This paper contains two directions of work. The first one gives material related to free action (an inner derivation) mappings on a group ring R[G] which is construction involving G and R the dependent elements those in R[G]. other direction deals with generalization definition actions. We concentrate our study elements, satisfy T(x)γ=δx,x∈R[G] some fixed γ,δ∈R[G]. In part we work element. word...

Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized v...

We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and show by explicit calculation that the minimum travel time and the optimal-speed Hamiltonians are determined by the metric operator (inner product...

Higher order generalizations of Lie algebras have equivalently been conceived as Lie n-algebras, as L∞-algebras, or, dually, as quasi-free differential graded commutative algebras. Here we discuss morphisms and higher morphisms of Lie n-algebras, the construction of inner derivation Lie (n+1)-algebras, and the existence of short exact sequences of Lie (2n + 1)-algebras for every transgressive L...

The Marton-Gelfand-Pinsker inner bound on the capacity region of broadcast channels was extended by HanCosta to include arbitrarily correlated sources where the capacity region is replaced by an admissible source region. The main arguments of Han-Costa are correct but unfortunately the authors overlooked an inequality in their derivation. The corrected region is presented and the absence of the...

Let be a nest and let be a subalgebra of L(H) containing all rank one operators of alg . We give several conditions under which any derivation δ from into L(H) must be inner. The conditions include (1) H− ≠H, (2) 0+ ≠ 0, (3) there is a nontrivial projection in which is in , and (4) δ is norm continuous. We also give some applications.

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with homomorphisms G→ H. (Precise statement in §1.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of G itself, is...

A simple derivation of a meaningful, manifestly covariant inner product for real KleinGordon (KG) fields with positive semi-definite norm is provided which turns out — assuming a symmetric bilinear form — to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, qu...

BACKGROUND The large number (30) of permanent human embryonic stem cell (hESC) lines and additional 29 which did not continue growing, in our laboratory at Karolinska Institutet have given us a possibility to analyse the relationship between embryo morphology and the success of derivation of hESC lines. The derivation method has been improved during the period 2002-2009, towards fewer xeno-comp...

Embryonic stem cells, derived from the inner cell mass of embryos in the blastocyst stage, are cells capable of perpetual self-renewal and long-term propagation and hold the potential to differentiate to progeny of the three embryonic germ layers. Since their derivation approximately two decades ago, exploration of mouse ES cells made major advances in ES cell differentiation research and in th...