Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.

On the water-induced critical double point in a polymer solution: the role of isotopic substitution

This paper examines the effect of substitution of water by heavy water in a polymer solution of polystyrene (molecular weight = 13000) and acetone. A critical double point (CDP), at which the upper and the lower partially-miscible regions merge, occurs at nearly the same coordinates as for the system [polystyrene + acetone + water]. The shape of the critical line for [polystyrene + acetone + heavy water] is highly asymmetric. An explanation for the occurrence of the water-induced CDP in [polystyrene + acetone] is advanced in terms of the interplay between contact energy dissimilarity and free-volume disparity of the polymer and the solvent. The question of the possible existence of a one-phase hole in an hourglass phase diagram is addressed in [polystyrene + acetone + water]. Our data exclude such a possibility.

Biochemical properties of C78SC96S rhFGF-2: A double point-mutated rhFGF-2 increases obviously its activity

Fibroblast growth factor-2 (FGF-2) is a multifunctional polypeptide that affects many cellular functions and phenomena. The wild-type recombinant human fibroblast growth factor rhFGF-2(W) and the mutant C78SC96S rhFGF-2(M) were expressed in Escherichia coli and their products were purified. The results by the means of fluorescence spectroscopy and CD spectrums, suggested that due to its decreased hydrophobicity rhFGF-2 is not deposited as an inclusion body. The mitogenic activity of the expressed rhFGF-2(M) on 3T3 fibroblasts was shown to be 10-fold more than the expressed rhFGF-2(W) of which the biological activity was a little less than that of the standard rhbFGF(W), indicating that the increased biological activity was due to the change of its secondary structure, dimerization and affinity binding to FGF receptor (FGFR).

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

De la paroleconsidérée áu double point de vue de la physiologie et de la grammaire : nouvelles études sur les divers ordres de phénomènes que présente le langage de la voix articulée /

Texto a dos columnas.

De l'enseignement des mathématiques dans les colléges, considéré sous le double point de vue des prescriptions réglementaires de l'université, et des principes fondamentaux de la science ...

Mémoire (A) couronné par l'Académie royale des sciences, belles-lettres et arts de Rouen.

La Russie en face de Constantinople et de l'Europe depuis son origine jusqu'à nos jours : son histoire diplomatique sous ce double point de vue, d'après les pièces officielles, les meilleurs recueils de traités, les auteurs russes et étrangers, les sources, en un mot, les plus authentiques et les plus estimées pour chaque époque /

Includes bibliographical references.

Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

EXCIMER FLUORESCENCE STUDY ON THE MISCIBILITY OF POLY(VINYL METHYL-ETHER) AND STYRENE-BUTADIENE STYRENE TRIBLOCK COPOLYMER

The excimer fluorescence of a triblock copolymer, styrene-butadiene-styrene (SBS) containing 48 wt% polystyrene was used to investigate its miscibility with poly(vinyl methyl ether) (PVME). The excimer-to-monomer emission intensity ratio I(M)/I(E) can be used as a sensitive probe to determine the miscibility level in SBS/PVME blends: I(M)/I(E) is a function of PVME concentration, and reaches a maximum when the blend contains 60% PVME. The cloud point curve determined by light scattering shows a pseudo upper critical solution temperature diagram, which can be attributed to the effect of PB segments in SBS. The thermally induced phase separation of SBS/PVME blends can be observed by measuring I(M)/I(E), and the phase dissolution process was followed by measuring I(M)/I(E) at different times.

五种红树植物光合产量模型及对环境因子的响应

以木榄（Bruguiera gymnorriza）、白骨壤（Avicennia marina）、桐花树（Aegiceras corniculata）、秋茄（Kandelia candel）和海漆（Excoecaria agallocha）为对象，以光合作用对环境因子的响应为主线，建立了从叶片水平到群体冠层水平上的光合产量模型，探讨了从器官、个体到群体的光合产量对环境因子响应的定量关系。 将Farquhar提出的单叶片光合作用生理生化模型与气孔导度B-B模型相结合，建立了光合作用－气孔导度耦合模型。模型模拟结果与实际测量结果具有较好的一致性。在温度为25.0℃，光合有效辐射为1000μmol•m-2s-1 的条件下，当外部CO2浓度倍增到720μmol•mol-1时，白骨壤、木榄、桐花树、秋茄、海漆的光合速率分别提高22.56%，17.13%，18.43%，18.63%和18.41%。在大气CO2浓度和光合有效辐射通量密度不变的条件下，光合作用速率对温度的响应呈单峰型曲线，即有一个最适温度，5种红树植物的最适温度值均为26.5℃左右。大气CO2浓度和温度固定不变（分别为350μmol•mol-1和25.0 ℃）时，光合作用对光合有效辐射的响应符合Michaelis-Menten反应曲线，模型在PAR<1800μmol•m-2s-1时模拟精度较高（P<0.01）。 在典型晴天条件下，5种红树植物的光合速率日变化都出现两个极大值（分别在11时和15时左右），中午前后光合速率较低，模型模拟光合速率日变化与实测数值日变化趋势一致。本模型能较好地模拟5种红树植物光合产量以及对环境因子的响应，模拟预测精度较高（P<0.01）。 以Ross和Nilson叶倾角分布模型为基础，分别建立了直接辐射和散射辐射在冠层内传输的子模型。冠层内的消光系数均有明显的日变化，且上午8时之前和下午16时之后随时间变化较大。在典型晴天条件下，单位土地面积日合成干物质总量（折合为CH2O）白骨壤为15.840g•m-2d-1，对于木榄、桐花树、秋茄、海漆其相应的值分别为 22.254 g•m-2d-1， 23.610 g•m-2d-1，24.525 g•m-2d-1和25.996 g•m-2d-1 。

Impacts of land use change and climate variations on annual inflow into Miyun Reservoir,Beijing, China

The Miyun Reservoir, the only surface water source for Beijing city, has experienced water supply decline in recent decades. Previous studies suggest that both land use change and climate contribute to the changes of water supply in this critical watershed. However, the specific causes of the decline in the Miyun Reservoir are debatable under a non-stationary climate in the past 4 decades. The central objective of this study was to quantify the separate and collective contributions of land use change and climate variability to the decreasing inflow into the Miyun Reservoir during 1961–2008. Different from previous studies on this watershed, we used a comprehensive approach to quantify the timing of changes in hydrology and associated environmental variables using the long-term historical hydrometeorology and remote-sensing-based land use records. To effectively quantify the different impacts of the climate variation and land use change on streamflow during different sub-periods, an annual water balance model (AWB), the climate elasticity model (CEM), and a rainfall–runoff model (RRM) were employed to conduct attribution analysis synthetically. We found a significant (p  <  0.01) decrease in annual streamflow, a significant positive trend in annual potential evapotranspiration (p  <  0.01), and an insignificant (p  >  0.1) negative trend in annual precipitation during 1961–2008. We identified two streamflow breakpoints, 1983 and 1999, by the sequential Mann–Kendall test and double-mass curve. Climate variability alone did not explain the decrease in inflow to the Miyun Reservoir. Reduction of water yield was closely related to increase in actual evapotranspiration due to the expansion of forestland and reduction in cropland and grassland, and was likely exacerbated by increased water consumption for domestic and industrial uses in the basin. The contribution to the observed streamflow decline from land use change fell from 64–92 % during 1984–1999 to 36–58 % during 2000–2008, whereas the contribution from climate variation climbed from 8–36 % during the 1984–1999 to 42–64 % during 2000–2008. Model uncertainty analysis further demonstrated that climate warming played a dominant role in streamflow reduction in the most recent decade (i.e., 2000s). We conclude that future climate change and variability will further challenge the water supply capacity of the Miyun Reservoir to meet water demand. A comprehensive watershed management strategy needs to consider the climate variations besides vegetation management in the study basin.

Exercise sheet 9

Exercises and solutions in LaTex