Limits of Julia Sets for Sums of Power Maps and Polynomials

Suppose f_{n,c} is a complex-valued mapping of one complex variable given by f_{n,c}(z) = z^n + p(z) + c, where p is a polynomial such that p(0) = 0 and c is a complex parameter such that |c| \u3c 1. We provide necessary and sufficient conditions that the geometric limit, as n approaches infinity, of the set of points that remain bounded under iteration by f_{n,c} is the disk of radius 1 centered at the origin

“Our Largest and Most Varied Life”: Walt Whitman’s Bicentennial

May 31, 2019 marks Walt Whitman’s two-hundredth birthday. In his lifetime, Whitman was a schoolmaster, journalist, editor, novelist, poet, and more, though his posthumous legacy has depended largely on his career as the author of a distinctly American volume of verse, Leaves of Grass, which begins famously: “I celebrate myself…” As a reviewer of his own work, his words rang true enough. But Whitman has also been celebrated by readers, scholars, and statesmen since the advent of his muscular, free verse, not to mention by devoted friends and followers such as Horace Traubel, who would describe Whitman on the occasion of his seventieth birthday as “our largest and most varied life.” We’re still coming to terms with exactly how large and varied Whitman’s life was, as new discoveries of lost volumes of his prose, including a novel, have landed him on the front page of the New York Times twice in as many years (2016 and 2017), and for the first time(s) since the Civil War. Whitman’s bicentennial occasions a look back not only at these new discoveries from Whitman’s lifetime, but also at Whitman’s influence that extended well past his own life into new centuries in which his democratic optimism and Jacksonian populism would be championed, utilized, and also called into crisis. This exhibition prompts such examination by presenting a retrospective glance at (1) the many faces of Walt Whitman as he self-fashioned from dandy to sage; (2) the process by which he developed his signature poetic line that would be a hallmark of Leaves of Grass; (3) his interventions in the American Civil War; (4) how Whitman’s legacy has been shaped by those who have come after.Englis

Are Private Automobile Insurance Companies Replacing Workers’ Compensation Coverage When the Employee/Insured is Injured in the Course and Scope of Employment by a Third-Party Tortfeasor?: Rubin v. State Farm Mutual Automobile Insurance Company

[Excerpt] “Multiple sources for recovery are available for an employee who is physically injured by a third-party tortfeasor in the course and scope of employment. This is especially true when the physical injury triggers coverage under a health insurance policy or other type of insurance policy for medical benefits. First, assuming that the employer participates in workers’ compensation insurance, the employee is entitled to receive workers’ compensation benefits for medical expenses. Second, the employee can also recover payments for medical benefits from the third-party tortfeasor in a common-law negligence lawsuit. Third, the employee, who in this context would be considered “the insured,” can also make a claim for medical benefits under a private health insurance policy, private automobile insurance policy, or some other variety of private insurance. […] In 2002, the Nevada Supreme Court held in Rubin v. State Farm Mutual Automobile Company that a workers’ compensation exclusionary clause in a private insurance contract does not apply where an injured employee subsequently recovers damages from a third-party tortfeasor. The recovery the employee receives from the third-party tortfeasor, however, is to be reimbursed to the workers’ compensation carrier until workers’ compensation is made whole. Finally, the Rubin court also allows the employee/insured to recover payments for medical benefits under the insured’s med-pay clause of his private automobile insurance policy. This Note contends that under Rubin when an employee recovers medical benefits from both workers’ compensation and the employee’s own private insurance, the insured employee should either not be entitled to med-pay benefits from the private insurance company, or the private automobile insurance company should be permitted to subrogate against the third-party tortfeasor for med-pay benefits already paid to the insured. Many other jurisdictions support this approach. This Note concedes, however, that Rubin was correctly decided under Nevada law since subrogation of med-pay benefits in Nevada is against public policy. Although some states have allowed the same result as the decision in Rubin, the opposing view is better because it serves the purpose of no-fault med-pay benefits, discourages the windfall of a double recovery, and requires that physical injuries sustained in the course and scope of employment are primarily covered by workers’ compensation. Part II of this Note will provide background information on no-fault medical benefits, subrogation and offsetting, and the collateral source rule as they relate to med-pay benefits. Part III of this Note will report the facts, procedural history, and reasoning of the Rubin decision. Part IV will analyze the Rubin decision using explanations from other jurisdictions that have reached similar results. Part V will explain the problems associated with the Rubin situation, and offer alternate solutions, as reached in jurisdictions other than Nevada. Part VI will briefly conclude this Note.

User interface and function library for ground robot navigation

Master's Project (M.S.) University of Alaska Fairbanks, 2017A web application user interface and function library were developed to enable a user to program a ground robot to navigate autonomously. The user interface includes modules for generating a grid of obstacles from a map image, setting waypoints for a path through the map, and programming a robot in a code editor to navigate autonomously. The algorithm used for navigation is an A* algorithm modified with obstacle padding to accommodate the width of the robot and path smoothing to simplify the paths. The user interface and functions were designed to be simple so that users without technical backgrounds can use them, and by doing so they can engage in the development process of human-centered robots. The navigation functions were successful in finding paths in test configurations, and the performance of the algorithms was fast enough for user interactivity up to a certain limit of grid cell sizes