scholarly journals Notes on the Distribution of Roots Modulo a Prime of a Polynomial III

2020 ◽  
Vol 15 (1) ◽  
pp. 93-104
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Irreducible Polynomial ◽  
The Other ◽  
One Dimensional ◽  
Integer Coefficients ◽  
The One ◽  
Distribution Of Roots

AbstractLet f (x) bea monicpolynomialwith integer coefficients and integers r1,..., rn with 0 ≤ r1 ≤··· ≤ rn <p the n roots of f (x) ≡ 0mod p for a prime p. We proposed conjectures on the distribution of the point (r1/p,...,rn/p) in the previous papers. One aim of this paper is to revise them for a reducible polynomial f (x), and the other is to show that they imply the one-dimensional equidistribution of r1/p,...,rn/p for an irreducible polynomial f (x) by a geometric way.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

Exploring the electron density localization in MoS2 nanoparticles using a localized-electron detector: Unraveling the origin of the one-dimensional metallic sites on MoS2 catalysts

2018 ◽  
Vol 20 (31) ◽  
pp. 20417-20426 ◽  
Author(s):  
Yosslen Aray ◽  
Antonio Díaz Barrios
Keyword(s):  
Electron Density ◽  
The Other ◽  
Local Moment ◽  
Electron Detector ◽  
Moment Representation ◽  
One Dimensional ◽  
Mos2 Nanoparticles ◽  
Mos2 Catalysts ◽  
The One

The nature of the electron density localization in two MoS2 nanoclusters containing eight rows of Mo atoms, one with 100% sulphur coverage at the Mo edges (n8_100S) and the other with 50% coverage (n8_50S) was studied using a localized-electron detector function defined in the local moment representation.

scholarly journals Feller chains and random functions

2015 ◽  
Vol 56 ◽  
Author(s):  
Vytautas Kazakevičius
Keyword(s):  
Random Function ◽  
Transition Probability ◽  
The Other ◽  
One Dimensional ◽  
Random Functions ◽  
Other Hand ◽  
Dimensional Distribution ◽  
The One

We prove that each Feller transition probability is the one-dimensional distribution of some stochastically continuous random function. We also introduce the notion of a regular random function and show, on one hand, that every random  function has a regular modification, and on the other hand, that the composition of independent regular stochastically continuous random functions is stochastically continuous as well.

scholarly journals A stronger recognizability condition for two-dimensional languages

2013 ◽  
Vol Vol. 15 no. 2 (Automata, Logic and Semantics) ◽  
Author(s):  
Marcella Anselmo ◽  
Maria Madonia
Keyword(s):  
Finite Automata ◽  
The Other ◽  
Two Dimensional ◽  
Minimal Size ◽  
One Dimensional ◽  
Tiling System ◽  
International Audience ◽  
The One

Automata, Logic and Semantics International audience The paper presents a condition necessarily satisfied by (tiling system) recognizable two-dimensional languages. The new recognizability condition is compared with all the other ones known in the literature (namely three conditions), once they are put in a uniform setting: they are stated as bounds on the growth of some complexity functions defined for two-dimensional languages. The gaps between such functions are analyzed and examples are shown that asymptotically separate them. Finally the new recognizability condition results to be the strongest one, while the remaining ones are its particular cases. The problem of deciding whether a two-dimensional language is recognizable is here related to the one of estimating the minimal size of finite automata recognizing a sequence of (one-dimensional) string languages.

The Problem of Radiation Reaction in Classical Electrodynamics

1976 ◽  
Vol 31 (10) ◽  
pp. 1133-1142 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Radiation Reaction ◽  
The Other ◽  
Classical Electrodynamics ◽  
Momentum Balance ◽  
Covariant Theory ◽  
Dirac Theory ◽  
Principle Of Equivalence ◽  
One Dimensional ◽  
General Energy ◽  
The One

Abstract A new covariant theory of the classical radiating electron is compared with other radiation reaction theories: On the one hand, the new theory can be deduced from Caldirola's finite-dif-ferences theory by suitable approximations; on the other hand, the Lorentz-Dirac theory and the theory of Mo and Papas are shown to be approximative forms of the new theory. The latter is free from the difficulties of the other theories: there are no undetermined internal oscillations, no runaway solutions and pre-acceleration effects, and radiation reaction exists in the case of one-dimensional motion. The general energy-momentum balance is studied, and the implications of the existence of radiation reaction in a static constant force field are discussed with regard to the principle of equivalence.

scholarly journals Internal Freezing of Snow Cover due to its Own Cold Heat Sources (Abstract)

1985 ◽  
Vol 6 ◽  
pp. 329-329
Author(s):  
Y. Yamada ◽  
T. Ikarashi
Keyword(s):  
Heat Conduction ◽  
Open System ◽  
The Other ◽  
Fundamental Aspect ◽  
Heat Sources ◽  
Field Observations ◽  
Snow Layer ◽  
One Dimensional ◽  
Wet Snow ◽  
The One

This report discusses the one-dimensional freezing of dry snow/ wet snow systems for the condition first examined by Stefan: the problem of heat conduction with phase change. There are two systems of internal freezing: one is a closed system of temperature rise in a dry snow layer sandwiched between upper and lower wet snow layers; the other an open system of freezing of a thin wet layer provoked mainly by an upper dry snow layer facing the atmosphere at its surface. The latter negatively concerns the release of some avalanches, because the weak layers of surface avalanches in districts where the melt-freeze metamorphism prevails (as in the Horuriku district of Japan) may be the thin wet granular snow layers.Numerical results are given for different conditions of internal freezing. A comparison with field observations reveals the fundamental aspect of this phenomenon and the possibility of avalanche release.

A New Method and Device for Temperature Measurement Using One-Dimensional Heat Equation

1994 ◽  
Author(s):  
Nicolae A. Damean
Keyword(s):  
Heat Equation ◽  
Temperature Measurement ◽  
Low Temperatures ◽  
Principal Component ◽  
The Other ◽  
New Method ◽  
Gradient Algorithm ◽  
One Dimensional ◽  
The One ◽  
The Mathematical Model

Abstract A new method and device for temperature measurement are presented. The method reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. The device consists of a hardware part including some conventional transducers and a software one. The problem of temperature measurement, according to this method, is mathematically modelled by means of the one-dimensional heat equation, describing the heat transfer through the device. The principal component of the device is a rod. The variation of the temperature which is produced near one end of the rod is determined using some temperature measurements in the other end of the rod, the mathematical model and a type of gradient algorithm. This device works as an attenuator of high temperatures and as an amplifier of low temperatures.

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