Holomorphic Variations of Minimal Disks with Boundary on a Lagrangian Surface

2010 ◽  
Vol 62 (6) ◽  
pp. 1264-1275
Author(s):  
Jingyi Chen ◽  
Ailana Fraser
Keyword(s):  
Morse Index ◽  
Kähler Manifold ◽  
Maslov Index ◽  
Minimal Immersion ◽  
Lagrangian Submanifold ◽  
Lagrangian Surface ◽  
Real Dimension ◽  
The Real ◽  
Linearly Independent ◽  
Minimal Disks

AbstractLet L be an oriented Lagrangian submanifold in an n-dimensional Kähler manifold M. Let u: D → M be a minimal immersion from a disk D with u(𝜕D) ⊂ L such that u(D) meets L orthogonally along u(𝜕D). Then the real dimension of the space of admissible holomorphic variations is at least n + μ(E, F), where μ(E, F) is a boundary Maslov index; the minimal disk is holomorphic if there exist n admissible holomorphic variations that are linearly independent over ℝ at some point p ∈ 𝜕D; if M = ℂPn and u intersects L positively, then u is holomorphic if it is stable, and its Morse index is at least n + μ(E, F) if u is unstable.

The real dimension of a vector bundle at the prime two

1983 ◽  
pp. 128-135
Author(s):  
Edgar H. Brown ◽  
Franklin P. Peterson
Keyword(s):  
Vector Bundle ◽  
Real Dimension ◽  
The Real

Islam and democracy*

2010 ◽  
Vol 3 (3) ◽  
pp. 297-333 ◽  
Author(s):  
Fahmy Howeidy
Keyword(s):  
Islamic State ◽  
Real Dimension ◽  
The Real ◽  
Knowing That ◽  
Fourth Part ◽  
Islam And Democracy

This paper reviews how the civilizational discourse of Islam differs from that of democracy but doesn't necessarily mean that it contradicts it. Knowing that this juxtaposition promotes diversity and distinction, this paper elucidates the factors of ambiguity that surround this religion and system in order to uncover the real dimension of their distinction. The paper is organized as follows: first, it presents seven characteristics of the Islamic state. Next, it discusses the importance of consultation (al-shūrā) and the necessity of questioning the rulers in Islam. Third, the article answers the question “Where does democracy correspond to Islam and where does it differ?”. Several prominent opinions are examined in the fourth part, before displaying the main positions from the 1980s, vis-à-vis democracy, in part five. Part six exhibits the fatwas of al-Qaradawi. At the end of the article, the paper emphasizes the approaches that can be taken towards Islamic ruling (sharīʿah).

scholarly journals Applying Benford’s Law to Monitor Death Registration Data: A Management Tool for the COVID-19 Pandemic

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 46
Author(s):  
Francisco Gabriel Morillas-Jurado ◽  
María Caballer-Tarazona ◽  
Vicent Caballer-Tarazona
Keyword(s):  
Central Government ◽  
National Level ◽  
Management Tool ◽  
Benford’S Law ◽  
Death Registration ◽  
Health Crisis ◽  
Real Dimension ◽  
The Real ◽  
Registration Data ◽  
Benford's Law

In Spain, the COVID-19 pandemic has impacted the various regions of the country differently. The availability of reliable and up-to-date information has proved to be fundamental for the management of this health crisis. However, especially during the first wave of the pandemic (February–August 2020), the disparity in the recording criteria and in the timing of providing these figures to the central government created controversy and confusion regarding the real dimension of the pandemic. It is therefore necessary to have objective and homogeneous criteria at the national level to guide health managers in the correct recording and evaluation of the magnitude of the pandemic. Within this context, we propose using Benford’s Law as an auditing tool to monitor the reliability of the number of daily COVID-related deaths to identify possible deviations from the expected trend.

Higher Monotonicity Properties of Certain Sturm-Liouville Functions. III

1970 ◽  
Vol 22 (6) ◽  
pp. 1238-1265 ◽  
Author(s):  
Lee Lorch ◽  
M. E. Muldoon ◽  
Peter Szego
Keyword(s):  
Differential Equation ◽  
Trivial Solution ◽  
Infinite Sequence ◽  
Liouville Function ◽  
The Real ◽  
Linearly Independent ◽  
Monotonicity Properties ◽  
Real Domain ◽  
Sturm Liouville ◽  
Image Position

A Sturm-Liouville function is simply a non-trivial solution of the Sturm-Liouville differential equation(1.1)considered, together with everything else in this study, in the real domain. The associated quantities whose higher monotonicity properties are determined here are defined, for fixed λ > –1, to be(1.2)where y(x) is an arbitrary (non-trivial) solution of (1.1) and x1, x2, … is any finite or infinite sequence of consecutive zeros of any non-trivial solution z(x) of (1.1) which may or may not be linearly independent of y(x). The condition λ > –1 is required to assure convergence of the integral defining Mk, and the function W(x) is taken subject to the same restriction.

scholarly journals Every conformal minimal surface in ℝ3 is isotopic to the real part of a holomorphic\break null curve

2018 ◽  
Vol 2018 (740) ◽  
pp. 77-109 ◽  
Author(s):  
Antonio Alarcón ◽  
Franc Forstnerič
Keyword(s):  
Riemann Surface ◽  
Minimal Surface ◽  
Minimal Immersion ◽  
Open Riemann Surface ◽  
The Real ◽  
Conformal Minimal Immersion ◽  
Null Curve ◽  
Minimal Immersions ◽  
Conformal Minimal Surface

Abstract We show that for every conformal minimal immersion {u:M\to\mathbb{R}^{3}} from an open Riemann surface M to {\mathbb{R}^{3}} there exists a smooth isotopy {u_{t}:M\to\mathbb{R}^{3}} ( {t\in[0,1]} ) of conformal minimal immersions, with {u_{0}=u} , such that {u_{1}} is the real part of a holomorphic null curve {M\to\mathbb{C}^{3}} (i.e. {u_{1}} has vanishing flux). If furthermore u is nonflat, then {u_{1}} can be chosen to have any prescribed flux and to be complete.

scholarly journals Diploma course: “Health Economy tools for taking decisions”, a useful tool for health managers

2020 ◽  
Vol 2 (2) ◽  
pp. 01-03
Author(s):  
Fé Fernández Hernández
Keyword(s):  
Public Health ◽  
Health Services ◽  
Population Health ◽  
Health Policies ◽  
Health Economy ◽  
Public Health Services ◽  
Real Dimension ◽  
The Real ◽  
The Public ◽  
Strong Relation

The Public Health services are closest related with the human develop. The strong relation between population health and labor productivity is determining the historical economic develop and the real capability to make sustainable the economic develop. Few sectors have an extensive and strong relation with the human develop as the Public Health. The health policies may insider over the whole population and can determine which population sector can access to the health services and the real dimension from the effective demand from these services too.

scholarly journals SUBJEKTIVITAS EKA KURNIAWAN MELALUI NOVEL LELAKI HARIMAU

TELAGA BAHASA ◽  
2020 ◽  
Vol 7 (1) ◽  
pp. 83-96
Author(s):  
Siti Hardiyanti Amri
Keyword(s):  
Human Life ◽  
Symbolic Order ◽  
False Consciousness ◽  
Literature Study ◽  
Slavoj Zizek ◽  
Real Dimension ◽  
The Real ◽  
Slavoj Žižek ◽  
The Subject ◽  
Ideological Fantasy

Paradigma humanis dalam kajian sastra memposisikan manusia sebagai pusat. Penelitian ini mengkaji subjektivitas tokoh dan pengarang dalam semesta novel Lelaki Harimau karya Eka Kurniawan menggunakan teori subjektivitas Slavoj Zizek. Zizek memfokuskan pemikirannya pada tatanan riil dan simbolik dalam kehidupan manusia. Menurutnya, manusia mampu meraih kebebasan dan keotentikan dirinya selama ia bertindak melampaui norma-norma simbolik dan bergerak menuju dimensi riil dalam kehidupannya. Sebaliknya, manusia akan tetap terpenjara dalam dimensi simbolik, selama ia membiarkan dirinya tetap hanyut dalam kesadaran palsu ideologi. Penelitian ini menunjukkan bahwa ada upaya radikal yang dilakukan oleh tokoh utama untuk mencapai kondisi riil melalui tindakan sadis dan tak berkeprimanusiaan yang melanggar aspek normatif dalam lingkaran simbolik. Akan tetapi, peristiwa yang dihadapi oleh tokoh tersebut berlawanan dengan diri pengarang sebagai subjek. Pengarang justru tidak menunjukkan adanya upaya radikal dalam kehidupannya sehingga ia tetap berada dalam fantasi ideologis.Kata Kunci:Subjektivitas, Slavoj Zizek, Eka Kurniawan, Tindakan Radikal, Fantasi ideologis. The humanist paradigm in literature study assigns humans as the center. This research examines the subjectivity of the characters and the author in Lelaki Harimau novel by Eka Kurniawan using Slavoj Zizek's theory of subjectivity. Zizek focused his thoughts on the real and symbolic order in human life. According to him, humans are able to achieve freedom and authenticity as long as they act beyond the symbolic norms and move towards the real dimension in their life. On the contrary, humans will remain imprisoned in a symbolic dimension as long as they allowed themselves drifted away on a false consciousness of ideology. This research indicates that there are radical efforts made by the main characters to achieve the real conditions through sadistic and inhumane actions that violate the normative aspects in a symbolic circle. However, the events faced by these characters are opposite to the author as the subject. In fact, the author does not perform any radical efforts in his life so that he remains in ideological fantasies.Keywords: subjectivity, Slavoj Zizek, Eka Kurniawan, radical act, ideological fantasy

Introduction

2021 ◽  
pp. 1-4
Author(s):  
Robert Alexy
Keyword(s):  
Human Rights ◽  
Legal Argumentation ◽  
Constitutional Rights ◽  
Dual Nature ◽  
Real Dimension ◽  
The Real ◽  
Main Thesis ◽  
Social Efficacy ◽  
The Ideal

This volume comprises three parts. The issue of Part I is the nature of law. The main thesis is that law has a dual nature. It comprises a real as well as an ideal dimension. The real dimension is defined by authoritative issuance and social efficacy, the ideal dimension by the claim to correctness, which includes a claim to justice. This connection of the real and the ideal dimension implies non-positivism. In Part II the connection between constitutional rights, human rights, and proportionality is taken up. The construction of constitutional rights as principles is to be found at the centre. The principles construction implies the necessity of proportionality analysis and, with this, the necessity of balancing. Balancing is defended against numerous critics as a form of rational legal argumentation. Part III concerns the relation between argumentation, correctness, and law.

scholarly journals On the topological complexity of Grassmann manifolds

2020 ◽  
Vol 70 (5) ◽  
pp. 1197-1210
Author(s):  
Vimala Ramani
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Zero Divisor ◽  
Flag Manifold ◽  
Topological Complexity ◽  
Grassmann Manifolds ◽  
Real Dimension ◽  
The Real ◽  
Rational Cohomology

AbstractWe prove that the topological complexity of a quaternionic flag manifold is half of its real dimension. For the real oriented Grassmann manifolds G͠n,k, 3 ≤ k ≤ [n/2], the zero-divisor cup-length of the rational cohomology of G͠n,k is computed in terms of n and k which gives a lower bound for the topological complexity of G͠n,k, TC(G͠n,k). When k = 3, it is observed in certain cases that better lower bounds for TC(G͠n,3) are obtained using ℤ2-cohomology.

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