طرح هاي مربع لاتين ناقص متعادل

چكيده انگليسي :

Balanced incomplete Latin square designs Seyed Mostafa Fatemi mostafa fatemi@math iut ac ir June 26 2018 M Sc Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac ir2000 MSC 62Kxx 62K05 62K10 Keywords Incomplete Latin square Information matrix Optimality Orthogonal Latin squares CrisscrossLatin square designs Knut Vik designs Abstract The Latin squares of order k are widely used to make a three factor experiment when each factor has klevels In some experiments the size of the blocks may be less than the numbers of treatments In orderto compare all treatments in each block a new class of Latin squares called incomplete Latin squares is introduced One of the most important types of incomplete Latin squares is the balanced incompleteLatin square with parameters k and r which is denoted by BILS k r It is obtained from an incompleteLatin square such that each of the k labels occurs exactly r times in the square A transversal in a Latinsquare of order k is a set of k entries one selected from each row and each column of the Latin squaresuch that no two entries contain the same symbol It is well known that a Latin square of order k has anorthogonal mate if and only if it can be decomposed into k disjoint transversals If an orthogonal Latinsquare is superimposed on another one then the k cells of one Latin square corresponding to the samesymbol of the other Latin square form a transversal A Latin square L is called a Knut Vik design if everyright and left diagonal of L is complete Also L is called right left semi Knut Vik design if all of theright left diagonals are complete A Latin square is said to be crisscross Latin square if each of the oddright and even left diagonals contains each of the symbols exactly once The BILS k r can be constructedfrom the orthogonal Latin squares Knut Vik designs semi Knut Vik designs or crisscross Latin squaredesigns It is important to consider the connectedness of BILS designs The BILS k r with informationmatrix C is called connected if the rank of C is equal to k 1 Therefore a connected BILS k r is constructedby choosing a Knut Vik design semi Knut Vik design or crisscross Latin square design of order k andthen removing the k r appropriate diagonals of the selected design such that the rank of its matrix C isequal to k 1 In this thesis the optimality of the proposed BILS k k 1 designs is investigated and the optimality functions which satisfy four conditions of isotonic to the Loewner ordering concavity positivehomogeneity and permutation invarient are considered A design is said to be universally optimal if itis optimal for all functions which satisfy these four conditions Unlike the relative efficiency of theBILS k k 1 designs for treatment effects the relative efficiency of the BILS k k 1 designs for the row column and treatment effects depend on the choice of the optimality function The BILS k k 1 designsare asymptotically universal optimal for treatment effects and also they are asymptotically p optimal forall row column and treatment effects

فاطمي، مصطفي

طرح هاي مربع لاتين ناقص متعادل

مربع لاتين ناقص , ماتريس اطلاع , بهينگي , مربع لاتين متعامد , مربع لاتين متقاطع , طرح نات ويك