We present two symmetric function operators H qt 3 and H qt 4 that have the property H qt 3 H (2 a 1 b) [X; q, t] = H (32 a 1 b) [X; q, t] and H qt 4 H (2 a 1 b) [X; q, t] = H (42 a 1 b) [X; q, t]. These operators are generalizations of the analogous operator H qt 2 and also have expressions in terms of Hall-Littlewood vertex operators. We also discuss statistics, a µ (T) and b µ (T), on standa...

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When regular steam ferry service between Brooklyn and Manhattan began in 1814, the first commuter suburb became possible. 1 Suburbs continued to develop slowly but steadily during the 19th and early 20th centuries, thanks to transportation advances such as commuter trains and streetcars, the innovations of early real estate developers, and the urge to live in pastoral tranquility rather than in...

Time-varying topological simplifications of the space of votes in the US House of Representatives (US HoR) display several interesting features unavailable with classical methods of machine learning. In this paper we demonstrate how a recently developed topological simplification method, MAPPER, can detect changes in collaboration structures within the US HoR over time.

Liver weight and function also are often used as the “canary in the mine” to test for adverse effects of chemical compounds and drugs. The largest single gland in the body and the secondlargest organ, the liver filters about a quart of blood every minute, detoxifying blood by filtering toxins and other chemicals from it. When possible, it converts toxics to less harmful chemicals through variou...

................................................................................................................................... v CHAPTER 1 GENERAL INTRODUCTION ................................................................................ 1 1.1 Background ........................................................................................................................... 1 1.2 Moti...

directly onto the hands, which were subsequently scrubbed, it would be improbable that " q u e n c h i n g " of activity would be an issue for concern. Regarding concern # 3 , single plates were not used, rather the solutions were plated in triplicate and a mean value used. The dilution fortunately did inactivate the formulation, but it also provided a comfortable number of colonies per plate f...

Data adaptation is an essential system component in a wide variety of application areas. Adaptation is performed to manage data in response to limited resources and changing system conditions. Recent research has led to the development of general models for adaptive systems, including our own general framework for multidimensional adaptation. In this article, we review our framework, which dist...

A coupled KdV system with a free parameter proposed by Nutku and Og̃uz is considered. It is shown that the system passes the WTC’s Painlevé test for arbitrary value of the parameter. A further analysis yields that the parameter can be scaled away and the system can be decoupled. Soliton or integrable equations are those systems which have rich structures, such as infinite number of conservation ...

Let A = (aj,k)j,k≥1 be a non-negative matrix. In this paper, we characterize those A for which ‖A‖E,F are determined by their actions on decreasing sequences, where E and F are suitable normed Riesz spaces of sequences. In particular, our results can apply to the following spaces: lp, d(w, p), and lp(w). The results established here generalize the corresponding ones given by Bennett in Quart. J...