Hasse-Schmidt Derivations and Coefficient Fields in Positive Characteristics

We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivationsComment: 14 pages; A gap in the statement of Proposition (2.7) has been fixed and the proof of Theorem (3.14) has been adapte

On the logarithmic comparison theorem for integrable logarithmic connections

Let $X$ be a complex analytic manifold, $D\subset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j: U=X-D \to X$ the corresponding open inclusion, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $U$. In this paper we prove that the canonical morphisms between the logarithmic de Rham complex of $E(kD)$ and $R j_* L$ (resp. the logarithmic de Rham complex of $E(-kD)$ and $j_!L$) are isomorphisms in the derived category of sheaves of complex vector spaces for $k\gg 0$ (locally on $X$)Comment: Terminology has changed: "linear jacobian type" instead of "commutative differential type"); no Koszul hypothesis is needed in theorem (2.1.1); minor changes. To appear in Proc. London Math. So

Dependence of the electronic structure of self-assembled InGaAs/GaAs quantum dots on height and composition

While electronic and spectroscopic properties of self-assembled In_{1-x}Ga_{x}As/GaAs dots depend on their shape, height and alloy compositions, these characteristics are often not known accurately from experiment. This creates a difficulty in comparing measured electronic and spectroscopic properties with calculated ones. Since simplified theoretical models (effective mass, k.p, parabolic models) do not fully convey the effects of shape, size and composition on the electronic and spectroscopic properties, we offer to bridge the gap by providing accurately calculated results as a function of the dot height and composition. Prominent results are the following. (i) Regardless of height and composition, the electron levels form shells of nearly degenerate states. In contrast, the hole levels form shells only in flat dots and near the highest hole level (HOMO). (ii) In alloy dots, the electrons' ``s-p'' splitting depends weakly on height, while the ``p-p'' splitting depends non-monotonically. In non-alloyed InAs/GaAs dots, both these splittings depend weakly on height. For holes in alloy dots, the ``s-p'' splitting decreases with increasing height, whereas the ``p-p'' splitting remains nearly unchaged. Shallow, non-alloyed dots have a ``s-p'' splitting of nearly the same magnitude, whereas the ``p-p'' splitting is larger. (iii) As height increases, the ``s'' and ``p'' character of the wavefunction of the HOMO becomes mixed, and so does the heavy- and light-hole character. (iv) In alloy dots, low-lying hole states are localized inside the dot. Remarkably, in non-alloyed InAs/GaAs dots these states become localized at the interface as height increases. This localization is driven by the biaxial strain present in the nanostructure.Comment: 14 pages, 12 figure

Mating Patterns and Post-Mating Isolation in Three Cryptic Species of the Engystomops Petersi Species Complex

Determining the extent of reproductive isolation in cryptic species with dynamic geographic ranges can yield important insights into the processes that generate and maintain genetic divergence in the absence of severe geographic barriers. We studied mating patterns, propensity to hybridize in nature and subsequent fertilization rates, as well as survival and development of hybrid F1 offspring for three nominal species of the Engystomops petersi species complex in Yasuní National Park, Ecuador. We found at least two species in four out of six locations sampled, and 14.3% of the wild pairs genotyped were mixed-species (heterospecific) crosses. We also found reduced fertilization rates in hybrid crosses between E. petersi females and E. “magnus” males, and between E. “magnus” females and E. “selva” males but not in the reciprocal crosses, suggesting asymmetric reproductive isolation for these species. Larval development times decreased in F1 hybrid crosses compared to same species (conspecific) crosses, but we did not find significant reduction in larval survival or early metamorph survival. Our results show evidence of post-mating isolation for at least two hybrid crosses of the cryptic species we studied. The general decrease in fertilization rates in heterospecific crosses suggests that sexual selection and reinforcement might have not only contributed to the pattern of call variation and behavioral isolation we see between species today, but they may also contribute to further signal divergence and behavioral evolution, especially in locations where hybridization is common and fertilization success is diminished

Mating Patterns and Post-Mating Isolation in Three Cryptic Species of the Engystomops Petersi Species Complex

Determining the extent of reproductive isolation in cryptic species with dynamic geographic ranges can yield important insights into the processes that generate and maintain genetic divergence in the absence of severe geographic barriers. We studied mating patterns, propensity to hybridize in nature and subsequent fertilization rates, as well as survival and development of hybrid F1 offspring for three nominal species of the Engystomops petersi species complex in Yasuní National Park, Ecuador. We found at least two species in four out of six locations sampled, and 14.3% of the wild pairs genotyped were mixed-species (heterospecific) crosses. We also found reduced fertilization rates in hybrid crosses between E. petersi females and E. “magnus” males, and between E. “magnus” females and E. “selva” males but not in the reciprocal crosses, suggesting asymmetric reproductive isolation for these species. Larval development times decreased in F1 hybrid crosses compared to same species (conspecific) crosses, but we did not find significant reduction in larval survival or early metamorph survival. Our results show evidence of post-mating isolation for at least two hybrid crosses of the cryptic species we studied. The general decrease in fertilization rates in heterospecific crosses suggests that sexual selection and reinforcement might have not only contributed to the pattern of call variation and behavioral isolation we see between species today, but they may also contribute to further signal divergence and behavioral evolution, especially in locations where hybridization is common and fertilization success is diminished

The architectural adaptation of urban economic life: Location, use and form of the commercial-residential building in Cardiff

Revisiting Jane Jacob's notion of locality knowledge, this paper argues that combining commercial space and dwelling fosters social, economic and architectural processes that come about by factors of local urban economies. The mixing of uses merges the relation of 'what one does' and 'where one lives' in a particular building whereby urban and architectural scale effects come into place. Comparisons of commercial-residential buildings in two local districts of contrasting morphologies in the city of Cardiff are studied in the context of their urban-architectural design scales. From an urban scale analysis, attention is given to the distribution of commercial-residential buildings in relation to spatial centrality; from an architectural perspective, it examines the way residential building adapts commercial additions, defining how different functions associate distinctive adaptable typologies depending on the building's urban location. By using syntactical and morphological approaches, the paper combines Depth Distance analysis with patterns of use and building form, drawing two reportable findings: The identification of corner shops located within one turn of direction from main high streets within gridiron urban forms, while activities combining retail or local office businesses with residential functions are located in corner blocks along streets within radial urban morphologies. These spatial attributes of location combine the adaptability of local property markets to mixed use with advantages in accessibility to produce an urban building that can flexibly accommodate innovation that is both a reflection of new skills and knowledge contributing to a local diversity

Effects of morphology on phonons of nanoscopic silver grains

The morphology of nanoscopic Ag grains significantly affects the phonons. Atomistic simulations show that realistic nanograin models display complex vibrational properties. (1) Single-crystalline grains. Nearly-pure torsional and radial phonons appear at low frequencies. For low-energy, faceted models, the breathing mode and acoustic gap (lowest frequency) are about 10% lower than predicted by elasticity theory (ET) for a continuum sphere of the same volume. The sharp edges and the atomic lattice split the ET-acoustic-gap quintet into a doublet and triplet. The surface protrusions associated with nearly spherical, high-energy models produce a smaller acoustic gap and a higher vibrational density of states (DOS) at frequencies \nu<2 THz. (2) Twined icosahedra. In contrast to the single-crystal case, the inherent strain produce a larger acoustic gap, while the core atoms yield a DOS tail extending beyond the highest frequency of single-crystalline grains. (3) Mark's decahedra, in contrast to (1) and (2), do not have a breathing mode; although twined and strained, do not exhibit a high-frequency tail in the DOS. (4) Irregular nanograins. Grain boundaries and surface disorder yield non-degenerate phonon frequencies, and significantly smaller acoustic gap. Only these nanograins exhibit a low-frequency \nu^2 DOS in the interval 1-2 THz.Comment: Version published in Phys. Rev.

The Architecture of Decision-Making Processes: A Game of Chess in the Spatial Configuration of the River Thames London

Urban forms emerge from the interplay of social, economic, political and cultural forces, which are partly attributed to decision-making processes of urban planning and design. However, decision-making involves the everyday life of using and navigating in the built environment to the management of urban space. This paper seeks to understand the basic notion of how pedestrian movement is related to land use choices in the built form. The hypothesis is that movement itself involves a choice; that is, a decision-making of direction and destination, of passing through or of static behaviour. The density of movement flow is seen as a result of locations that potentially become attractors that have a rich distribution of land use. How we accommodate and modulate movement is thus important in helping us understand the multiple effects of everyday use that arises from decision-making processes and its subsequent effectuation in the configuration of urban space. Therefore, two key questions are addressed: first, how the types of movement choices influence and are influenced by the spatial layout; and second, how the distribution of land uses is affected by such choices. The paper uses Space Syntax and Game theory as a combination of theoretical frameworks that study independent and interdependent decision-making processes in urban space, to answer these questions. Taking the River Thames Path as an example, the research project focuses on the unconnected section of the river walk between London Bridge and Southwark Bridge. In analogy with a game of chess, the results demonstrate how different kinds of choices are ruled primarily by the location of commercial uses in the urban grid