1: Introduction to Lattices
... distance at least kx − yk ≥ . Not every subgroup of Rn is a lattice. Example 1. Qn is a subgroup of Rn , but not a lattice, because it is not discrete. The simplest example of lattice is the set of all n-dimensional vectors with integer entries. Example 2. The set Zn is a lattice because integer ve ...
... distance at least kx − yk ≥ . Not every subgroup of Rn is a lattice. Example 1. Qn is a subgroup of Rn , but not a lattice, because it is not discrete. The simplest example of lattice is the set of all n-dimensional vectors with integer entries. Example 2. The set Zn is a lattice because integer ve ...
![arXiv:math/0106066v1 [math.CO] 10 Jun 2001](http://s1.studyres.com/store/data/017702261_1-bfc5908794194e67b6dcd68ae33c70f9-300x300.png)
arXiv:math/0106066v1 [math.CO] 10 Jun 2001
... between the average degree of G, d¯ = v∈V dG (v)/|V | and its maximal degree ∆(G) = maxv∈V dG (v). As for all p(n) ≫ log n the last two quantities are both asymptotically equal to np, it follows that in this range of edge probabilities a.s. λ1 (G(n, p)) = (1 + o(1))np. In fact, much more is known fo ...
... between the average degree of G, d¯ = v∈V dG (v)/|V | and its maximal degree ∆(G) = maxv∈V dG (v). As for all p(n) ≫ log n the last two quantities are both asymptotically equal to np, it follows that in this range of edge probabilities a.s. λ1 (G(n, p)) = (1 + o(1))np. In fact, much more is known fo ...
The largest eigenvalue of sparse random graphs
... between the average degree of G, d¯ = v∈V dG (v)/|V | and its maximal degree ∆(G) = maxv∈V dG (v). As for all p(n) ≫ log n the last two quantities are both asymptotically equal to np, it follows that in this range of edge probabilities a.s. λ1 (G(n, p)) = (1 + o(1))np. In fact, much more is known fo ...
... between the average degree of G, d¯ = v∈V dG (v)/|V | and its maximal degree ∆(G) = maxv∈V dG (v). As for all p(n) ≫ log n the last two quantities are both asymptotically equal to np, it follows that in this range of edge probabilities a.s. λ1 (G(n, p)) = (1 + o(1))np. In fact, much more is known fo ...
Lower Bounds in Communication Complexity: A Survey
... extrema of a smooth real-valued function than a discrete valued function. For example, for smooth functions the powerful tools of calculus are available. To illustrate, think of integer programming vs. linear programming. The latter problem can be solved in polynomial time, while even simple instanc ...
... extrema of a smooth real-valued function than a discrete valued function. For example, for smooth functions the powerful tools of calculus are available. To illustrate, think of integer programming vs. linear programming. The latter problem can be solved in polynomial time, while even simple instanc ...
Full text - Toulouse School of Economics
... Surprisingly, the argument used to compare mixture distributions can also be used in a completely different analytical environment, to compare distributions generated by lotteries, and yields similar sufficient conditions. We consider the class of n-dimensional random vectors representing n independ ...
... Surprisingly, the argument used to compare mixture distributions can also be used in a completely different analytical environment, to compare distributions generated by lotteries, and yields similar sufficient conditions. We consider the class of n-dimensional random vectors representing n independ ...
Introduction to Algebraic Coding Theory
... more with this example in Chapter 2.) In general, if a message has length k, the encoded message, i.e. codeword, will have length n > k. Algebraic coding theory is an area of discrete applied mathematics that is concerned (in part) with developing error-control codes and encoding/decoding procedures ...
... more with this example in Chapter 2.) In general, if a message has length k, the encoded message, i.e. codeword, will have length n > k. Algebraic coding theory is an area of discrete applied mathematics that is concerned (in part) with developing error-control codes and encoding/decoding procedures ...
On anti-automorphisms of von Neumann algebras
... real algebra into another we shall mean a one-to-one real linear map φ such that φ(A*) = Φ(A)*y and φ(AB) = φ(A)φ(B) for all A, B in the algebra. By a ^-anti-automorphism (or just anti-automorphism) of a von Neumann algebra 21 we shall mean a one-to-one (complex) linear map φ of 31 onto itself such ...
... real algebra into another we shall mean a one-to-one real linear map φ such that φ(A*) = Φ(A)*y and φ(AB) = φ(A)φ(B) for all A, B in the algebra. By a ^-anti-automorphism (or just anti-automorphism) of a von Neumann algebra 21 we shall mean a one-to-one (complex) linear map φ of 31 onto itself such ...
