fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

a note on a paper by e khorram and a ghodousian abstract the aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 may not lead to the optimal solution in some cases besides it will be pointed out that the other algorithm correct but unfortunately ineffective for larger problems proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 can be extended to a wider class of non convex optimization problems

on a special type of solutions of arbitrary higher spin dirac operators in this paper an explicit expression is determined for the elliptic higher spin dirac operator acting on functions f x taking values in an arbitrary irreducible finite dimensional module for the group spin m characterized by a half integer highest weight also a special class of solutions of these operators is constructed and the connection between these solutions and transvector algebras is explained

deriving minimal solutions for fuzzy relation equations with max product composition this work considers fuzzy relation equations with max product composition the critical problem in solving such equations is to determine the minimal solutions when an equation is solvable however this problem is np hard and difficult to solve a v markovskii on the relation between equations with max product composition and the covering problem fuzzy sets and systems 153 2005 261 273 this work first examines the attributes of a solvable equation and characteristics of minimal solutions then reduces the equation to an irreducible form and converts the problem into a covering problem for which minimal solutions are correspondingly determined furthermore for theoretical and practical applications this work presents a novel method for obtaining minimal solutions the proposed method easily derives a minimal solution and obtains other minimal solutions from this predecessor using a back tracking step the proposed method is compared with an existing algorithm and some applications are described in detail

the higher spin laplace operator in several vector variables in this paper an explicit expression is obtained for the conformally invariant higher spin laplace operator which acts on functions taking values in an arbitrary finite dimensional irreducible representation for the orthogonal group with integer valued highest weight once an explicit expression is obtained a special kind of polynomial solutions of this operator is determined

minimizing a linear function under a fuzzy max min relational equation constraint in this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint a necessary condition for optimal solution is proposed based on this necessary condition we propose three rules to simplify the work of computing an optimal solution numerical examples are provided to illustrate the procedure experimental results are reported showing that our new procedure systematically outperforms our previous work

spinor valued l2 spaces on sm 1 and representations of spin 1 m abstract we show that the l 2 spaces of spinor valued functions on s m 1 provide models for the unitary principal series representations of spin 1 m which are characterized by the feature that they contain the fundamental spinor representation s of spin m the novelty of our approach is that we use tools characteristic of hypercomplex analysis the group spin 1 m is realized as a group of vahlen matrices and the harish chandra modules of such representations are expressed in terms of spherical monogenics which generalize the classical spherical harmonics by switching to the framework of hypercomplex analysis on the sphere we are able to extend part of the well known results for the scalar spherical principal series representations of so 1 m to the spinor setting in the process we introduce a clifford algebra valued riesz transform on the sphere

assessing large sets of rank correlations summary a recent poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors this allows the asymptotic distribution of the largest of the rank correlations to be derived simulations show that the asymptotic approximations are close in the tails of the distributions an example indicates how these approximations can be used to assess the significance of the large correlation coefficients given the measurement of k characteristics on each of n individuals one often wishes to determine which if any of the characteristics are associated suppose one has a measure of association between two n vectors standardized so that large positive and negative values indicate positive and negative association respectively one could calculate the k k 1 different values taken by this measure when the k observed vectors are compared two at a time those observed values which are largest in modulus may then be used to determine which pairs of characteristics are possibly associated the difficult problem of course is to decide when a large value is significant one must take account not only of the fact that we are making multiple comparisons but also of the fact that values calculated for different pairs of vectors may be dependent when the observations on a particular characteristic are independent and identically distributed normal random variables and the measure of association is the product moment correlation there are a number of procedures available for testing for association the standard likelihood ratio test for a general alternative based on the logarithm of the determinant of the observed correlation matrix gives an overall test however this test does have some drawbacks the observed correlation matrix is singular if k n so that the test cannot be used furthermore simulations show that the asymptotic distribution of the test statistic is not a good approximation when k n unless n is large there are graphical techniques for the normal case hills 1969 schweder spj0tvoll 1982 which are designed to identify those coefficients which seem to be suspiciously large but as with many graphical techniques no probability statements can be made still considering normal observations moran 1980 studied the distribution of the maximum of the lk k 1 correlation coefficients for this distribution he derived accurate bounds which can be used to construct a formal test recently cameron eagleson 1985 constructed a test based on a few of the large correlation coefficients using an asymptotic result for u statistics with a varying kernel silverman brown 1978 here the asymptotics are when k the number of characteristics is large their

optimization of fuzzy relational equations with max av composition max min and max product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations both are members in the class of max t norm composition in this study the max av composition is considered for the same optimization model which does not belong to the max t norm composition however max av composition generates some properties of the solution set that are similar to the max product composition thanks to these properties a simple value matrix with rules can be applied to reduce problem size thus this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub problems or finding all the potential minimal solutions

rarita schwinger type operators in clifford analysis abstract in this paper we investigate a generalization of the classical rarita schwinger equations for spin 3 2 fields to the case of functions taking values in irreducible representation spaces with weight k 1 2 these fields may be realised as functions taking values in spaces of spherical monogenics earlier considered in f sommen and n van acker 1993 in clifford algebras and their applications in mathematical physics kluwer academic dordrecht norwell ma in this paper we develop the main function theoretic results

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

a limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials a sequence of independent experiments is performed each one producing a letter from a given alphabet we study the number of overlapping appearances of a given pattern of letters and we prove that under quite general conditions the number of overlapping appearances of long patterns is approximately distributed according to a polya aeppli distribution

spherical monogenics on the lie sphere abstract in this paper spherical monogenics on the lie sphere ls m 1 are introduced leading to a refinement of the theory of spherical harmonics on ls m 1 developed by morimoto furthermore the explicit decomposition in spherical monogenics of the cauchy hua kernel is given and the theory is applied to classes of spin m invariant operators on r m and on ls m 1 itself finally the theory is applied to the spherical means of functions defined on the unit sphere which satisfy a spin m invariant darboux type system on the lie sphere

testing for correlated errors in the analysis of variance summary in a two way analysis of variance one factor may have a spatial or temporal structure in which case correlation may be expected between the errors for the different levels of that factor this note suggests a procedure for checking this in analyses with just one observation per combination of levels of the two factors the procedure involves calculation of correlation coefficients it is illustrated on measurements of the size of mitral cells in the olfactory bulbs of rats it is now standard practice when fitting a model to data to use residuals to check for inadequacies in the fit in an analysis of variance the residuals may be checked for nonnormality or for an effect not included in the model an interaction for example this note suggests a further test for the adequacy of the model in the two way analysis of variance with just one observation per combination of levels of the two factors the test is based on the correlations between the residuals and can be used to detect whether the errors are contrary to assumption correlated such a test is applicable if one factor in an experiment has some spatial or temporal structure so that neighbouring units may have error structures that are associated a biological example of such a factor is time of observation that the existence of serial correlations amongst the errors can invalidate the usual f test has been noted by for example andersen jensen and schou 1981 box 1954 daniels 1938 fisher 1941 p 226 and hearne clark and hatch 1983 a simple approach is to compute an overall estimate of the lag i serial correlation coefficient this is inappropriate however if the true serial correlations vary with the levels of the spatial or temporal factor the correlations may even have opposite signs at different levels in the case of a two way analysis of variance where the first factor is spatial or temporal the observations at the different levels of the second factor provide replicates that can be used to calculate sample correlation coefficients between the residuals at the different levels of the first factor these correlation coefficients can then be assessed to determine whether there are any unusually large ones the only difficulty is that there may be a large number of coefficients to consider so that the problem of multiple comparisons arises if there are k levels of the spatial temporal factor there are up to ok correlation coeffi1cients that may be of interest thus if an overall test at the a level of significance is required the critical point for comparing each correlation must depend on the number of comparisons to be made

an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition abstract fuzzy sets as the feasible region for optimization problems is an interesting and on going research topic s c fang g li solving fuzzy relations equations with a linear objective function fuzzy sets syst 103 1999 107 113 7 j lu s c fang solving nonlinear optimization problems with fuzzy relation constraints fuzzy sets syst 119 2001 1 20 16 e khorram a ghodpusian linear objective function optimization with fuzzy relation constraints regarding max av composition appl math comput in press doi 10 1016 j amc 2005 04 021 in this paper we focus on these kind problems in which the solutions region is the fuzzy relation equation with max prod composition and the objective function is linear whereas one of the major difficulties in such problems is non convexity of the feasible region it is preferable to study these regions in the first step hence we have primarily investigated two methods and their relationship and then we have determined the feasible region via them after determining the feasible set we have given an algorithm to optimize the linear objective function on such these regions finally we have presented two examples to illustrate the methods and algorithms

asymptotic distribution of the largest off diagonal entry of correlation matrices suppose that we have observations from a dimensional population we are interested in testing that the variates of the population are independent under the situation where goes to infinity as a test statistic is chosen to be where is the sample correlation coefficient between the th coordinate and the th coordinate of the population under an independent hypothesis we prove that the asymptotic distribution of is an extreme distribution of type by using the chen stein poisson approximation method and the moderate deviations for sample correlation coefficients as a statistically more relevant result a limit distribution for where is spearman s rank correlation coefficient between the th coordinate and the th coordinate of the population is derived

decomposition of the polynomial kernel of arbitrary higher spin dirac operators in a series of recent papers we have introduced higher spin dirac operators which are generalisations of the classical dirac operator whereas the latter acts on spinor valued functions the former acts on functions taking values in arbitrary irreducible half integer highest weight representations for the spin group in this paper we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group we will hereby make use of results from representation theory

on the fundamental solution for higher spin dirac operators abstract in this paper we will determine the fundamental solution for the higher spin dirac operator q which is a generalisation of the classical rarita schwinger operator to more complicated irreducible half integer representations for the spin group in m dimensions this will allow us to generalise the stokes theorem the cauchy pompeiu theorem and the cauchy integral formula which lie at the very heart of the function theory behind arbitrary elliptic higher spin operators

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

poisson convergence for dissociated statistics summary a poisson limit theorem is derived for the number of large values observed among comparisons of independent but not necessarily identically distributed random variables the comparisons made need not be the same and may depend on the two variables being compared an application to the assessment of large numbers of correlation coefficients is given

on the relation between equations with max product composition and the covering problem systems of equations with max product composition are considered it is shown that solving these equations is closely related with the covering problem which belongs to the category of np hard problems it is proved that minimal solutions of equations correspond to irredundant coverings in terms of the covering problem the conditions of compatibility of equations of redundancy of equations of uniqueness of solution of uniqueness of minimal solution are determined concepts of essential non essential semi essential and super essential variables are suggested ways of simplification of a covering problem and methods of its solving are considered

a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian abstract in this paper we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition that it has been proposed by ghodousian and khorram a ghodousian e khorram an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition appl math comput 178 2006 502 509 firstly we show that the algorithm may not lead to the optimal solution in some cases secondly we propose a new algorithm for solving the presented model by ghodousian and khorram 2006 as mentioned above in fact it modifies the presented algorithm in the ghodousian and khorram s paper also this algorithm is extended to the presented model by khorram and ghodousian e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 with max av composition finally some numerical examples are given for illustrating the purposes

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

functional poisson approximation in kantorovich rubinstein distance with applications to u statistics and stochastic geometry a poisson or a binomial process on an abstract state space and a symmetric function f acting on k tuples of its points are considered they induce a point process on the target space of f the main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a poisson process on the target space the technical background are a version of stein s method for poisson process approximation a glauber dynamics representation for the poisson process and the malliavin formalism as applications of the main result error bounds for approximations of u statistics by poisson compound poisson and stable random variables are derived and examples from stochastic geometry are investigated

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

a note on a paper by molai and khorram abstract the aim of this note is to show that the optimization algorithm proposed in 6 may not lead to the optimal solution in some cases in fact the optimization problem remains open if we do not apply the branch and bound method to solve it or compute all the objective values of minimal solutions of the feasible domain