Showing papers on "Pencil (mathematics) published in 2018"
01 Sep 2018
TL;DR: In this paper, the authors consider the geometry of the Wiman-Edge pencil from a more modern, conceptual perspective, whereby explicit equations are reincarnated as geometric objects, and they consider hyperbolic, conformal and modular aspects.
Abstract: In 1981 William L. Edge discovered and studied a pencil $$\mathscr {C}$$
of highly symmetric genus 6 projective curves with remarkable properties. Edge’s work was based on an 1895 paper of Anders Wiman. Both papers were written in the satisfying style of 19th century algebraic geometry. In this paper and its sequel Geometry of the Wiman–Edge pencil, II: hyperbolic, conformal and modular aspects (in preparation), we consider $$\mathscr {C}$$
from a more modern, conceptual perspective, whereby explicit equations are reincarnated as geometric objects.
20 citations
01 May 2018
TL;DR: In this article, the authors studied the Jacobian of a regular pencil of quadrics over an arbitrary base field of characteristic not equal to 2 and showed how these Fano schemes are related to the Jacobians of hyperelliptic curves.
Abstract: The geometry of the Fano scheme of maximal linear spaces contained in the base locus of a pencil of quadrics has been studied by algebraic geometers when the base field is algebraically closed. In this paper, we work over an arbitrary base field of characteristic not equal to 2 and show how these Fano schemes are related to the Jacobians of hyperelliptic curves. In particular, if B is the base locus of a generic pencil of quadrics in P, and F is the Fano variety of n− 1 planes contained in B, then F is a component of a disconnected commutative algebraic group G = Pic(C) ∪F ∪Pic(C) ∪F ′, where C is the hyperelliptic curve defined by the discriminant form of the pencil. In the second half of this paper, we study regular pencils of quadrics, where the hyperelliptic curve defined by the discriminant is singular.
19 citations
TL;DR: In this study, the estimation of array parameters is recast as a 2-D poles extraction problem, and the number of antenna elements is minimized by the reduced rank processing.
11 citations
Posted Content•
TL;DR: In this paper, the authors generalize this construction to explicit birational maps of the plane that preserve quadratic resp. certain quartic pencils, and show that they are measure-preserving and hence integrable.
Abstract: Manin transformations are maps of the plane that preserve a pencil of cubic curves. They are the composition of two involutions. Each involution is constructed in terms of an involution point that is required to be one of the base points of the pencil. We generalise this construction to explicit birational maps of the plane that preserve quadratic resp. certain quartic pencils, and show that they are measure-preserving and hence integrable. In the quartic construction the two involution points are required to be base points of the pencil of multiplicity 2. On the other hand, for the quadratic pencils the involution points can be any two distinct points in the plane (except for base points). We employ Pascal's theorem to show that the maps that preserve a quadratic pencil admit infinitely many symmetries. The full 18-parameter QRT map is obtained as a special instance of the quartic case in a limit where the two involution points go to infinity. We show by construction that each generalised Manin transformation can be brought to QRT form by a fractional affine transformation. We also specify classes of generalised Manin transformations which admit a root.
10 citations
TL;DR: The present study maps the cloth model to the dummy model to make the garment form and thus represents draping more closely and can be made employing the proposed method.
8 citations
01 May 2018
TL;DR: In this paper, a pencil of sextic nodal curves admitting A5 as its group of automorphism is presented, along with some other aspects of this pencil, such as the associated fibration and its connection to the singularities of the moduli of six-dimensional abelian varieties.
Abstract: We rewrite in modern language a classical construction by W. E. Edge showing a pencil of sextic nodal curves admitting A5 as its group of automorphism. Next, we discuss some other aspects of this pencil, such as the associated fibration and its connection to the singularities of the moduli of six-dimensional abelian varieties.
7 citations
01 Jan 2018
TL;DR: It is shown that deciding whether a given instance of each puzzle has a solution is NP-complete.
Abstract: Herugolf and Makaro are Nikoli's pencil puzzles. We study the computational complexity of Herugolf and Makaro puzzles. It is shown that deciding whether a given instance of each puzzle has a solution is NP-complete.
7 citations
TL;DR: In this article, the topological properties of holomorphic Lefschetz pencils on the four-torus were studied and a system of vanishing cycles of the genus-3 holomorphism of Smith's pencil was given.
Abstract: We discuss topological properties of holomorphic Lefschetz pencils on the four-torus. Relying on the theory of moduli spaces of polarized abelian surfaces, we first prove that, under some mild assumptions, the (smooth) isomorphism class of a holomorphic Lefschetz pencil on the four-torus is uniquely determined by its genus and divisibility. We then explicitly give a system of vanishing cycles of the genus- 3 holomorphic Lefschetz pencil on the four-torus due to Smith, and obtain those of holomorphic pencils with higher genera by taking finite unbranched coverings. One can also obtain the monodromy factorization associated with Smith’s pencil in a combinatorial way. This construction allows us to generalize Smith’s pencil to higher genera, which is a good source of pencils on the (topological) four-torus. As another application of the combinatorial construction, for any torus bundle over the torus with a section we construct a genus- 3 Lefschetz pencil whose total space is homeomorphic to that of the given bundle.
7 citations
6 citations
Journal Article•
01 Jan 2018-International journal of education and development using information and communication technology
TL;DR: It was revealed that mobile photo note-taking was a common practice at DUCE and the distraction of concentration, impairment of handwriting skills and speed, poor attendance to the lecture sessions, and distortion of students’ ability to compose and organize their own work were the impact of the practice.
Abstract: This study examined the extent, motives and impact of mobile phone photo note-taking on students’ learning at Dar es Salaam University College of Education (DUCE) in Tanzania. It employed the mixed methods approach. A sample of 310 respondents was drawn using a multi stage sampling technique which involved stratified random sampling at the first stage and convenient sampling at the second stage. Questionnaires and interviews were used to obtain data for the study. The findings revealed that mobile photo note-taking was a common practice at DUCE. The time consuming nature of handwritten notes, Speedy lecturing, easy access to notes, peer and technological influence were claimed to be the motives behind students’ fondness to the practice. It was also revealed that the distraction of concentration, impairment of handwriting skills and speed, poor attendance to the lecture sessions, and distortion of students’ ability to compose and organize their own work were the impact of the practice. The study recommends that the University should create better teaching and learning environment to allow university students to use variables and multiple note-taking methods for best results underlying each method.
6 citations
01 Jan 2018
TL;DR: In this article, simultaneous feedback and output injection on descriptor linear systems described by a quadruple of matrices (E,A,B,C) is studied, and the possible Kronecker invariants of the resulting pencil λE−(A+BF + KC) when F and K vary, in the case when the pencil corresponding to the system has no infinite elementary divisors of the second, third and fourth type.
Abstract: In this paper we study simultaneous feedback and output injection on descriptor linear system described by a quadruple of matrices (E,A,B,C). We describe the possible Kronecker invariants of the resulting pencil λE−(A+ BF + KC), when F and K vary, in the case when the pencil corresponding to the system (E,A,B,C) has no infinite elementary divisors of the second, third and fourth type. The solution is constructive and explicit, and is given over algebraically closed fields.
TL;DR: In this paper, a correspondence theorem for singular tropical surfaces in real three space was proved, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface.
Abstract: We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we develop a three-dimensional version of Mikhalkin's lattice path algorithm that enumerates singular tropical surfaces passing through an appropriate configuration of points in real three space. As application we show that there are pencils of real surfaces of degree $d$ in projective three space containing at least $(3/2)d^3+O(d^2)$ singular surfaces, which is asymptotically comparable to the number $4(d-1)^3$ of all complex singular surfaces in the pencil. Our result relies on the classification of singular tropical surfaces (arXiv:1106.2676).
01 Jan 2018
TL;DR: In this article, the difference equations related to Jacobi-type pencils were studied, where a Jacobi type pencil is defined as the following pencil: J5−λJ3, where J3 is a Jacobian matrix and J5 is a sigmoid.
Abstract: In this paper we study various difference equations related to Jacobi-type pencils. By a Jacobi-type pencil one means the following pencil: J5−λJ3, where J3 is a Jacobi matrix and J5 is a s...
TL;DR: In this paper, the completeness of commutative subalgebras in S(gl(n)) constructed from the Sokolov-Odesskii Lie pencil with generic parameters was proved.
Abstract: We prove the completeness of commutative subalgebras in S(gl(n)) constructed from the Sokolov–Odesskii Lie pencil with generic parameters.
01 Jan 2018
TL;DR: In this article, the locus of the Brocard points of a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle is studied.
Abstract: In this paper we consider a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle. We study the locus of their Brocard points, two curves of order 4.
TL;DR: In this article, it was shown that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane, i.e., it is the same graph as a stable map.
01 Jan 2018
TL;DR: Neller presented games such as Dots and Boxes, Sprouts, Jotto, Chomp, and Pentominoes in order to illustrate the diversity of existing pencil and paper games.
Abstract: Neller presented games such as Dots and Boxes, Sprouts, Jotto, Chomp, and Pentominoes in order to illustrate the diversity of existing pencil and paper games. Additionally, he presented his own pencil and paper game design, Paper Penguins, and discussed the game design process.
01 Jan 2018
TL;DR: This study examined whether the testing medium impacts student performance in math assessment by addressing three questions: does a test mode effect exist, as evidenced by mean score difference between a CBT and a PPT?
Abstract: Today’s schools turn to computers for all aspects of learning, including assessment. While advantages to computer testing do exist, the comparability between paper pencil tests (PPT) and computer-based tests (CBT) must be considered. This study examined whether the testing medium impacts student performance in math assessment by addressing three questions. First, does a test mode effect exist, as evidenced by mean score difference between a CBT and a PPT? Second, does question type: multiple choice, constructed response, or extended response, relate to student performance? Third, does either gender or computer experience and familiarity impact CBT and PPT scores? Eighty 6th grade students took math tests with half of the questions on a PPT and half of the questions on a CBT. A computer familiarity survey was completed prior to the unit tests. Significant differences were found for one of the unit tests and for some of the question types.
27 Jan 2018
TL;DR: Large-scale bound-constrained optimization (L-BFGS) is applied to synthesize the new pencil sketch whose style is similar to the exemplar pencil sketch, and results demonstrate that the proposed method is better than conventional method in clarity and color tone.
Abstract: In most cases, the conventional pencil-drawing-synthesized methods were in terms of geometry and stroke, or only used classic edge detection method to extract image edge characters. In this paper, we propose a new method to produce pencil drawing from natural image. The synthesized result can not only generate pencil sketch drawing, but also can save the color tone of natural image and the drawing style is flexible. The sketch and style are learned from the edge of original natural image and one pencil image exemplar of artist’s work. They are accomplished through using the convolutional neural network feature maps of a natural image and an exemplar pencil drawing style image. Large-scale bound-constrained optimization (L-BFGS) is applied to synthesize the new pencil sketch whose style is similar to the exemplar pencil sketch. We evaluate the proposed method by applying it to different kinds of images and textures. Experimental results demonstrate that our method is better than conventional method in clarity and color tone. Besides, our method is also flexible in drawing style.
Patent•
23 Jan 2018
TL;DR: In this paper, an intelligent grip strength reminding and monitoring method was proposed, where a pencil holder, an auxiliary pencil gripper arranged outside the pencil holder in a sleeving mode and a microprocessor are involved in the method.
Abstract: The invention discloses an intelligent grip strength reminding and monitoring method. A pencil holder, an auxiliary pencil gripper arranged outside the pencil holder in a sleeving mode and a microprocessor are involved in the method, a pencil lead sleeve is arranged in the pencil holder, a first miniature pressure sensor is arranged below each concave face of the auxiliary pencil gripper, a circleof second miniature pressure sensors are arranged on the inner wall of the head of the pencil lead sleeve, and the first miniature pressure sensors and the second miniature pressure sensors are connected with the microprocessor; a circle of LED lamps are arranged outside the pencil holder and connected with the miniature sensors and correspond to the miniature sensors in position one to one; a sound generating device is further involved and is connected with the microcomputer. According to the intelligent grip strength reminding and monitoring method, a child can be reminded when holding theauxiliary pencil gripper with the hand and applying inappropriate force, a corresponding reminder is sent by the LEDs on the outer wall of the pencil holder when pressure on the inner wall of the pencil lead sleeve is too large, and the child is reminded to keep correct pencil grip strength and direction.
Patent•
01 May 2018
TL;DR: In this article, the pencil lead barrel conveying mechanism was used to achieve automatic pencil pencil pencil-lead positioning and feeding, and the production efficiency was improved; and through the technology, automatic pencil lead feeding and positioning are achieved, automatic lead filling is achieved, and manual work is replaced.
Abstract: The invention relates to the field of pencil pencil-lead manufacturing, in particular to a pencil lead feeding and positioning device of a full-automatic pencil pencil-lead filling machine. The pencillead feeding and positioning device comprises a pencil lead barrel conveying mechanism, a pencil lead conveying mechanism, a second falling mechanism, a third falling mechanism and an induction mechanism. The pencil lead barrel conveying mechanism comprises a first rack and a conveying assembly, an installing groove is formed in the top of the first rack, the conveying assembly is fixed in the installing groove, and the first rack is provided with a first supporting block and a second supporting block which are symmetrically arranged. The side, facing the second supporting block, of the firstsupporting block is provided with a first sliding way. The second falling mechanism is fixed to the pencil lead conveying mechanism. The third falling mechanism is located between the first rack andthe pencil lead conveying mechanism. The first supporting block is provided with a third containing groove, and the induction mechanism is located in the third containing groove. The pencil lead feeding and positioning device achieves automatic pencil pencil-lead positioning and feeding, and the production efficiency is improved; and through the technology, automatic pencil lead feeding and positioning are achieved, automatic pencil lead filling is achieved, and manual work is replaced.
Posted Content•
TL;DR: In this article, the spectral properties of the truncated Jacobi-type pencil and some special matrix orthogonality relations are investigated, and the basic set of solutions for the corresponding $4$-th order difference equation is constructed.
Abstract: In this paper we study various difference equations related to Jacobi-type pencils. By a Jacobi-type pencil one means the following pencil: $J_5 - \lambda J_3$, where $J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. The basic set of solutions for the corresponding $4$-th order difference equation is constructed. Spectral properties of the truncated pencil and some special matrix orthogonality relations are investigated. Classical type orthogonal polynomials satisfying a $4$-th order differential equation are constructed.
TL;DR: In this paper, the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries.
Abstract: Spine spaces can be considered as fragments of a projective Grassmann space We prove that the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries It is also shown that, over a spine space, the geometry of pencils of lines can be reconstructed in terms of the two binary relations
TL;DR: In this article, the authors present a critical review of several selected methods used for assessment of children's mathematical abilities, including traditional paper-pencil tasks as well as computer-assisted ones.
Abstract: Nowadays the development and use of the computerised variant of methods is an obvious part of research and diagnosis, which is widely used in psychological practice. Will these computer-assisted tools used for this purpose replace the traditional paper-pencil tools? What are their advantages and disadvantages in comparison to traditional methods? What could such tools never provide to psychologists? The computerised tests are commonly used for assessment of a broad range of cognitive functions as well as capacities, among others for measurement of mathematical competencies and for diagnosis of deficiencies observed in the case of number processing. It allows us to measure the disorder’s indices in a precise way, which is unobtainable in the case of paper-pencil tools (or it is possible only to a limited extent). This paper presents the critical review of several selected methods, which are used for assessment of children’s mathematical abilities. Here we describe both traditional paper-pencil tasks as well as computer-assisted ones. The aim of this review is to compare these methods in terms of their reliability, advantages and disadvantages, as well as the details of the data provided by both type of tools used for the measurement of mathematical skills in the case of normal development and in the case of cognitive deficits (e.g. dyscalculia).
TL;DR: In this paper, the authors investigated light dual multinets labeled by a finite group in the projective plane P G ( 2, K ) defined over a field K, under some conditions on the characteristic of K, and classified group-labeled light dual multiinets with lines of length at least 9.
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TL;DR: In this article, a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering was identified as the Apery-Fermi pencil.
Abstract: We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Apery--Fermi pencil, that was related to Apery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.
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TL;DR: In this paper, the authors used the Kneser-Nishiyama technique to determine all the non-isomorphic elliptic fibrations of the Ap\'ery-Fermi pencil.
Abstract: Given a generic $K3$ surface $Y_k$ of the Ap\'ery-Fermi pencil, we use the Kneser-Nishiyama technique to determine all its non isomorphic elliptic fibrations. These computations lead to determine those fibrations with 2-torsion sections T. We classify the fibrations such that the translation by T gives a Shioda-Inose structure. The other fibrations correspond to a K3 surface identified by it transcendental lattice. The same problem is solved for a singular member $Y_2$ of the family showing the differences with the generic case. In conclusion we put our results in the context of relations between $2$-isogenies and isometries on the singular surfaces of the family.