The three-dimensional assignment and partition problems. New lower bounds

2006 ◽  
Vol 67 (2) ◽  
pp. 242-250 ◽  
Author(s):  
S. I. Sergeev
Keyword(s):  
Lower Bounds ◽  
Three Dimensional

Complete caps in AG(3, q) from elliptic curves

2014 ◽  
Vol 13 (08) ◽  
pp. 1450050 ◽  
Author(s):  
Irene Platoni
Keyword(s):  
Elliptic Curves ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Complete Caps ◽  
Odd Order ◽  
Galois Space

In a three-dimensional Galois space of odd order q, the known infinite families of complete caps have size far from the theoretical lower bounds. In this paper, we investigate some caps defined from elliptic curves. In particular, we show that for each q between 100 and 350 they can be extended to complete caps, which turn out to be the smallest complete caps known in the literature.

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.

TIME LOWER BOUNDS FOR PERMUTATION ROUTING ON MULTI-DIMENSIONAL BUSED MESHES

1993 ◽  
Vol 03 (02) ◽  
pp. 129-138
Author(s):  
STEVEN CHEUNG ◽  
FRANCIS C.M. LAU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Routing Problem ◽  
Higher Dimensional ◽  
Low Dimensional ◽  
Permutation Routing

We present time lower bounds for the permutation routing problem on three- and higher-dimensional n x…x n meshes with buses. We prove an (r–1)n/r lower bound for the general case of an r-dimensional bused mesh, r≥2, which is not as strong for low-dimensional as for higher-dimensional cases. We then use a different approach to construct a 0.705n lower bound for the three-dimensional case.

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.

DIOPHANTINE APPROXIMATION IN IMAGINARY QUADRATIC FIELDS

2010 ◽  
Vol 06 (04) ◽  
pp. 731-766 ◽  
Author(s):  
L. YA. VULAKH
Keyword(s):  
Half Space ◽  
Hyperbolic Space ◽  
Lower Bounds ◽  
Diophantine Approximation ◽  
Three Dimensional ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Space Model ◽  
Limit Points ◽  
Group B

Let H3 be the upper half-space model of the three-dimensional hyperbolic space. For certain cocompact Fuchsian subgroups Γ of an extended Bianchi group Bd, the extremality of the axis of hyperbolic F ∈ Γ in H3 with respect to Γ implies its extremality with respect to Bd. This reduction is used to obtain sharp lower bounds for the Hurwitz constants and lower bounds for the highest limit points in the Markov spectra of Bd for some d < 1000. In particular, such bounds are found for all non-Euclidean class one imaginary quadratic fields. The Hurwitz constants for the imaginary quadratic fields with discriminants -120 and -132 are given. The second minima are also indicated for these fields.

scholarly journals Lower Bounds on Blowing-Up Solutions of the Three-Dimensional Navier--Stokes Equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$

2016 ◽  
Vol 48 (3) ◽  
pp. 2119-2132 ◽  
Author(s):  
David S. McCormick ◽  
Eric J. Olson ◽  
James C. Robinson ◽  
Jose L. Rodrigo ◽  
Alejandro Vidal-López ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blowing Up ◽  
Blowing Up Solutions

scholarly journals A Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Lower Bounded Variables

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 339
Author(s):  
Yi-Fang Chen ◽  
Hui-Chin Tang
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Single Constraint ◽  
Bounded Variables ◽  
Aggregation Problem

We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution(x1',x2',x3') depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution(x1',x2',x3') types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables.

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