)}.In this paper,we prove that L2(16) is recognizable byτe (L2(16)).In other words,we prove that if G is a group such that τe(G)=τe(L2(16))={1,255,272,544,1088,1920},then G is isomorphic to L2(16). 相似文献