a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

We compute the Grothendieck group K0 of non-commutative analogues of projective space bundles. Our results specialize to give the K0-groups of non-commutative analogues of projective spaces, and specialize to recover the K0-group of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection theory for quantum ruled surfaces.

This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized. A connection between some space-time supersymmetric theories and non-commutative geometry is made. The advantages and prolems of this direction are discussed.

Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SUq(2), the Green function and the Kernel on the q-homogeneous space M = SU(2)q/U(1) are derived. A path integration is formulated. Green function for the free massive scalar field on the non-commutative Einstein space R ×M is presented.

We present a self-contained and comprehensive study of the Fisher-Rao space matrix-valued non-commutative probability measures, related Hellinger space. Our is natural generalization classical commutative measures Bures-Wasserstein Hermitian positive-definite matrices. introduce justify canonical entropy on space, which differs from von Neumann entropy. consequently derive analogues heat flow, ...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrödinger equation for a free particle is investigated in such a non-commutative plane and ...