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### Unitarity triangle test of the extra factor of two in particle oscillation phases

S. M. Bilenky, W. Grimus, T. Schwetz
2005 European Physical Journal C: Particles and Fields
We demonstrate that the unitarity triangle (UT) fit in the Standard Model with three families is a suitable means to discriminate between the standard oscillation phase and the phase with an extra factor  ...  There are claims in the literature that in neutrino oscillations and oscillations of neutral kaons and B-mesons the oscillation phase differs from the standard one by a factor of two.  ...  It is likely that in the future, with accumulated data used in the unitarity triangle fit, the exclusion of the extra factor of two will become even more significant.  ...

### Maximal sets of triangle-factors onv = 6m vertices

Rolf S. Rees
1998 Journal of combinatorial designs (Print)
A collection of edge-disjoint triangle-factors on K 3n is called maximal if it cannot be extended by a further triangle-factor.  ...  It is well-known that a maximal set must therefore contain at least % triangle factors.  ...  triangle-factors with the two triangle-factors in the RRP (12, 9) ; this gives two triangle-factors on AU B.  ...

### Heronian Triangles

Wm. Fitch Cheney
1929 The American mathematical monthly
This paper presents some theorems regarding factors of the sides and area of Heronian triangles. 2. Rational triangles. In the July, 1921, issue of this Monthly, Professor L. E.  ...  Any factor common to two v's is prime to all the d’s and n’s. Now since every d and 1 is 1 or greater, the minimum value of d?+n? is 2. (In this case only, our Heronian triangle is a right triangle.)  ...

### Theorem on a Matrix of Right-Angled Triangles

Martin W. Bredenkamp
2013 Applied and Computational Mathematics
even number and have no common factor.  ...  The sides of every positive integer right angled triangle are then defined by the indices as follows: For hypotenuse h, uneven leg u and even leg e, h = i 2 + ij + j 2 /2, e = ij + j 2 /2, u = i 2 + ij  ...  Likewise, the triangles in a horizontal row, having index j in common, have their even sides e increase by a factor of 2j in the triangle sequence from left to right.  ...

### Semi-uniform, 2-Different Tessellation of Triangular Parametric Surfaces [chapter]

Ashish Amresh, Christoph Fünfzig
2010 Lecture Notes in Computer Science
The factors are then used to steer the tessellation of the parametric surface into a collection of triangle strips in a single pass.  ...  In this paper, we present SD-2 (Semi-uniform, 2-Different), an adaptive tessellation algorithm for triangular parametric surfaces.  ...  Adaptive Tessellation Pattern with 2-Different Factors In case of triangles with only two different edge tessellation factors f u = f v and f w , it is possible to tessellate in an especially simple way  ...

### Triangle-factors in a balanced blown-up triangle

Robert Johansson
2000 Discrete Mathematics
Let G be a 3-partite graph with 3n vertices, n in each class, such that each vertex is connected to at least 2 3 n + √ n of the vertices in each of the other two classes.  ...  In this paper it will be proved that G contains n vertex-disjoint triangles, it will also be shown by example that this is close to being sharp.  ...  Therefore some triangle T = T i in F must satisfy |E(P; T )|¿4l + 2.  ...

### Page 27 of The American Mathematical Monthly Vol. 36, Issue 1 [page]

1929 The American Mathematical Monthly
Probably the easiest way to make a list of Heronian triangles is to develop the method suggested in paragraph 2.  ...  This keeps the point P of paragraph 2 in the shaded area of the loop in the diagram.  ...

### Simple models of the impact of overlap in bucket rendering

Milton Chen, Gordon Stoll, Homan Igehy, Kekoa Proudfoot, Pat Hanrahan
1998 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware - HWWS '98
If triangles are small, the overlap factor itself is also small. If triangles are large, overlap is high but pixel work dominates the rendering time.  ...  The drawbacks of this technique are the cost of computing the regions overlapped by each triangle and the redundant work required in processing triangles multiple times when they overlap multiple regions  ...  Head Cylhead Studio Flight Quake APPENDIX Worst-Case Overlap Factor The expected number of tiles overlapped by two triangles of total bounding-box area 2B is: 2 2 2         + +        ...

### Ascending subgraph decompositions of oriented graphs that factor into triangles

Andrea D. Austin, Brian C. Wagner
2020 Discussiones Mathematicae Graph Theory
In this paper, we will show that all orientations of an oriented graph that can be factored into triangles with a large portion of the triangles being transitive have an ASD.  ...  We will also use the result to obtain an ASD for any orientation of complete multipartite graphs with 3n partite classes each containing 2 vertices (a K(2 : 3n)) or 4 vertices (a K(4 : 3n)).  ...  Acknowledgments The research for this paper was funded in part by the Bill and Roberta Blankenship Undergraduate Research Endowment.  ...

### Packing 3-Vertex Paths in Claw-Free Graphs [article]

Alexander Kelmans
2007 arXiv   pre-print
is not a claw and not a triangle.  ...  Then (c1) if v(G) = 0 mod 3, then G has an L-factor containing (avoiding) e, (c2) if v(G) = 1 mod 3, then G - x has a L-factor, (c3) if v(G) = 2 mod 3, then G - x -y has an L-factor, (c4) if v(G) = 0 mod  ...  Moreover, (a1) if L induces a triangle in G, then G has a Λ-factor R containing L and such that each component of R induces a triangle (a2) if L does not induce a triangle in G, then G has a Λ-factor R  ...

### A simple and effective element distortion factor

A. El-Hamalawi
2000 Computers & structures
Lo  also defined a distortion coefficient β in the form of equation (2) , for quadrilaterals based on the triangular coefficient α.  ...  A given quadrilateral ABCD is cut along the two diagonals AC and BD into four triangles, and their corresponding α i are calculated.  ...  Figure 2 . 2 Distortion factors for typical (a) triangles and (b) quadrilaterals Figure 2 ( 2 a) shows some typical triangles with the new distortion factors computed and compared with Lo's α factors  ...

### Efficient computation of marginal reliability-importance for reducible/sup +/ networks

S.J. Hsu, M.C. Yuang
2001 IEEE Transactions on Reliability
In phase 2, the 2-P algorithm backtracks the reduction steps and computes MRI, based on the reduction factors generated in phase 1 and a set of closed-form TR formulas.  ...  In each reduction step, the 2-P algorithm generates the correlation, quantified by a reduction factor, between the original network and the reduced network.  ...  The new success probabilities are recomputed, as shown in Fig. 2 . , because of a transformation factor of 1 in this step.  ...

### Empirical Analysis of Claims Development Trapezoids following Benford's Law

Jochen Heberle, Tobias Gummersbach
2018 Financial Statistical Journal
In particular we determine Benfors's law fordifferent characteristic factors depending on claims development triangles/trapezoids.These characteristic factors are the cumulative claims payments, the incrementalclaims  ...  In this paper we make an empirical analysis of a wide range of claims developmenttrapezoids following Benford's law.  ...  The characteristic factors, namely the cumulative and incremental claims payments and the individual development factors are also introduced in Section 2.  ...

### Note on the Steiner Point

W. Gallatly
1908 The American mathematical monthly
only in (2. 2b and 3b, where b is any prime of form 24z+5 and 24z+11, can be resolved into complex factors in only one way since 2 and 3 have no complex factors in ?  ...  complex factors in only one way and 27, 3%, or 2y 31 have no complex factors in the domain.  ...

### A derivation of an affine plane of order 4 from a triangle-free 3-colored K16

Charles F. Laywine
2001 Discrete Mathematics
In this paper a new relationship is given through the derivation of AG(2,4), the a ne plane of order 4, from the 3-colored, triangle-free K16 constructed by Greenwood and Gleason in the proof that the  ...  In the derivation each line of this a ne plane is deÿned by a set of 4 vertices of the K16, which are mutually connected by edges of three colors so that each color deÿnes one of three 1-factor of that  ...  If two vertices are in one 1-factored K 4 and the third in a second K 4 , Fig. 2 shows that no monochromatic triangle exists.  ...
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