scholarly journals Splitting Lemma for Biholomorphic Mappings with Smooth Dependence on Parameters

2020 ◽  
Author(s):  
Arkadiusz Lewandowski
Keyword(s):  
Precise Formulation ◽  
Smooth Dependence

Abstract We prove that the mappings obtained in Forstnerič splitting lemma vary in a $$\mathcal {C}^{\lfloor {\frac{l-1}{2}}\rfloor }$$ C ⌊ l - 1 2 ⌋ -continuous way if only the input family of biholomorphic mappings close to Id (and their domains) is $$\mathcal {C}^l$$ C l -continuous (see Theorem 1.3 for a precise formulation).

scholarly journals II.—A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F. R. S

1925 ◽  
Vol 213 (402-410) ◽  
pp. 21-87 ◽  
Keyword(s):  
Mathematical Theory ◽  
Small Areas ◽  
Theory Of Evolution ◽  
Precise Formulation ◽  
Statistical Studies

The following work is founded on that conception of evolution, the most recent and precise formulation of which is due to Dr. J. C. Willis, and represents an attempt to develop the quantitative consequences of the conception. By his statistical studies of distribution Dr. Willis was led to two conclusions:— (1) Species occupying large areas are, on the whole , older than those occupying small areas, provided that allied forms are compared.

A precise formulation of spontaneous breaking of grand unified theories

1980 ◽  
Vol 97 (3-4) ◽  
pp. 367-370 ◽  
Author(s):  
I. Antoniadis ◽  
C. Bouchiat ◽  
J. Iliopoulos
Keyword(s):  
Spontaneous Breaking ◽  
Precise Formulation ◽  
Grand Unified Theories ◽  
Unified Theories

Equilibrium Theory: A Simple Production Model

2019 ◽  
pp. 451-457
Author(s):  
Tomas Björk
Keyword(s):  
Equilibrium Problem ◽  
Optimization Problem ◽  
Dynamic Equilibrium ◽  
Equilibrium Theory ◽  
Production Model ◽  
Stochastic Discount Factor ◽  
Equilibrium Concept ◽  
Precise Formulation ◽  
Central Planner ◽  
Simple Production

This is the first of several chapters dealing with the dynamic equilibrium theory. As an instructive first example we study a simple Cox–Ingersoll–Ross type of production model. The equilibrium concept is given a precise formulation and we derive the equilibrium short rate as well as the equilibrium stochastic discount factor. We also study the associated optimization problem for a central planner and prove that this is equivalent to the equilibrium problem.

scholarly journals Helix-Free Ferroelectric Liquid Crystals: Electro Optics and Possible Applications

2018 ◽  
Vol 8 (12) ◽  
pp. 2429 ◽  
Author(s):  
Alexander Andreev ◽  
Tatiana Andreeva ◽  
Igor Kompanets ◽  
Nikolay Zalyapin
Keyword(s):  
Liquid Crystals ◽  
Low Voltage ◽  
Light Transmission ◽  
Optical Response ◽  
Phase Delay ◽  
High Rate ◽  
Ferroelectric Liquid Crystals ◽  
Light Modulators ◽  
Director Reorientation ◽  
Smooth Dependence

This is a review of results from studying ferroelectric liquid crystals (FLCs) of a new type developed for fast low-voltage displays and light modulators. These materials are helix-free FLCs, which are characterized by spatially periodic deformation of smectic layers and a small value of spontaneous polarization (less than 50 nC/cm2). The FLC director is reoriented due to the motion of solitons at the transition to the Maxwellian mechanism of energy dissipation. A theoretical model is proposed for describing the FLC deformation and director reorientation. The frequency and field dependences of the optical response time are studied experimentally for modulation of light transmission, scattering, and phase delay with a high rate. The hysteresis-free nature and smooth dependence of the optical response on the external electric field in the frequency range up to 6 kHz is demonstrated, as well as bistable light scattering with memorization of an optical state for a time exceeding the switching time by up to 6 orders of magnitude. Due to the spatially inhomogeneous light phase delay, the ability of a laser beam to cause interference is effectively suppressed. The fastest FLCs under study are compatible with 3D, FLC on Silicon (FLCoS), and Field Sequential Colors (FSC) technologies.

The Politics of Human Rights Diplomacy

2020 ◽  
pp. 097359842094343
Author(s):  
Anupama Ghosal ◽  
Sreeja Pal
Keyword(s):  
Human Rights ◽  
Foreign Policy ◽  
United Nations ◽  
National Security ◽  
International Organizations ◽  
Human Rights Violations ◽  
Precise Formulation ◽  
The United Nations ◽  
The Relationship

The issue of Human Rights features as a prominent agenda of the United Nations and its related international organizations. However, when it comes to precise formulation of a country’s foreign policy in bilateral or multilateral forums, the issues of trade and national security find priority over pressing human rights violations occurring within the countries engaged in the diplomatic dialogue. An often-employed reason behind such an approach is the need to respect sovereignty and non-interference of a country in diplomacy. This article aims at analysing the potential which diplomacy holds to pressurize recalcitrant regimes to respect human rights. In doing so, the article tries to explore the ambit of Human Rights Diplomacy and the relationship between agenda of politics and human rights.

Normal and osculating maps for submanifolds of RN

1990 ◽  
Vol 114 (1-2) ◽  
pp. 39-55 ◽  
Author(s):  
I. Cattaneo Gasparini ◽  
G. Romani
Keyword(s):  
Isometric Immersion ◽  
Normal Bundle ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Gauss Map ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Precise Formulation ◽  
Parallel Case ◽  
Necessary And Sufficient

SynopsisLet Mn be a manifold supposed “nicely curved” isometrically immersed in ℝn+p. Starting from a generalised Gauss map associated to the splitting of the normal bundle defined from the values of the fundamental forms of M of order k (k ≧ 0), we give necessary and sufficient conditions for the map to be totally geodesic and harmonic . For k = 0 is the classical Gauss map and our formula reduces to Ruh–Vilm's formula with a more precise formulation due to the consideration of the splitting of the normal bundle.We also give necessary conditions for M, supposed complete, to admit an isometric immersion with . This theorem generalises a theorem of Vilms on the manifolds with second fundamental forms parallel (case k = 0). The result is interesting as the class of manifolds satisfying the condition is larger than the class of manifolds satisfying .

Precise formulation of the vibroacoustic effects of an added constrained damping layer on a plane structure.

1996 ◽  
Vol 99 (4) ◽  
pp. 2520-2520
Author(s):  
Jean Nicolas ◽  
Noureddine Atalla ◽  
Olivier Foin ◽  
Bertrand Mercier
Keyword(s):  
Precise Formulation ◽  
Constrained Damping

scholarly journals Discovery of the Odderon by TOTEM experiments and the FMO approach

2019 ◽  
Vol 206 ◽  
pp. 06001
Author(s):  
Evgenij Martynov ◽  
Basarab Nicolescu
Keyword(s):  
Experimental Data ◽  
International Symposium ◽  
Momentum Transfer ◽  
Experimental Observation ◽  
Theoretical Basis ◽  
Extended Version ◽  
Precise Formulation ◽  
Wide Interval ◽  
History Of

This paper is an extended version of the talk by B. Nicolescu at the XLVIII International Symposium on Multiparticle Dynamics (ISMD2018) at Singapore, 3-7 September, 2018. Theoretical basis and history of the Froissaron and Maximal Odderon (FMO) approach for elastic pp and $ \bar {p} $ p scattering is presented. Precise formulation of the FMO model at any momentum transfer squared t is given. The model is applied to description and analysis of the experimental data in a wide interval of energy $ \sqrt s $ and t. The special attention is given for the latest TOTEM data at 13 TeV, both at t = 0 and at t ≠ 0 and to their interpretation in the FMO model. It is emphasized that the last TOTEM results can be considered as clear evidence for the first experimental observation of the Odderon, predicted theoretically about 50 years ago.

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