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11	The University of Hong Kong DEPARTMENT OF MATHEMATICS MATH3302/MATH4302 Algebra II Suggested Solution to Assignment 4 In the following, E, F, K are fields. 1. (a) Prove that K Emb (K/F ) = F ⇔ for all u ∈ K − F , M Add to Reading List Source URL: hkumath.hku.hk Language: English - Date: 2015-03-31 04:58:08 Galois theory Algebraic number theory Group theory Field Normal extension Galois extension Separable extension Fundamental theorem of Galois theory Abstract algebra Algebra Field theory
12	FACTS YOU CAN USE To Prove That High-Skilled Immigration is Good for America’s Workforce and Economy Immigrants Create Jobs for U.S.-Born Workers • Add to Reading List Source URL: www.renewoureconomy.org Language: English - Date: 2015-04-27 14:41:29 Foreign relations of the United States Education United States visas Foreign worker STEM fields Visa Nursing shortage Optional Practical Training United States Immigration to the United States Human migration H-1B visa
13	P r o o f m ar k f o r des k t o p Cost-effectively safeguard the integrity of your documents and prove the authenticity of electronic records to clients, Add to Reading List Source URL: www.proofspace.com Language: English - Date: 2013-06-11 17:07:31 Ü Paperless office Public-key cryptography Business Security Environment Computer security Time Trusted timestamping
14	t he sin g u l a rit y \| specia l rep o rt Can Machines Be Conscious? Yes—and a new Turing test might prove it By Christof Koch and Giulio Tononi Add to Reading List Source URL: www.klab.caltech.edu Language: English - Date: 2008-06-06 23:10:51 Cognition Artificial intelligence Computational neuroscience Cognitive psychology Consciousness Artificial consciousness Integrated Information Theory Philosophical zombie Strong AI Cognitive science Mind Philosophy of mind
15	for C O U N S E L Safeguard the integrity of legal records and prove the authenticity of evidence to clients, auditors, and courts. Can you reliably prevail Add to Reading List Source URL: www.proofspace.com Language: English - Date: 2013-06-11 17:07:41 Time Civil law Notary Electronic documents Aesthetics Trusted timestamping Tamper-evident Timestamp Authentication Cryptography Security Packaging
16	t he sin g u l a rit y \| specia l rep o rt Can Machines Be Conscious? Yes—and a new Turing test might prove it By Christof Koch and Giulio Tononi Add to Reading List Source URL: www.klab.caltech.edu Language: English - Date: 2008-06-06 23:10:51 Cognition Artificial intelligence Computational neuroscience Cognitive psychology Consciousness Artificial consciousness Integrated Information Theory Philosophical zombie Strong AI Cognitive science Mind Philosophy of mind
17	GORENSTEIN INJECTIVE, PROJECTIVE AND FLAT (PRE)COVERS E. ENOCHS, S. ESTRADA and A. IACOB Abstract. We prove that if the ring R is left noetherian and if the class GI of Gorenstein injective modules is closed under filtra Add to Reading List Source URL: www.kurims.kyoto-u.ac.jp Language: English - Date: 2014-05-23 08:15:45 Homological algebra Ring theory Commutative algebra Algebraic geometry Injective module Gorenstein ring Flat module Finitely-generated module Projective module Abstract algebra Algebra Module theory
18	BLOW-UP SOLUTIONS ON A SPHERE FOR THE 3D QUINTIC NLS IN THE ENERGY SPACE JUSTIN HOLMER AND SVETLANA ROUDENKO Abstract. We prove that if u(t) is a log-log blow-up solution, of the type studied by Merle-Rapha¨el [14], to Add to Reading List Source URL: www.math.brown.edu Language: English - Date: 2010-07-08 10:13:52 Hilbert transform Signal processing Fourier transform Symbol Mathematical analysis Integral transforms Functional analysis
19	Boundary regularity results for variational integrals Lisa Beck∗ Abstract: We prove partial H¨ older continuity for the gradient of minimizers u ∈ W 1,p (Ω, RN ), Ω ⊂ Rn a bounded domain, of variational integr Add to Reading List Source URL: www.math.uni-augsburg.de Language: English - Date: 2014-01-20 11:25:26 Calculus Fourier analysis Fractional calculus Connection Sobolev inequality Calculus of variations Harmonic function Ordinal number Symbol Mathematical analysis Mathematics Sobolev spaces
20	Important Change in International Land and Sea Travel Document Procedures Effective January 31, 2008, U.S. and Canadian citizens ages 19 and older should no longer expect that they will be able to prove identity and citi Add to Reading List Source URL: www.peacebridge.com Language: English - Date: 2014-08-29 16:28:29 Public records Canada–United States relations Borders of the United States Passports Radio-frequency identification Western Hemisphere Travel Initiative Identity document Canadian passport United States passport Government Security United States Department of Homeland Security

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