Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

Is the dynamics of open quantum systems always linear?

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.Comment: 19 pages, 3 figures, minor changes to improve readability, discussion on Mori's linear regime and references adde

Enzymatic hydrolysis of lentil protein concentrate for modification of physicochemical and techno-functional properties

The effects of hydrolysis by commercial food-grade proteases on the physicochemical and techno-functional properties of lentil protein concentrate were investigated. Lentil protein concentrate was hydrolysed with Alcalase, Novozym 11028 or Flavourzyme, and a control was prepared without enzyme addition under the same conditions. Differences in specificity between the three proteases were evident in the electrophoretic protein profile, reversed-phase HPLC peptide profile, and free amino acid composition. Alcalase and Novozym were capable of extensively degrading all the major protein fractions. Alcalase or Novozym treatment resulted in considerably higher solubility under acidic conditions compared to the control. Flavourzyme treatment resulted in moderately improved solubility in the acidic range, but slightly lower solubility at pH 7. Alcalase treatment resulted in slightly larger particle size and slightly higher viscosity. The foaming properties of the protein concentrate were not significantly affected by hydrolysis. Increased solubility in acidic conditions with hydrolysis could broaden the range of food and beverage applications for lentil protein concentrate

Nutritional and rheological features of lentil protein isolate for yoghurt-like application

The substitution of animal protein with proteins of plant origin is a viable way to decrease the negative impact caused by animal husbandry on the environment. Pulse consumption has been widely promoted as a nutritious contribution to protein supplementation. In this study, an emulsion of lentil (Lens culinaris) protein isolate is fermented with lactic acid bacteria (LAB) to manufacture a yoghurt alternative and the techno-functional properties compared to a dairy- and a soy-based product with similar protein contents. The yoghurt-like products are subjected to large and small deformation analysis, quantification of fermentable oligosaccharides, disaccharides, monosaccharides and polyols (FODMAP), water holding capacity tests, protein profile analysis and the gel structure is visualised by confocal laser scanning microscopy (CLSM). The lentil yoghurt alternative shows good water holding capacity, high firmness and consistency values in large deformation analysis, with cohesiveness and viscosity not significantly different from that of dairy yoghurt. The high gel strength and rigidity of the lentil yoghurt gels measured by small deformation analysis is well-reflected in the dense protein matrix in the CLSM graphs. FODMAP content of the lentil yoghurt is very low, making it suitable for consumption by irritable bowel syndrome (IBS) patients. Our results show that lentil protein isolate is an excellent base material for producing a plant-based yoghurt alternative

Leuconostoc citreum TR116 as a microbial cell factory to functionalise high-protein faba bean ingredients for bakery applications

Grain legumes, such as faba beans, have been investigated as promising ingredients to enhance the nutritional value of wheat bread. However, a detrimental effect on technological bread quality was often reported. Furthermore, considerable amounts of antinutritional compounds present in faba beans are a subject of concern. Sourdough-like fermentation can positively affect baking performance and nutritional attributes of faba bean flours. The multifunctional lactic acid bacteria strain Leuconostoc citreum TR116 was employed to ferment two faba bean flours with different protein contents (dehulled flour (DF); high-protein flour (PR)). The strain's fermentation profile (growth, acidification, carbohydrate metabolism and antifungal phenolic acids) was monitored in both substrates. The fermentates were applied in regular wheat bread by replacing 15% of wheat flour. Water absorption, gluten aggregation behaviour, bread quality characteristics and in vitro starch digestibility were compared to formulations containing unfermented DF and PR and to a control wheat bread. Similar microbial growth, carbohydrate consumption as well as production of lactic and acetic acid were observed in both faba bean ingredients. A less pronounced pH drop as well as a slightly higher amount of antifungal phenolic acids were measured in the PR fermentate. Fermentation caused a striking improvement of the ingredients' baking performance. GlutoPeak measurements allowed for an association of this observation with an improved gluten aggregation. Given its higher potential to improve protein quality in cereal products, the PR fermentate seemed generally more promising as functional ingredient due to its positive impact on bread quality and only moderately increased starch digestibility in bread

Closure properties of solutions to heat inequalities

We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by $u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2}$ also satisfies a heat inequality of a similar type provided $\tfrac{1}{p_1} + \tfrac{1}{p_2} = 1 + \tfrac{1}{p}$. On iterating, this result leads to an analogous statement concerning $n$-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp $n$-fold Young convolution inequality and its reverse form.Comment: 12 page

Süsswasseralgen [Material gráfico]

Contiene: I. Cyanophyceae, grünalgen I ; II. Bacillariaceae, kieselalgen (Diatomeen) ; III. Conjugatae, jochalgen ; IV. Chorophyceae, grünalgen I ; V. Chorophyceae, grünalgen II ; VI. Characeae, phaeophyceae, rhodophyceaeMención de responsabilidad tomada de una de las láminasEn el catálogo de Cultura aparece el tit. de esta colección en castellano: "Algas de agua dulce"Las dos primeras lám. editadas por Lith. & Verlag Gummer & Ruge, Glindom Bez, Postda

Adaptive Significance of the Formation of Multi-Species Fish Spawning Aggregations near Submerged Capes

BACKGROUND: Many fishes are known to spawn at distinct geomorphological features such as submerged capes or "promontories," and the widespread use of these sites for spawning must imply some evolutionary advantage. Spawning at these capes is thought to result in rapid offshore transport of eggs, thereby reducing predation levels and facilitating dispersal to areas of suitable habitat. METHODOLOGY/PRINCIPAL FINDINGS: To test this "off-reef transport" hypothesis, we use a hydrodynamic model and explore the effects of topography on currents at submerged capes where spawning occurs and at similar capes where spawning does not occur, along the Mesoamerican Barrier Reef. All capes modeled in this study produced eddy-shedding regimes, but specific eddy attributes differed between spawning and non-spawning sites. Eddies at spawning sites were significantly stronger than those at non-spawning sites, and upwelling and fronts were the products of the eddy formation process. Frontal zones, present particularly at the edges of eddies near the shelf, may serve to retain larvae and nutrients. Spawning site eddies were also more predictable in terms of diameter and longevity. Passive particles released at spawning and control sites were dispersed from the release site at similar rates, but particles from spawning sites were more highly aggregated in their distributions than those from control sites, and remained closer to shore at all times. CONCLUSIONS/SIGNIFICANCE: Our findings contradict previous hypotheses that cape spawning leads to high egg dispersion due to offshore transport, and that they are attractive for spawning due to high, variable currents. Rather, we show that current regimes at spawning sites are more predictable, concentrate the eggs, and keep larvae closer to shore. These attributes would confer evolutionary advantages by maintaining relatively similar recruitment patterns year after year

Some recent progress on sharp Fourier restriction theory

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several concrete examples of underlying manifolds with large groups of symmetries, which sometimes allow for simple geometric proofs. We mention several open problems along the way, and include an appendix on integration on manifolds using delta calculus