explicit relation
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Author(s):  
David P. Bourne ◽  
Charlie P. Egan ◽  
Beatrice Pelloni ◽  
Mark Wilkinson

AbstractWe give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver.


2021 ◽  
Vol 13 (1) ◽  
pp. 207-225
Author(s):  
Urška Valenčič Arh

The article deals with the use of the phraseological units in print advertisements in the German print media. The focus is the relations between phraseological units in the texts and images of the advertisements. The introductory part provides a brief overview of phraseology as a linguistic discipline and its role in advertisements, the structure of advertisements and possible modifications of phraseological units. The results of the analysis of semantic modifications showed certain relations between phraseological units in texts and images of the advertisements. According to the typology of Hartmut Stöckl (2004), we first defined the relation between a phraseological unit as a latent or explicit relation. In the latent relation phraseological units create a certain relation between text and image. There are two subgroups of the latent relation: phraseological units, which are visually evoked, and phraseological units, which are textually evoked and expressed. In the explicit relation phraseological units are materialized in image and text. Phraseological units, which appear isolated only in one place, are classified in the subgroup of the punctual relation. In the subgroup of the connected relation are phraseological units, to which other linguistic elements and structures refer. The analysis of 84 print advertisements showed that phraseological units are mostly used explicitly and in a connecting manner. This means phraseological units are not used isolated, but the text is characterized by an expressive or phraseological language that is linked to the advertisement’s message in image and text at the same time. The research confirmed that phraseological units are very popular as fixed and idiomatic units in advertisements, because they take on the persuasive functions and represent understandable, connotative and easily memorable structures.


2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Nuno Barros e Sá ◽  
Cláudio Gomes

AbstractThe purpose of this article is to construct an explicit relation between the field operators in Quantum Field Theory and the relevant operators in Quantum Mechanics for a system of N identical particles, which are the symmetrised functions of the canonical operators of position and momentum, thus providing a clear relation between Quantum Field Theory and Quantum Mechanics. This is achieved in the context of the non-interacting Klein–Gordon field. Though this procedure may not be extendible to interacting field theories, since it relies crucially on particle number conservation, we find it nevertheless important that such an explicit relation can be found at least for free fields. It also comes out that whatever statistics the field operators obey (either commuting or anticommuting), the position and momentum operators obey commutation relations. The construction of position operators raises the issue of localizability of particles in Relativistic Quantum Mechanics, as the position operator for a single particle turns out to be the Newton–Wigner position operator. We make some clarifications on the interpretation of Newton–Wigner localized states and we consider the transformation properties of position operators under Lorentz transformations, showing that they do not transform as tensors, rather in a manner that preserves the canonical commutation relations. From a complex Klein–Gordon field, position and momentum operators can be constructed for both particles and antiparticles.


Author(s):  
Claudio Meneses ◽  
Leon A. Takhtajan

AbstractModuli spaces of stable parabolic bundles of parabolic degree 0 over the Riemann sphere are stratified according to the Harder–Narasimhan filtration of underlying vector bundles. Over a Zariski open subset $$\mathscr {N}_{0}$$ N 0 of the open stratum depending explicitly on a choice of parabolic weights, a real-valued function $$\mathscr {S}$$ S is defined as the regularized critical value of the non-compact Wess–Zumino–Novikov–Witten action functional. The definition of $$\mathscr {S}$$ S depends on a suitable notion of parabolic bundle ‘uniformization map’ following from the Mehta–Seshadri and Birkhoff–Grothendieck theorems. It is shown that $$-\mathscr {S}$$ - S is a primitive for a (1,0)-form $$\vartheta $$ ϑ on $$\mathscr {N}_{0}$$ N 0 associated with the uniformization data of each intrinsic irreducible unitary logarithmic connection. Moreover, it is proved that $$-\mathscr {S}$$ - S is a Kähler potential for $$(\Omega -\Omega _{\mathrm {T}})|_{\mathscr {N}_{0}}$$ ( Ω - Ω T ) | N 0 , where $$\Omega $$ Ω is the Narasimhan–Atiyah–Bott Kähler form in $$\mathscr {N}$$ N and $$\Omega _{\mathrm {T}}$$ Ω T is a certain linear combination of tautological (1, 1)-forms associated with the marked points. These results provide an explicit relation between the cohomology class $$[\Omega ]$$ [ Ω ] and tautological classes, which holds globally over certain open chambers of parabolic weights where $$\mathscr {N}_{0} = \mathscr {N}$$ N 0 = N .


Author(s):  
Andrey A. Kostoglotov ◽  
Anton S. Penkov ◽  
Sergey V. Lazarenko

A method of synthesis of a filter for estimating the state of dynamic systems of Kalman type with an adaptive model built on the basis of the principle of decomposition of the system using kinematic relations from the condition of constancy of motion invariants has been developed. The structure of the model is determined from the condition of the maximum function of the generalized power up to a nonlinear synthesizing function that determines the rate of dissipation and, accordingly, the degree of structural adaptation. The resulting model has an explicit relation with the gradient of the estimation error functional, which makes it possible to adapt to the intensity of regular and random influences and can be used to construct a filter for estimating the state of the Kalman structure. On the basis of the developed method, a discrete algorithm is obtained and its comparative analysis with the classical Kalman filter is carried out.


2020 ◽  
Vol 6 (1) ◽  
Author(s):  
George Morrison ◽  
Ali Taheri

AbstractWe establish the existence of multiple whirling solutions to a class of nonlinear elliptic systems in variational form subject to pointwise gradient constraint and pure Dirichlet type boundary conditions. A reduced system for certain $$\mathbf{SO}(n)$$ SO ( n ) -valued matrix fields, a description of its solutions via Lie exponentials, a structure theorem for multi-dimensional curl free vector fields and a remarkable explicit relation between two Euler–Lagrange operators of constrained and unconstrained types are the underlying tools and ideas in proving the main result.


Author(s):  
Fiona E. Raitt ◽  
M. Suzanne Zeedyk
Keyword(s):  

2020 ◽  
Author(s):  
Ali Teimouri

AbstractIn December 2019 a severe acute respiratory syndrome now known as SARS-CoV-2 began to surge in Wuhan, China. The virus soon spread throughout the world to become a pandemic. Since the outbreak various measures were put in place to contain and control the spread, these interventions were mostly based on compartmental models in epidemiology with the main goal of controlling and monitoring the rate of the basic and effective reproduction number. In this paper, we propose an SEIR model where we incorporate contact tracing and age-structured social mixing. We show the explicit relation between contact tracing and social mixing and other relevant parameters of the proposed model. We derive a formula for the effective reproduction number which is expressed in terms of reported cases, tracing quantities and social mixing. We use this formula to determine the expectation value of the effective reproduction number in London, UK.


Author(s):  
Abigail C. Saguy

This chapter traces the origin of the term coming out to gay men in pre–World War II urban communities, who spoke of coming out into gay society. It recounts how, by the 1970s, coming out had become a political tactic by which people revealed their sexual orientation to friends, neighbors, and co-workers or—in the case of celebrities—more publicly via the mass media in an effort to challenge harmful stereotypes and gain sympathy. It reviews how, in the 1980s and 1990s, coming out was set up in explicit relation to the metaphor of the closet and how the mantra “Come Out, Come Out, Wherever You Are” became a demand for members of sexual minorities to declare their sexual orientation—bringing forth the “closet case” and “outing.” It considers critiques of the imperative to come out and arguments that gay men and lesbians have moved “beyond the closet.”


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