Ostrowski type fractional integral operators for generalized (;,,)−preinvex functions

In the present paper, the notion of generalized (;,,)−preinvex function is applied to establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature but also provide new estimates on these type

Globally Convergent Algorithms for Maximum a Posteriori Transmission Tomography

This paper reviews and compares three maximum likelihood algorithms for transmission tomography. One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro in the context of emission tomography, and one is an ad hoc gradient algorithm. The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors. Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm. This superiority stems from the larger number of exponentiations required by the EM algorithm. The convex and gradient algorithms are well adapted to parallel computing.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86016/1/Fessler101.pd

Historical development of the BFGS secant method and its characterization properties

The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe that the secant method arose from Newton's method using finite difference approximations to the derivative. We compile historical evidence revealing that a special case of the secant method predated Newton's method by more than 3000 years. We trace the evolution of secant methods from 18th-century B.C. Babylonian clay tablets and the Egyptian Rhind Papyrus. Modifications to Newton's method yielding secant methods are discussed and methods we believe influenced and led to the construction of the BFGS secant method are explored. In the second part of our research, we examine the construction of several rank-two secant update classes that had not received much recognition in the literature. Our study of the underlying mathematical principles and characterizations inherent in the updates classes led to theorems and their proofs concerning secant updates. One class of symmetric rank-two updates that we investigate is the Dennis class. We demonstrate how it can be derived from the general rank-one update formula in a purely algebraic manner not utilizing Powell's method of iterated projections as Dennis did it. The literature abounds with update classes; we show how some are related and show containment when possible. We derive the general formula that could be used to represent all symmetric rank-two secant updates. From this, particular parameter choices yielding well-known updates and update classes are presented. We include two derivations of the Davidon class and prove that it is a maximal class. We detail known characterization properties of the BFGS secant method and describe new characterizations of several secant update classes known to contain the BFGS update. Included is a formal proof of the conjecture made by Schnabel in his 1977 Ph.D. thesis that the BFGS update is in some asymptotic sense the average of the DFP update and the Greenstadt update

Coronal magnetic energy release by current sheet reconnection

In this thesis we investigate the rapid release of energy in the solar corona, with a particular view to understanding the solar flare in which magnetic reconnection is thought to play a key role. A review of existing reconnection solutions is given in Chapters 2 and 3, with new analytic and numeric results are presented in subsequent chapters. Although much of the work in this thesis is computational, numerical investigations are always motivated theoretically. In Chapters 4 and 5 several aspects of two dimensional reconnection are investigated using a periodic time-dependent incompressible code. One of the main points is to check the veracity of the analytic solution of Craig and Henton (1995) by running the code from general initial conditions. Other aspects of 2-D merging covered include the tearing mode instability, osculation and the effects of finite compressibility. We employ a 3-D time-dependent code, in Chapter 4, to check that the analytically predicted spine and fan forms develop from general initial conditions. Scalings with resistivity of the associated current structures are also investigated. Most of the analytic work so far has revolved around single null magnetic configurations. Chapter 6 focuses on reconnection solutions in the presence of multiple nulls. Finally, we look at an application of the analytic theory in the context of particle acceleration. In Chapter 7 we trace proton orbits using a physically plausible analytic current sheet solution

The transmission of digitally-coded-speech signals by means of random access discrete address systems

Imperial Users onl

Coupled and separable iterations in nonlinear estimation

This thesis deals with algorithms to fit certain statistical models. We are concerned with the interplay between the numerical properties of the algorithm and the statistical properties of the model fitted. Chapter 1 outlines some results, concerning the construction of tests and the convergence of algorithms, based on quadratic approximations to the likelihood surface. These include the relationship between statistical curvature and the convergence of the scoring algorithm, separable regression, and a Gauss-Seidel process which we called coupled iterations. Chapters 2, 3 and 4 are concerned with varying parameter models. Chapter 2 proposes an extension of generalized linear models by including a linear predictor for (a function of) the dispersion parameter also. Chapter 3 deals with various ways to go outside this extended generalized linear model framework for normally distributed data. Chapter 4 briefly describes how coupled iterations may be applied to autoregressive and multinormal models. Chapters 5 to 8 apply a generalization of Prony's classical parametrization to solve separable regression problems which satisfy a linear homogeneous difference equation. Chapter 5 introduces the problem, specifies the assumptions under which asymptotic results are proved, and shows that the reduced normal equations may be expressed as a nonlinear eigenproblem in terms of the Prony parameters. Chapter 6 describes the algorithm which results from solving the eigenproblem, including some computational details. Chapter 7 proves that the algorithm is asymptotically stable. Chapter 8 compares the convergence of the algorithm with that of Gauss-Newton by way of simulations

Commission of Two Narratives of the Psyche: Reading Poqeakh in Nella Larsen's Quicksand and Ralph Ellison's Invisible Man, 2019

This study focuses on the novels of Quicksand by Nella Larsen and Invisible Man by Ralph Ellison to explore the phenomenon of poqakh (???????) through the fictionalized lived experiences of their protagonists, Helga Crane and invisible man. Each novelists representation of poqakh offers a portrait of the protagonists psyches. The narratives reveal an unsettling truth for the protagonists, who are members of a population often targeted, stigmatized, and fashioned or re-fashioned by Americans and various environs in American society, that they must assimilatenot only their bodies, but their psyches too to fit the white mans pattern (Larsen 4). Their realities inform them that non-conformity and/or developing or utilizing their intellect is disadvantageousperceiving is unfavorable. Each protagonist learns that she and he will not only be limited by their imaginations or abilities, but also by persons and constructs within American society keeping them witless and amenable. The environs presented in forms such as schools, jobs, even people who prepare each protagonist to accept all and any disparity (inequality and inequity), they are made to be persistently and surreptitiously instructive. As such, these environs are always educating (or training), always molding the psyches of the protagonists to live within a framethe construct (American society). These ever informing boundaries thoroughly acquaint each protagonist on how to scale down [their] desires and dreams so that they will come within reach of possibility (Thurman 115). Poqakh leads Helga Crane to perceive the boundaries while it prevents the invisible man from returning to unblissful ignorance, thus, for him, providing momentary periods of lucidity. This study utilizes a qualitative research design and method, and relies on phenomenological theory to successfully analyze the novels and explicate on the representations of poqakh. As this study will illustrate, Larsen and Ellison offer as representative via their novels two narratives of the diasporic psyche (mind), wherein their protagonists experiences of poqakh lead to some unmitigated facts and disturbing truths about their reality. KEYWORDS: Ancient Philosophy, Asian History, Classical Literature and Philology, Cultural History, Metaphysics, Nonfictio

New Generalizations of Ostrowski's Inequality on Time Scales

In this short paper, a time scales version of Ostrowski’s inequality is further generalized