I. N. Herstein  proved that a prime ring of characteristic not two with a nonzero derivation d satisfying d(x)d(y) = d(y)d(x) for all x, y must be commutative, and H. E. Bell and M. N. Daif  showed that a prime ring of arbitrary characteristic with nonzero
derivation d satisfying d(xy) = d(yx) for all x, y in some nonzero ideal must also be commutative. For semiprime rings, we show that an inner derivation satisfying the condition
of Bell and Daif on a nonzero ideal must be zero on that ideal, and for rings with identity, we generalize all three results
to conditions on derivations of powers and powers of derivations. For example, let R be a prime ring with identity and nonzero derivation d, and let m and n be positive integers such that, when charR is finite, m ∨ n < charR. If d(xmyn) = d(ynxm) for all x, y ∈ R, then R is commutative. If, in addition, charR≠ 2 and the identity is in the image of an ideal I under d, then d(x)md(y)n = d(y)nd(x)m for all x, y ∈ I also implies that R is commutative.
Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on X, and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D: A(X) → L(X) satisfying the relation D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras.
Authors:Qinyi Fu, Hongwei Zheng, Xiangning Han, Limin Cao, and Jianxin Sui
aquatic products, the existing HPLC methods show some disadvantages. Firstly, because most biogenic amines lack a suitable chromophore, they have to be derived with dansyl chloride (Dns-Cl), o-phthalaldehyde or other reagents before analyzing with
Authors:S. Casu, S. Galvagno, A. Calabrese, G. Casciaro, M. Martino, A. Russo, and Sabrina Portofino
Summary Refuse derived fuels (RDF) characterization and pyrolysis behaviour, carried out by means of thermogravimetric analysis, infrared and mass spectroscopy, are presented. Thermal degradation of RDF takes place through three main mass loss stages; the analyses of evolved gas allow us to discriminate the contributions of the different fractions (paper, LDPE, wood, rubber, etc.) to the global decomposition. Furthermore thermogravimetry (TG) was used for the determination of kinetic parameters, using the differential method. In order to set up the conditions of production of a good quality pyrolysis gas, the operating conditions of RDF in a pyrolysis reactor have been simulated. Data show that the volatile fraction grows with the temperature, together with the relative conversion, and that light volatile fraction (hydrogen, ethyne, etc.) gets richer, at the expense of superior homologous hydrocarbons.
Authors:Luciano N. Batista, Rosane A. S. San Gil, Luciana B. R. Lopes, and Vera L. P. Soares
-product. As the amount of glycerol predicted would be more than could be absorbed in a single industrial segment, a molecule derived from glycerol with biofuel features was tailored. One of the main requirements for a compound to act as a fuel is that it must
Authors:A. Nath, S. Mondal, A. Csighy, M.A. Molnár, K. Pásztorné-Huszár, Z. Kovács, A. Koris, and Gy. Vatai
, A. , Verasztó , B. , Basak , S. , Koris , A. , Kovács , Z. & Vatai , G. ( 2016 ): Synthesis of lactose-derived nutraceuticals from dairy waste whey — A review . Food Bioprocess Tech. , 9 , 16 – 48