In the first part, we introduce randomized algorithms as a new notion of efficient algorithms for decision problems. We classify randomized algorithms according to their error probabilities, and define appropriate complexity classes. (RP, coRP, ZPP, BPP, PP). We discuss which classes are realistic proposals for design of probabilistic algorithms. We cover the implementation of randomized algori...

Introduction. The purpose of this report is to draw attention to some nontrivial connections between the ("continuous") theory of irregularities of distribution and discrete mathematics. The object of the theory of irregularities of distribution is to measure the uniformity (or nonuniformity) of sequences and point sets. For instance: how uniformly can an arbitrary set of N points in the unit c...

Background: Due to the small size of the beamlets in IMRT (intensity modulated radiotherapy), physical penumbra is one of the important dosimetric parameters and small changes in the penumbra have a notable impact on the results. The physical penumbra width is defined as the lateral distance between two specified isodose curves at a specified depth of phantom. In this study, after demonstrating...

Abstract Timely and quality planting of soybean is important to achieve maximum yield potential. Wet spring soil conditions rain frequently shorten the time for farmers plant crops within optimal conditions. New planter technology has been introduced that enables their fields faster more precisely than with traditional planters. Large plot field studies were conducted in Indiana from 2015 2017 ...

First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the po...