The abstract economy defined by Debreu (1952) generalizes the Nash non-cooperative game in that a player’s strategy set depends on the strategy choices of all the other players. Debreu (1952) proved the existence of equilibrium in abstract economies with finitely many agents, finite dimensional strategy space, and quasi-concave utility functions. Since then, the Debreu’s result has been extende...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

in this paper, using a one-dimensional simulation model, the reforming process of sour gas, i.e. ch4, co2, and h2s, to the various charged particles and syngas in a dielectric barrier discharge (dbd) reactor is studied. an electric field is applied across the reactor radius, and thus a non-thermal plasma discharge is formed within the reactor. based on the space-time coupled finite element meth...

We give the infinite-dimensional representation for the elliptic K-operator satisfying the boundary Yang-Baxter equation. By restricting the functional space to finite-dimensional space, we construct the elliptic K-matrix associated to Belavin's completely Z-symmetric R-matrix.

A reflection in a real vector space equipped with a positive definite symmetric bilinear form is any automorphism that sends some nonzero vector v to its negative and pointwise fixes its orthogonal complement, and a finite reflection group is a discrete group generated by such transformations. We note two important classes of groups which occur as finite reflection groups: for a 2-dimensional v...

A double algebra is a linear space V equipped with linear map V ⊗ V → V ⊗ V . Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double algebras do not exist over an arbitrary field, and all simple finite-dimensional associative double algebras over an algebraically closed field are trivial. Over an arbitrary...

Dimensionality reduction is a generic name for any procedure that takes a complicated object living in a high-dimensional (or possibly even infinite-dimensional) space and approximates it in some sense by a finite-dimensional vector. We are interested in a particular class of dimensionality reduction methods. Consider a data source that generates vectors in some Hilbert space H , which is eithe...