Generalized*-Lie Higher Derivable Mappings on*-Rings

Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△={G_(n)}_(n∈N)associated with a*-Lie higher derivable mapping L={L_(n)}_(n∈N),then for any X,Y in R and for each n in N there exists an element Z_(X,Y)(depending on X and Y)in the center Z(R)such that G_(n)(X+Y)=G_(n)(X)+G_(n)(Y)+Z_(X,Y).

Jordan Higher Derivable Maps on Triangular Algebras by Commutative Zero Products

In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained.

*-Lie Derivable Mappings on Von Neumann Algebras

In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.

CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Evaluation of Structural Framework and Depth Estimates Using High Resolution Airborne Magnetic Data over Some Parts of Middle Benue Trough, Nigeria

High-resolution aeromagnetic data of parts of Middle Benue Trough, Nigeria (sheets 212, 213, 233 and 234) was interpreted by applying source Parameter Imaging (SPI) and Spectral Depth analysis with the aim of mapping out the magnetic lineaments and analysing magnetic signals coming from different sources. The results from the derivatives maps show major and minor lineaments trends in the NE-SW and NW-SE directions respectively. Results from SPI show the maximum sedimentary thickness of about -4546.7 m (-4.5467 km) around the region of Awe, Aman, Langtang south, Gassol and the north-eastern part of Donga. Minimum depth of -167.9 m (-0.1679 km) around the region of north of Shendam, north of Wase, north-eastern part of Aman, Bantaji, Donga, Ibi and Bali. The residual map was divided into twenty-five sections. Spectral Depth was run for each of these twenty-five sections, the result shows that the depth to the deep magnetic source ranges between -0.65 km and -3.35 km. The depth to the shallow magnetic sources ranges between -0.03 km and -0.44 km showing the presence of magnetic intrusive bodies within the sediments. Since the sedimentary thickness of 3.0 km and above is only sufficient for hydrocarbon maturation and accumulation, then the results from this present study show that the study area might be sufficient enough for hydrocarbon maturation and accumulation.

Nonlinear Maps Satisfying Derivability on the Parabolic Subalgebras of the Full Matrix Algebras

Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.

Rational maps as Schwarzian primitives

We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.

A Characterization of Generalized Derivations of JSL Algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.