Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...

Reflexive methodology was used to identify music collectors’ needs, that informed the development of conceptual prototypes which create moments of delightful distraction in their everyday lives. ARON: music lives in the cloud is a music listening and sharing system that enables ambient, non-task oriented experiences through networked biomorphic light forms equipped with a presence interface. AR...

Prior studies on online sentence processing have shown that the parser can resolve non-local dependencies rapidly and accurately. This study investigates the interaction between the processing of two such non-local dependencies: wh-filler-gap dependencies (WhFGD) and reflexive-antecedent dependencies. We show that reflexive-antecedent dependency resolution is sensitive to the presence of a WhFG...

We derive consequences from the existence of a term which satisfies Mal’cev identities (characterizing permutability) modulo two functions F and G from admissible relations to admissible relations. We also provide characterizations of varieties having a Mal’cev term modulo F and G. Given an algebra A, let Adm(A) denote the set of all reflexive and admissible relations on A (we shall use the wor...

It was observed by Gilfeather, Hopenwasser, and Larson in [1] that Tomita's commutation formula for tensor products of von Neumann algebras can be rewritten in a way that makes sense for tensor products of arbitrary reflexive algebras. The tensor product problem for reflexive algebras is to decide for which pairs of reflexive algebras this tensor product formula is valid. Recall that a subalgeb...

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. This is used to prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a ...

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflex...

A novel two-step paradigm was used to investigate the parallel programming of consecutive, stimulus-elicited ('reflexive') and endogenous ('voluntary') saccades. The mean latency of voluntary saccades, made following the first reflexive saccades in two-step conditions, was significantly reduced compared to that of voluntary saccades made in the single-step control trials. The latency of the fir...

This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The major advantages of RGT are its ability to predict human behavior and unfold the entire spectra of reflexion in the human mind. On the other ha...