Representation of a granule, relation and operation between two granules are mainly researched in granular computing. Hyperbox granular computing classification algorithms (HBGrC) are proposed based on interval analysis. Firstly, a granule is represented as the hyperbox which is the Cartesian product of $N$ intervals for classification in the $N$-dimensional space. Secondly, the relation betwee...

We show that the infinite-dimensional Teichmüller space of a Riemann surface whose boundary consists of n closed curves is a holomorphic fiber space over the Teichmüller space of n-punctured surfaces. Each fiber is a complex Banach manifold modeled on a twodimensional extension of the universal Teichmüller space. The local model of the fiber, together with the coordinates from internal Schiffer...

Sufficient conditions are established for the solvability of the boundary value problem x(t) = f(x)(t), hi(x) = 0 (i = 1, . . . , n), where f is an operator (hi (i = 1, . . . , n) are operators) acting from some subspace of the space of (n − 1)-times differentiable on the interval ]a, b[ m-dimensional vector functions into the space of locally integrable on ]a, b[ m-dimensional vector functions...

2. Abstract space-time. We need first an axiomatic foundation strong enough to support both our mathematical considerations and their applications to physics. DEFINITION. An n+1 dimensional space-time (n*tl) consists of (A) An n+1 dimensional vector space V over the real numbers plus a symmetric bilinear real form A »B (inner product) such that: (1) There exists a vector A with A -A <0 . (2) An...

We argue that the string theory dual to a certain sector of the four-dimensional Yang-Mills theory at large-N is the A-model wrapping N Lagrangian Dbranes on the twistor space of the complex two-dimensional projective space, with a certain flux and Wilson loop background, by finding that the targetspace beta function of this A-model coincides with the large-N beta function of the Yang-Mills the...