A probabilistic approach to spectral analysis of growth-fragmentation equations

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.     

为什么要引入溶剂的渗透因子

阐明了引入溶剂渗透因子的必要性,较详细地介绍了两种渗透因子及它们间的关系。     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

A rational approximation and its applications to nonlinear partial differential equations on the whole line

An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach.     

T-型树谱唯一性的一个简单刻画

图G称为谱唯一的,如果任何与G谱相同的图一定与G同构.一棵树称为T-型树如果其仅有一个最大度为3的顶点.本文给出了T-型树谱唯一性的一个简单刻画,从而完全解决了T-型树的谱唯一性问题.     

TOF-SIMS imaging of chlorhexidine-digluconate transport in frozen hydrated biofilms of the fungus Candida albicans

The diffusion of the anti-microbial chlorhexidine digluconate (CHG) has been studied in C. albicans biofilms by time-of-flight secondary-ion mass spectrometry (TOF-SIMS). C. albicans has been shown to become resistant to common anti-microbial agents, including CHG, when growing as a biofilm. Mass transport resistance within biofilms has commonly been suggested as a resistance mechanism, but measurement of transport for most anti-microbial agents in biofilms has proven extremely difficult because of the heterogeneity of the biofilms and the difficulty in detecting these agents within an intact biofilm. In this study, TOF-SIMS has been used to study the transport of CHG and glucose in a frozen hydrated biofilm. The TOF-SIMS images reveal a progression of CHG from the top of the biofilm to its base with time. Images suggest that there are channels within the biofilm and show preferential binding of CHG to cellular components of the biofilm. Additionally, both living and dead cells can be identified in the TOF-SIMS images by the sequestration of K⁺ and the presence of cell markers. This study demonstrates that TOF-SIMS has the unique potential to simultaneously observe the presence of an antimicrobial agent, concentration of nutrients, and the viability of the cell population.     

Hypernormal form theory: foundations and algorithms

Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the smallest substages into which the hypernormalization process can be divided. This leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work. A concrete interpretation of Jan Sanders’ spectral sequence for hypernormal forms is presented. Examples are given, and a proof is given for a little-known theorem of Belitskii expressing the hypernormal form space (in the inner product style) as the kernel of a higher-order differential operator.     

Design of an experimental procedure for energy evaluation from biomass

The rational and sustainable exploitation of nature resources is one of the priority objectives of our society. In this article a method is proposed to evaluate and exploit the energetic resources contained in different forest formations. This method is based on the use of a combustion bomb calorimeter to determine the calorific values of the different samples studied. These results were complemented with chemical analysis of the samples and with environmental and geomorphological studies of the zones were samples were taken. The results obtained during the last 3 years for the residual biomass originated from the forest formations existing in Galicia ensure the reliability and usefulness of the method that can be extended to any forest formation all over the world.     

若干具有[(PO_4)_4Mo_6~ⅤO_(15)]~(12-)簇骼的化合物的光谱研究

用FTIR ,NIRFT Raman ,UV VisDRS和荧光光谱等对五个新型具有 [(PO4) 4 MoⅤ6O15]12 -阴离子簇的化合物 :Na·(H4TETA) 3 ·(H3 O) 5·{Zn[(HPO4) 2 (PO4) 2 Mo6O15]2 } (2 ) ,(H2 en) 7·(H3 O) 4 ·{Cu[(HPO4) 2(PO4) 2 Mo6O15]2 }·H2 O (3) ,(H3 DETA) 2 ·(H3 O) 3 ·{Co0 5[(HPO4) 2 (PO4) 2 Mo6O15]}·H2 O (4) ,[Co(H3 TETA) ]2 {Co0 5[(HPO4) (PO4) 3 Mo6O15]}· 3 5H2 O (5 )和 (H3 DETA)· (H3 O ) 4 · {Co1 5[(HPO4) 2(PO4) 2 Mo6O15]}·0 5H2 O (6 ) ,进行研究 ,并探讨其结构和性能的关系。这些化合物具有 {M [(PO4) 4 Mo6O15]2 }二聚体单元 ,化合物 2～ 4的二聚体间通过与有机分子和水分子的氢键形成三维网状结构 ;化合物 5和 6的 {Co[(PO4) 4 Mo6O15]2 }二聚体间是分别通过 [CoH3 TEATA]基团和CoO4四面体组成网状结构。磷钼酸盐的特征振动频率和这些化合物的结构相关 ;化合物的三个UV VisDRS特征谱带分别属于Od→Mo,Oμ→Mo和O→M电荷转移 ;观察到以 2 4 0nm激发 ,在 4 10nm附近出现的由Oμ→Mo跃迁激发引起的较强的荧光发射谱带。