scholarly journals Asymptotes of Plane Curves - Revisited

KoG ◽  
2021 ◽  
pp. 78-86
Author(s):  
Ana Katalenić ◽  
Aleksandra Čižmešija ◽  
Željka Milin Šipuš
Keyword(s):  
Algebraic Curves ◽  
Tangent Line ◽  
Plane Curves ◽  
Asymptotic Line ◽  
Basic Ideas ◽  
The One ◽  
Asymptotic Lines

In this paper we present a review of the basic ideas and results concerning asymptotic lines of plane curves. We discuss their different definitions, namely that of a limiting position of tangent lines, of the tangent line at infinity, and finally the one that requires that the distance between points of a curve and asymptotic line tends to 0 as the point moves along an infinite branch of the curve. We also recall the method of determining asymptotes of algebraic curves from the leading coefficients in their equation and provide examples.

scholarly journals Providing Meaningful Interactions at KOSEN between Japanese and International Students

2018 ◽  
Vol 53 ◽  
pp. 01003
Author(s):  
Richard Grumbine ◽  
Natsuki Aka ◽  
Riho Hirano
Keyword(s):  
International Students ◽  
International Student ◽  
Traditional Classroom ◽  
Learning Goals ◽  
Student Body ◽  
Japanese Students ◽  
Japanese Student ◽  
Basic Ideas ◽  
The One ◽  
In The Beginning

Internationalizing the Japanese students at KOSEN has proven difficult. While KOSEN welcomes international students with the hope of internationalizing the almost entirely Japanese student body, the challenge has been to get the Japanese students to interact with the international students and take advantage of the opportunity. Far too often international students live in a bubble and have meaningful contact with only a few students. This leaves the international students feeling isolated and the Japanese students not benefiting from the opportunity that KOSEN is trying to provide. Ariake KOSEN attempted to address this problem in two ways. A discussion class which included international students was created where the students were expected to discuss pre-assigned topics in small groups over the course of a semester. These groups often contained an international student. This forced exposure created a chance for Japanese students to communicate with international students. This communication was then seen continuing well beyond the discussion exercises. A survey was given at the completion of the one semester class to evaluate effectiveness. The results show that students found the opportunity to be helpful and in line with their own learning goals. Another approach was to create a more casual place for students to gather and interact with international students. An English Lab was created to give the students a place to interact outside of the traditional classroom atmosphere. This second effort is just in the beginning stages but the basic ideas are laid out in this paper. Anecdotal evidence seems to suggest that the Lab is working, with usage on the part of Japanese students being high, but the international students seem less inclined to use the room.

Negative Pedal of the Ellipse with Respect to A Focus

1957 ◽  
Vol 41 (338) ◽  
pp. 254-257
Author(s):  
E. H. Lockwood
Keyword(s):  
Algebraic Curves ◽  
General Treatment ◽  
Plane Curves

My attention was first called to this attractive curve by a pupil, M. J. Burleigh; so, lacking any other name, we called it “Burleigh’s Oval”. It is mentioned in Salmon’s Higher Plane Curves (p. 107), where a cartesian equation is given; and in Hilton’s Plane Algebraic Curves (p. 64), where it is described, with a diagram, as the reciprocal of the Limaçon. It also occurs in a very interesting general treatment of negative pedals by A. Ameseder, (Archiv der Mathematik und Physic, LXIV, 1879).

CLUSTER STATE QUANTUM COMPUTATION AND THE REPEAT-UNTIL-SUCCESS SCHEME

2008 ◽  
Vol 22 (01n02) ◽  
pp. 33-43 ◽  
Author(s):  
L. C. KWEK
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Cluster State ◽  
Entangled State ◽  
Single Qubit ◽  
Computation Process ◽  
Measurement Results ◽  
Basic Ideas ◽  
The One ◽  
Computational Basis

Cluster state computation or the one way quantum computation (1WQC) relies on an initially highly entangled state (called a cluster state) and an appropriate sequence of single qubit measurements along different directions, together with feed-forward based on the measurement results, to realize a quantum computation process. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. In this short tutorial on cluster state quantum computation, we will also describe the basic ideas of a cluster state and proceed to describe how a single qubit operation can be done on a cluster state. Recently, we proposed a repeat-until-success (RUS) scheme that could effectively be used to realize one-way quantum computer on a hybrid system of photons and atoms. We will briefly describe this RUS scheme and show how it can be used to entangled two distant stationary qubits.

scholarly journals AN APPROXIMATE ARRANGEMENT ALGORITHM FOR SEMI-ALGEBRAIC CURVES

2007 ◽  
Vol 17 (02) ◽  
pp. 175-198 ◽  
Author(s):  
VICTOR MILENKOVIC ◽  
ELISHA SACKS
Keyword(s):  
Computational Model ◽  
Linear Order ◽  
General Position ◽  
Algebraic Curves ◽  
Vertical Line ◽  
Floating Point ◽  
Plane Curves ◽  
Data Sets ◽  
Running Time

We present an arrangement algorithm for plane curves. The inputs are (1) continuous, compact, x-monotone curves and (2) a module that computes approximate crossing points of these curves. There are no general position requirements. We assume that the crossing module output is ∊ accurate, but allow it to be inconsistent, meaning that three curves are in cyclic y order over an x interval. The curves are swept with a vertical line using the crossing module to compute and process sweep events. When the sweep detects an inconsistency, the algorithm breaks the cycle to obtain a linear order. We prove correctness in a realistic computational model of the crossing module. The number of vertices in the output is V = 2n + N + min (3kn,n2/2) and the running time is O (V log n) for n curves with N crossings and k inconsistencies. The output arrangement is realizable by curves that are O (∊ + kn∊) close to the input curves, except in kn∊ neighborhoods of the curve tails. The accuracy can be guaranteed everywhere by adding tiny horizontal extensions to the segment tails, but without the running time bound. An implementation is described for semi-algebraic curves based on a numerical equation solver. Experiments show that the extensions only slightly increase the running time and have little effect on the error. On challenging data sets, the number of inconsistencies is at most 3N, the output accuracy is close to ∊, and the running time is close to that of the standard, non-robust floating point sweep.

scholarly journals Kötter's synthetic geometry of algebraic curves

1888 ◽  
Vol 7 ◽  
pp. 46-61
Author(s):  
Norman Fraser
Keyword(s):  
Algebraic Curves ◽  
Royal Academy ◽  
Plane Curves ◽  
Geometrical Theory ◽  
Short Account ◽  
University Of Berlin ◽  
The University

In the following paper I propose to give a short account of Dr Ernst Kötter's purely geometrical theory of the algebraic plane curves. This theory is developed in a treatise which, in 1886, gained the prize of the Berlin Royal Academy; but the contents of my paper are also partly drawn from a course of lectures delivered by Dr Kötter in the University of Berlin, W.S. 1887–88.

scholarly journals A New Look for Hamiltonian Dynamics

1961 ◽  
Vol 44 ◽  
pp. 9-12
Author(s):  
C. W. Kilmister
Keyword(s):  
Hamiltonian Dynamics ◽  
New Developments ◽  
Basic Ideas ◽  
The One ◽  
Contact Transformations ◽  
New Look

It seems a pity that Hamiltonian dynamics—contact transformations and so on—is regarded as a fearsome subject, too time-consuming to teach to most students; for it is the one branch of dynamics to point a way to new developments in this century. Moreover the basic ideas are extremely simple, but presented in an unfortunate way in all the text-books.

scholarly journals Approximation the geometric objects of multidimensional space using arcs of curves passing through the given points

2019 ◽  
Author(s):  
Евгений Конопацкий ◽  
Evgeniy Konopatskiy ◽  
Сергей Ротков ◽  
Sergey Rotkov
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Influence Factors ◽  
Geometric Object ◽  
Multidimensional Space ◽  
Global Coordinate System ◽  
Factors Affecting ◽  
Geometric Objects ◽  
Basic Ideas ◽  
The Given

The paper presents the basic ideas of geometric objects approximation in multidimensional space by means the arcs of algebraic curves passing through given points, which is as follows. A special network of points with a dimension one less than the dimension of the space in which the simulated geometric object is located is formed. Taking into account the special properties the arcs of algebraic curves passing through the given points, a linear relationship between the parameters of the geometric object and the influence factors corresponding to the axes of the global coordinate system is established. Next, the nodes of the network are calculated such values of the response function, which provide the minimum value of the quadratic residual function. The proposed method allows to perform the generalization the method of least squares in the direction of increasing space dimension and, consequently, the number of investigated factors affecting the response function, which is especially important for modeling and optimization of multifactorial processes and phenomena.

scholarly journals Ego States and the Image of God in Personal Prayer: Psycholinguistic Analysis

2020 ◽  
Vol 27 (1) ◽  
pp. 219-236
Author(s):  
Nataliya Savelyuk
Keyword(s):  
Computer Software ◽  
Interdisciplinary Approach ◽  
Religious Activity ◽  
Current Crisis ◽  
Theoretical Substantiation ◽  
Ego States ◽  
Basic Ideas ◽  
The One ◽  
Theological Understanding ◽  
Personal Prayer

Introduction. The results of theoretical substantiation and empirical study of personal prayer in the context of an interdisciplinary approach, which combines, on the one hand, the basic ideas and positions of the theory of transactional analysis and Ego states according to E. Bern, on the other hand, the ideas and techniques of modern psycholinguistics are describes and interprets in the article. It is substantiated that such an approach makes it possible to constructively supplement the basic metaphysical, spiritual, theological understanding of prayer with its full-fledged scientific analysis. Methods & Techniques. The sample of Ukrainian respondents of different ages and social status, self-identified as «Christians», according to the «Techniques of Studying Religious Activity» (D. Smirnov), is divided into four subgroups: the lowest, the lowest than the average, the highest than the average and the highest level of religious activity. Each was offered two related tasks («My Prayer» and «God’s Answer») with special instructions, after which the texts of personalized prayers as discourses of two «Ego states» were received and analyzed. In the context of the psycholinguistic direction of the study, the method of predicative text analysis was used (А. Leontiev, T. Dridze, N. Zhinkin). For the sake of clarification, the qualitative data was supplemented by a quantitative content analysis method using the «Textanz» computer software (version 2.4.2.0). And the results were summarized and compared in the context of four previously separated subgroups of respondents. Results. It is theoretically substantiated that prayer as a religious discourse should be considered not only in the context of broad social cognition and interaction, but also as a component of self-knowledge, self-understanding, self-construction of Personality. It has been empirically established that in the process of personal prayer as a reference to God with certain requests, thanksgiving, repentance and praise, the harmonious communicative transaction «Child»/«Father» is most often implicated (31.45% persons). So, for almost a third of the surveyed God, God is definitely a loving Father. However, disharmonious, conflicting transactions of various types – «Child» / «Parent», «Child» / «Adult», «Adult» / «Adult», are found quite frequently (approximately 40% persons). Conclusions. The results are viewed as one of the consequences and manifestations of the current crisis of the whole society, when, in the context of chronic and global distrust of any authority, centuries-old sacral values are also partially negated, and God begins to be perceived as an indifferent «Father» or an too liberal «Head».

scholarly journals The one-dimensional hydrogen atom revisited

2006 ◽  
Vol 84 (9) ◽  
pp. 787-800 ◽  
Author(s):  
Guillermo Palma ◽  
Ulrich Raff
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Controversial Problem ◽  
Representation Method ◽  
Basic Ideas ◽  
The One ◽  
Infinite Energy ◽  
Symmetric Operators

The one-dimensional Schrödinger hydrogen atom is an interesting mathematical and physical problem for the study of bound states, eigenfunctions, and quantum-degeneracy issues. This one-dimensional physical system has given rise to some intriguing controversy for more than four decades. Presently, still no definite consensus seems to have been reached. We reanalyzed this apparently controversial problem, approaching it from a Fourier-transform representation method combined with some fundamental (basic) ideas found in self-adjoint extensions of symmetric operators. In disagreement with some previous claims, we found that the complete Balmer energy spectrum is obtained together with an odd-parity set of eigenfunctions. Closed-form solutions in both coordinate and momentum spaces were obtained. No twofold degeneracy was observed as predicted by the degeneracy theorem in one dimension, though it does not necessarily have to hold for potentials with singularities. No ground state with infinite energy exists since the corresponding eigenfunction does not satisfy the Schrödinger equation at the origin.PACS Nos.: 03.65.Ge, 03.65.–w

Envelope of a Family of Curves

2016 ◽  
Vol 4 (4) ◽  
pp. 14-18 ◽  
Author(s):  
Гирш ◽  
A. Girsh
Keyword(s):  
Real Number ◽  
Euclidean Plane ◽  
Euclidean Geometry ◽  
Algebraic Curves ◽  
Geometric Object ◽  
Parameter Family ◽  
Visualization Method ◽  
Family Of Curves ◽  
Geometric Space ◽  
The One

A one-parameter family of algebraic curves has an envelope line, which may be imaginary in certain cases. Jakob Steiner was right, considering the imaginary images as creation of analysis. In the analysis a real number is just a part of a complex number and in certain conditions the initial real values can give an imaginary result. But Steiner was wrong in denying the imaginary images in geometry. The geometry, in contrast to the single analytical space exists in several spaces: Euclidean geometry operates only on real figures valid and does not contain imaginary figures by definition; pseudo-Euclidean geometry operates on imaginary images and constructs their images, taking into account its own features. Geometric space is complex and each geometric object in it is the complex one, consisting of the real figure (core) having the "aura" of an imaginary extension. Thus, any analytical figure of the plane is present at every point of the plane or by its real part or by its imaginary extension. Would the figure’s imaginary extension be visible or not depends on the visualization method, whether the image has been assumed on superimposed epures – the Euclideanpseudo-Euclidean plane, or the image has been traditionally assumed only in the Euclidean plane. In this paper are discussed cases when a family of algebraic curves has an envelope, and is given an answer to a question what means cases of complete or partial absence of the envelope for the one-parameter family of curves. Casts some doubt on widely known categorical st

Sign in / Sign up

Export Citation Format

Share Document