A Few Basics of Probability
... New example solution: The probability that all land heads, P(AllHeads) = P(H1 ∧ H2 ∧ H3 ) is P(H1 )P(H2 )P(H3 ) = 21 12 12 = 18 because the coin is fair and flips are independent. In fact, any particular sequence has the same probability. The probability that at least two of the coins land heads, P( ...
... New example solution: The probability that all land heads, P(AllHeads) = P(H1 ∧ H2 ∧ H3 ) is P(H1 )P(H2 )P(H3 ) = 21 12 12 = 18 because the coin is fair and flips are independent. In fact, any particular sequence has the same probability. The probability that at least two of the coins land heads, P( ...
Proof Nets Sequentialisation In Multiplicative Linear Logic
... Definition 5 (Constrainted Structure). A constrainted structure (or Cstructure) Rc is a d.a.g. obtained from a proof structure R (whose links have been given ports as in Definition 3), by adding untyped edges, called sequential edges, in such a way that each node n has the same label as in R, and ea ...
... Definition 5 (Constrainted Structure). A constrainted structure (or Cstructure) Rc is a d.a.g. obtained from a proof structure R (whose links have been given ports as in Definition 3), by adding untyped edges, called sequential edges, in such a way that each node n has the same label as in R, and ea ...
p-ADIC QUOTIENT SETS
... element of A. If b is squarefree, a result of Hasse ensures that R(A) is dense in Qp for infinitely many p [18]. Fibonacci and Lucas numbers are considered in Section 7. Corollary 7.1 recovers the main result of [13]: the set of quotients of Fibonacci numbers is dense in each Qp . The situation for ...
... element of A. If b is squarefree, a result of Hasse ensures that R(A) is dense in Qp for infinitely many p [18]. Fibonacci and Lucas numbers are considered in Section 7. Corollary 7.1 recovers the main result of [13]: the set of quotients of Fibonacci numbers is dense in each Qp . The situation for ...
Algebraic Number Theory - School of Mathematics, TIFR
... xn = (x−1 )−n for n < 0 in Z. It is also customary to write the composition law in an abelian group additively, i.e. to write x + y for what has been denoted by x · y above. In this case, one writes 0 for e, −x for x−1 , mx for xm , and refers to the composition law as addition. Definition 1.3 An ab ...
... xn = (x−1 )−n for n < 0 in Z. It is also customary to write the composition law in an abelian group additively, i.e. to write x + y for what has been denoted by x · y above. In this case, one writes 0 for e, −x for x−1 , mx for xm , and refers to the composition law as addition. Definition 1.3 An ab ...
PARTIALIZATION OF CATEGORIES AND INVERSE BRAID
... induces a functor from P(C ) to P(C 0 ), which we will denote by P(F ). In particular, P becomes a functor from the category of all small categories, satisfying Condition 1, where morphisms are all functors, preserving monomorphisms, to the category of all small categories. We will call P the (first ...
... induces a functor from P(C ) to P(C 0 ), which we will denote by P(F ). In particular, P becomes a functor from the category of all small categories, satisfying Condition 1, where morphisms are all functors, preserving monomorphisms, to the category of all small categories. We will call P the (first ...
Compactifications and Function Spaces
... is such that f −1 (r) is infinite and not compact, then there is some x ∈ αX \ X so that x ∈ cl(f −1 (r)). This shows that whether a function f extends to a compactification αX depends on whether there are enough “points” in αX \ X to capture the “behavior” of f at “∞”. This is very close to the pre ...
... is such that f −1 (r) is infinite and not compact, then there is some x ∈ αX \ X so that x ∈ cl(f −1 (r)). This shows that whether a function f extends to a compactification αX depends on whether there are enough “points” in αX \ X to capture the “behavior” of f at “∞”. This is very close to the pre ...
The Coinductive Formulation of Common Knowledge
... is interpreted epistemically, that is, K is read “it is known that”. If we want to reason about the knowledge of multiple agents, we can extend S5 by introducing multiple modal operators, each written Ka for some agent a and read “a knows that”. S5 provides an idealised model for knowledge: in short ...
... is interpreted epistemically, that is, K is read “it is known that”. If we want to reason about the knowledge of multiple agents, we can extend S5 by introducing multiple modal operators, each written Ka for some agent a and read “a knows that”. S5 provides an idealised model for knowledge: in short ...
ON SEQUENTIALLY COHEN-MACAULAY
... The result follows from the fact that k∆hmi k = k∆khmi , for all m = 0, 1, . . . , dim ∆, where k∆k denotes the geometric realization of ∆. There is a characterization of SCMness due to Duval [10] which involves the pure r-skeleton of a simplicial complex. The pure r-skeleton ∆[r] of a simplicial ...
... The result follows from the fact that k∆hmi k = k∆khmi , for all m = 0, 1, . . . , dim ∆, where k∆k denotes the geometric realization of ∆. There is a characterization of SCMness due to Duval [10] which involves the pure r-skeleton of a simplicial complex. The pure r-skeleton ∆[r] of a simplicial ...
