Given an approximate solution to a data least squares (DLS) problem, we would like to know its minimal backward error. Here we derive formulas for what we call an “extended” minimal backward error, which is at worst a lower bound on the minimal backward error. When the given approximate solution is a good enough approximation to the exact solution of the DLS problem (which is the aim in practic...

This paper presents some novel theoretical results as well as practical algorithms and computational procedures on fuzzy relation equations (FRE). These results refine and improve what has already been reported in a significant manner. In the previous paper, the authors have already proved that the problem of solving the system of fuzzy relation equations is an N P-hard problem. Therefore, it i...

We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimaltime solution. Both solutions use fewer states than the previous bestknown minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We sh...

PCOS is still a problem in gynecology and infertility. Especially in ART the problem of PCOS patients is bigger and more highlighted. These patients are prone to over and under stimulation. Strategies to overcome hyper stimulation are: use of metformin, ovarian drilling, use of minimal stimulation, suppressing LH with use of OCP or GnRh analogues, use of GnRh antagonist in COH. But none of thes...

In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

plays central role in the linear control theory. It occurs in optimal control synthesis, in dead-beat as well as in quadratic criteria [1, 2, 3]. In this equation, a(X), b(X), c(X) are given polynomials, x(X), y(X) are unknown ones. We suppose a(X), b(X) are not both identically zero. Main tool for studying this Euclidean equation is the Euclidean algorithm. It yields general solution and can s...

In this paper we study two-sided, one-to-one matching problems and consider the most wellknown solution concept: the men-optimal solution. The men-optimal solution fails to satisfy consistency as well as converse consistency. Thanks to Sasaki and Toda (1992), we know that the minimal consistent extension of the men-optimal solution equals the core (Thomson, 1994a). In this paper, we compute the...

(4) 0 < a1 < a2 < . . . < ak and ai ∈ A for i = 1, . . . , k. The set A is called an asymptotic basis of order k if there exists a natural number n1 such that rA(n) > 0 for all n ≥ n1. The set A is called a strict asymptotic basis of order k if there exists a natural number n1 such that r′ A(n) > 0 for all n ≥ n1. All bases considered in this paper will be either asymptotic or strict asymptotic...

In this paper we solve the problem of estimating the relative pose between a robot’s gripper and a camera mounted rigidly on the gripper in situations where the rotation of the gripper w.r.t. the robot global coordinate system is not known. It is a variation of the so called hand-eye calibration problem. We formulate it as a problem of seven equations in seven unknowns and solve it using the Gr...