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1.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
2.
Aminonaphthols are easily transformed into a variety of 1- and 2-naphthyl piperazines using a sequence of diazotization, iodide substitution and Pd(0) catalyzed coupling reactions. 相似文献
3.
The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated. 相似文献
4.
In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices). 相似文献
5.
This study analyzes the economics of transshipping biomass from truck to train in a North American setting. Transshipment
will only be economic when the cost per unit distance of a second transportation mode is less than the original mode. There
is an optimum number of transshipment terminals which is related to biomass yield. Transshipment incurs incremental fixed
costs, and hence there is a minimum shipping distance for rail transport above which lower costs/km offset the incremental
fixed costs. For transport by dedicated unit train with an optimum number of terminals, the minimum economic rail shipping
distance for straw is 170 km, and for boreal forest harvest residue wood chips is 145 km. The minimum economic shipping distance
for straw exceeds the biomass draw distance for economically sized centrally located power plants, and hence the prospects
for rail transport are limited to cases in which traffic congestion from truck transport would otherwise preclude project
development. Ideally, wood chip transport costs would be lowered by rail transshipment for an economically sized centrally
located power plant, but in a specific case in Alberta, Canada, the layout of existing rail lines precludes a centrally located
plant supplied by rail, whereas a more versatile road system enables it by truck. Hence for wood chips as well as straw the
economic incentive for rail transport to centrally located processing plants is limited. Rail transshipment may still be preferred
in cases in which road congestion precludes truck delivery, for example as result of community objections. 相似文献
6.
G. A. Watson 《Advances in Computational Mathematics》1994,2(4):393-405
The orthogonal Procrustes problem involves finding an orthogonal matrix which transforms one given matrix into another in
the least-squares sense, and thus it requires the minimization of the Frobenius matrix norm. We consider, the solution of
this problem for a family of orthogonally invariant norms which includes the Frobenius norm as a special case. 相似文献
7.
8.
Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem. 相似文献
9.
10.
It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map. 相似文献