A classical problem in logic synthesis is to find a sum-of-product (SOP) Boolean expression with the minimum number of product terms that implements a Boolean function. In this paper, we focus on a related yet different synthesis problem targeted toward probabilistic computation. In our scenario, we want to synthesize a Boolean function that covers an exact number of minterms, say m minterms. T...

This paper considers the problem of scheduling a single machine, in which the objective function is to minimize the weighted quadratic earliness and tardiness penalties and no machine idle time is allowed. We develop a branch and bound algorithm involving the implementation of lower and upper bounding procedures as well as some dominance rules. The lower bound is designed based on a lagrangian ...

One can apply Bonse’s inequality to points on the real line to find an upper bound on any prime gap, including both for first occurrences and for maximal prime gaps. However, such a result is neither as fine as the upper bound found by Mozzochi, nor as fine as the lower bound obtained by Rankin for maximal prime gaps. Without deep sieve methods, such as those used by Maier and Pomerance to comp...

In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. We demonstrate an O(d...

In this research, flat rolling process of bonded sandwich sheets is investigated by the method of upper bound. A kinematically admissible velocity field is developed for a single layer sheet and is extended into the rolling of the symmetrical sandwich sheets. The internal, shear and frictional power terms are derived and they are used in the upper bound model. Through the analysis, the rolling ...

This paper describes an upper bound analysis of cold forward extrusion of spur gears with modified tooth profile. Spur gear geometrical parameters such as module, number of teeth, pressure angle, bore radius and addendum modification factor were input to a computer program written in Visual Basic. Then spur gear, billet and extrusion die cavity were modeled automatically in SolidWorks. For uppe...

air defense is a crucial area for all naval combat systems. in this study, we consider a warship equipped with an air-defense weapon that targets incoming threats using surface-to-air missiles. we define the weapon scheduling problem as the optimal scheduling of a set of surface-to-air missiles of a warship to a set of attacking air threats. the optimal scheduling of the weapon results in an in...

New upper and lower bounds are presented for a multi-dimensional generalization of bin pa king alled box pa king. Several variants of this problem, in luding bounded spa e box pa king, square pa king, variable sized box pa king and resour e augmented box pa king are also studied. The main results, stated for d = 2, are as follows: A new upper bound of 2.66013 for online box pa king, a new 14=9 ...

I’ll use the symbol R to denote the set of real numbers. Let A be a nonempty subset of R. A number u is an upper bound for A if a ≤ u for all a ∈ A. We say that A is bounded above if it has an upper bound. Note that saying that a number t is not an upper bound for A is equivalent to the statement “There is some a ∈ A such that t < a.” A number s is called the supremum of A (sup) if it is the le...

We consider linear stability of three-layer Hele-Shaw flows with each layer having constant viscosity and viscosity increasing in the direction of a basic uniform flow. While the upper bound results on the growth rate of long waves are well known from our earlier works, lower bound results on the growth rate of short stable waves are not known to-date. In this paper we obtain such a lower bound...