Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions

Inverse problem for Dirac systems with locally square summable potentials and rectangular Weyl functions is solved. For that purpose we use a new result on the linear similarity between operators from a subclass of triangular integral operators and the operator of integration.Comment: Some of the main results from [16] (A. Sakhnovich, Inverse Problems 18 (2002), 331--348) and the submitted to ArXiv papers[2] and [5] (see arXiv:0912.4444 and arXiv:1106.1263) are generalized for the case of the locally square-summable potentials and rectangular Weyl function

Simon Grant, Monti, Martin Osherson, Daniel

The classical theory of preference among monetary bets represents people as expected utility maximizers with nondecreasing concave utility functions. Critics of this account often rely on assumptions about preferences over wide ranges of total wealth. We derive a prediction of the theory that bears on bets at any fixed level of wealth, and test the prediction behaviorally. Our results are discrepant with the classical account. Competing theories are also examined in light of our data.

Analysis techniques for complex-field radiation pattern measurements

Complex field measurements are increasingly becoming the standard for state-of-the-art astronomical instrumentation. Complex field measurements have been used to characterize a suite of ground, airborne, and space-based heterodyne receiver missions [1], [2], [3], [4], [5], [6], and a description of how to acquire coherent field maps for direct detector arrays was demonstrated in Davis et. al. 2017. This technique has the ability to determine both amplitude and phase radiation patterns from individual pixels on an array. Phase information helps to better characterize the optical performance of the array (as compared to total power radiation patterns) by constraining the fit in an additional plane [4]. Here we discuss the mathematical framework used in an analysis pipeline developed to process complex field radiation pattern measurements. This routine determines and compensates misalignments of the instrument and scanning system. We begin with an overview of Gaussian beam formalism and how it relates to complex field pattern measurements. Next we discuss a scan strategy using an offset in z along the optical axis that allows first-order optical standing waves between the scanned source and optical system to be removed in post-processing. Also discussed is a method by which the co- and cross-polarization fields can be extracted individually for each pixel by rotating the two orthogonal measurement planes until the signal is the co-polarization map is maximized (and the signal in the cross-polarization field is minimized). We detail a minimization function that can fit measurement data to an arbitrary beam shape model. We conclude by discussing the angular plane wave spectral (APWS) method for beam propagation, including the near-field to far-field transformation

Flyer: University Lecture Series Featuring Dr. Jacqueline Wexler

“The Emerging Nation of Women”-- Dr. Jacqueline Wexler -- University Auditorium Wednesday May 29 (no year) 8:00PM, No Admission Charge -- Presented By University Public Functions Committee. Dr. Jacqueline Wexler -- As Sister Jacqueline, she developed Webster College’s Dept. of Education into a pioneering Teacher -Training and Curriculum Research Center - As a member of LBJ’s Educational Advisory council, she helped set up Project Head Start – As President of New York’s Hunter College, she speaks for the role of women in higher education and in the nation today

The Reachability Problem for Petri Nets is Not Elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.Comment: Final version of STOC'1

Language Functions Used by the Main Character in Sherlock Holmes II: a Game of Shadows Movie

This research focused on language functions used by the main character in “Sherlock Holmes” movie. The aims were to find the use of language functions and describe the dominant types of language functions used in “Sherlock Holmes” movie. The data were the dialogue of the main character in “Sherlock Holmes” movie in the first forty minutes of the movie. The research was conducted by using descriptive qualitative research. The findings show that there are six types of language functions used by the main character in “Sherlock Holmes” movie. They are expressive, directive, referential, metalinguistic, phatic, and poetic. The most dominant type of language function is metalinguistic. It means that the main character conveys code analysis by asking questions to the people so that he might invent clue for the sake of his investigation

Busemann functions and barrier functions

We show that Busemann functions on a smooth, non-compact, complete, boundaryless, connected Riemannian manifold are viscosity solutions with respect to the Hamilton-Jacobi equation determined by the Riemannian metric and consequently they are locally semi-concave with linear modulus. We also analysis the structure of singularity sets of Busemann functions. Moreover we study barrier functions, which are analogues to Mather's barrier functions in Mather theory, and provide some fundamental properties. Based on barrier functions, we could define some relations on the set of lines and thus classify them. We also discuss some initial relations with the ideal boundary of the Riemannian manifold.Comment: comments are welcome

Heun functions versus elliptic functions

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard's generalization of Floquet's theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integral representation which, at level one, is shown to be equivalent to their elliptic form.Comment: Communication at the International Conference on Difference Equations, Special Functions and Applications, Munich, 25-30 july 2005, latex 2e, 20 page

Lyapunov functions via Whitney's size functions

In this paper we present a technique for constructing Lyapunov functions based on Whitney's size functions. Applications to asymptotically stable equilibrium points, isolated sets, expansive homeomorphisms and continuum-wise expansive homeomorphisms are given