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    Topology

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    Topology The two main figures of Topology, the spheroid and the torus. Shown together like this, they create the symbol for the sun in ancient times (2, 1). The field of mathematics encompasses many different sub-fields which have been studied and researched for a very long time. One of the most intriguing divisions of mathematics is topology. Topology, the mathematical study of the properties of objects which are preserved through deformations, twistings, and stretchings (4, 1), is rooted far

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    tessellations. This brings me to my research question: how does Maurits Cornelis Escher’s Regular Division of the Plane with Birds relate to the tiling view of the torus? Tessellations and the torus are related to mathematics in the areas of geometry, topology, and the geometry of space. “A regular tiling of polygons (in two dimensions), polyhedras (three dimensions), or polytopes (n dimensions) is called a tessellation.” (Weisstein, Eric W.). Tessellations, or regular divisions of the plane, cover the

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    Differential Scientists

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    Differential Scientists If at a social gathering a man or woman with a nicely tucked in shirt and shoes that do not quite match their outfit regales listeners with the musical version of the quadratic formula (set to the tune of “Jingle Bells”), chances are that that person is either a mathematician or a physicist. But how does one know whether the clever soul selflessly sharing their dry wit studies numbers or physical science? Does it even matter? Are not the words “physicist” and “mathematician”

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    Maxwell Relations

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    (1-1)     U = U(S, V, XI) In system of constant mass and composition, whose work can be expressed only in terms of its PV properties, there are no X’s and U is changed only by reversible heat and P dV work. Therefore (1-2) dU = T dS – P dV. The differential of the accumulated internal energy in a fixed-composition, P dV – work system is. = dH = dU + d(PV) (1-3)      = dU + P dV + V dP. Substituting equation (1-2) in equation (1-3), we obtain (1-4)                         dH = T dS + V dP. From the

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    The Seven Bridges of Königsberg

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    of the ancient city of Königsberg posed a famous and almost problematic challenge a few centuries ago. But this isn’t just about the math problem; it’s also a story about a famous Swiss mathematician named Leonhard Euler who founded the study of topology and graph theory by solving this problem. The effects of this problem have lasted centuries, and have helped develop several parts of our understanding of mathematics. We don’t hear too much about Euler, but he is one of the most important and influential

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    in 4-dimensional space. Brouwer was a Dutch mathematician who founded mathematical intuitionism, which is a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws, and whose work completely transformed topology which is the study of the most basic properties of geometric surfaces and configurations. The life of Brouwer is easily summarized. His upbringing was entirely uneventful. Luitzen Egbertus Jan Brouwer was born on February 27, 1881 in Overschie, Amsterdam

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    Ip History

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    Task Force (IETF) to handle all of these problems and was first presented on July 25, 1994 in Toronto. Thou structurally it is very different from IPv4; it still incorporates all the successful features of IPv4 like its ability to adapt to many topologies or technologies at the same time. IPv6 is increasing address format from 32 bits to 128 bits. This increase gave 340,282,366,920,938,463,463,374,607,431,768,211,456 addresses (should be more that the packet since switching the paths for each packet

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    With economic decline in full effect, the city of Anderson is on track to become a ghost town. Anderson is located in Northern California, 150 miles north of Sacramento, and a 10-minute drive to Redding. The primary source of the problem is in Anderson’s Downtown which is defined as I-5 to 273 and North Street to Balls Ferry (See Reference 1). Nearby attractions include the Sacramento River, Turtle Bay Exploration Park, and the Mt Shasta Mall (Things Web). However, all the main attractions are found

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    Differential Effects of American Destabilization Policy in Chile in the 1970s and Cuba in the 1990s Just three years after taking office in 1970, Chile’s military removed the leftist President Salvador Allende from power. In Cuba, nearly forty years after his ascension to power in 1959, Fidel Castro continues to control a communist regime. In Chile in the early 1970s and in Cuba in the early 1990s, the United States exasperated severe economic crises. In addition, the United States attempted

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    Differential Association

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    Sutherland’s Differential Association Born August 13, 1883 in Gibbon, Nebraska, Edwin H. Sutherland grew up and studied in Ottawa, Kansas, and Grand Island, Nebraska. After receiving his B.A degree from Grand Island College in 1904, he taught Latin, Greek, History, and shorthand for two years at Sioux Falls College in South Dakota. In 1906 he left Sioux Falls College and entered graduate school at the University of Chicago from which he received his doctorate. (Gaylord, 1988:7-12) While attending

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    Topology

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    Topology Topology is the study of those properties of geometric figures that are unchanged when the shape of the figure is twisted, stretched, shrunk, or otherwise distorted without breaking. It is sometimes referred to as "rubber sheet geometry" (West 577). Topology is a basic and essential part of any post school mathematics curriculum. Johann Benedict Listing introduced this subject, while Euler is regarded as the founder of topology. Mathematicians such as August Ferdinand Möbius, Felix

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    Bernard Tschumi was a one of the few architects that connected with the people and essential focused on the inhabitants. He did not care how you should inhabit it, but what you experience from it. These experiences essentially become stories of events that are eventually retold events. Tschumi argues that these events or in other words sequences that establish a memory of the proceeding frame or space. These sequences often tell a story or follow a scenario. The architecture itself becomes part of

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    Frequency Data

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    As a student of Saint Leo, it is our responsibility to uphold and utilize our core values. The core vale of “Excellence” states as follows, “All of us, individually and collectively, work hard to ensure that our students develop the character, learn the skills, and assimilate the knowledge essential to become morally responsible leaders” (Florida Catholic University). Using and creating opinions on data leaves one vulnerable to data fraud and other unethical qualms. In order to uphold the integrity

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    Mesh, Bus, Ring and Star Topologies Mesh A mesh topology typically refers to a Wide Area Network where there are multiple paths connecting multiple sites. A router is used to search multiple paths and determine the best path for the data. Routes are determined by least cost, time of day and performance. A three or four site mesh network is relatively easy to create, whereas it is impractical to set up a mesh network of 100 sites or nodes. Mesh networks are used in Wide Area Networks (WANs) where

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    Topology

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    Topology Topology is a modern branch of geometry. It has been called qualitative geometry because instead of thinking about the traditional characteristics of an object (like angles, length, etc.), topologists study features that can’t be altered by stretching, twisting or shrinking the object. After any alteration all points in the object that were connected must still be connected and all points separated by a hole must remain separated. Topology also attempts to explain objects that cannot

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    The Seven Bridges of Königsberg

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    Around the date 1763, a problem arose in Königsberg, Germany (Diestel). This problem began with a few curious citizens but soon spread to scientists and other intellects, and eventually became known as the Königsberg Bridge Problem. The town of Königsberg was cut into four separate land masses by the river Pregel (Green). At the time, Königsberg was a large trading city, valuable because of its position on the river. The prosperity of the city allowed the people to build seven bridges so citizens

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    Mr. McCoy’s testimony revealed that his first issue is regarding the custodial parent (CP), Sabrina Durant Hawthorne. He stated the CP has not had his daughter, Daisha Durant, since she was three years old. He stated he mailed the court order that stated that the child support was to stop to the DHR. He stated he received a garnishment from his bank account and did not understand why. He stated that he called Child Support and was told that he owed the CP $3,000.00; he did not understand why

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    A Kantian Interpretation of Demonstrative Reference ABSTRACT: According to Kant, we refer to what is out there in the world by performing a demonstrative act, like pointing at an object with a finger. A Kantian mode of demonstrative reference is characterized by the existence of a real, 2-placed affective relation between an intuiting subject and the referent. Parsons suggests that Kantian intuition is both singular and immediate, and immediacy demands an object of intuition to be present, a condition

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    Topology

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    Topology Mathematics is a field so vast and diverse that it is impossible to be an expert in all areas. It is also a field that is constantly evolving and branching outward. The field of topology is one of the newest intensively studied branches of mathematics. “A simple way to describe topology is as rubber sheet geometry” [2]. “Topology is an offshoot of geometry that originated during the 19th century and that studies those properties an object retains under deformation - specifically

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    <a href="http://philosophos.tripod.com">http://philosophos.tripod.com The problem of continuum versus discreteness seems to be related to the issue of infinity and finiteness. The number of points in a line served as the logical floodgate which led to the development of Set Theory by Cantor at the end of the 19th century. It took almost another century to demonstrate the problematic nature of some of Cantor's thinking (Cohen completed Godel's work in 1963). But continuity can be finite and the connection

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