Inductive reasoning
... 2-1 Make Conjectures When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclu ...
... 2-1 Make Conjectures When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclu ...
Trees and amenable equivalence relations
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Unit F: Quadrilaterals (1.6, 5.3-5.7)
... □ I will explain and use the relationship between the nonvertex angles of a kite. □ I will explain and use the relationships formed by the diagonals of a kite. □ I can apply the properties of a trapezoid to solve problems. □ I will explain and use the relationships between the angles of trapezoids a ...
... □ I will explain and use the relationship between the nonvertex angles of a kite. □ I will explain and use the relationships formed by the diagonals of a kite. □ I can apply the properties of a trapezoid to solve problems. □ I will explain and use the relationships between the angles of trapezoids a ...
Belief Propagation in Monoidal Categories
... categories means those word problems can be reduced to e.g. graph isomorphism [DK13], and produces normal forms by word7→graph7→word. Hence the word problem for the free closed category and free compact closed category over a finite tensor scheme are in LOGSPACE and P [Luk82] respectively. Adding ad ...
... categories means those word problems can be reduced to e.g. graph isomorphism [DK13], and produces normal forms by word7→graph7→word. Hence the word problem for the free closed category and free compact closed category over a finite tensor scheme are in LOGSPACE and P [Luk82] respectively. Adding ad ...
Ch 2 Review SG - Miss S. Harvey
... 7. Jessica noticed a pattern when dividing these numbers by 4: 53, 93, 133. Determine the pattern and make a conjecture. a. When the cube of an odd number that is 1 more than a multiple of 4 is divided by 4, the decimal part of the result will be .75. b. When the cube of an odd number that is 1 less ...
... 7. Jessica noticed a pattern when dividing these numbers by 4: 53, 93, 133. Determine the pattern and make a conjecture. a. When the cube of an odd number that is 1 more than a multiple of 4 is divided by 4, the decimal part of the result will be .75. b. When the cube of an odd number that is 1 less ...
THE INVERSE PROBLEM OF GALOIS THEORY 1. Introduction Let
... associated embedding problems of the first and second kind. The obstructions are interpreted as elements of the groups H 1 , H 2 , Ext1 and Ext2 . This brought a number of new results or new proofs of well-known facts, e.g. the second Kochendörffer reduction theorem, which states that every embeddi ...
... associated embedding problems of the first and second kind. The obstructions are interpreted as elements of the groups H 1 , H 2 , Ext1 and Ext2 . This brought a number of new results or new proofs of well-known facts, e.g. the second Kochendörffer reduction theorem, which states that every embeddi ...
the usual castelnuovo s argument and special subhomaloidal
... subvariety X ⊂ Pr . Special (sub)homaloidal systems of quadrics deserved great interest. Well known examples are given by quadrics through a rational normal curve of degree 4 (general representation of G(1, 3), see [17], [18]), by quadrics through a normal elliptic quintic curve (quadro-cubo transfo ...
... subvariety X ⊂ Pr . Special (sub)homaloidal systems of quadrics deserved great interest. Well known examples are given by quadrics through a rational normal curve of degree 4 (general representation of G(1, 3), see [17], [18]), by quadrics through a normal elliptic quintic curve (quadro-cubo transfo ...
conjecture. - Nutley Public Schools
... Show that the conjecture is false by finding a counterexample. The monthly high temperature in Abilene is never below 90°F for two months in a row. Monthly High Temperatures (ºF) in Abilene, Texas ...
... Show that the conjecture is false by finding a counterexample. The monthly high temperature in Abilene is never below 90°F for two months in a row. Monthly High Temperatures (ºF) in Abilene, Texas ...
A refinement of the Artin conductor and the base change conductor
... then de Shalit’s recipe [CY01, A1.9] shows that c(T ) = cGal (T̂ ), where c(T ) is the classical base change conductor of T , which is defined in terms of algebraic Néron models, and where cGal (T̂ ) is the base change conductor of T̂ , defined Galois-theoretically. It is easily seen that ˆ· induce ...
... then de Shalit’s recipe [CY01, A1.9] shows that c(T ) = cGal (T̂ ), where c(T ) is the classical base change conductor of T , which is defined in terms of algebraic Néron models, and where cGal (T̂ ) is the base change conductor of T̂ , defined Galois-theoretically. It is easily seen that ˆ· induce ...
Covering Groupoids of Categorical Rings - PMF-a
... A group-groupoid is a group object in the category of groupoids [7]; equivalently, it is an internal category and hence an internal groupoid in the category of groups ([18], [1]) . An alternative name, quite generally used, is “2-group”, see for example [4]. Recently for example in [1], [12] and [13 ...
... A group-groupoid is a group object in the category of groupoids [7]; equivalently, it is an internal category and hence an internal groupoid in the category of groups ([18], [1]) . An alternative name, quite generally used, is “2-group”, see for example [4]. Recently for example in [1], [12] and [13 ...
Several approaches to non-archimedean geometry
... residue class field Tn /m that has finite degree over k. (2) The ring Tn is Jacobson: every prime ideal p of Tn is the intersection of the maximal ideals containing it. In particular, if I is an ideal of Tn then an element of Tn /I is nilpotent if and only if it lies in every maximal ideal of Tn /I. ...
... residue class field Tn /m that has finite degree over k. (2) The ring Tn is Jacobson: every prime ideal p of Tn is the intersection of the maximal ideals containing it. In particular, if I is an ideal of Tn then an element of Tn /I is nilpotent if and only if it lies in every maximal ideal of Tn /I. ...
ABELIAN VARIETIES A canonical reference for the subject is
... Proof. Choose a nonempty open affine U ⊂ X and let D = X \ U with the reduced structure. We claim that D is a Cartier divisor (that is, its coherent ideal sheaf is invertible). Since X is regular, it is equivalent to say that all generic points of D have codimension 1. Mumford omits this explanation ...
... Proof. Choose a nonempty open affine U ⊂ X and let D = X \ U with the reduced structure. We claim that D is a Cartier divisor (that is, its coherent ideal sheaf is invertible). Since X is regular, it is equivalent to say that all generic points of D have codimension 1. Mumford omits this explanation ...
Homological algebra
... MATH 101B: ALGEBRA II PART A: HOMOLOGICAL ALGEBRA These are notes for our first unit on the algebraic side of homological algebra. While this is the last topic (Chap XX) in the book, it makes sense to do this first so that grad students will be more familiar with the ideas when they are applied to a ...
... MATH 101B: ALGEBRA II PART A: HOMOLOGICAL ALGEBRA These are notes for our first unit on the algebraic side of homological algebra. While this is the last topic (Chap XX) in the book, it makes sense to do this first so that grad students will be more familiar with the ideas when they are applied to a ...
MARCH 10 Contents 1. Strongly rational cones 1 2. Normal toric
... Let σ be a smooth cone in Rn . Then it is σ = Cone(e1 , ..., er ) for a lattice basisi (e1 , ..., er ). It follows that σ̌ = Cone(e1 , ..., er , ±er+1 , ..., ±en ), and thus Uσ ∼ = Cr × (C∗ )n−r . We see that if σ is smooth then: • dim(σ̌) = n and thus σ a strongly rational smooth cone. • Uσ is a no ...
... Let σ be a smooth cone in Rn . Then it is σ = Cone(e1 , ..., er ) for a lattice basisi (e1 , ..., er ). It follows that σ̌ = Cone(e1 , ..., er , ±er+1 , ..., ±en ), and thus Uσ ∼ = Cr × (C∗ )n−r . We see that if σ is smooth then: • dim(σ̌) = n and thus σ a strongly rational smooth cone. • Uσ is a no ...
Cyclic A structures and Deligne`s conjecture
... by Kn the associahedron of dimension n 2. Recall the associahedron Kn is an abstract polytope whose vertices correspond to full bracketings of n letters and whose codimension m faces correspond to partial bracketings with m brackets. Hence K2 is a point, K3 is an interval, K4 is a pentagon. For more ...
... by Kn the associahedron of dimension n 2. Recall the associahedron Kn is an abstract polytope whose vertices correspond to full bracketings of n letters and whose codimension m faces correspond to partial bracketings with m brackets. Hence K2 is a point, K3 is an interval, K4 is a pentagon. For more ...
ON THE IRREDUCIBILITY OF SECANT CONES, AND
... these is easily determined, a natural question is: are CY and DY irreducible? This question plays an important role, for instance, in Pinkham’s work on regularity bounds for surfaces [Pi]. The purpose of this note is to show that this irreducibility holds provided the codimension of Y is sufficientl ...
... these is easily determined, a natural question is: are CY and DY irreducible? This question plays an important role, for instance, in Pinkham’s work on regularity bounds for surfaces [Pi]. The purpose of this note is to show that this irreducibility holds provided the codimension of Y is sufficientl ...
AN INTRODUCTION TO (∞,n)-CATEGORIES, FULLY EXTENDED
... Remark 1.3. In general, if we replace Vect(k) by an arbitrary symmetric monoidal category C, we get a C-valued TQFT. It is worth noting that the idea behind Atiyah’s definition of TQFT is that such a theory should be, in some sense, local: one can to compute what is attached to a n-manifold by cutti ...
... Remark 1.3. In general, if we replace Vect(k) by an arbitrary symmetric monoidal category C, we get a C-valued TQFT. It is worth noting that the idea behind Atiyah’s definition of TQFT is that such a theory should be, in some sense, local: one can to compute what is attached to a n-manifold by cutti ...
Derived splinters in positive characteristic
... Returning to affine D-splinters, we note that in positive characteristic p, by Theorem 1.4 this class of singularities is closely related to other classes of singularities, the so-called F-singularities, defined using the Frobenius action. For example, locally excellent affine Q-Gorenstein splinters ...
... Returning to affine D-splinters, we note that in positive characteristic p, by Theorem 1.4 this class of singularities is closely related to other classes of singularities, the so-called F-singularities, defined using the Frobenius action. For example, locally excellent affine Q-Gorenstein splinters ...
Unit 5 * Triangles
... Directions: For each section, use the indicated GeoGebra applet, along with the Word Bank, to fill in the blanks below. adjacent bisect(s) ...
... Directions: For each section, use the indicated GeoGebra applet, along with the Word Bank, to fill in the blanks below. adjacent bisect(s) ...
Intersection Theory course notes
... pair (M, N ) an integer number M · N satisfying the “conservation of number principle”, that is, if we move subvarieties M and N inside X in a certain way then their intersection index does not change. We will formulate this principle explicitly for some interesting examples and see why it is useful ...
... pair (M, N ) an integer number M · N satisfying the “conservation of number principle”, that is, if we move subvarieties M and N inside X in a certain way then their intersection index does not change. We will formulate this principle explicitly for some interesting examples and see why it is useful ...
