We construct a linear interval system Ax = b with a 4 × 4 interval matrix whose all proper interval coefficients (there are also some noninterval ones) are of the form [−ε, ε]. It is proved that for each ε > 0, the interval hull [x, x] and interval hull of the midpoint preconditioned system [x, x] satisfy x1 = 0.6 and x1 = 1.2, hence midpoint preconditioning produces a 100% overestimation of x1...

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros ...

Inbreeding coefficients of artificially bred Ayrshire, Guernsey, Holstein, Jersey, and Brown Swiss cows were calculated from relationships between sires and maternal male ancestors. Percentages of inbred cows and average inbreeding coefficients of inbred cows were: Ayrshire, 26 and 11%; Guernsey, 11 and 4%; Holstein, 31 and 1%; Jersey 23 and 2%; and Brown Swiss, 23 and 2%. Percentages of inbred...

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that LFPP RICs function can be converted into (LPP) by using variable transformations. To solve this problem, we will make two LPP (ICs). Next, those four LPPs constructed under these assumptions; solved classical simplex method and used MS Excel Solver....

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

‎we consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎we present a class of problems that are easily solved by reduction to the classi...

Hemodynamic variability in patients with atrial fibrillation may originate from a direct influence of the variations in RR intervals on myocardial contractility. With the aid of a computer the serial autocorrelation function and the histogram of the RR intervals of patients with atrial fibrillation receiving no medication were produced. The RR intervals were randomly distributed and the histogr...

The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval ∆t was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as n!. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is not excluded that for number of the potentia...