10
10.0
Apr 24, 2021
04/21
by
Elahe Mohammadzadeh; Akbar Rezaei
texts
eye 10
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In this paper, we introduce the notion of commutator of two elements in a specific NeutroGroup. Then we define the notion of a NeutroNilpotentGroup and we study some of their properties. Moreover, we show that the intersection of two NeutroNilpotentGroups is a NeutroNilpotentGroup. Also, we show that the quotient of a NeutroNilpotentGroup is a NeutroNilpotentGroup. Specially, using NeutroHomomorphism we prove the NeutroNilpotentcy is closed with respect to homomorphic image.
37
37
Apr 24, 2021
04/21
by
Florentin Smarandache
texts
eye 37
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comment 0
In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.
17
17
Apr 24, 2021
04/21
by
Mohammad Hamidi; Florentin Smarandache
texts
eye 17
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This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCKalgebra.
18
18
Apr 24, 2021
04/21
by
F. Smarandache
texts
eye 18
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comment 0
In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that...
8
8.0
Apr 24, 2021
04/21
by
M.A. Ibrahim; A.A.A. Agboola
texts
eye 8
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comment 0
NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures.
20
20
Apr 24, 2021
04/21
by
Madeleine Al-Tahan; F. Smarandache; Bijan Davvaz
texts
eye 20
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comment 0
Starting with a partial order on a NeutroAlgebra, we get a NeutroStructure. The latter if it satisfies the conditions of NeutroOrder, it becomes a NeutroOrderedAlgebra. In this paper, we apply our new defined notion to semigroups by studying NeutroOrderedSemigroups. More precisely, we define some related terms like NeutrosOrderedSemigroup, NeutroOrderedIdeal, NeutroOrderedFilter, NeutroOrderedHomomorphism, etc., illustrate them via some examples, and study some of their properties.
13
13
Apr 24, 2021
04/21
by
A.A.A. Agboola
texts
eye 13
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comment 0
NeutroRings are alternatives to the classical rings and they are of different types. NeutroRings in some cases exhibit different algebraic properties, and in some cases they exhibit algebraic properties similar to the classical rings. The objective of this paper is to revisit the concept of NeutroRings and study finite and infinite NeutroRings of type-NR.
19
19
Apr 25, 2021
04/21
by
F. Smarandache; A. Rezaei; S. Mirvakilii
texts
eye 19
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As generalizations and alternatives of classical algebraic structures Florentin Smarandache has introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well-defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras the operations may be partially well-defined and the axioms partially true or respectively totally outerdefined and the axioms totally...
22
22
Apr 24, 2021
04/21
by
Madeleine Al-Tahan; Bijan Davvaz; Florentin Smarandache
texts
eye 22
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comment 0
Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structuresí operations and/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as...
18
18
Apr 24, 2021
04/21
by
A.A.A. Agboola; M.A. Ibrahim; E.O. Adeleke
texts
eye 18
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comment 0
The objective of this paper is to examine NeutroAlgebras and AntiAlgebras viz-a-viz the classical number systems.
13
13
Apr 24, 2021
04/21
by
Florentin Smarandache
texts
eye 13
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comment 0
In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.
12
12
Apr 24, 2021
04/21
by
Florentin Smarandache; Akbar Rezaei; Hee Sik Kim
texts
eye 12
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comment 0
In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CIalgebras are not BE-algebras.
14
14
Apr 24, 2021
04/21
by
A. Rezaei; F. Smarandache; S. Mirvakili
texts
eye 14
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comment 0
In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups (resp. neutrohypergroups). We investigate the property of anti-semihypergroups (resp. anti-hypergroups). We also give a new alternative of neutro-hyperoperations (resp. anti-hyperoperations), neutro-hyperoperation-sophications (resp. anti-hypersophications). Moreover, we show that these new concepts are different from classical concepts by several examples.
17
17
Apr 24, 2021
04/21
by
A.A.A. Agboola
texts
eye 17
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comment 0
In this paper, we are going to study a class of NeutroGroups of type-NG[1,2,4]. In this class of NeutroGroups, the closure law, the axiom of associativity and existence of inverse are taking to be either partially true or partially false for some elements; while the existence of identity element and axiom of commutativity are taking to be totally true for all the elements.
24
24
Apr 24, 2021
04/21
by
A.A.A. Agboola
texts
eye 24
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comment 0
The objective of this paper is to introduce the concept of NeutroRings by considering three NeutroAxioms (NeutroAbelianGroup (additive), NeutroSemigroup (multiplicative) and NeutroDistributivity (multiplication over addition)). Several interesting results and examples on NeutroRings, NeutroSubgrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms are presented. It is shown that the 1st isomorphism theorem of the classical rings holds in the class of NeutroRings.
22
22
Apr 24, 2021
04/21
by
Diego Silva JimÈnez; Juan Alexis Valenzuela Mayorga; Mara Esther Roja Ubilla
texts
eye 22
favorite 0
comment 0
In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that...
24
24
Apr 24, 2021
04/21
by
Akbar Rezaei; Florentin Smarandache
texts
eye 24
favorite 0
comment 0
In this paper, the concepts of Neutro-algebra and Anti-algebra are introduced, and some related properties and four theoremsare investigated. We show that the classes of Neutro-algebra and Anti-algebras are alternatives of the class of algebras.
20
20
Apr 24, 2021
04/21
by
A.A.A. Agboola
texts
eye 20
favorite 0
comment 0
The notion of AntiGroups is formally presented in this paper. A particular class of AntiGroups of type-AG[4] is studied with several examples and basic properties presented. In AntiGroups of type-AG[4], the existence of an inverse is taking to be totally false for all the elements while the closure law, the existence of identity element, the axioms of associativity and commutativity are taking to be either partially true, partially indeterminate or partially false for some elements
32
32
Apr 24, 2021
04/21
by
Florentin Smarandache
texts
eye 32
favorite 0
comment 0
We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.
24
24
Apr 24, 2021
04/21
by
A.A.A. Agboola
texts
eye 24
favorite 0
comment 0
The objective of this paper is to formally present the concept of NeutroGroups by considering three NeutroAxioms (NeutroAssociativity, existence of NeutroNeutral element and existence of NeutroInverse element). Several interesting results and examples of NeutroGroups, NeutroSubgroups, NeutroCyclicGroups, NeutroQuotientGroups and NeutroGroupHomomorphisms are presented.
13
13
Apr 24, 2021
04/21
by
Florentin Smarandache
texts
eye 13
favorite 0
comment 0
In all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations in science and in any domain of knowledge when an Axiom defined on a set may be only partially-true (and partially-false), that we call NeutroAxiom, or totally false that we call AntiAxiom. Therefore, we open for the first time in 2019 new fields of research called NeutroStructures and...
47
47
Apr 24, 2021
04/21
by
Florentin Smarandache
texts
eye 47
favorite 0
comment 0
In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras, also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures
19
19
Apr 23, 2021
04/21
by
Soumyadip Dhar; Malay K. Kundu
texts
eye 19
favorite 0
comment 0
37
37
Apr 25, 2021
04/21
by
Madeleine Al-Tahan
texts
eye 37
favorite 0
comment 0
In this talk, we firstly review some basic concepts related to neutrosophy. Also, we discuss NeutroAlgebra. Next, we present some of our results related to our new defined concept NeutroOrderedAlgebra and compare it to the well known concept of Ordered Algebra. Finally, we leave with some questions that open new research options in this field.
11
11
Apr 23, 2021
04/21
by
Muhammad Aslam
texts
eye 11
favorite 0
comment 0
16
16
Apr 23, 2021
04/21
by
O.H. Arif; Muhammad Aslam
texts
eye 16
favorite 0
comment 0
104
104
Nov 14, 2013
11/13
by
Daniel H. Rothman
texts
eye 104
favorite 0
comment 0
The chaotic phenomena of the Lorenz equations may be exhibited by even simpler systems.
Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics
Source: http://www.flooved.com/reader/1837
64
64
Nov 14, 2013
11/13
by
Tomasz S. Mrowka
texts
eye 64
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
Source: http://www.flooved.com/reader/2149
132
132
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 132
favorite 0
comment 0
Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics,...
Source: http://www.flooved.com/reader/2602
98
98
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 98
favorite 0
comment 0
Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics,...
Source: http://www.flooved.com/reader/2624
127
127
Nov 14, 2013
11/13
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
texts
eye 127
favorite 0
comment 0
Introduction: Before we try to solve higher order equations with discontinuous or impulsive input we need to think carefully about what happens to the solution at the point of discontinuity.
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs), Second...
Source: http://www.flooved.com/reader/1401
172
172
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 172
favorite 0
comment 0
Covariance of X and Y is de�ned as: ... Positive when both high or low in deviation
Topics: Maths, Statistics and Probability, Mathematics
Source: http://www.flooved.com/reader/1625
79
79
Nov 14, 2013
11/13
by
Scott Aaronson
texts
eye 79
favorite 0
comment 0
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1301
195
195
Nov 14, 2013
11/13
by
Albert R. Meyer
texts
eye 195
favorite 0
comment 0
We need to know one more property of planar graphs in order to prove that planar graphs are 5-colorable.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1709
92
92
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 92
favorite 0
comment 0
Topics: Physics, Classical Mechanics, Fluid Mechanics�, General Theory in Fluid Dynamics, Fluid Dynamics,...
Source: http://www.flooved.com/reader/2596
84
84
Nov 14, 2013
11/13
by
David Tong
texts
eye 84
favorite 0
comment 0
So far, we�ve only discussed strings propagating in �at spacetime. In this section we will consider strings propagating in di_erent backgrounds. This is equivalent to having di_erent CFTs on the world sheet of the string.
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...
Source: http://www.flooved.com/reader/3183
9
9.0
Apr 23, 2021
04/21
by
Muhammad Aslam
texts
eye 9
favorite 0
comment 0
53
53
Sep 26, 2014
09/14
by
Schmidt, Julius J; Lorenzen, Johan; Chatzikyrkou, Christos; Lichtinghagen, Ralf; Kielstein, Jan T
texts
eye 53
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This article is from BMC Pharmacology & Toxicology , volume 15 . Abstract Background: Lithium intoxication has potentially fatal neurologic and cardiac side effects. Extracorporeal removal can therefore be lifesaving. The dialysance of lithium is high as it is a small molecule. Comparable to its neighbor in the periodic table, sodium, its intracellular accumulation hampers its removal by renal replacement therapy, despite its favorable size. For this reason the combination of short...
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4172392
61
61
Sep 26, 2014
09/14
by
Sato, Hiroe; Kobayashi, Daisuke; Abe, Asami; Ito, Satoshi; Ishikawa, Hajime; Nakazono, Kiyoshi; Murasawa, Akira; Kuroda, Takeshi; Nakano, Masaaki; Narita, Ichiei
texts
eye 61
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comment 0
This article is from BMC Research Notes , volume 7 . Abstract Background: Multiple sclerosis is a relatively rare disease, and complications of multiple sclerosis and rheumatoid arthritis are much rarer. Since anti-tumor necrosis factor therapy increases exacerbations of multiple sclerosis, complications of demyelinating diseases contraindicate anti-tumor necrosis factor therapy. There have been few reports of anti-interleukin-6 receptor therapy for patients with rheumatoid arthritis...
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4171561
87
87
Sep 26, 2014
09/14
by
Verdegem, Dries; Moens, Stijn; Stapor, Peter; Carmeliet, Peter
texts
eye 87
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comment 0
This article is from Cancer & Metabolism , volume 2 . Abstract The stromal vasculature in tumors is a vital conduit of nutrients and oxygen for cancer cells. To date, the vast majority of studies have focused on unraveling the genetic basis of vessel sprouting (also termed angiogenesis). In contrast to the widely studied changes in cancer cell metabolism, insight in the metabolic regulation of angiogenesis is only just emerging. These studies show that metabolic pathways in endothelial...
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4171726
34
34
Apr 23, 2021
04/21
by
Muhammad Aslam; Nasrullah Khan; Ali Hussein AL-Marshadi
texts
eye 34
favorite 0
comment 0
134
134
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 134
favorite 0
comment 0
In this chapter we examine high-speed �ows of a viscous �uid. As a prelude, the limit ofinviscid �ows is brei�y discussed.
Topics: Physics, Classical Mechanics, Electromagnetism and Electromagnetic Radiation, Fluid Mechanics�,...
Source: http://www.flooved.com/reader/2585
114
114
Nov 14, 2013
11/13
by
Kiran S. Kedlaya
texts
eye 114
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comment 0
In this unit, we derive von Mangoldt�s formula estimating _(x) _ x in terms of the critical zeroes of the Riemann zeta function. This �nishes the derivation of a form of the prime number theorem with error bounds. It also serves as another good example of how to use contour integration to derive bounds on number-theoretic quantities; we will return to this strategy in the context of the work of Goldston-Pintz-Y�ld�r�m.
Topics: Maths, Algebra, Number Theory, Mathematics
Source: http://www.flooved.com/reader/2093
88
88
Nov 14, 2013
11/13
by
Kiran S. Kedlaya
texts
eye 88
favorite 0
comment 0
Topics: Maths, Number Theory, Mathematics
Source: http://www.flooved.com/reader/2100
102
102
Nov 14, 2013
11/13
by
K. Venkatram
texts
eye 102
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Topology and Metric Spaces, Geometry, Differential Geometry,...
Source: http://www.flooved.com/reader/1952
107
107
Nov 14, 2013
11/13
by
Emma Carberry
texts
eye 107
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Geometry, Differential Geometry, Inverse Function Theorem,...
Source: http://www.flooved.com/reader/1102
227
227
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 227
favorite 0
comment 0
Topics: Maths, Analysis and Calculus, Statistics and Probability, Measure Theory, Probability,...
Source: http://www.flooved.com/reader/1033
181
181
Nov 14, 2013
11/13
by
Andrew Snowden
texts
eye 181
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comment 0
In this paper, we �rst develop and prove a special case of the Hurewicz theorem. We then give a few results from the theory of the higher homotopy groups. Finally, we state the full form of the Hurewicz theorem (without proof). We discuss some applications throughout the paper.
Topics: Maths, Algebra, Topology and Metric Spaces, Mathematics
Source: http://www.flooved.com/reader/1114
130
130
Nov 14, 2013
11/13
by
Hung Cheng
texts
eye 130
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comment 0
In this lecture and the next two lectures, we�ll briefly review partial differential equations (PDEs). As PDEs are much more difficult to solve than ODEs, we shall start with the simplest of PDEs, those of the first order.
Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1336
110
110
Nov 14, 2013
11/13
by
Katrin Wehrheim
texts
eye 110
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comment 0
Topics: Maths, Analysis and Calculus, Topology and Metric Spaces, Analysis, Measure Theory, Cauchy...
Source: http://www.flooved.com/reader/1274
121
121
Nov 14, 2013
11/13
by
Hung Cheng
texts
eye 121
favorite 0
comment 0
Solutions expanded around an irregular singular point are distinctive in one aspect: they are usually in the form of an exponential function times a Frobenius series. Due to the factor of the exponential function, a solution near an irregular singular point behaves very differently from that near a regular singular point. It may blow up exponentially, or vanish exponentially, or oscillate wildly.
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs),...
Source: http://www.flooved.com/reader/1338
170
170
Nov 14, 2013
11/13
by
Abhinav Kumar
texts
eye 170
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comment 0
First, what is number theory? At the most basic level, it�s the study of the properties of the integers Z = {. . . , _2, _1, 0, 1, 2, . . . } or the natu-ral numbers N = {0, 1, 2, . . . }
Topics: Maths, Algebra, Number Theory, Mathematics
Source: http://www.flooved.com/reader/1118
114
114
Nov 14, 2013
11/13
by
Vera Mikyoung Hur
texts
eye 114
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comment 0
We give a comprehensive development of the theory of linear differential equations with constant coef�cients. We use the operator calculus to deduce the existence and uniqueness. We presents techniques for �nding a complete solution of the inhomogeneous equation from solu-tions of the homogeneous equation. We also give qualitative results on asymptotic stability.
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs),...
Source: http://www.flooved.com/reader/1562
81
81
Nov 14, 2013
11/13
by
Vera Mikyoung Hur
texts
eye 81
favorite 0
comment 0
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1538
114
114
Nov 14, 2013
11/13
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis
texts
eye 114
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comment 0
Our goal in this session is to derive formulas for solving both homo_geneous and inhomogeneous �rst order linear ODE�s. For the inhomoge_neous equations we will use what are called integrating factors.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1433
113
113
Nov 14, 2013
11/13
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis
texts
eye 113
favorite 0
comment 0
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1422
98
98
Nov 14, 2013
11/13
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
texts
eye 98
favorite 0
comment 0
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1445
139
139
Nov 14, 2013
11/13
by
Pavel Etingof
texts
eye 139
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comment 0
In this section, we begin a systematic development of representation theory of �nite groups.
Topics: Maths, Algebra, Representation Theory, Mathematics
Source: http://www.flooved.com/reader/1656
90
90
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 90
favorite 0
comment 0
Topics: Maths, Statistics and Probability, Mathematics
Source: http://www.flooved.com/reader/1635
168
168
Nov 14, 2013
11/13
by
Richard Melrose
texts
eye 168
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comment 0
I �rst discussed the de�nition of preHilbert and Hilbert spaces and proved Cauchy�s inequality and the parallelogram law.
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Functional...
Source: http://www.flooved.com/reader/1590
256
256
Nov 14, 2013
11/13
by
Albert R. Meyer
texts
eye 256
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comment 0
So far we focused on probabilities of events �that you win the Monty Hall game; that you have a rare medical condition, given that you tested positive; . . . . Now we focus on quantitative questions: How many contestants must play the Monty Hall game until one of them �nally wins? . . . How long will this condition last? How much will I lose playing 6.042 games all day? Random variables are the mathematical tool for addressing such questions.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1718
146
146
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 146
favorite 0
comment 0
Topics: Maths, Statistics and Probability, Mathematics
Source: http://www.flooved.com/reader/1644
477
477
Nov 14, 2013
11/13
by
Gilbert Strang
texts
eye 477
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comment 0
One theme of this book is the relation of equations to minimum principles. To minimize P is to solve P' = 0. There may be more to it, but that is the main point. This section is also the opening to control theory � the modern form of the calculus of variations. Its constraints are di_erential equations, and Pontryagin�s maximum principle yields solutions.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1687
177
177
Nov 14, 2013
11/13
by
Matthew Herman
texts
eye 177
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comment 0
We can now define an abstract root system in a Eucledian space.
Topics: Maths, Linear Algebra and Geometry, Linear Algebra, Mathematics
Source: http://www.flooved.com/reader/1661
97
97
Nov 14, 2013
11/13
by
Jared Speck
texts
eye 97
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comment 0
In this section, we will study (scalar-valued) functions _ on R^(1+n). They are sometimes called (scalar-valued) �elds on R^(1+n)
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Mathematics
Source: http://www.flooved.com/reader/1609
240
240
Nov 14, 2013
11/13
by
Albert R. Meyer
texts
eye 240
favorite 0
comment 0
Recursive data types play a central role in programming. From a mathematical point of view, recursive data types are what induction is about. Recursive data types are speci�ed by recursive de�nitions that say how to build something from its parts.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1708
107
107
Nov 14, 2013
11/13
by
Albert R. Meyer
texts
eye 107
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comment 0
We will start the chapter with a motivating example involving annuities. Figuring out the value of the annuity will involve a large and nasty-looking sum. We will then describe several methods for �nding closed forms for all sorts of sums, including the annuity sums. In some cases, a closed form for a sum may not exist and so we will provide a general method for �nding good upper and lower bounds on the sum (which are closed form, of course).
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1777
97
97
Nov 14, 2013
11/13
by
Jeff Viaclovsky
texts
eye 97
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Convergence almost everywhere. Lebesgue�s dominated conver_gence theorem (LDCT) in the case of almost everywhere.
Topics: Maths, Analysis and Calculus, Analysis, Integration, Mathematics
Source: http://www.flooved.com/reader/1783
168
168
Nov 14, 2013
11/13
by
Daniel Kleitman;Peter Shor
texts
eye 168
favorite 0
comment 0
We now explain the algorithm that Lempel and Ziv gave in a 1978 paper, and generally called LZ78. This is opposed to LZ77, an earlier algorithm which di_ered signi�cantly in the implementation details but is based on the same general idea. This idea is that if some text is not random, a substring that you see once is more likely to appear again than substrings you haven�t seen.
Topics: Maths, Algebra, Coding and Cryptography, Codes, Mathematics
Source: http://www.flooved.com/reader/1881
143
143
Nov 14, 2013
11/13
by
Daniel Kleitman;Peter Shor
texts
eye 143
favorite 0
comment 0
Unfortunately, the OCW notes on Kuratowski�s theorem seem to have several things substantially wrong with the proof, and the notes from Prof. Kleitman�s website are too vague to be able to deduce the proof from them. I�m just going to type in the OCW notes, changing things to make the proofs correct.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1880
109
109
Nov 14, 2013
11/13
by
Daniel H. Rothman
texts
eye 109
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comment 0
Summary Finally, we summarize the characteristics of dissipative systems: � Energy not conserved. � Irreversible. � Contraction of areas (volumes) in phase space.
Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics
Source: http://www.flooved.com/reader/1830
240
240
Nov 14, 2013
11/13
by
Daniel H. Rothman
texts
eye 240
favorite 0
comment 0
Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics
Source: http://www.flooved.com/reader/1836
186
186
Nov 14, 2013
11/13
by
Kiran S. Kedlaya
texts
eye 186
favorite 0
comment 0
We�re going to use the language of category theory freely. Fortunately, it�s easy to learn because it corresponds naturally to the way you (hopefully) already think about mathemat_ical objects. (I could give a reference, but in fact you should be �ne just looking these things up in Wikipedia.)
Topics: Maths, Linear Algebra and Geometry, Algebraic Geometry, Mathematics
Source: http://www.flooved.com/reader/2052
98
98
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 98
favorite 0
comment 0
Topics: Physics, Classical Mechanics, Fluid Mechanics�, General Theory in Fluid Dynamics, Fluid Dynamics,...
Source: http://www.flooved.com/reader/2607
71
71
Nov 14, 2013
11/13
by
Denis Auroux
texts
eye 71
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
Source: http://www.flooved.com/reader/2124
73
73
Nov 14, 2013
11/13
by
Tomasz S. Mrowka
texts
eye 73
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Differential Geometry, Geometry of Manifolds, Smooth Manifold,...
Source: http://www.flooved.com/reader/2132
85
85
Nov 14, 2013
11/13
by
Chiang C. Mei
texts
eye 85
favorite 0
comment 0
Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics,...
Source: http://www.flooved.com/reader/2623
140
140
Nov 14, 2013
11/13
by
Jerry Griffiths
texts
eye 140
favorite 0
comment 0
It is �nally appropriate to review a series of results which are related to the analysis of exact solutions describing the collision of plane waves in a �at background, which is the main subject of this book. The results described in this chapter di_er from those given in previous chapters in a variety of ways. A number of interesting results have been obtained using di_erent approaches, by considering the background in region I tobe non-�at, or by considering alternative gravitational...
Topics: Physics, Special Relativity, General Relativity and Gravitation, Classical General Relativity,...
Source: http://www.flooved.com/reader/2796
138
138
Nov 14, 2013
11/13
by
Peter Dourmashkin;Kate Scholberg
texts
eye 138
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comment 0
In this demo we measured the value of Young�s modulus for a copper wire. The setup is shown in the �gure (not to scale!).
Topics: Physics, Classical Mechanics, Continuum Mechanics of Solids�, Stress, Physics
Source: http://www.flooved.com/reader/3028
182
182
Nov 14, 2013
11/13
by
Joel Kamnitzer
texts
eye 182
favorite 0
comment 0
Topic: Maths
Source: http://www.flooved.com/reader/3400
244
244
Nov 14, 2013
11/13
by
Victor Flynn
texts
eye 244
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comment 0
These notes are modi�ed from previous versions (due to Neil Dummigan,Alan Lauder and Roger Heath-Brown) and have been recently revised by me. They draw mainly upon �A Classical Introduction to Modern Number Theory�, by Ireland and Rosen, and �Algebraic Number Theory�, by Stewart and Tall. While I take full responsibility for their current contents, considerable thanks are clearly due to Neil, Alan and Roger.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1060
116
116
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 116
favorite 0
comment 0
In this section we will make several connections between the Kantorovich-Rubinstein theorem and other classical objects. Let us start with the following classical inequality.
Topics: Maths, Analysis and Calculus, Statistics and Probability, Mathematics
Source: http://www.flooved.com/reader/1038
134
134
Nov 14, 2013
11/13
by
Dmitry Panchenko
texts
eye 134
favorite 0
comment 0
Topics: Maths, Analysis and Calculus, Statistics and Probability, Measure Theory, Probability, ?-Algebras,...
Source: http://www.flooved.com/reader/1035
133
133
Nov 14, 2013
11/13
by
Rodolfo R. Rosales
texts
eye 133
favorite 0
comment 0
When nonlinearities are "small" there are various ways one can exploit this fact - and the fact that the linearized problem can be solved exactly - to produce useful approximations to the solutions. We illustrate two of these techniques here, with examples from phase plane analysis: The Poincare-Lindstedt method and the (more exible) Two Timing method. This second method is a particular case of the Multiple Scales approximation technique, which is useful whenever the solution of a...
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Mathematics
Source: http://www.flooved.com/reader/1181
91
91
Nov 14, 2013
11/13
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
texts
eye 91
favorite 0
comment 0
De�nition: 1. The gain is de�ned to be the the ratio of the amplitude of the output sinusoid to the amplitude of the input sinusoid. 2. The phase lag is de�ned to be the angle by which the output sinusoid is shifted relative to the input sinusoid.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1417
163
163
Nov 14, 2013
11/13
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
texts
eye 163
favorite 0
comment 0
In this section we will compute the unit impulse response as the limit of the responses to these box functions.
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs),...
Source: http://www.flooved.com/reader/1392
107
107
Nov 14, 2013
11/13
by
Scott Aaronson
texts
eye 107
favorite 0
comment 0
Of course the real question is: can quantum computers actually do something more e_ciently than classical computers? In this lecture, we�ll see why the modern consensus is that they can.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1307
102
102
Nov 14, 2013
11/13
by
Jeff Viaclovsky
texts
eye 102
favorite 0
comment 0
In this course, we will mainly be concerned with the following problems: 1) Harmonic functions. 2) Heat equation. 3) Poisson Equation
Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1326
110
110
Nov 14, 2013
11/13
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis
texts
eye 110
favorite 0
comment 0
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs),...
Source: http://www.flooved.com/reader/1388
387
387
Nov 14, 2013
11/13
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
texts
eye 387
favorite 0
comment 0
We say an eigenvalue _1 of A is repeated if it is a multiple root of the characteristic equation of A; in our case, as this is a quadratic equation, the only possible case is when _1 is a double real root.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1424
138
138
Nov 14, 2013
11/13
by
Vera Mikyoung Hur
texts
eye 138
favorite 0
comment 0
We discuss various techniques for solving inhomogeneous linear differential equations.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
Source: http://www.flooved.com/reader/1539
94
94
Nov 14, 2013
11/13
by
Lawrence Baggett
texts
eye 94
favorite 0
comment 0
Abstract: We motivate our third definition of an integral over a curve by returning to physics. This definition is very much a real variable one, so that we think of the plane as R^2 instead of C. A connection between this real variable definition and the complex variable definition of a contour integral will emerge later.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1566
102
102
Nov 14, 2013
11/13
by
Richard Melrose
texts
eye 102
favorite 0
comment 0
So, recall the de�nitions of a Lebesgue integrable function on the line (forming the linear space L^1(R)) and of a set of measure zero E _ R. The �rst thing we want to show is that the putative norm on L^1 does make sense.
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Functional...
Source: http://www.flooved.com/reader/1588
80
80
Nov 14, 2013
11/13
by
Jeff Viaclovsky
texts
eye 80
favorite 0
comment 0
Lebesgue measurable sets (with �nite outer measure). Let A _ Rn and __(A) < � (A has �nite outer measure). Then we write that ... and de�ne measure of A to be ...
Topics: Maths, Analysis and Calculus, Analysis, Integration, Mathematics
Source: http://www.flooved.com/reader/1800
62
62
Nov 14, 2013
11/13
by
Tom Leighton
texts
eye 62
favorite 0
comment 0
This class will discuss several research problems that are related to the Internet. Each lecture will discuss How a particular Internet component or technology works today: Issues and problems with the current technology, Potential new lines of research, Formulation of concrete problems and solutions.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/2005
128
128
Nov 14, 2013
11/13
by
Michel X. Goemans
texts
eye 128
favorite 0
comment 0
Last lecture we covered matroid intersection, and de�ned matroid union. In this lecture we review the de�nitions of matroid intersection, and then show that the matroid intersection polytope is TDI. This is Chapter 41 in Schrijver�s book. Next we review matroid union, and show that unlike matroid intersection, the union of two matroids is again a matroid. This material is largely contained in Chapter 42 in Schrijver�s book. We leave testing independence in the union matroid for the next...
Topics: Maths, Optimization and Control, Statistics and Probability, Optimization, Probability,...
Source: http://www.flooved.com/reader/1926
105
105
Nov 14, 2013
11/13
by
Rahul Hariharan
texts
eye 105
favorite 0
comment 0
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/2006
171
171
Nov 14, 2013
11/13
by
Jonathan Kelner
texts
eye 171
favorite 0
comment 0
Today�s lecture covers three main parts: � Courant-Fischer formula and Rayleigh quotients � The connection of _2 to graph cutting � Cheeger�s Inequality
Topics: Maths, Linear Algebra and Geometry, Graph Theory, Optimization and Control, Vectors and Matrices,...
Source: http://www.flooved.com/reader/2019
75
75
Nov 14, 2013
11/13
by
Abhinav Kumar
texts
eye 75
favorite 0
comment 0
Topics: Maths, Linear Algebra and Geometry, Algebraic Geometry, Mathematics
Source: http://www.flooved.com/reader/2210
84
84
Nov 14, 2013
11/13
by
Richard M. Dudley
texts
eye 84
favorite 0
comment 0
Topics: Maths, Statistics and Probability, Statistics, Mathematics
Source: http://www.flooved.com/reader/2163
