An energy balance climate model with hysteresis

Energy balance climate models of Budyko type lead to reaction–diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line). Here we introduce a Babuška–Duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data. Existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode.     

Reconstructibility of a general DNA evolution model

In this paper, we analyze the tree reconstruction problem, to identify whether there is non-vanishing information of the root, as the level of the tree goes to infinity. Although it has been studied in numerous contexts, the existing literature with rigorous reconstruction thresholds established are very limited, and it becomes extremely challenging when the model under investigation has 4 states, one of whose interpretations is the four main bases found in Deoxyribonucleic acid (DNA) and Ribonucleic acid (RNA): guanine [G], cytosine [C], adenine [A], and thymine [T]. In this paper, we study a general DNA evolution model, which distinguishes between transitions and transversions, and allow transversions to occur at the same rate but that rate can be different from the rates for transitions. The sufficient condition for reconstruction is rigorously established.     

Periodicity and repetitions in parameterized strings

One of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation a^M=b^Nc^P in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and Wilf [Uniqueness theorems for periodic functions, Proc. Amer. Math. Soc. 16 (1965) 109–114]. In this paper, we investigate the notion of periodicity and the closely related one of repetition in connection with parameterized strings as introduced by Baker [Parameterized pattern matching: algorithms and applications, J. Comput. System Sci. 52(1) (1996) 28–42; Parameterized duplication in strings: algorithms and an application to software maintenance, SIAM J. Comput. 26(5) (1997) 1343–1362]. In such strings, the notion of pairwise match or “equivalence” of symbols is more relaxed than the usual one, in that it rests on some mapping, rather than identity, of symbols. It seems natural to try and extend notions of periods and periodicities to encompass parameterized strings. However, we know of no previous attempt in this direction. Our preliminary investigation yields results as follows. For periodicity, we get (a) a generalization of the Weak Version of the Periodicity Lemma for parameterized strings, showing that it is essential that the two mappings inducing the periodicity must commute; (b) a proof that an analogous of the Lemma by Fine and Wilf [Uniqueness theorems for periodic functions, Proc. Amer. Math. Soc. 16 (1965) 109–114] cannot hold for parameterized strings, even if the mappings inducing the periodicity “commute”, in a sense to be specified below; (c) a proof that parameterized strings over an alphabet of at least three letters may have a set of periods which differ from those of any binary string of the same length—whereby the parameterized analog of a classic result by Guibas and Odlyzko [String overlaps, pattern matching, and nontransitive games, J. Combin. Theory Ser. A 30 (1981) 183–208] cannot hold. We also derive necessary and sufficient conditions characterizing parameterized repetitions, which are patterns of length at least twice that of the period, and show how the notion of root differs from the standard case, and highlight some of the implications on extending algorithmic criteria previously adopted for string searching, detection of repetitions and the likes. Finally, as a corollary of our main results, we also show that binary parameterized strings behave much in the same way as non-parameterized ones with respect to periodicity and repetitions, while there is a substantial difference for strings over alphabets of at least three symbols.     

A Periodicity Theorem in K-Theory for Finite Covariant Systems

Let A be a complex Banach algebra. In this paper, we prove a periodicity theorem that K(S ² A, G, )K(A, G,), where (A,G,) is a finite covariant system and K(A,G,) is an Abelian group associated with (A,G,).     

Homogenization of an Elliptic System as the Cells of Periodicity are Refined in One Direction

We homogenize a second-order elliptic system with anisotropic fractal structure characteristic of many real objects: the cells of periodicity are refined in one direction. This problem is considered in the rectangle with Dirichlet conditions given on two sides and periodicity conditions on two other sides. An explicit formula for the homogenized operator is established, and an asymptotic estimate of the remainder is obtained. The accuracy of approximation depends on the exponent $\kappa$ ∈ (0, 1/2] of smoothness of the right-hand side with respect to slow variables (the Sobolev-Slobodetskii space) and is estimated by $O(h^\kappa )$ for $\kappa$ ∈ (0, 1/2) and by O(h ^1/2(1 + |log h|)) for $\kappa$ = 1/2.     

Periodicity and global dynamics of an impulsive delay Lasota-Wazewska model

The periodicity of an impulsive delay Lasota-Wazewska model is discussed. Sufficient and necessary condition for the existence of a positive periodic solution is established. Sufficient conditions for its global attractivity are also obtained via the methods of Lyapunov function and comparison.     

An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification

The bioconversion of glycerol to 1,3-propanediol is a complex bioprocess. In this study, we aim to explore a novel model for describing the multistage cell growth in batch culture. This is achieved by a modification at the specific rate of cell growth in consideration of its time-dependent changes. The existence, uniqueness and boundedness of solutions to the system and the continuity of solutions with respect to the parameters are discussed. In addition, a parameter identification problem of the system is developed and a feasible optimization algorithm is constructed to solve it. Numerical result shows that the improved model could describe the batch culture well.     

模情况下对称代数在亚循环群作用下的周期性质

在本文中,我们考虑在亚循环群$G=C_p \times H$作用下将对称代数$\mathbb{F}[V]$分解为不可分解模的直和,其中$H$是一个$p^{\prime}$-模.当向量空间$V$作为$G$-模的不可分解直和部分对应的单$H$-模的规范多项式是它的对偶模的基底元素乘积的幂时, 我们证明了对称代数 $\mathbb{F}[V]$的周期性质.     

Persistent oscillations in a threshold adjustment model

In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic fluctuations of the consumption rate, the habit and the threshold. It turns out that both a low adjustment rate of the threshold as well as a steep consumption function favour oscillatory patterns.     

最小偏差分析法在经济周期分析中的应用

利用最小偏差分析法,分析了我国GDP增长率的周期性特征,并对我国今后几年的GDP增长率进行了预测.分析的结果是:从1953—2006年,我国GDP增长率存在着7年左右的小周期,15年左右的中周期,19年左右的中长周期和28年左右的大周期,而且随着时间的推移,经济周期的波动幅度逐渐趋小,反映出经济增长的稳定性增强.预测的结果是:今后几年(2年或更长一段时间)我国GDP增长率应该保持在10%左右,波动的区间为[9%,11%].     

关于随机动力系统的Fatou－Julia猜测

设Ｆ＝｛ｆ１，…，ｆＭ｝是一个次数大于１的多项式集合。我们证明了在一定条件下Ｆａｔｏｕ集Ｆ（Ｆ）没有游荡区域。更确切地说，对于Ｆ（Ｆ）的每一个分支Ω，存在整数ｍ≥０，ｎ≥０，ｍ≠ｎ和λ∈∑Ｍ使得Ｗｍα（Ω）和Ｗｎα（Ω）落入Ｆ（Ｆ）的同一分支     

一个具有年龄阶段结构的流行病-种群混合动力系统的数学分析

研究一个捕食者具有年龄阶段结构的流行病-种群混合动力系统.得到系统的平衡点的存在性,局部稳定性,Hopf分支及其分支出的极限环的轨道稳定性,进一步地,考虑脉冲影响下系统的灭绝性和持久性.最后,用数值模拟说明所得到的结果.     

On a dynamical hierarchical model for prismatic shells in the theory of elastic mixtures

The present paper is devoted to the design of a hierarchy of two‐dimensional models for dynamical problems within the theory of multicomponent linearly elastic mixtures in the case of prismatic shells with thickness which may vanish on some part of its boundary. The hierarchical model is obtained by a semidiscretization of the three‐dimensional problem in the transverse direction. In suitable weighted Sobolev spaces we investigate the well‐posedness of the two‐dimensional problems, prove pointwise convergence of the sequence of approximate solutions restored from the solutions of the reduced problems to the exact solution of the original problem and estimate the rate of convergence. Copyright © 2005 John Wiley & Sons, Ltd.     

Determination of the insolation function in the nonlinear Sellers climate model

We are interested in the climate model introduced by Sellers in 1969 which takes the form of some nonlinear parabolic equation with a degenerate diffusion coefficient. We investigate here some inverse problem issue that consists in recovering the so-called insolation function. We not only solve the uniqueness question but also provide some strong stability result, more precisely unconditional Lipschitz stability in the spirit of the well-known result by Imanuvilov and Yamamoto (1998) [22]. The main novelties rely in the fact that the considered model is degenerate and above all nonlinear. Indeed we provide here one of the first result of Lipschitz stability in a nonlinear case.     

On the Module of Almost Periodic Output for Sampled-Data Feedback Control Systems

The present paper is concerned with the module containment of almost periodic output for sampled-data feedback control system. Some known (periodic, quasi-periodic) results would be expanded. A special case of sampled-data feedback control systems is detailed. This work was partially supported by the National Natural Science Foundation of China and RFDP.     

A finite element model for nonlinear behaviour of piezoceramics under weak electric fields

It has been experimentally observed that piezoceramic materials exhibit different types of nonlinearities under different combinations of electric and mechanical fields. When excited near resonance in the presence of weak e to a Duffinor such as jump phenomena and presence of superharmonics in the response spectra. There has not been much work in the litrature to model these types of nonlinearities. Some authors have developed one-dimensional models for the above phenomenon and derived closed-form solutions for the displacement response of piezo-actuators. However, the generalized three-dimensional (3-D) formulation of electric enthalpy, the variational formulation and the FEM implementation have not yet been addressed, which are the focus of this paper. In this work, these nonlinearities have been modelled in a 3-D piezoelectric continuum using higher order quadratic and cubic terms in the generalized electric enthalpy density function. The coupled nonlinear finite element equations have been derived using variational formulation. A special linearization technique for assembling the nonlinear matrices and solution of the resulting nonlinear equations has been developed. The method has been used for simulating the nonlinear frequency response of a lead zirconate titanate plate excited near its first in-plane vibration resonance frequency with sinusoidal excitations of different electric field strengths. The results have been compared with those of the experiment.