Here CH0(X) denotes the Chow group of zero-cycles on X modulo rational equivalence and π̃ 1 (X) ab is the modified abelianized étale fundamental group, which classifies finite abelian étale coverings of X in which every real point splits completely (if X is defined over a totally imaginary number field, then this is just the usual abelianized étale fundamental group). By Lang [La], the homomorph...

In his work about Galois representations, R. Greenberg conjectured the existence, for any odd prime p and positive integer t, of a multiquadratic p-rational number field degree 2t. this article, we prove that there exists infinitely many primes such triquadratic Q(p(p+2),p(p−2),−1) is p-rational. To do this, use an analytic result providing us with p−2 p+2 simultaneously have large square facto...

it is said that the theory of active intellect is among the most ambiguous and controversial topics of aristotle’s philosophy. this ambiguity is generally regarded as being resulted from the brevity and vagueness of aristotle’s speech in his on the soul. however; is the ambiguity of aristotle’s speech to such an extent that the active intellect attributed to him can be regarded as separate from...

Unlike the Metelli monochrome transparencies, when overlays and their backgrounds have chromatic content, the inferred surface colors may not always be physically realizable, and are in some sense "imaginary." In these cases, the inferred chromatic transmittance or reflectance of the overlay lies outside the RGB spectral boundaries. Using the classical Metelli configuration, we demonstrate this...

BACKGROUND Previous research has reported a link between imaginary companions (ICs) in middle childhood and the perception of verbal material in ambiguous auditory stimuli. These findings have been interpreted in terms of commonalities in the cognitive processes underlying children's engagement with ICs and adults' reporting of imaginary verbal experiences such as auditory verbal hallucinations...

Background: Majority of high altitude residents have certain clinical, physiological, anatomical and biochemical changes. Pain threshold is one of the numerable changes that may occur due to chronic hypoxia. The aim of this research was to study the long term effects of high altitude exposure on pain perception among healthy volunteer subjects. Methods: This is an observational case-control stu...