An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics

A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.BERC 2022-2025 Severo Ochoa CEX2021-001142-S / MCIN / AEI / 10.13039/50110001103

Algebraic equations for constant width curves and Zindler curves

An explicit method to compute algebraic equations of curves of constant width and Zindler curves generated by a family of middle hedgehogs is given thanks to a property of Chebyshev polynomials. This extends the methodology used by Rabinowitz and Martinez-Maure in particular constant width curves to generate a full family of algebraic equations, both of curves of constant width and Zindler curves, defined by trigonometric polynomials as support functions

On isoptics and isochordal-viewed curves

In this paper, some results involving isoptic curves and constant $\phi$-width curves are given for any closed curve. The non-convex case, as well as non-simple shapes with or without cusps are considered. Relating the construction of isoptics to the construction given in Holditch’s theorem, a kind of curves is defined: the isochordal-viewed curves. The explicit expression of these curves is given together with some examples. Integral formulae on the area of their isoptics are obtained and a Barbier-type theorem is derived. Finally, a characterization for isochordal-viewed hedgehogs and curves of constant $\phi$-width is given in terms of an angle function

Generalized plane offsets and rational parameterizations

In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown

S&O House - Benicàssim, Castellón. Spain

[EN] The S&O House is located in surroundings highlighted by the serene image of the Mediterranean Sea. The front of the plot borders the coast, and this proximity determines the main strategies planned for this assignment. The Mediterranean spirit of these surroundings was transferred to the design by designing the house on the basis of its relationship with the elements closest to hand: the sea, the light, the landscape and Mediterranean culture in general. The programme was developed on three levels through a simple composition and based on an appropriate use of materials, where the volumes of exposed concrete framing the landscape acquire special prominence[ES] La Casa S&O se ubica en un entorno protagonizado por la serena imagen del mar Mediterráneo. El frente de la parcela limita con la costa y dicha proximidad determina las principales estrategias proyectuales de la obra. La esencia mediterránea presente en el lugar se traslada al diseño al proyectar la casa desde su relación con los elementos más próximos: el mar, la luz, el paisaje y la cultura mediterránea. El programa se desarrolla en tres niveles a través de una composición sencilla y basada en una utilización adecuada de materiales, donde los volúmenes de hormigón visto que enmarcan el paisaje adquieren un especial protagonismoSanahuja Rochera, V. (2020). Casa S&O - Benicàssim, Castellón. España. En IX Congreso Internacional Arquitectura Blanca. Editorial Universitat Politècnica de València. https://doi.org/10.4995/CIAB9.2020.10651OC

On inverse construction of isoptics and isochordal-viewed curves

Given a regular closed curve α in the plane, a $\phi$-isoptic of $\alpha$ is a locus of points from which pairs of tangent lines to $\alpha$ span a fixed angle $\phi$. If, in addition, the chord that connects the two points delimiting the visibility angle is of constant length $\ell$, then $\alpha$ is said to be $(\phi,\ell)$-isochordal viewed. Some properties of these curves have been studied, yet their full classification is not known. We approach the problem in an inverse manner, namely that we consider a $\phi$-isoptic curve $c$ as an input and construct a curve whose $\phi$-isoptic is $c$. We provide thus a sufficient condition that constitutes a partial solution to the inverse isoptic problem. In the process, we also study a relation of isoptics to multihedgehogs. Moreover, we formulate conditions on the behavior of the visibility lines so as their envelope is a $(\phi,\ell)$-isochordal-viewed curve with a prescribed $\phi$-isoptic $c$. Our results are constructive and offer a tool to easily generate this type of curves. In particular, we show examples of $(\phi,\ell)$-isochordal-viewed curves whose $\phi$-isoptic is not circular. Finally, we prove that these curves allow the motion of a regular polygon whose vertices lie along the $(\phi,\ell)$-isochordal-viewed curve

Guest Editors’ Introduction Formative Feedback in Digital Learning Environments

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Zindler-type hypersurfaces in R^4

In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symplectic geometry are used. Moreover, each Zindler hypersurface is fibrated by space Zindler curves that correspond, in the convex case, to some space curves of constant width lying on the associated hypersurface of constant width and with the same symplectic area

Guest Editors' Introduction: Formative feedback in digital learning environments

Formative feedback is widely considered one of the most influential elements within teaching and learning processes, as evidenced by a range of articles and reviews conducted primarily in face-toface environments (see, for example, Evans, 2013; Kluger & DeNisi, 1998; Hattie & Timperley, 2007; Kulhavy & Stock, 1989; Mory, 2004; Narciss & Huth, 2004; Shute, 2008). A review of the literature shows that feedback has been conceptualized according to specific learning viewpoints. Different psychological perspectives -objectivism, information processing, socioculturalism, visible learning theory- provide distinct frameworks for describing different views of learning and the nature, characteristics and function of feedback (Hattie & Gan, 2011)..

Mechanism of allosteric modulation of Escherichia coli carbamoyl phosphate synthetase probed by site-directed mutagenesis of ornithine site residues

AbstractThe role of residues of the ornithine activator site is probed by mutagenesis in Escherichia coli carbamoyl phosphate synthetase (CPS). Mutations E783A, E783L, E892A and E892L abolish ornithine binding, E783D and T1042V decrease 2–3 orders of magnitude and E892D decreased 10-fold apparent affinity for ornithine. None of the mutations inactivates CPS. E783 mutations hamper carbamate phosphorylation and increase K+ and MgATP requirements, possibly by perturbing the K+-loop near the carbamate phosphorylation site. Mutation E892A activates the enzyme similarly to ornithine, possibly by altering the position of K891 at the opening of the tunnel that delivers the carbamate to its phosphorylation site. T1042V also influences modulation by IMP and UMP, supporting signal transmission from the nucleotide effector to the ornithine site mediated by a hydrogen bond network involving T1042. Ornithine activation of CPS may be mediated by K+-loop and tunnel gating changes