Analysis Commons^™

More Properties Of Optimal Polynomial Approximants In Hardy Spaces, Raymond Cheng, Christopher Felder

Mathematics & Statistics Faculty Publications

We study optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, H^p (1 < p < ∞). For fixed f ∈ H^p and n ∈ N, the OPA of degree n associated to f is the polynomial which minimizes the quantity ∥qf −1∥_p over all complex polynomials q of degree less than or equal to n. We begin with some examples which illustrate, when p ≠ 2, how the Banach space geometry makes the above minimization problem interesting. We then weave through various results concerning limits and roots of these polynomials, including results which show that OPAs can be witnessed as solutions …

Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, Ashutosh Timilsina

Theses and Dissertations--Computer Science

Electric power systems are transforming from a centralized unidirectional market to a decentralized open market. With this shift, the end-users have the possibility to actively participate in local energy exchanges, with or without the involvement of the main grid. Rapidly reducing prices for Renewable Energy Technologies (RETs), supported by their ease of installation and operation, with the facilitation of Electric Vehicles (EV) and Smart Grid (SG) technologies to make bidirectional flow of energy possible, has contributed to this changing landscape in the distribution side of the traditional power grid.

Trading energy among users in a decentralized fashion has been referred …

Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong

Honors Theses

Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …

Stochastic Optimization To Reduce Aircraft Taxi-In Time At Igia, New Delhi, Rajib Das, Saileswar Ghosh, Rajendra Desai, Pijus Kanti Bhuin, Stuti Agarwal

International Journal of Aviation, Aeronautics, and Aerospace

Since there is an uncertainty in the arrival times of flights, pre-scheduled allocation of runways and stands and the subsequent first-come-first-served treatment results in a sub-optimal allocation of runways and stands, this is the prime reason for the unusual delays in taxi-in times at IGIA, New Delhi.

We simulated the arrival pattern of aircraft and utilized stochastic optimization to arrive at the best runway-stands allocation for a day. Optimization is done using a GRG Non-Linear algorithm in the Frontline Systems Analytic Solver platform. We applied this model to eight representative scenarios of two different days. Our results show that without …

Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad

Graduate Theses, Dissertations, and Problem Reports (ETD)

The purpose of this thesis is to present new different spaces as attempts to generalize the concept of topological vector spaces. A topological vector space, a well-known concept in mathematics, is a vector space over a field \mathbb{F} with a topology that makes the addition and scalar multiplication operations of the vector space continuous functions. The field \mathbb{F} is usually \mathbb{R} or \mathbb{C} with their standard topologies. Since every vector space is a finitary matroid, we define two spaces called finite matroidal spaces and matrological spaces by replacing the linear structure of the topological vector space with a finitary matroidal …

Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans

UNF Graduate Theses and Dissertations

Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …