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INFINITE CLASS FIELD TOWERS
, 802
"... Abstract. This paper studies infinite class field towers of number fields K that are ramified over Q only at one finite prime. In particular, we show the existence of such towers for a general family of primes including p = 2, 3 and 5. 1. ..."
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Abstract. This paper studies infinite class field towers of number fields K that are ramified over Q only at one finite prime. In particular, we show the existence of such towers for a general family of primes including p = 2, 3 and 5. 1.
Infinite Classes of Covering Numbers
 CANAD. MATH. BULL
, 1998
"... Let D be a family of ksubsets (called blocks) of a vset X(v). Then D is a (v; k; t) covering design or covering if every tsubset of X(v) is contained in at least one block of D. The number of blocks is the size of the covering, and the minimum size of the covering is called the covering number. I ..."
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. In this paper we consider the case t = 2, and find several infinite classes of covering numbers. We also give upper bounds on other classes of covering numbers.
An Infinite Class Field Tower
, 2012
"... In 1964, Golod and Shafarevich provided the first example of a number field with infinite class field tower [1]. Since then, attempts have been made to construct number fields with various properties that have infinite class field tower. Using a theorem of Schoof, we give an example of a class of S3 ..."
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In 1964, Golod and Shafarevich provided the first example of a number field with infinite class field tower [1]. Since then, attempts have been made to construct number fields with various properties that have infinite class field tower. Using a theorem of Schoof, we give an example of a class of S
AN INFINITE CLASS OF FUNCTIONS IDENTIFIABLE USING
"... Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal ’ and ‘nearly minimal ’ programs for functions from their graphs. Freivalds showed that there exists a Gö ..."
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, showed that for every Kolmogorov numbering there exists an infinite class of functions which can be identified using minimal programs. Note that these infinite classes of functions may depend on the Kolmogorov numbering. It was left open whether there exists an infinite class of functions, C
New infinite classes of weighing matrices
 Sankhya Ser. B
"... SUMMARY. In this paper we use a new algorithm to find weighing matrices W (2n, 9) constructed using two circulant matrices. The basic idea of this algorithm is to investigate all possible ways the weight 9 can be split into two weights of the corresponding sequences. Solutions for each split, if th ..."
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, if they exist, are given for weighing matrices W (2n, 9), for all n up to 100. Many of these sequences are new and given here for the first time. Using these sequences we can obtain many new infinite classes of weighing matricesW (2n, k).
Two Infinite Classes of Cryptographic Hash Functions
, 2003
"... We o#er two new definitions of two infinite classes of strongly collision free hash functions that we gave a name "Edon"C and "Edon" R. ..."
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We o#er two new definitions of two infinite classes of strongly collision free hash functions that we gave a name "Edon"C and "Edon" R.
Some Infinite Classes of Fullerene Graphs
 International Mathematical Forum
"... A fullerene graph is a 3 regular planar simple finite graph with pentagon or hexagon faces. In these graphs the number of pentagon faces is 12. Therefore, any fullerene graph can be characterized by number of its hexagon faces. In this note, for any h> 1, we will construct a fullerene graph with ..."
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A fullerene graph is a 3 regular planar simple finite graph with pentagon or hexagon faces. In these graphs the number of pentagon faces is 12. Therefore, any fullerene graph can be characterized by number of its hexagon faces. In this note, for any h> 1, we will construct a fullerene graph with h hexagon faces. Then, using the leapfrogging process we will construct stable fullerenes with 20 + 3h hexagon faces, for any h> 1.
An infinite class of sparseyao spanners
 In SODA
, 2013
"... We show that, for any integer k ≥ 6, the SparseYao graph Y Y6k (also known as YaoYao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k ≥ 8. 1 ..."
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We show that, for any integer k ≥ 6, the SparseYao graph Y Y6k (also known as YaoYao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k ≥ 8. 1
An Infinite Class of Convex Tangent Cones
, 1997
"... Since the early 1970's there have been many papers devoted to tangent cones and their applications to optimization. Much of the debate over which tangent cone is "best" has centered on the properties of Clarke's tangent cone and whether other cones have these properties. In this ..."
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. In this paper it is shown that there are an infinite number of tangent cones with some of the nicest properties of Clarke's cone. These properties are convexity, multiple characterizations, and proximal normal formulas. The nature of these cones indicates that the two extremes of this family of cones
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