We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, variables inhabit certain Hilbert bundles, and computations are interpreted as the appropriate inner product preserving maps between Hilbert bundles. These bundles and maps form a symmetric monoidal...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

With a detailed investigation of n linear algebraic equations Bx = b, we find that the scaled residual dynamics for y ∈ Sn−1 is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm...

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

Many authors have studied the local dynamics of holomorphic maps in C around a fixed point; see, for example, [4; 6] for an introduction to this field and known results. Most of the results are obtained under the assumption that the linear part of the map at the fixed point is diagonalizable. There are few results in the nondiagonalizable case. In [8], Coman and Dabija studied a special map wit...

Let (R;G) be a marked elliptic root system and let ' (R;G) be the characteristic polynomial of its Coxeter element. According to the decomposition ' (R;G) = Q i ( i 1) e(i) , we attach the product (R;G) ( ) := Q i (i ) e(i) of Dedekind eta-function and call it an elliptic eta-product (1.2.1). The elliptic eta-product turns out to be holomorphic at every cusps. The main goal of the present artic...

The eta-subunit of the TCR is derived from an alternative splice product of the TCR-zeta gene. The eta-subunit has been extensively characterized in murine T cells, where up to 10% of TCR bear zeta-eta heterodimers rather than zeta-homodimers. In contrast to the significant levels of eta found in murine T cells, in human PBL an eta-like region is expressed spliced to upstream exons of the zeta-...