We quantise complex, infinite–dimensional projective space CP(H). We apply the result to quantise a complex, finite–dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The embedding is univocally determined by requiring it to be an isometry between the Bergman metric on C and the Fubini–Study metric on CP(H). Then the Hilbert–spa...

1. In the mathematical theory of fields of elementary particles one has to do with a representation of the unitary group on a Hilbert space 77. With any such representation T and subspace M of 77 there is associated a self-adjoint operator called the "number of particles in M." The particle interpretation of general wave fields is made possible in the first instance by the fact that these opera...

In this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. Weshow that obtained result is an extension of the result ofRodr'{i}guez-L'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

We show that an infinite-dimensional real Banach space with numerical index 1 satisfying the Radon– Nikodỳm property contains l1. It follows that a reflexive or quasi-reflexive real Banach space cannot be re-normed to have numerical index 1, unless it is finite-dimensional.

In this paper we give sufficient conditions for a bang-bang regular extremal to be a strong local optimum for a control problem in the Mayer form; strong means that we consider the C0 topology in the state space. The controls appear linearly and take values in a polyhedron, and the state space and the end point constraints are finite-dimensional smooth manifolds. In the case of bang-bang extrem...

The edge space of a finite graph G = (V,E) over a field F is simply an assignment of field elements to the edges of the graph. The edge space can equally be thought of us an |E|-dimensional vector space over F. The cycle space and bond space are the subspaces of the edge space generated by the cycle and bonds of the graph respectively. It is easy to prove that the cycle space and bond space are...

We study homological structure of the filtration of the space of selfadjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.

Set-valued mappings play an important role in a number of optimization problems. We examine several of those problems in these notes. We discuss iterative algorithms for solving these problems and prove convergence. We use the finite-dimensional space RJ through-out, although the results also hold for weak convergence in infinite-dimensional Hilbert space.