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Effective analytic functions

Joris van der Hoeven
2005 Journal of symbolic computation  
This naturally leads to problems of how to answer questions about analytic functions in a fully effective way.  ...  In this paper, we propose a first definition for the notion of an effective analytic function and we show how to effectively solve several types of differential equations in this context.  ...  Operations on effective analytic functions In this section we will show how to effectively construct elementary analytic functions from the constants in Complex and the identity function z, using the operations  ... 
doi:10.1016/j.jsc.2004.11.012 fatcat:mu2ht4cixjdn5hdoi5vctu2vyu

Effective certification of approximate solutions to systems of equations involving analytic functions [article]

Michael Burr, Kisun Lee, Anton Leykin
2019 arXiv   pre-print
These algorithms are based on the existence of oracles for evaluating basic data about the input analytic functions.  ...  We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions.  ...  Certification using α-theory In this section, we introduce an effective extension of α-theory for analytic functions.  ... 
arXiv:1901.10384v2 fatcat:h27vya6vfrgxhnkc27nk4atuta

Excitonic effects in time-dependent density-functional theory: An analytically solvable model

R. Stubner, I. V. Tokatly, O. Pankratov
2004 Physical Review B  
We investigate the description of excitonic effects within time-dependent density-functional theory (TDDFT).  ...  Using a diagrammatic representation for f_xc, we express its excitonic part f_xc^Ex in terms of the effective vertex function Lambda.  ...  MODEL SYSTEM In this section we consider a model system that reveals both bound and unbound excitonic effects and where both the BSE and the equation for ⌳ can be solved analytically.  ... 
doi:10.1103/physrevb.70.245119 fatcat:fu6uo2iatbfpro3qzdpsp7nccm

An Analytical Approach to the Universal Wave Function and its Gravitational Effect [article]

Yunuo Xiong, Hongwei Xiong
2021 arXiv   pre-print
derive gravitational effects corresponding to dark matter, without modifying any physical principles or hypothesizing the existence of new elementary particles.  ...  We find that an auxiliary function having formal symmetry is very useful to predict the evolution of the classical information in the universal wave function.  ...  An Analytical Approach to the Universal Wave Function In the 1950s, Everett [3] analyzed the following formal solution for the universal wave function: Ψ u ( r 1 , · · · , r N , t) = P(t) ∑ κ=1 α κ (  ... 
arXiv:2104.13770v1 fatcat:btzy3xym7jfwlpmqa6wmcpnipq

Effective potential analytic continuation calculations of real time quantum correlation functions: Asymmetric systems

Atsushi Horikoshi, Kenichi Kinugawa
2004 Journal of Chemical Physics  
We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures.  ...  EFFECTIVE POTENTIAL ANALYTIC CONTINUATION METHOD A. Effective potentials and analytic continuation We first introduce the effective classical potential defined by Feynman [1] .  ...  As new quantum dynamics methods to calculate the real time quantum correlation functions at finite temperature, the centroid molecular dynamics (CMD) method [7] and the effective potential analytic continuation  ... 
doi:10.1063/1.1774161 pmid:15291599 fatcat:xmzdwojthfe7lgolllxvplxraq

A predictive analytic model for high-performance tunneling field-effect transistors approaching non-equilibrium Green's function simulations

Ramon B. Salazar, Hesameddin Ilatikhameneh, Rajib Rahman, Gerhard Klimeck, Joerg Appenzeller
2015 Journal of Applied Physics  
A new compact modeling approach is presented which describes the full current-voltage (I-V) characteristic of high-performance (aggressively scaled-down) tunneling field-effect-transistors (TFETs) based  ...  The compact model is validated by comparison with state-of-the-art quantum transport simulations using a 3D full band atomistic approach based on Non-Equilibrium Green's Functions (NEGF).  ...  The ad-hoc analytic potential shown in (4) is proposed as a simple and adequate solution without resorting to piecewise functions.  ... 
doi:10.1063/1.4934682 fatcat:hcuyrgiatngtvbh3jadc6izxou

Hawking radiation as perceived by different observers: an analytic expression for the effective-temperature function

L C Barbado, C Barceló, L J Garay
2012 Classical and quantum gravity  
In this work, we find a general analytic expression for the effective-temperature function which, apart from the vacuum state choice, depends on the position, the local velocity and the acceleration of  ...  This can be done by means of the effective-temperature function introduced by Barcel\'o et al. in [1].  ...  In section section 3, we write down the general analytic expression for the effective-temperature function and show how it is derived.  ... 
doi:10.1088/0264-9381/29/7/075013 fatcat:ppnsgf2zz5eg5amwyl6yysbjpa

An Analytical Approach to the Universal Wave Function and Its Gravitational Effect

Yunuo Xiong, Hongwei Xiong
2021 Symmetry  
derive gravitational effects corresponding to dark matter, without modifying any physical principles or hypothesizing the existence of new elementary particles.  ...  We find that an auxiliary function having formal symmetry is very useful to predict the evolution of the classical information in the universal wave function.  ...  An Analytical Approach to the Universal Wave Function In the 1950s, Everett [3] analyzed the following formal solution for the universal wave function: Ψ u ( r 1 , · · · , r N , t) = P(t) ∑ κ=1 α κ (  ... 
doi:10.3390/sym13020193 fatcat:pqkmnfzklfgzfllfuhglqdajge

Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

Atsushi Horikoshi, Kenichi Kinugawa
2005 Journal of Chemical Physics  
We apply the effective potential analytic continuation (EPAC) method to the calculation of real time quantum correlation functions involving operators nonlinear in the position operator q̂.  ...  Finally, we propose a simplified version of the EPAC method to reduce the computational cost required for the calculation of the standard effective potential.  ...  Consequently, the real time quantum correlation function q n (t)q n (0) β should be obtained by means of the effective action formalism and the analytic continuation.  ... 
doi:10.1063/1.1888576 pmid:15910020 fatcat:xgelsiqokbg3dk5vkizpeuvzfa

Effect of the Molecular Size of Analytes on Polydiacetylene Chromism

Donghwan Seo, Jinsang Kim
2010 Advanced Functional Materials  
The spectral intensity of 'photopolymerized' (blue phase) shown in all figures are simply ½ of that of original ones for a better comparison with the spectra after addition of acid analytes.  ...  Absorption transition with respect to time duration after addition of acid analytes Figure S1 .  ... 
doi:10.1002/adfm.201000262 fatcat:flg3bhhleve5pdem2xu34o642a

Approximate analytical effective phase function obtained for a thin slab geometry

F. Vaudelle
2017 Journal of Quantitative Spectroscopy and Radiative Transfer  
Therefore, with a modified Gegenbauer or a Two-Terms Henyey-Greenstein phase function, some adjustable analytic functions are proposed in order to fit the measurements linked to the true effective phase  ...  This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/17255 To cite this version : Fabrice VAUDELLE -Approximate analytical effective phase function  ...  Analytical solutions of the effective phase function can be made.  ... 
doi:10.1016/j.jqsrt.2017.03.016 fatcat:hwfihbl5izg43cfntaeify6dsy

Analysis of Thickness and Roughness Effects of Artificial Basement Membranes on Endothelial Cell Functions

Jinfeng Zeng, Michiya Matsusaki
2020 Analytical Sciences  
In this study, we investigated both thickness and roughness-dependent effects of A-BMs on the functions of endothelial cells (ECs), which resulted from different assembly concentrations.  ...  Our study highlights the influence of LbL assembly conditions on endothelial functions, which offers a new criterion for the design of A-BMs in well-organized 3D tissues.  ...  This study aims to explore the effects of thickness and surface morphology of Col-IV/LM LbL nanofilms on the functions of ECs.  ... 
doi:10.2116/analsci.20scp10 pmid:33310992 fatcat:wz57p2ygizeglozdnkiblnrf4m

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

Carmem Lucia de Souza Batista, Dingping Li
1997 Physical Review B (Condensed Matter)  
We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective  ...  This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory and the composite fermion theory, are physically equivalent.  ...  In this paper, we present a framework for the analytic calculations of the two wave functions on the sphere by using projective (or stereographic) coordinates on the sphere.  ... 
doi:10.1103/physrevb.55.1582 fatcat:bc3iudbnuff5dbwn3steo37l5y

Analytical expressions for effective weighting functions used during simulations of water hammer

Kamil Urbanowicz
2017 Journal of Theoretical and Applied Mechanics  
In this work, it has been decided to present certain analytical formulas using which it will be possible to determine the coefficients of simplified effective weighting functions in a simple direct way  ...  The recently completed work shows that during efficient calculations of the convolution integral, the effective weighting function used does not have to be characterised by large convergence with a classical  ...  functions or 10% for three-expression functions and that the optimal range of applicability of these functions should be from ∆t to When searching for an analytical solution for the effective two-expression  ... 
doi:10.15632/jtam-pl.55.3.1029 fatcat:7bvz2lkffnfk3jldze62335qvy

Effects of Subanesthetic Ketamine on Pain and Cognitive Functions in TIVA

Yeliz Özhan
2015 Journal of Clinical and Analytical Medicine  
There are many studies evaluating effects of general anesthetics on cognitive functions in the current literature.  ...  It is known that ketamine use at anesthetic doses affects cognitive functions, but with the new drug combinations such as remifentanyl, dexmedetomidine and propofol, studies evaluating the effects of subanesthetic  ... 
doi:10.4328/jcam.2161 fatcat:htvqmtz5svcedajz57r7ceh2gq
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