## Related Articles

- Split Rank of Triangle and Quadrilateral Inequalities. Dey, Santanu S.; Louveaux, Quentin // Mathematics of Operations Research;Aug2011, Vol. 36 Issue 3, p432
A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and CornuÃ©jols and Margot showed that the facet-defining inequalities of this set are either...

- Representing Sets with Sums of Triangular Numbers. Kane, Benjamin // IMRN: International Mathematics Research Notices;Sep2009, Vol. 2009 Issue 17, p3264
We investigate here sums of triangular numbers where Tn is the nth triangular number. We show that for a set of positive integers S, there is a finite subset S0 such that f represents S if and only if f represents S0. However, computationally determining S0 is ineffective for many choices of S....

- A CLASSROOM NOTE ON GENERATING EXAMPLES FOR THE LAWS OF SINES AND COSINES FROM PYTHAGOREAN TRIANGLES. Sher, Lawrence; Sher, David // Mathematics & Computer Education;Spring2007, Vol. 41 Issue 2, p168
The article discusses generating examples for the laws of sines and cosines from pythagorean triangles. It explains that in teaching the laws of sines and cosines, one can use integer-sided right triangles to create integer sided general triangles with rational and one decimal place...

- THE DURATION OF PLAY IN GAMES OF CHANCE WITH WIN-OR-LOSE OUTCOMES AND GENERAL PAYOFFS. Estafanous, Marc; Ethier, S. N. // Mathematical Scientist;Dec2009, Vol. 34 Issue 2, p99
The duration of play formulae of De Moivre are generalized, using restricted Pascal triangles, to games in which the gambler wins Î¼ units or loses v units at each play, where Î¼ and v are positive integers. We treat the cases of both one and two barriers.

- A note on Smarandache number related triangles. Gunarto, H.; Majumdar, A. A. K. // Scientia Magna;2010, Vol. 6 Issue 1, p1
The triangle T(a, b, c) with angles a, b, c, and the triangle T(aâ€², bâ€², câ€²) with angles aâ€², bâ€², câ€² are said to be pseudo Smarandache related if Z(a) =Z(aâ€²), Z(b) =Z(bâ€²), Z(c) =Z(câ€²), and the pair of triangles T(a,b, c) and T(aâ€²,...

- Fractions eliminate floating-point multiply. Gauland, Michael // EDN;02/15/96 Supplement, Vol. 41 Issue 4, p134
Focuses on the use of two integers to approximate a floating-point constant to achieve excellent accuracy. Examination of an example; Advantages of this circuit.

- Lower Bounds in Lot-Sizing Models: A Polyhedral Study. Constantino, Miguel // Mathematics of Operations Research;Feb98, Vol. 23 Issue 1, p101
Variable lower bounds in Mixed Integer Programs are constraints with the general form x greater than or equal to Ly, where x is a continuous variable and y is a binary or an integer variable.This type of constraints is present in some Lot-Sizing models, where x represents the amount of some...

- New class of 0-1 integer programs with tight approximation via linear relaxations. Asratian, A. S.; Kuzjurin, N. N. // Mathematical Methods of Operations Research;2001, Vol. 53 Issue 3, p363
We consider the problem of estimating optima of integer programs { max cx | Axâ‰¤b,0â‰¤xâ‰¤1, x - integral} where b>0, câ‰¥0 are rational vectors and A is an arbitrary rational m Ã—n matrix. Using randomized rounding we find an efficiently verifiable sufficient condition for...

- The integral basis method for integer programming. Haus, Utz-Uwe; Köppe, Matthias; Weismantel, Robert // Mathematical Methods of Operations Research;2001, Vol. 53 Issue 3, p353
This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear...