International Journal of Mathematics and Mathematical Sciences, 1989
Let E be a topological vector space of scalar sequences, with topologyτ;(E,τ)satisfies the closed... more Let E be a topological vector space of scalar sequences, with topologyτ;(E,τ)satisfies the closed neighborhood condition iff there is a basis of neighborhoods at the origin, forτ, consisting of sets whlch are closed with respect to the topologyπof coordinate-wise convergence on E;(E,τ)satisfies the filter condition iff every filter, Cauchy with respect toτ, convergent with respect toπ, converges with respect toτ.Examples are given of solid (definition below) normed spaces of sequences which (a) fail to satisfy the filter condition, or (b) satisfy the filter condition, but not the closed neighborhood condition. (Robertson and others have given examples fulfilling (a), and examples fulfilling (b), but these examples were not solid, normed sequence spaces.) However, it is shown that among separated, separable solid pairs(E,τ), the filter and closed neighborhood conditions are equivalent, and equivalent to the usual coordinate sequences constituting an unconditional Schauder basis for(E...
An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices ... more An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices have exactly $\lambda$ common neighbors. This paper is about the existence and structure of edge-regular graphs with $\lambda =1$ and about edge-regular graphs with $\lambda >1$ which have local neighborhood structure analogous to that of the edge-regular graphs with $\lambda =1$.
If you treasure semantic precision, you might name the volcano that erupted (figuratively speakin... more If you treasure semantic precision, you might name the volcano that erupted (figuratively speaking!) in 1973: Coloring Problems in Geometrically Defined Hypergraphs.
Page 1. Darrel Hankerson Greg A. Harris Peter D. Johnson, Jr. Introduction to &am... more Page 1. Darrel Hankerson Greg A. Harris Peter D. Johnson, Jr. Introduction to < Information Theory and Data Compression Second Edition Page 2. Page 3. Page 4. Page 5. Introduction to Information Theory and Data Compression Second Edition This One DOE3-9KT-6615 ...
... of [1]. The Babai numbers were also discovered independently by Paul Erdös in [8]; the defini... more ... of [1]. The Babai numbers were also discovered independently by Paul Erdös in [8]; the definition is confined to the case XDR2, but it ... the 20-year-old Francis Guthrie started a mathe-matical avalanche by posing the four-color conjecture to his brother Frederick, who transmitted ...
Let P denote the set of positive integers. For m, n ∈ P, n ⩾ 2, a Kraft sequence of length m for ... more Let P denote the set of positive integers. For m, n ∈ P, n ⩾ 2, a Kraft sequence of length m for alphabet size n is a sequence (l1,...,lm) of the lengths of the words in a prefix-free list of words formed from an alphabet of n letters. For instance, because none of the binary words ...
International Journal of Mathematics and Mathematical Sciences, 2005
In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included ... more In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, with equality only if the hypergraph is regular. Here, we prove a wider class of inequalities in a wider context, that of edge-weighted uniform hypergraphs.
International Journal of Mathematics and Mathematical Sciences, 1989
Let E be a topological vector space of scalar sequences, with topologyτ;(E,τ)satisfies the closed... more Let E be a topological vector space of scalar sequences, with topologyτ;(E,τ)satisfies the closed neighborhood condition iff there is a basis of neighborhoods at the origin, forτ, consisting of sets whlch are closed with respect to the topologyπof coordinate-wise convergence on E;(E,τ)satisfies the filter condition iff every filter, Cauchy with respect toτ, convergent with respect toπ, converges with respect toτ.Examples are given of solid (definition below) normed spaces of sequences which (a) fail to satisfy the filter condition, or (b) satisfy the filter condition, but not the closed neighborhood condition. (Robertson and others have given examples fulfilling (a), and examples fulfilling (b), but these examples were not solid, normed sequence spaces.) However, it is shown that among separated, separable solid pairs(E,τ), the filter and closed neighborhood conditions are equivalent, and equivalent to the usual coordinate sequences constituting an unconditional Schauder basis for(E...
An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices ... more An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices have exactly $\lambda$ common neighbors. This paper is about the existence and structure of edge-regular graphs with $\lambda =1$ and about edge-regular graphs with $\lambda >1$ which have local neighborhood structure analogous to that of the edge-regular graphs with $\lambda =1$.
If you treasure semantic precision, you might name the volcano that erupted (figuratively speakin... more If you treasure semantic precision, you might name the volcano that erupted (figuratively speaking!) in 1973: Coloring Problems in Geometrically Defined Hypergraphs.
Page 1. Darrel Hankerson Greg A. Harris Peter D. Johnson, Jr. Introduction to &am... more Page 1. Darrel Hankerson Greg A. Harris Peter D. Johnson, Jr. Introduction to < Information Theory and Data Compression Second Edition Page 2. Page 3. Page 4. Page 5. Introduction to Information Theory and Data Compression Second Edition This One DOE3-9KT-6615 ...
... of [1]. The Babai numbers were also discovered independently by Paul Erdös in [8]; the defini... more ... of [1]. The Babai numbers were also discovered independently by Paul Erdös in [8]; the definition is confined to the case XDR2, but it ... the 20-year-old Francis Guthrie started a mathe-matical avalanche by posing the four-color conjecture to his brother Frederick, who transmitted ...
Let P denote the set of positive integers. For m, n ∈ P, n ⩾ 2, a Kraft sequence of length m for ... more Let P denote the set of positive integers. For m, n ∈ P, n ⩾ 2, a Kraft sequence of length m for alphabet size n is a sequence (l1,...,lm) of the lengths of the words in a prefix-free list of words formed from an alphabet of n letters. For instance, because none of the binary words ...
International Journal of Mathematics and Mathematical Sciences, 2005
In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included ... more In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, with equality only if the hypergraph is regular. Here, we prove a wider class of inequalities in a wider context, that of edge-weighted uniform hypergraphs.
Uploads