ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

1995 ◽  
Vol 05 (02) ◽  
pp. 275-280 ◽  
Author(s):  
BEATE BOLLIG ◽  
MARTIN HÜHNE ◽  
STEFAN PÖLT ◽  
PETR SAVICKÝ
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Time Complexity ◽  
Upper And Lower Bounds ◽  
Average Case ◽  
Asymptotically Optimal ◽  
Circuit Delay ◽  
Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

scholarly journals The stretch-length tradeoff in geometric networks: average case and worst case study

2015 ◽  
Vol 159 (1) ◽  
pp. 125-151
Author(s):  
DAVID ALDOUS ◽  
TAMAR LANDO
Keyword(s):  
Lower Bounds ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Unit Area ◽  
Average Density ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Average Case ◽  
Route Length

AbstractConsider a network linking the points of a rate-1 Poisson point process on the plane. Write Ψave(s) for the minimum possible mean length per unit area of such a network, subject to the constraint that the route-length between every pair of points is at moststimes the Euclidean distance. We give upper and lower bounds on the function Ψave(s), and on the analogous “worst-case” function Ψworst(s) where the point configuration is arbitrary subject to average density one per unit area. Our bounds are numerically crude, but raise the question of whether there is an exponent α such that each function has Ψ(s) ≍ (s− 1)−αass↓ 1.

Some applications of extremum principles to magnetohydrodynamic pipe flow

1974 ◽  
Vol 336 (1605) ◽  
pp. 211-222 ◽  
Keyword(s):  
Laminar Flow ◽  
Mass Flow Rate ◽  
Lower Bounds ◽  
Flow Rate ◽  
Wide Class ◽  
Pipe Flow ◽  
Asymptotic Series ◽  
Upper And Lower Bounds ◽  
Thin Wall ◽  
Square Channel

This paper is concerned with the application of extremum principles to the laminar flow of a conducting fluid along a pipe with conducting walls. The extremum principles provide upper and lower bounds to the mass-flow rate Q . While these may supply numerical bounds for Q their main application lies in the construction of asymptotic series at large Hartmann numbers. The most important result is a formula for the leading coefficient in the asymptotic series for Q for a wide class of pipe sections with thick conducting walls. A number of examples are given. A particular example is the square channel with thin conducting walls and it is shown how the ‘thin wall’ approximation can be derived from the extremum principles.

scholarly journals Cuckoo Hashing

2001 ◽  
Vol 8 (32) ◽  
Author(s):  
Rasmus Pagh ◽  
Flemming Friche Rodler
Keyword(s):  
Lower Bounds ◽  
Binary Search ◽  
Upper And Lower Bounds ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Average Case ◽  
Cuckoo Hashing ◽  
Perfect Hashing ◽  
Theoretical Performance

We present a simple and efficient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (<em>Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738-761, 1994</em>). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of the scheme is backed by extensive experiments and comparisons with known methods, showing it to be quite competitive also in the average case.

Bounds for Initial Value Problems

1973 ◽  
Vol 40 (4) ◽  
pp. 1097-1102 ◽  
Author(s):  
C. A. Bell ◽  
F. C. Appl
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Initial Value Problems ◽  
Numerical Technique ◽  
Analytic Form ◽  
New Method ◽  
Upper And Lower Bounds ◽  
Initial Value ◽  
Linear Combinations

A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type: x(¨t)+f(t,x,x)˙=0,x(0)=X0,x(˙0)=V0, where f is continuous with continuous first derivatives, Lipschitzian, and ∂f/∂x ≥ 0. An original bounding theorem has been formulated and proven and a numerical technique has been developed for finding the bounding functions in analytic form as linear combinations of Tchebyshev polynomials. The method has been applied to several problems of engineering interest.

TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)

2012 ◽  
Vol 09 (02) ◽  
pp. 447-479 ◽  
Author(s):  
PETE L. CLARK ◽  
BRIAN COOK ◽  
JAMES STANKEWICZ
Keyword(s):  
Elliptic Curves ◽  
Lower Bounds ◽  
Prime Order ◽  
Complex Multiplication ◽  
Number Fields ◽  
Upper And Lower Bounds ◽  
Torsion Points ◽  
Asymptotically Optimal ◽  
Large N ◽  
Cm Points

We present seven theorems on the structure of prime order torsion points on CM elliptic curves defined over number fields. The first three results refine bounds of Silverberg and Prasad–Yogananda by taking into account the class number of the CM order and the splitting of the prime in the CM field. In many cases we can show that our refined bounds are optimal or asymptotically optimal. We also derive asymptotic upper and lower bounds on the least degree of a CM-point on X1(N). Upon comparison to bounds for the least degree for which there exist infinitely many rational points on X1(N), we deduce that, for sufficiently large N, X1(N) will have a rational CM point of degree smaller than the degrees of at least all but finitely many non-CM points.

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.

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