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.

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 Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Faris Alzahrani ◽  
Ahmed Salem ◽  
Moustafa El-Shahed
Keyword(s):  
Real Number ◽  
Lower Bounds ◽  
Gamma Function ◽  
Open Problem ◽  
Upper And Lower Bounds ◽  
Digamma Function ◽  
Sharp Bounds ◽  
Gamma Functions ◽  
Numer Math

AbstractIn the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ Γ q ( x + 1 ) / Γ q ( x + s ) for all real number s and $0< q\neq1$ 0 < q ≠ 1 in terms of the q-digamma function. Our results refine the results of Ismail and Muldoon (Internat. Ser. Numer. Math., vol. 119, pp. 309–323, 1994) and give the answer to the open problem posed by Alzer (Math. Nachr. 222(1):5–14, 2001). Also, for the classical gamma function, our results give a Kershaw inequality for all $0< s<1$ 0 < s < 1 when letting $q\to 1$ q → 1 and a new inequality for all $s>1$ s > 1 .

A NOTE ON SPIRALLIKE FUNCTIONS

2021 ◽  
pp. 1-7
Author(s):  
Y. J. SIM ◽  
D. K. THOMAS
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Open Problem ◽  
Univalent Functions ◽  
Inverse Function ◽  
Upper And Lower Bounds ◽  
Spirallike Functions ◽  
New Inequalities

Abstract Let f be analytic in the unit disk $\mathbb {D}=\{z\in \mathbb {C}:|z|<1 \}$ and let ${\mathcal S}$ be the subclass of normalised univalent functions with $f(0)=0$ and $f'(0)=1$ , given by $f(z)=z+\sum _{n=2}^{\infty }a_n z^n$ . Let F be the inverse function of f, given by $F(\omega )=\omega +\sum _{n=2}^{\infty }A_n \omega ^n$ for $|\omega |\le r_0(f)$ . Denote by $ \mathcal {S}_p^{* }(\alpha )$ the subset of $ \mathcal {S}$ consisting of the spirallike functions of order $\alpha $ in $\mathbb {D}$ , that is, functions satisfying $$\begin{align*}{\mathrm{Re}} \ \bigg\{e^{-i\gamma}\dfrac{zf'(z)}{f(z)}\bigg\}>\alpha\cos \gamma, \end{align*}$$ for $z\in \mathbb {D}$ , $0\le \alpha <1$ and $\gamma \in (-\pi /2,\pi /2)$ . We give sharp upper and lower bounds for both $ |a_3|-|a_2| $ and $ |A_3|-|A_2| $ when $f\in \mathcal {S}_p^{* }(\alpha )$ , thus solving an open problem and presenting some new inequalities for coefficient differences.

scholarly journals Infinite-order laminates in a model in crystal plasticity

2009 ◽  
Vol 139 (4) ◽  
pp. 685-708 ◽  
Author(s):  
Nathan Albin ◽  
Sergio Conti ◽  
Georg Dolzmann
Keyword(s):  
Energy Density ◽  
Lower Bounds ◽  
Crystal Plasticity ◽  
Infinite Order ◽  
Two Dimensions ◽  
Upper And Lower Bounds ◽  
Geometrically Nonlinear ◽  
Slip Systems ◽  
Quasiconvex Envelope ◽  
Active Slip

We consider a geometrically nonlinear model for crystal plasticity in two dimensions, with two active slip systems and rigid elasticity. We prove that the rank-1 convex envelope of the condensed energy density is obtained by infinite-order laminates, and express it explicitly via the 2F1 hypergeometric function. We also determine the polyconvex envelope, leading to upper and lower bounds on the quasiconvex envelope. The two bounds differ by less than 2%.

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.

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

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

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