Automorphism groups of rational elliptic surfaces with section and constant J-map

In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ?. The automorphism group of such a surface β: B → ?¹, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ? Aut _σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut _σ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Aut _σ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.     

Response to “The Mössbauer rotor experiment and the general theory of relativity” by C. Corda

We show that a new attempt by Corda (2016), just like his previous attempt (Corda, 2015) that we had answered before (A.L. Kholmetskii et al., 2015), to reinterpret Mössbauer experiments in a rotating system as a “new, strong and independent proof of the correctness of Einstein’s vision of gravity” is erroneous. In addition, we demonstrate that Corda’s criticism of Yarman–Arik–Kholmetskii gravitation theory (in short YARK), is based on the application of ill-posed logic; thus rendering his claims against YARK as unfounded.     

Certain positive linear operators with better approximation properties

The present paper deals with a new positive linear operator which gives a connection between the Bernstein operators and their genuine Bernstein‐Durrmeyer variants. These new operators depend on a certain function τ defined on [0,1] and improve the classical results in some particular cases. Some approximation properties of the new operators in terms of first and second modulus of continuity and the Ditzian‐Totik modulus of smoothness are studied. Quantitative Voronovskaja–type theorems and Grüss‐Voronovskaja–type theorems constitute a great deal of interest of the present work. Some numerical results that compare the rate of convergence of these operators with the classical ones and illustrate the relevance of the theoretical results are given.     

Novel Methods for the Synthesis of 4‐Arylisoquinolinium Perchlorates and 4‐Arylisoquinolin‐1‐ones

2‐Benzylamino‐1‐phenyl‐ethanones 1 were converted to the corresponding isoquinolinium perchlorates 2 in high yields using 70% HClO₄‐FeCl₃ mixture as a cyclization and oxidation reagent. A mild and high yielding method for the oxidation of perchlorates 2 to isoquinolin‐1‐ones 3 involving the treatment of 2 with KOH and K₃[Fe(CN)₆] in THF‐H₂O two‐phase system at room temperature was developed. Compounds 2a–g were shown to be disproportionate to 3 and the corresponding 1,2‐dihydroisoquinoline 4 in the presence of base, which in turn is oxidized by K₃[Fe(CN)₆] to 2.     

Dielectric‐loaded plasmonic waveguide components: Going practical

Surface plasmon propagating modes supported by metal/dielectric interfaces in various configurations can be used for radiation guiding similarly to conventional dielectric waveguides. Plasmonic waveguides offer two attractive features: subdiffraction mode confinement and the presence of conducting elements at the mode‐field maximum. The first feature can be exploited to realize ultrahigh density of nanophotonics components, whereas the second feature enables the development of dynamic components controlling the plasmon propagation with ultralow signals, minimizing heat dissipation in switching elements. While the first feature is yet to be brought close to the domain of practical applications because of high propagation losses, the second one is already being investigated for bringing down power requirements in optical communication systems. In this review, the latest application‐oriented research on radiation modulation and routing using thermo‐optic dielectric‐loaded plasmonic waveguide components integrated with silicon‐based photonic waveguides is overviewed. Their employment under conditions of real telecommunications is addressed, highlighting challenges and perspectives.     

Letter: Three Dimensional Gravity in the Presence of Scalar Fields

We study a scalar field in curved space in three dimensions. We obtain a static perturbative solution and show that this solution satisfies the exact equations in the asymptotic region at infinity. The new solution gives rise to a singularity in the curvature scalar at the origin. Our solution, however, necessitates the excising the region near the origin, thus avoiding the naked singularity.     

q‐Voronovskaya type theorems for q‐Baskakov operators

In the present paper, we prove quantitative q‐Voronovskaya type theorems for q‐Baskakov operators in terms of weighted modulus of continuity. We also present a new form of Voronovskaya theorem, that is, q‐Grüss‐Voronovskaya type theorem for q‐Baskakov operators in quantitative mean. Hence, we describe the rate of convergence and upper bound for the error of approximation, simultaneously. Our results are valid for the subspace of continuous functions although classical ones is valid for differentiable functions. Copyright © 2015 John Wiley & Sons, Ltd.     

Understanding the hierarchical classification of quadrilaterals through the ordered relation according to diagonal properties

This article's aim is to suggest a supplementary learning environment to understand the hierarchical classification of quadrilaterals for high school or higher degree learners. Three diagonal properties, ‘being congruent’, ‘being perpendicular’ and ‘dividing each other in particular ratio,’ and all possible combinations of these properties, were used to construct the quadrilaterals in a dynamic geometry environment. According to the diagonal properties, 15 quadrilaterals could be constructed and an order relation was constituted on 16 quadrilaterals including the quadrilateral that did not have any diagonal property. The definition of order relation is ‘any quadrilateral Q_i is included by another quadrilateral Q_j, if and only if Q_i has all diagonal properties of Q_j.’ According to this relation, an ordered relation diagram was created, and it was found that this relation was not well ordered. After the dynamic geometry construction of each quadrilateral, observations about the diagonal properties of special quadrilaterals were noted. Furthermore, the conditions under which a quadrilateral can be concave are examined. This alternative approach to the construction of quadrilaterals provided an opportunity to define quadrilaterals with more economical and less confusing way than using angle and side properties. For example, ‘a Kite is a quadrilateral whose diagonals are perpendicular and at least one of the diagonals bisects the other’ and ‘a Trapezoid is a quadrilateral whose diagonals divide each other in same ratio.’     

Matheuristics for solving a multi-attribute collection problem for a charity organisation

This paper studies a real-life multi-attribute profit collecting vehicle routing problem, arising in the collection operations of a charity organisation in the United Kingdom. The problem involves a heterogeneous fleet of vehicles of different capacities, mandatory visits to a subset of vertices, time windows, rest requirements associated with maximum driving and working times, and partial collection. A mixed integer programming formulation of the problem is described, along with three matheuristics based on Tabu Search and Large Neighbourhood Search. Computational results on instances derived from the case study are presented, and insights are given from a practical implementation.