We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths.

The study aims to understand the underlying factor why McDonald's customers return despite previous failure customer experiences. Why do customers come back to the company that contributes to the former dissatisfaction? McDonald's attempt to maintain unceasing purposeful emergence fail at the local level, where the customer contact occurs. McDonald's offerings and customers' bounded rationality results in that customers are satisfied with an "ok" experience, which adds to their low expectations of McDonalds. This makes clear that McDonald's does not have to make an effort through constant adaptation at the local level to achieve a "great" level of satisfaction. Because the customer is satisfied with an "ok" experience, and not require more to return to McDonalds. If you can lower your customers' expectations so much that they do not care about the previous failure customer experiences, the company's competitive invincible, even without continuous adjustment.

This thesis is an exposition of spectral theory for bounded operators on Hilbert space. Detailed proofs are given for the functional calculus, the multiplication operator, and the projection-valued measure versions of the spectral theorem for self-adjoint bounded operators. These theorems are then generalized to finite sequences of self-adjoint and commuting bounded operators. Finally, normal bounded operators are discussed, as a particular case of the generalization.

The notion that corporations would voluntarily devote resources to serve non-shareholder interests seems to contradict the purpose of commerce. Yet, corporate social responsibility ranks among the most prominent aspects of contemporary capitalism, reaching – in the words of one author – a point of nearly universal adoption among businesses. Over four decades of empirical testing has provided no incontrovertible evidence to support the belief that businesses benefit, even in the long run, from responsible behaviour. Peculiarly, then, it appears that corporations are defying the logic of competitive markets by investing in CSR en masse without an established business case for doing so. Inspiring the work is a research question rooted in the observation of a counter-intuitive: if not profit, in every circumstance, what is turning the attention of nearly every major corporation away from their bottom line and towards social interests? The thesis explores what other factors may lay behind the business community’s curious adoption of CSR, including a new hypothesis that corporate leaders may be diverging from the normative ideal of rational choice and following boundedly-rational patterns of behaviour. It argues that CSR is a form of risk-averse corporate behaviour from a private sector that has seen tremendous growth and gain since the end of the Second World War.

This thesis has two parts. The first part deals with some questions in amenability. We show that for a Banach algebra A with a bounded approximate identity, the amenability of the projective tensor product of A with itself, the amenability of the projective tensor product of A with A^op and the amenability of A are equivalent. Also if A is a closed ideal in a commutative Banach algebra B, then the (weak) amenability of the projective tensor product of A and B implies the (weak) amenability of A. Finally, we show that if the Banach algebra A is amenable through multiplication π then is also amenable through any multiplication ρ such that the norm of π-ρ is less than 1/( 11). The second part deals with questions in generalized notions of amenability such as approximate amenability and bounded approximate amenability. First we prove some new results about approximately amenable Banach algebras. Then we state a characterization of approximately amenable Banach algebras and a characterization of boundedly approximately amenable Banach algebras. Finally, we prove that B(l^p (E)) is not approximately amenable for Banach spaces E with certain properties. As a corollary of this part, we give a new proof that B(l^2) is not approximately amenable.

This thesis has two parts. The first part deals with some questions in amenability. We show that for a Banach algebra A with a bounded approximate identity, the amenability of the projective tensor product of A with itself, the amenability of the projective tensor product of A with A^op and the amenability of A are equivalent. Also if A is a closed ideal in a commutative Banach algebra B, then the (weak) amenability of the projective tensor product of A and B implies the (weak) amenability of A. Finally, we show that if the Banach algebra A is amenable through multiplication π then is also amenable through any multiplication ρ such that the norm of π-ρ is less than 1/( 11). The second part deals with questions in generalized notions of amenability such as approximate amenability and bounded approximate amenability. First we prove some new results about approximately amenable Banach algebras. Then we state a characterization of approximately amenable Banach algebras and a characterization of boundedly approximately amenable Banach algebras. Finally, we prove that B(l^p (E)) is not approximately amenable for Banach spaces E with certain properties. As a corollary of this part, we give a new proof that B(l^2) is not approximately amenable.

Thesis (M.S.)--Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaf 41).

Techn. University, Diss., 2003--Kaiserslautern.

abstract: Swarms of animals, fish, birds, locusts etc. are a common occurrence but their coherence and method of organization poses a major question for mathematics and biology.The Vicsek and the Attraction-Repulsion are two models that have been proposed to explain the emergence of collective motion. A major issue for the Vicsek Model is that its particles are not attracted to each other, leaving the swarm with alignment in velocity but without spatial coherence. Restricting the particles to a bounded domain generates global spatial coherence of swarms while maintaining velocity alignment. While individual particles are specularly reflected at the boundary, the swarm as a whole is not. As a result, new dynamical swarming solutions are found. The Attraction-Repulsion Model set with a long-range attraction and short-range repulsion interaction potential typically stabilizes to a well-studied flock steady state solution. The particles for a flock remain spatially coherent but have no spatial bound and explore all space. A bounded domain with specularly reflecting walls traps the particles within a specific region. A fundamental refraction law for a swarm impacting on a planar boundary is derived. The swarm reflection varies from specular for a swarm dominated by kinetic energy to inelastic for a swarm dominated by potential energy. Inelastic collisions lead to alignment with the wall and to damped pulsating oscillations of the swarm. The fundamental refraction law provides a one-dimensional iterative map that allows for a prediction and analysis of the trajectory of the center of mass of a flock in a channel and a square domain. The extension of the wall collisions to a scattering experiment is conducted by setting two identical flocks to collide. The two particle dynamics is studied analytically and shows a transition from scattering: diverging flocks to bound states in the form of oscillations or parallel motions. Numerical studies of collisions of flocks show the same transition where the bound states become either a single translating flock or a rotating (mill). / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2015

We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths. / Science, Faculty of / Computer Science, Department of / Graduate