Spherical trigonometry Spherical trigonometry is that branch of spherical geometry which deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy‚ geodesy and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics
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1. (a) Let A be the set of all 2 × 2 matrices of the form ‚ where a and b are real numbers‚ and a2 + b2 0. Prove that A is a group under matrix multiplication. (10) (b) Show that the set: M = forms a group under matrix multiplication. (5) (c) Can M have a subgroup of order 3? Justify your answer. (2) (Total 17 marks) 3. (a) Define an isomorphism between two groups (G‚ o) and (H‚ •). (2) (b) Let e and e be the identity elements of groups G and H respectively. Let f be
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path‚ and the length of a longest increasing subsequencee in a random permutation. In this introduction‚ I will survey some of the work inn the area and describe my results. Furthermore I will explain how all three subjects fit intoo the framework of random walks in stochastic surroundings. Section 1 is dedicated to reinforcedd random walks. Section 2 describes scenery reconstruction problems. Section 33 deals with random permutations and explains the connection with up-right paths in a Poissoniann field
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them. According to the planners ‘gridded’ is what is desired. It also describes layout of the city which is very boxed in. In the following line the phrase “permutation of possibilities” suggests that there are various different methods to make the cities perfect and the alliteration of the letter ‘P’ also show the endlessness of the permutation of possibilities. In the third line which is “The buildings are in alignment with the road” reinforces the image of the very planned environment and urban
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Asymptotes‚ Standard Hyperbola Equation for a Hyperbola Solving a Rational Expression Using Exponents‚ Solving a Rational Expression Rational Functions from a Graph Binomial Theorem Expansion Binomial Theorem Combinations and Combinations‚ Permutation Permutations Points 3 The
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Breaking 104 bit WEP in less than 60 seconds Erik Tews‚ Ralf-Philipp Weinmann‚ and Andrei Pyshkin <e tews‚weinmann‚pyshkin@cdc.informatik.tu-darmstadt.de> TU Darmstadt‚ FB Informatik Hochschulstrasse 10‚ 64289 Darmstadt‚ Germany Abstract. We demonstrate an active attack on the WEP protocol that is able to recover a 104-bit WEP key using less than 40‚000 frames with a success probability of 50%. In order to succeed in 95% of all cases‚ 85‚000 packets are needed. The IV of these packets can be randomly
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COURSE SYLLABUS SICS 1533: FOUNDATIONS OF COMPUTER SCIENCE "Whatever you vividly imagine‚ ardently desire‚ sincerely believe and enthusiastically act upon must inevitably come to pass!" Paul J. Meyer a "To be successful‚ you must decide exactly what you want to accomplish‚ then resolve to pay the price to get it." - Bunker Hunt b [Academic Year / Semester] 2013 / 2014‚ First Semester [Class Location] City Campus‚ Computer Lab [Class Meeting Time(s)] (Depending
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The Mean and Median: Measures of Central Tendency The Mean and the Median The difference between the mean and median can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds‚ 100 pounds‚ 130 pounds‚ 140 pounds‚ and 150 pounds. To find the median‚ we arrange the observations in order from smallest to largest value. If there is an odd number of observations‚ the median is the middle value. If there is an even number of observations
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Graphs‚ Groups and Surfaces 1 Introduction In this paper‚ we will discuss the interactions among graphs‚ groups and surfaces. For any given graph‚ we know that there is an automorphism group associated with it. On the other hand‚ for any group‚ we could associate with it a graph representation‚ namely a Cayley graph of presentations of the group. We will first describe such a correspondence. Also‚ a graph is always embeddable in some surface. So we will then focus on properties of graphs
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adjustment in the property of genes. In the sequencing operators‚ it only makes adjustment in the process of parent genes. The major issue of application of crossover or mutation with the operation scheduling is the precedence constraints. The permutation of certain work‚ which should be completed before the next step‚ is to start. In the genetic modification of the human body‚ there is always the requirement of complete gene structure (guanine-cytosine and adenine-thymine) to build the whole structure
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