The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

It is well-known that self-linking is the only Z valued Vassiliev invariant of framed knots in S^3. However for most 3-manifolds, in particular for the total spaces of S^1-bundles over an orientable surface F not S^2, the space of Z-valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S^1-bundles over an orientable not necessarily compact surface F not S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order one invariant, i.e. it distinguishes every two framed knots that can be distinguished by order one invariants with values in an Abelian group.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.htm

From Golden Spirals to Constant Slope Surfaces

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure

A systematic review of normative studies using images of common objects

Common objects comprise living and non-living things people interact with in their daily-lives. Images depicting common objects are extensively used in different fields of research and intervention, such as linguistics, psychology, and education. Nevertheless, their adequate use requires the consideration of several factors (e.g., item-differences, cultural-context and confounding correlated variables), and careful validation procedures. The current study presents a systematic review of the available published norms for images of common objects. A systematic search using PRISMA guidelines indicated that despite their extensive use, the production of norms for such stimuli with adult populations is quite limited (N = 55), particularly for more ecological images, such as photos (N = 14). Among the several dimensions in which the items were assessed, the most commonly referred in our sample were familiarity, visual complexity and name agreement, illustrating some consistency across the reported dimensions while also indicating the limited examination of other potentially relevant dimensions for image processing. The lack of normative studies simultaneously examining affective, perceptive and semantic dimensions was also documented. The number of such normative studies has been increasing in the last years and published in relevant peer-reviewed journals. Moreover, their datasets and norms have been complying with current open science practices. Nevertheless, they are still scarcely cited and replicated in different linguistic and cultural contexts. The current study brings important theoretical contributions by characterizing images of common objects stimuli and their culturally-based norms while highlighting several important features that are likely to be relevant for future stimuli selection and evaluative procedures. The systematic scrutiny of these normative studies is likely to stimulate the production of new, robust and contextually-relevant normative datasets and to provide tools for enhancing the quality of future research and intervention.info:eu-repo/semantics/publishedVersio

Variação de procedências para a produção de sementes de Araucaria angustifolia Bert. O. Ktze.

Resumo

Trayectoria de paradigmas que explican la fecundidad

El objetivo principal de este estudio es identificar la posible conexión entre la propuesta original de la teoría de la transición demográfica y otros paradigmas que explican los cambios en el comportamiento reproductivo de las poblaciones, aparecidos en la segunda mitad del siglo XX. Las principales conclusiones se refieren a las continuidades y rupturas en la trayectoria de las teorías escogidas en el estudio: transición de la fecundidad, teoría del costo beneficio de los hijos, modelo de los determinantes próximos de la fecundidad, teoría del flujo intergeneracional de riquezas y estudios de población con enfoque de género. Además, la discusión de los cambios entre paradigmas y distintas políticas de intervención en la fecundidad es otro foco de interés en este estudio.transición de la fecundidad, costo beneficio de los hijos, determinantes próximos de la fecundidad, flujo intergeneracional de riquezas, estatus de la mujer, fecundidad y género, políticas de población, intervención de la fecundidad

Frenet-Serret dynamics

We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincar\'e symmetry of Minkowski space, the mass and the spin of the particle, are expressed in a simple way in terms of these curvatures. The simplest non-trivial model of this form, with the lagrangian depending on the first FS (or geodesic) curvature, is integrable. We show how this integrability can be deduced from the Poincar\'e invariants of the motion. We go on to explore the structure of these invariants in higher-order models. In particular, the integrability of the model described by a lagrangian that is a function of the second FS curvature (or torsion) is established in a three dimensional ambient spacetime.Comment: 20 pages, no figures - replaced with version to appear in Class. Quant. Grav. - minor changes, added Conclusions sectio

Toward a general theory of linking invariants

Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2 disjoint. The classical linking number lk(phi_1,phi_2) is defined only when phi_1*[N_1] = phi_2*[N_2] = 0 in H_*(M). The affine linking invariant alk is a generalization of lk to the case where phi_1*[N_1] or phi_2*[N_2] are not zero-homologous. In arXiv:math.GT/0207219 we constructed the first examples of affine linking invariants of nonzero-homologous spheres in the spherical tangent bundle of a manifold, and showed that alk is intimately related to the causality relation of wave fronts on manifolds. In this paper we develop the general theory. The invariant alk appears to be a universal Vassiliev-Goussarov invariant of order < 2. In the case where phi_1*[N_1] and phi_2*[N_2] are 0 in homology it is a splitting of the classical linking number into a collection of independent invariants. To construct alk we introduce a new pairing mu on the bordism groups of spaces of mappings of N_1 and N_2 into M, not necessarily under the restriction dim N_1 + dim N_2 +1 = dim M. For the zero-dimensional bordism groups, mu can be related to the Hatcher-Quinn invariant. In the case N_1=N_2=S^1, it is related to the Chas-Sullivan string homology super Lie bracket, and to the Goldman Lie bracket of free loops on surfaces.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper42.abs.htm

RealPic: Picture norms of real-world common items

Pictures are often used as stimuli in several fields, such as psychology and neuroscience. However, co-occurring image-related properties might impact their processing, emphasizing the importance of validating such materials to guarantee the quality of research and professional practices. This is particularly relevant for pictures of common items because of their wide applicability potential. Normative studies have already been conducted to create and validate such pictures, yet most of them focused on stimulus without naturalistic elements (e.g., line drawings). Norms for real-world pictures of common items are rare, and their normative examination does not always simultaneously assess affective, semantic and perceptive dimensions, namely in the Portuguese context. Real-world pictures constitute pictorial representations of the world with realistic details (e.g., natural color or position), thus improving their ecological validity and their suitability for empirical studies or intervention purposes. Consequently, the establishment of norms for real-world pictures is mandatory for exploring their ecological richness and to uncover their impact across several relevant dimensions. In this study, we established norms for 596 real-world pictures of common items (e.g., tomato, drum) selected from existing databases and distributed into 12 categories. The pictures were evaluated on nine dimensions by a Portuguese sample. The results present the norms by item, by dimension and their correlations as well as cross-cultural analyses. RealPic is a culturally based dataset that offers systematic and flexible standards and is suitable for selecting stimuli while controlling for confounding effects in empirical tasks and interventional applications.info:eu-repo/semantics/acceptedVersio

Nutritional composition of omnivorous and carnivorous wild freshwater fish from Tagus river basin

Portugal is one of the countries in the world with highest per capita fish consumption (59.9 kg/year) (1), mainly saltwater fish from Atlantic Northwest and marine aquaculture. However, in the interior of Portugal is traditional the consumption of wild freshwater fish (common carp [CC], iberian barbel [IB], crucian carp [CrC] and largemouth bass [LB]). These species are very interesting as game fishing and also very important in the local cuisine due to their characteristic flavor.CERNAS-IPCB [UIDB/00681/2020] funding by the Portuguese National Funding Agency for Science, Research and Technology (FCT).info:eu-repo/semantics/publishedVersio