Physical Sciences and Mathematics Commons^™

A New Error Analysis For Brun's Constant, Thomas R. Nicely

Virginia Journal of Science

Enumeration of the twin primes, and the sum of their reciprocals, is extended to 3 x 10¹⁵, yielding the count π₂(3 x 10¹⁵) = 3310517800844. A more accurate estimate is obtained for Brun’s constant, B2 = 1.90216 05823 ± 0.00000 00008 . Error analysis is presented to support the contentioli that this estimate produces a 95 % confidence interval for B₂. In addition, published values of the count π(x) of primes, obtained previously by indirect means, are verified by direct coiiIit to x = 3 x 10¹⁵

Efficient Algorithms For Graphs With Few P-4’S, Luitpold Babel, Ton Kloks, Jan Kratochvíl, Dieter Kratsch, Kaiko Müller, Stephan Olariu

Computer Science Faculty Publications

We show that a large variety of NP-complete problems can be solved efficiently for graphs with 'few' P₄'s. We consider domination problems (domination, total domination, independent domination. connected domination and dominating clique), the Steiner tree problem, the vertex ranking problem, the pathwidth problem, the path cover number problem, the hamiltonian circuit problem, the list coloring problem and the precoloring extension problem. We show that all these problems can be solved in linear time for the class of (q,q - 4)-graphs, for every fixed q. These are graphs for which no set of at most q. vertices induces more …

Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees

Mathematics & Statistics Faculty Publications

If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b₁;r;k₁) are each partitioned into sub-blocks of size k₂, and the b₂ =b₁k₁=k2 sub-blocks themselves constitute a BIBD with parameters (v; b₂;r;k₂), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k₁ =2k₂= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, …

Mathematical Models Of Quiescent Solar Prominences, Iain Mckaig

Mathematics & Statistics Theses & Dissertations

Magnetic fields in the solar atmosphere suspend and insulate dense regions of cool plasma known as prominences. The convection zone may be the mechanism that both generates and expels this magnetic flux through the photosphere in order to make these formations possible. The connection is examined here by modeling the convection zone as both one-dimensional, then more realistically, two-dimensional.

First a Dirichlet problem on a semi-infinite strip is solved using conformal mapping and the method of images. The base of the strip represents the photosphere where a current distribution can be given as a boundary condition, and the strip extends …