206 research outputs found
Computational advances in Rado numbers
No full textIn this dissertation, we present new methods in the computation of Rado numbers. These methods are applied to several families of equations. The Rado number of an equation is a Ramsey-theoretic quantity associated to the equation. For any particular equation E, the Rado number R_r(E) is the smallest N such that any r-coloring chi:{1,2,...,N} -> {1,2,...,r} must induce a monochromatic solution to E. We will lay out the history of this field and provide some structure as context for new results. Then we will discuss the new methods and computational tools that provide the foundation of the thesis. The 2-color Rado numbers R_2(2x+2y+kz = 3w) and R_2(kx+(k+1)y = (k+2)z) are computed for small values of the parameter k. The 2-color off-diagonal Rado numbers R_2(x + ay = z; x + by = z) are provided for 1 = (3^r - 1)(c+1)/2 for c >= 0. We also compute the precise values for r = 4 and -20 = 3 variables. We provide the 2-color Rado numbers for 1/x + 1/y = 1/z and a few other equations involving reciprocals. We also construct a coloring proving R_2(x^2 + y^2 = z^2) > 6500. (It is not known whether this Rado number is finite.) We compute the 2- and 3-color Rado numbers for other sums-of-squares equations, sum_{i=1}^a x_i^2) = sum_{i=1}^b y_i^2, and we prove a universal upper bound for a <= b <= ca for a constant c between 1 and 2 (different values of c give different upper bounds). We follow this with Rado numbers for other assorted families of quadratic equations. We also present quantitative analogues of Hindman's theorem, which guarantees monochromatic solutions to systems like {x+y+z = w; x*y*z = v}. We conclude by suggesting a number of conjectures, extensions, and generalizations of these results for future work.Ph.D.Includes bibliographical referencesby Kellen John Myer
Pemodelan hujan Denyut Segi Empat Neyman Scott (NSRP) terbaik di semenanjung Malaysia
No full textKajian ini bertujuan mendapatkan gabungan statistik untuk pemodelan hujan kelompok berstokastik Denyut Segi Empat Neyman-Scott (NSRP) yang mampu memberikan pemadanan terbaik bagi hujan di stesen hujan Semenanjung Malaysia. Enam set gabungan statistik, yang setiap setnya mengandungi gabungan statistik momen (1, 2 dan 3) dan kebarangkalian hujan dalam selang masa yang singkat (jam) dan panjang (harian), serta empat taburan yang berbeza bagi kelebatan sel hujan (Eksponen, Campuran Eksponen, Gamma dan Weibull) telah dikaji. Penyelidikan telah dilakukan ke atas sembilan stesen hujan yang mewakili rantau yang berbeza di Semenanjung Malaysia. Hasil mendapati bahawa statistik momen ke-3 (kepencongan) tidak memberikan sumbangan yang baik dalam menjayakan model. Selang masa 1, 6 dan 24 jam didapati yang terbaik bagi statistik momen kedua (variasi) bagi menjayakan model. Kajian ini juga mendapati bahawa taburan eksponen adalah yang terbaik bagi pemodelan hujan NSRP di Semenanjung Malaysia
ANALYSIS OF THE BEST HIGH SCHOOL RANKING DETERMINATION WITH TECHNIQUE METHODS OR OTHERS PREFERENCE BY SIMILARITY TO IDEAL SOLUTION (TOPSIS)
No full textAn educational quality depends heavily on the quality of the educational institution
such as the senior high school and level above. The quality of senior high school level is
often served as a benchmark for people to choose the right school for the community
Hartono, Helmiati, Rado Yendra, Khairil Anwar, M Nizam Muhaijir, Ade Novia Rahma and
Ahmad Fudholi
http://www.iaeme.com/IJMET/index.asp 651 [email protected]
through the educational institutions. This research aims to determine the best rank of
senior high school in Pekanbaru using a Technique for others preference by similarity to
ideal solution (TOPSIS) method. This method of weighted TOPSIS requires range
criterions. To determine the weight of each criterion, this study uses AHP method as the
supporter for determining the weight of each criterion and gives the rank to the senior
high school in which majors are the natural science and the social science department.
The results obtained are the best rank for natural science majors of senior high schools
in Pekanbaru is SMAN 1 Pekanbaru and the best rank for social science majors of senior
high schools in Pekanbaru is SMAN 8 Pekanbaru. For the private high school, it can be
said that Pekanbaru Djuwita private high school becomes the first rank of science majors
and the Private high school of Witama Nasional Plus Pekanbaru becomes the first rank
of the social science Department. For the high school and the private high school, SMAN
8 Pekanbaru obtains the first rank in the science majors and the first rank in the social
science department.
Key words: Multicriteria decision making, priority ranking, TOPSIS, AHP method,
SMAN, Pekanbar
On Erdős-Ko-Rado for random hypergraphs
No full textOn Erdős-Ko-Rado for Random Hypergraphs o by Arran Hamm Dissertation Director: Jeff Kahn Denote by Hk (n, p) the random k-graph in which each k-subset of {1, . . . , n} is present with probability p, independent of other choices. This dissertation addresses the question: for which p0 will Hk (n, p) satisfy the “Erd˝s-Ko-Rado property” provided that o p > p0 ? This question was first studied by Balogh, Bohman, and Mubayi where they dealt mainly with k 0). Our first main result gives the desired p0 when k 0 such that if n = 2k + 1 and p > 1 − ε, then Hk (n, p) has the EKR property a.s. iiPh.D.Includes bibliographical referencesby Arran Ham
Element-Distinct Solution For Rado\u27s Theorem
No full textIn this paper, we present a simplified proof of Rado\u27s Theorem and demonstrate that when an integer matrix satisfies the column condition and has an element-distinct solution on , then under any finite coloring of , the equation has a monochromatic element-distinct solution. This gives a positive answer to a problem of Di Nasso in 2016.The main conclusions presented in this paper have been proven previously by others, and the original author has contacted me. I believe the paper should be withdraw
A numerical study on natural convection in a square inclined porous enclosure filled with an Ag nanoliquids
No full textErdős-Ko-Rado theorems for set partitions with certain block size
No full textIn this paper, we prove Erdős-Ko-Rado type results for (a) family of set partitions where the size of each block is a multiple of k; and (b) family of set partitions with minimum block size k.The author Kok Bin Wong was supported by the University of Malaya Research Grant GPF025B-2018
Erdos--Ko--Rado Theorems: New Generalizations, Stability Analysis and Chvatal's Conjecture
No full textabstract: The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma.Dissertation/ThesisPh.D. Mathematics 201
Aplikasi Sistem Bilangan Basis pada Analisis Rentetan Data Binari (Hujan dan Tidak Hujan) sebagai Antisipasi Bencana Banjir
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