Upper and lower bounds for three-dimensional undrained stability of shallow tunnels

2021 ◽  
Vol 27 ◽  
pp. 100491
Author(s):  
A.N. Antão ◽  
M. Vicente da Silva ◽  
N. Monteiro ◽  
N. Deusdado
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Shallow Tunnels

UPPER AND LOWER BOUNDS FOR THE VOLUME OF A COMPACT SPACELIKE HYPERSURFACE IN A GENERALIZED ROBERTSON–WALKER SPACETIME

2013 ◽  
Vol 11 (01) ◽  
pp. 1450006 ◽  
Author(s):  
JUAN ÁNGEL ALEDO ◽  
ALFONSO ROMERO ◽  
RAFAEL M. RUBIO
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Upper And Lower Bounds ◽  
Warping Function ◽  
First Eigenvalue ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Angle Function ◽  
Spacelike Hypersurfaces

We provide upper and lower bounds for the volume of a compact spacelike hypersurface in an (n + 1)-dimensional Generalized Robertson–Walker (GRW) spacetime in terms of the volume of the fiber, the hyperbolic angle function and the warping function. Under several geometrical and physical assumptions, we characterize the spacelike slices as the only spacelike hypersurfaces where these bounds are attained. As a consequence of these results, we get an upper bound for the first eigenvalue of a compact spacelike surface in a three-dimensional GRW spacetime whose fiber is a topological sphere, which includes the case of the three-dimensional De Sitter spacetime, and show that the bound is attained if and only if M is a spacelike slice.

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.

SIGNATURE AND RELIABILITY OF CONDITIONAL THREE-DIMENSIONAL CONSECUTIVE-(s, s, s)-OUT-OF-(s, s, m):F SYSTEM

2014 ◽  
Vol 21 (02) ◽  
pp. 1450009 ◽  
Author(s):  
MADHURI G. KULKARNI ◽  
AKANKSHA S. KASHIKAR
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
System Failure ◽  
Three Dimension ◽  
Two Dimensional ◽  
Math Model ◽  
The Moment ◽  
Appl Math ◽  
F System

A three-dimensional consecutive (r1, r2, r3)-out-of-(m1, m2, m3):F system was introduced by Akiba et al. [J. Qual. Mainten. Eng.11(3) (2005) 254–266]. They computed upper and lower bounds on the reliability of this system. Habib et al. [Appl. Math. Model.34 (2010) 531–538] introduced a conditional type of two-dimensional consecutive-(r, s)-out-of-(m, n):F system, where the number of failed components in the system at the moment of system failure cannot be more than 2rs. We extend this concept to three dimension and introduce a conditional three-dimensional consecutive (s, s, s)-out-of-(s, s, m):F system. It is an arrangement of ms2 components like a cuboid and it fails if it contains either a cube of failed components of size (s, s, s) or 2s3 failed components. We derive an expression for the signature of this system and also obtain reliability of this system using system signature.

scholarly journals Bounds on integrals with respect to multivariate copulas

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Michael Preischl
Keyword(s):  
Lower Bounds ◽  
Open Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Upper And Lower Bounds ◽  
Multidimensional Case ◽  
Assignment Problems ◽  
Dimensional Dependence ◽  
Dependence Measures

AbstractIn this paper, we present a method to obtain upper and lower bounds on integrals with respect to copulas by solving the corresponding assignment problems (AP’s). In their 2014 paper, Hofer and Iacó proposed this approach for two dimensions and stated the generalization to arbitrary dimensons as an open problem. We will clarify the connection between copulas and AP’s and thus find an extension to the multidimensional case. Furthermore, we provide convergence statements and, as applications, we consider three dimensional dependence measures as well as an example from finance.

Localization of Eigenvalues by a Modification of Müller′s Variational Principle in Some Exactly Solvable Cases

1983 ◽  
Vol 38 (5) ◽  
pp. 493-496 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Variational Principle ◽  
Lower Bounds ◽  
Schrödinger Operators ◽  
Three Dimensional ◽  
Finite Depth ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Potential Well ◽  
Rough Approximation ◽  
Exactly Solvable

Upper and lower bounds on the eigenvalues of Schrödinger operators with simple one and a simple three dimensional potential (well of finite depth, spherical δ-potential) are given by means of a modification of Müller′s variational principle. The estimates, comparing them with the exact eigenvalues, show a localization of the eigenvalues even in a rough approximation for the trial operator.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

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