On a family of models of cell division cycle

The aim of this work is to generalize and study a model of cell division cycle proposed recently by Zheng et al. [Zheng Z, Zhou T, Zhang S. Dynamical behavior in the modeling of cell division cycle. Chaos, Solitons & Fractals 2000;11:2371–8]. Here we study the qualitative properties of a general family to which the above model belongs. The global asymptotic stability (GAS) of the unique equilibrium point E (idest of the arrest of cell cycling) is investigated and some conditions are given. Hopf’s bifurcation is showed to happen. In the second part of the work, the theorems given in the first part are used to analyze the GAS of E and improved conditions are given. Theorem on uniqueness of limit cycle in Lienard’s systems are used to show that, for some combination of parameters, the model has GAS limit cycles.     

The asynchronous exponential growth property in a model for the kinetic heterogeneity of tumour cell populations

A continuous cell population model, which represents both the cell cycle phase structure and the kinetic heterogeneity of the population following Shackney's ideas [J. Theor. Biol. 38 (1973) 305-333], is studied. The asynchronous exponential growth property is proved in the framework of the theory of strongly continuous semigroups of bounded linear operators.     

An existence and uniqueness principle for a nonlinear version of the Lebowitz‐Rubinow model with infinite maximum cycle length

The present article deals with existence and uniqueness results for a nonlinear evolution initial‐boundary value problem, which originates in an age‐structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.     

Dynamical behavior in the modeling of cell division cycle

In this paper we qualitatively analyze mathematical modeling of the cell division cycle established by Novak and Tyson (Novak B, Tyson JJ. J Theor Biol 1993;165:101–34) and discuss the existence, uniqueness, stability and unstability of its singular point and the system boundedness, existence and nonexistence of closed orbit and its global structure.     

On the stability of hematopoietic model with feedback control

We propose and analyze a mathematical model of the production and regulation of blood cell population in the bone marrow (hematopoiesis). This model includes the primitive hematopoietic stem cells (PHSC), the three lineages of their progenitors and the corresponding mature blood cells (red blood cells, white cells and platelets). The resulting mathematical model is a nonlinear system of differential equations with several delays corresponding to the cell cycle durations for each type of cells. We investigate the local asymptotic stability of the trivial steady state by analyzing the roots of the characteristic equation. We also prove by a Lyapunov function the global asymptotic stability of this steady state. This situation illustrates the extinction of the cell population in some pathological cases.     

A Model of Proliferating Cell Populations with Infinite Cell Cycle Length: Semigroup Existence

In this paper we are concerned with a mathematical model of an age structured cell population endowed with general reproduction laws. Individual cells are distinguished by age and cell cycle length. The cell cycle length is considered as an inherited property determined at birth and can be between zero and infinity. We show that the model is well-posed in the sense of the semigroup theory and we give its explicit expression.     

一类二次系统极限环的唯一性与极限环不存在的充分条件

本文通过计算二次系统（１）在唯一奇点ｏ（０,０）的焦点量,证明了（１）最多只有一个极限环;并且给出了（１）不存在极限环的充分条件：（ｉ）当δｌｍ≥０时,（１）无极限环;（ｉ）当δｌｍ＜０,｜δ｜≥ｌｍ时,（１）无极限环     

Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots

This paper addresses cyclic scheduling of a no-wait robotic cell with multiple robots. In contrast to many previous studies, we consider r-degree cyclic (r > 1) schedules, in which r identical parts with constant processing times enter and leave the cell in each cycle. We propose an algorithm to find the minimal number of robots for all feasible r-degree cycle times for a given r (r > 1). Consequently, the optimal r-degree cycle time for any given number of robots for this given r can be obtained with the algorithm. To develop the algorithm, we first show that if the entering times of r parts, relative to the start of a cycle, and the cycle time are fixed, minimizing the number of robots for the corresponding r-degree schedule can be transformed into an assignment problem. We then demonstrate that the cost matrix for the assignment problem changes only at some special values of the cycle time and the part entering times, and identify all special values for them. We solve our problem by enumerating all possible cost matrices for the assignment problem, which is subsequently accomplished by enumerating intervals for the cycle time and linear functions of the part entering times due to the identification of the special values. The algorithm developed is shown to be polynomial in the number of machines for a fixed r, but exponential if r is arbitrary.     

A Model of Proliferating Cell Populations with Infinite Cell Cycle Length: Asymptotic Behavior

In this paper we are concerned with a mathematical model of an age structured cell population endowed with general reproduction laws. Individual cells are distinguished by age and cell cycle length. The cell cycle length is considered as an inherited property determined at birth and can be between zero and infinity. We show that the model is well-posed in the sense of the semigroup theory and we give its explicit expression.     

基于滤波技术的首都旅游贸易发展趋势与周期研究

运用HP滤波技术,实证拟合了首都旅游贸易的发展趋势和周期.在对时间序列分离出趋势和周期之后,采用多项式拟合给出了趋势值的经验回归表达式,在此基础上,分析了剔除趋势后的贸易周期特征.研究表明,改革开放的前10年,首都旅游贸易的出口周期性表现并不明显;之后至今的20年,则呈现显著周期特征,周期长度大约5-7年,但这种周期变化也不具有稳定性.对比我国经济发展历程,首都旅游贸易出口周期与宏观经济增长周期高度一致,显示出其对宏观经济发展具有高度敏感性,因此必须重视宏观经济减速给首都旅游贸易带来的衰退影响.另外,重大事件对首都旅游贸易的影响也不容忽视.     

An exact calculation of the cycle service level in a generalized periodic review system

This paper is focused on the exact calculation of the cycle service level for a generalized periodic review system accepting any discrete demand with a known probability function and any cycle service target. Previously, it was necessary to modify the definition of the cycle service level metric (also known as non stock out probability) so that it could be applied to these cases. The purpose of the proposed (R, S) system is to handle simultaneously fast-moving items, slow-moving items and intermittent or sporadic demand items any of them with high, medium or low cycle service targets.     

On a mathematical model of age‐cycle length structured cell population with non‐compact boundary conditions

This work deals with a mathematical model of an age‐cycle length structured cell population. Each cell is distinguished by its age and its cycle length. The cellular mitosis is mathematically described by non‐compact boundary conditions. We prove then that this mathematical model is governed by a positive C₀‐semigroup. Copyright © 2014 John Wiley & Sons, Ltd.     

Date identification of the Zhouji materials during the period of King Xin

By identifying the dates of the Zhouji materials (one kind of oracle bone) during the period of King Xin (also called Zhou the last monarch in Shang Dynasty), this paper establishes a new “Direct Solving Method” (DSM) to solve the chronology problems in the Shang and Zhou dynasties. The mathematical models are more suitable for those materials with the Ganzhi (the Heavenly Stems and Earthly Branches, the Chinese ancient date recorded method being of the 60-day cycle, that the repetitive cycle is independent of any astronomical parameter, each day within this cycle has its own name and can also be expressed by the numbers from 1 to 60) record of the date, lunar month, and their year intervals and all of them are in history documents, oracle bones and bronze vessels. For example, taking the 12 Zhouji materials in the period of King Xin, we derive the two best results of the first year when Xin assumed the reins of government in probably 1063 BC or 1052 BC.     

A fully polynomial time approximation scheme for the Replenishment Storage problem

The Replenishment Storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system with specified individual reorder cycle lengths. The reorders can only take place at integer time units. This problem was shown to be weakly NP-hard for constant joint cycle length (the least common multiple of all individual cycle lengths). We devise here the first known FPTAS for the RSP with different individual cycle lengths and constant joint cycle length.     

Integer Functions on the Cycle Space and Edges of a Graph

A directed graph has a natural \mathbb Z{\mathbb {Z}} -module homomorphism from the underlying graph’s cycle space to \mathbb Z{\mathbb {Z}} where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any \mathbb Z{\mathbb {Z}} -module homomorphism of a graph’s cycle space to \mathbb Z{\mathbb {Z}} that satisfies these two properties for all cycles must be such a map induced from an edge direction on the graph. In this paper we will prove a generalization of this theorem and an analogue as well.     

Modeling the role of the cell cycle in regulating Proteus mirabilis swarm-colony development

We present models and computational results which indicate that the spatial and temporal regularity seen in Proteus mirabilis swarm-colony development is largely an expression of a specific, nearly precise age of dedifferentiation in the cell cycle from motile swarmer cells to immotile dividing cells. This contrasts strongly with reaction–diffusion models of Proteus behavior that ignore or average out the age structure of the cell population and instead use only density-dependent mechanisms. We argue the necessity of retaining this known biological feature using explicit age structure in the model, and suggest that certain experiments may validate this underlying mechanism empirically.     

Effects of engine design and operating parameters on the performance of a spark ignition (SI) engine with steam injection method (SIM)

The effects of engine design and operating parameters such as equivalence ratio (ER), compression ratio (CR), cycle pressure ratio (CPR), cycle temperature ratio (CTR), bore-stroke length ratio (D/L) inlet pressure, inlet temperature, friction coefficient (FC), mean piston speed (MPS) and engine speed on the performance characteristics such as brake thermal efficiency (BTE) and brake power output (BPO) are investigated for a steam injected gasoline engine (SIGE) with a simulation model validated with experiments using a realistic finite-time thermodynamics model (FTTM). Moreover, the energy losses arising from exhaust output (EO), heat transfer (HT), friction (FR) and incomplete combustion (IC), are illustrated by using graphs. The optimum values of engine speed, compression ratio, equivalence ratio, cycle temperature ratio and pressure ratio are presented by grid curves. Also, they are called performance maps. The results showed that the performance characteristics improve with enhancing inlet pressure, cycle pressure ratio and cycle temperature ratio; with diminishing inlet temperature and friction coefficient. The BPO can be increased up to 42%, 55% and 62% by using the optimum values of cycle pressure ratio, cycle temperature ratio and inlet pressure, respectively. Also, the BTE can be increased up to 8%, 12% and 15%, by the same way. On the other hand, the performance characteristics can improve or deteriorate with respect to different conditions of compression ratio, engine speed, equivalence ratio, stroke length and mean piston speed. Therefore, the optimum values should be determined to obtain the maximum performance conditions.     

平面自治系统极限环的存在性

本文研究一般自治系统的极限环存在性问题，在一定条件下，我们证明该系统极限环的存在性，所得结果推广和改进了文［５—７］的相应结论．     

Date identification of the Zhouji materials during the period of King Xin--The chronology Solving method of oracle boneS and bronzes in the Shang and Zhou dynasties

By identifying the dates of the Zhouji materials (one kind of oracle bone) during the period of King Xin (also called Zhou the last monarch in Shang Dynasty), this paper establishes a new "Direct Solving Method" (DSM) to solve the chronology problems in the Shang and Zhou dynasties. The mathematical models are more suitable for those materials with the Ganzhi (the Heavenly Stems and Earthly Branches, the Chinese ancient date recorded method being of the 60-day cycle, that the repetitive cycle is independent of any astronomical parameter, each day within this cycle has its own name and can also be expressed by the numbers from l to 60) record of the date, lunar month, and their year intervals and all of them are in history documents, oracle bones and bronze vessels. For example, taking the 12 Zhouji materials in the period of King Xin,we derive the two best results of the first year when Xin assumed the reins of government in probably 1063 BC or 1052 BC.