Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

The nested association mapping (NAM) strategy promises to combine the advantages of linkage mapping and association mapping. The objectives of my research were to (i) investigate by computer simulations the power and type I error rate for detecting quantitative trait loci (QTL) with additive effects using recombinant inbred line (RIL) populations of maize derived from various mating designs, (i...

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

The concurrent-memory-load technique identifies attention demands with interactions between reaction-time-task parameters and the size of the load on memory. Three experiments are reported in which a multiple-choice, reaction time task involving two, four, and eig-ht stimulus-response (S-R) alternatives was performed alone and in the retention interval of a short-termmemory task involving order...

Identification of environment-specific QTL and stable QTL having consistent genetic effects across a wide range of environments is of great importance in plant breeding. Inclusive Composite Interval Mapping (ICIM) has been proposed for additive, dominant and epistatic QTL mapping in biparental populations for single environment. In this study, ICIM was extended to QTL by environment interaction...

Dwarf resources in Brassica napus are very important for developing high-yield cultivars through dwarf-type and lodging-resistant breeding. However, few dwarf varieties have been available for this species. Here, we reported a new rapeseed dwarf mutant GRC1157, which exhibits obvious phenotypic variations on dwarf. Six generations (P1, P2, F1, F2, B1, and B2) were produced from a cross between ...

Here we describe a method for separating the sum of chaotic signals into the individual components, using the inherent underlying dynamics of the chaotic sources. Capabilities of the method are demostrated on example of discrete-time systems, one-dimensional logistic maps. We demonstrate that the proposed approach based on backward iteration of the mapping equations describing the chaotic sourc...

In this paper, we investigate homomorphisms between JB∗ -triples, and derivations on JB∗ -triples associated to the following Cauchy–Jensen type additive functional equation f ( x + y 2 + z ) + f ( x + z 2 + y ) + f ( y + z 2 + x ) = 2[f (x) + f (y) + f (z)]. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stabilit...

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) ⊆ L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T (A2n+1) = 2n+1 ∑ i=1 (−1)i+1Ai−1T (A)A2n+1−i, for all A ∈ A(X) and some fixed integer n ≥ 1. In this case T ...

In this paper we prove the following result. LetH be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D : A(H) → L(H) satisfying the relation D(An) = D(A)A∗n−1 + AD(An−2)A∗ + An−1D(A) for all A ∈ A(H) and some fixed integer n > 1. In this case there exists a uniqu...