The question of the existence and uniqueness of an M-matrix which is a square root of an M-matrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an M-matrix.

In this paper, we consider a generalization of binomial coe¢ cients, called C– nomial coe¢ cients, dependent upon a sequence fungn, with indices in arithmetic progressions. We obtain a general recurrence relation and a generating matrix, and point out some new relationships between these coe¢ cients and the generalized Pascal matrices. Further, we obtain generating functions, combinatorial repr...

Matricaria chamomilla is a medicinal plant that is widely cultivated in salt affected soils. This investigation was undertaken to study the effect of NaCl concentration on germination, and the physiological, biochemical and growth characteristics of chamomile. Seed germination and growth were studied at five NaCl concentration levels (0, 40, 80, 120 and 190 mM NaCl concentration). Increasing th...

In this paper, we study the nth-bias optimality problem for finite continuous-time Markov decision processes (MDPs) with a multichain structure. We first provide nth-bias difference formulas for two policies and present some interesting characterizations of an nth-bias optimal policy by using these difference formulas. Then, we prove the existence of an nth-bias optimal policy by using nth-bias...

In this paper, we first show that the exponential Diophantine equation 2x + 1 = z2has unique solution (x, z) (3, 3). We then for n > 1, exponential. M 2y z2 where Mn := 2n − is nth Mersenne number, has exactly two solutions in non-negative integers viz., 0, 3) and (n 2, 1). Also, prove w4 y, w, n) (5, 3, . Finally, w2m, m 2 no integral solutions. conclude with some examples to illustrate our...

a hydroponic experiment was carried out to compare root anatomy and hydraulic conductivity of four barley cultivars including valfajr, karoon, afzal and zarjo under salt stress conditions. the results showed that under salt stress, the minimum diameter of vessels was observed in the peripheral metaxylem of seminal roots of valfajr cultivar and in adventitious roots; karoon with 19±3 µm had maxi...

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear...