in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

New data is emerging from evolutionary anthropology and the neuroscience of social cognition on our species-specific hyper-cooperation (HC). This paper attempts an integration of third-person archaeological and second-person, neuroscientific perspectives on the structure of HC, through a post-Ricoeurian development in hermeneutical phenomenology. We argue for the relatively late evolution of ad...

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive sheaves of any rank; on the contrary fo...

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetr...

The cardinal pathophysiology of Parkinson's disease (PD) is considered to be the increase in the activities of basal ganglia (BG) output nuclei, which excessively inhibits the thalamus and superior colliculus (SC) and causes preferential impairment of internal over external movements. Here we recorded saccade performance in 66 patients with PD and 87 age-matched controls, and studied how the ab...

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very str...

The communication (and reflexive translation) of denotations between semantic domains can generate “horizons of meaning” as reflexive orders that remain structurally coupled to individual minds. Luhmann noted that this elusive order contains a trade-off between “organization” at interfaces integrating (differently coded) expectations at each moment of time, and the potential of further differen...