For x x1, x2, . . . , xn ∈ R , the symmetric function φn x, r is defined by φn x, r φn x1, x2, . . . , xn; r ∏ 1≤i1<i2 ···<ir≤n ∑r j 1 xij / 1 xij 1/r , where r 1, 2, . . . , n and i1, i2, . . . , in are positive integers. In this article, the Schur convexity, Schur multiplicative convexity and Schur harmonic convexity of φn x, r are discussed. As applications, some inequalities are established...

One of several major contributions of Edmonds to combinatorial optimization is algorithms and polyhedral theorems for matroid intersection, and more generally polymatroid intersection. From an optimization point of view, the matroid intersection problem is the following: Let M1 = (S, I1) and M2 = (S, I2) be two matroids on the same ground set S. Then I1 ∩ I2 is the collection of all sets that a...

The imidazoline system consists in imidazoline receptors I1, I2 and I3 and the active as well as that there are some endogenous ligands. We consider that one of the most important functions of this system is modulation of different types of behavior. Existent data show that I1 and I2 receptors have different effects on some behavior components, such as suicidal behavior, stress, anxiety, food i...

Potatoes are a high-value crop with shallow root system and high fertilizer requirements. The primary emphasis in potato production is minimizing nitrogen-leaching losses from the zone through fertigation. Therefore, field experiment was conducted for two consecutive years, 2018–2019 2019–2020 to assess effect of nitrogen irrigation amount frequency on tuber yield, water balance components prod...

Let p be a large prime number, K,L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I2(M ; K, L) of solutions of the congruence xy ≡ λ (mod p), K + 1 ≤ x ≤ K + M, L + 1 ≤ y ≤ L + M and for the number I3(M ; L) of solutions of the congruence xyz ≡ λ (mod p), L + 1 ≤ x, y, z ≤ L + M. Using the idea of Heath-Brown from...

Let ξ be a random integer vector, having uniform distribution P{ξ = (i1, i2, . . . , in) = 1/n} for 1 ≤ i1, i2, . . . , in ≤ n. A realization (i1, i2, . . . , in) of ξ is called good, if its elements are different. We present algorithms Backward, Forward, Linear, Random, Tree, Garbage, Bucket which decide whether a given realization is good. We analyse the running time of these algorithms using...

The influence of in vivo melatonin administration on in vitro pituitary follicle stimulating hormone (FSH), growth hormone (GH) and prolactin secretion, as well as the possible influence of dopamine (DA) were evaluated in prepubertal (31-day-old), pubertal (33-day-old) and adult female rats at diestrus phase of the sexual cycle. The in vitro pituitary hormone secretions were evaluated at basal ...

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies. 1. Definition of the Neutrosophic Logic/Set: Let T, I, F be real standard or non-standard subsets of ]0, 1[, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf...

Abstract. If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for matrices with multiple symmetries. In this paper we consider how to exploit and preserve structure in the pivoted Cholesky factorization when appro...

In this paper we present a decoupling inequality that shows that multivariate Ustatistics can be studied as sums of (conditionally) independent random variables. This result has important implications in several areas of probability and statistics including the study random graphs and multiple stochastic integration. More precisely, we get the following result: Theorem 1. Let {Xj} be a sequence...