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.

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.

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.

NOTES ON THE DISTRIBUTION OF PHASE SHIFTS

2008 ◽  
Vol 22 (23) ◽  
pp. 2163-2175 ◽  
Author(s):  
MIKLÓS HORVÁTH
Keyword(s):  
Inverse Scattering ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Variational Formula ◽  
Phase Shifts ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Fixed Energy ◽  
Symmetrical Potential ◽  
The One

We consider three-dimensional inverse scattering with fixed energy for which the spherically symmetrical potential is nonvanishing only in a ball. We give exact upper and lower bounds for the phase shifts. We provide a variational formula for the Weyl–Titchmarsh m-function of the one-dimensional Schrödinger operator defined on the half-line.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

scholarly journals Relative annihilators in semilattices

1973 ◽  
Vol 9 (2) ◽  
pp. 169-185 ◽  
Author(s):  
J.C. Varlet
Keyword(s):  
Lower Bound ◽  
Principal Ideal ◽  
The Other ◽  
Fixed Element ◽  
Other Hand ◽  
The One ◽  
Implicative Semilattices

An α-distributive (respectively α-implicative) semilattice S is a lower semilattice (with greatest lower bound denoted by juxtaposition) in which the annihilator 〈x, a〉, that is {y ∈ S: xy ≤ α}, is an ideal (respectively a principal ideal) for the fixed element α and any x of S. These semilattices appear as natural links between general and distributive semi-lattices on the one hand, and between pseudo-complemented and implicative semilattices on the other hand. Prime and dense elements, as well as maximal and prime filters, are essential. Mandelker's result, a lattice L is distributive if and only if 〈x, y〉 is an ideal for any x, y ∈ L is extended to semi-lattices.

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 Testing methods for quantifying Monte Carlo variation for categorical variables in Probabilistic Genotyping

2021 ◽  
Author(s):  
Jo-Anne Bright ◽  
Duncan Alexander Taylor ◽  
James Michael Curran ◽  
JOHN BUCKLETON
Keyword(s):  
Monte Carlo ◽  
Lower Bound ◽  
Lower Bounds ◽  
Population Model ◽  
The Other ◽  
Categorical Variables ◽  
Testing Methods ◽  
Resampling Method

Two methods for applying a lower bound to the variation induced by the Monte Carlo effect are trialled. One of these is implemented in the widely used probabilistic genotyping system, STRmix Neither approach is giving the desired 99% coverage. In some cases the coverage is much lower than the desired 99%. The discrepancy (i.e. the distance between the LR corresponding to the desired coverage and the LR observed coverage at 99%) is not large. For example, the discrepancy of 0.23 for approach 1 suggests the lower bounds should be moved downwards by a factor of 1.7 to achieve the desired 99% coverage. Although less effective than desired these methods provide a layer of conservatism that is additional to the other layers. These other layers are from factors such as the conservatism within the sub-population model, the choice of conservative measures of co-ancestry, the consideration of relatives within the population and the resampling method used for allele probabilities, all of which tend to understate the strength of the findings.

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.

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