Transcendental Bézout estimate by the logarithmic function in ℂn

1985 ◽  
pp. 204-210
Author(s):  
Masami Okada
Keyword(s):  
Logarithmic Function

scholarly journals Testing and Formal Verification of Logarithmic Function Design

2010 ◽  
Author(s):  
Sanjeev Agarwal ◽  
Indu Bhuria ◽  
R. B. Patel ◽  
B. P. Singh
Keyword(s):  
Formal Verification ◽  
Logarithmic Function ◽  
Function Design

ON THE MODEL THEORY OF THE LOGARITHMIC FUNCTION IN COMPACT LIE GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350055
Author(s):  
SONIA L'INNOCENTE ◽  
FRANÇOISE POINT ◽  
CARLO TOFFALORI
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Model Theory ◽  
Effective Model ◽  
Logarithmic Function ◽  
Compact Lie Groups ◽  
Model Completeness ◽  
Schanuel's Conjecture ◽  
Logarithm Function ◽  
Natural Expansion

Given a compact linear Lie group G, we form a natural expansion of the theory of the reals where G and the graph of a logarithm function on G live. We prove its effective model-completeness and decidability modulo a suitable variant of Schanuel's Conjecture.

scholarly journals F-centers mechanism of long-term relaxation in lead zirconate-titanate based piezoelectric ceramics. 2. After-field relaxation

2016 ◽  
Vol 06 (03) ◽  
pp. 1650019 ◽  
Author(s):  
V. M. Ishchuk ◽  
D. V. Kuzenko
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Lead Zirconate Titanate ◽  
Oxygen Vacancies ◽  
Lead Zirconate ◽  
Relaxation Processes ◽  
Logarithmic Function ◽  
External Effects ◽  
Dc Electric Field

The paper presents results of experimental study of the dielectric constant relaxation during aging process in Pb(Zr,Ti)O3based solid solutions (PZT) after action of external DC electric field. The said process is a long-term one and is described by the logarithmic function of time. Reversible and nonreversible relaxation process takes place depending on the field intensity. The relaxation rate depends on the field strength also, and the said dependence has nonlinear and nonmonotonic form, if external field leads to domain disordering. The oxygen vacancies-based model for description of the long-term relaxation processes is suggested. The model takes into account the oxygen vacancies on the sample's surface ends, their conversion into [Formula: see text]- and [Formula: see text]-centers under external effects and subsequent relaxation of these centers into the simple oxygen vacancies after the action termination. [Formula: see text]-centers formation leads to the violation of the original sample's electroneutrality, and generate intrinsic DC electric field into the sample. Relaxation of [Formula: see text]-centers is accompanied by the reduction of the electric field, induced by them, and relaxation of the dielectric constant, as consequent effect.

scholarly journals Strengthened convexity of positive operator monotone decreasing functions

2020 ◽  
Vol 126 (3) ◽  
pp. 559-567
Author(s):  
Megumi Kirihata ◽  
Makoto Yamashita
Keyword(s):  
Logarithmic Function ◽  
Monotone Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Positive Maps ◽  
Operator Monotone ◽  
Strengthened Form ◽  
Operator Monotone Functions ◽  
Positive Functions ◽  
Decreasing Functions

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.

scholarly journals Is our perception of the spread of COVID-19 inherently inaccurate?

2021 ◽  
Author(s):  
Alexander Maier
Keyword(s):  
Decision Making ◽  
Subjective Perception ◽  
Logarithmic Function ◽  
Original Formulation ◽  
Global Crisis ◽  
New Information ◽  
The World ◽  
Non Linear ◽  
The Future ◽  
Linear Nature

One of the most fundamental insights into the nature of our subjective perception of the world around us is that it is not veridical. In other words, we tend to not perceive information about the world around us accurately. Instead, our brains interpret new information through a host of innate and learned mechanisms that can introduce bias and distortions One of the best studied mechanisms that guide – and distort – our perception is the psychophysical Weber-Fechner law. According to this empirically derived, mathematically formulated law we tend to put more emphasis on smaller deviations in size while underestimating larger changes. The original formulation of the Weber-Fechner law takes the shape of a logarithmic function and is commonly applied to somatosensory perception such as the weight of an object. However, later work showed that the Weber-Fechner law can be generalized and describe a large variety of perceived changes in magnitude that even go beyond the sensory domain. Here we investigate the hypothesis that our perception of data associated with the spread of COVID-19 and similar pandemics is governed by the same psychophysical laws. Based on several recently published studies, we demonstrate that the Weber-Fechner law can be shown to directly affect the decision-making of officials in response to this global crisis as well as the greater public at large. We discuss how heightened awareness of the non-linear nature of subjective perception could help alleviate problematic judgements in similar situations in the future.

scholarly journals On quantum quasi-relative entropy

2019 ◽  
Vol 31 (07) ◽  
pp. 1950022
Author(s):  
Anna Vershynina
Keyword(s):  
Relative Entropy ◽  
Logarithmic Function ◽  
Operator Inequalities ◽  
Operator Convex Function ◽  
Strong Subadditivity ◽  
Entropy Formula ◽  
Quantum Relative Entropy ◽  
Skew Information ◽  
Explicit Bounds ◽  
Joint Convexity

We consider a quantum quasi-relative entropy [Formula: see text] for an operator [Formula: see text] and an operator convex function [Formula: see text]. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the [Formula: see text]-divergences (i.e. [Formula: see text]). We also provide an error term for a class of operator inequalities, that generalizes operator strong subadditivity inequality. We apply those results to demonstrate explicit bounds for the logarithmic function, that leads to the quantum relative entropy, and the power function, which gives, in particular, a Wigner–Yanase–Dyson skew information. In particular, we provide the remainder terms for the strong subadditivity inequality, operator strong subadditivity inequality, WYD-type inequalities, and the Cauchy–Schwartz inequality.

Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies

2020 ◽  
pp. 1-38
Author(s):  
Jiu-Gang Dong ◽  
Seung-Yeal Ha ◽  
Doheon Kim
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Dynamical Variable ◽  
Switching Network ◽  
Logarithmic Function ◽  
System Parameters ◽  
Network Topologies ◽  
Isothermal Case ◽  
Uniformly Bounded ◽  
Emergent Dynamics

We study the emergent dynamics of the thermomechanical Cucker–Smale (TCS) model with switching network topologies. The TCS model is a generalized CS model with extra internal dynamical variable called “temperature” in which isothermal case exactly coincides with the CS model for flocking. In previous studies, emergent dynamics of the TCS model has been mostly restricted to some static network topologies such as complete graph, connected graph with positive in and out degrees at each node, and digraphs with spanning trees. In this paper, we consider switching network topologies with a spanning tree in a sequence of time-blocks, and present two sufficient frameworks leading to the asymptotic mono-cluster flocking in terms of initial data and system parameters. In the first framework in which the sizes of time-blocks are uniformly bounded by some positive constant, we show that temperature and velocity diameters tend to zero exponentially fast, and spatial diameter is uniformly bounded. In the second framework, we admit a situation in which the sizes of time-blocks may grow mildly by a logarithmic function. In latter framework, our temperature and velocity diameters tend to zero at least algebraically slow.

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