Abstract. In this paper we introduce the notion of "generalized" interpolation space, and state and prove a "generalized" interpolation theorem. This apparently provides a foundation for an axiomatic treatment of interpolation space theory, for subsequently we show that the "mean" interpolation spaces of Lions-Peetre, the "complex" interpolation spaces of A. P. Calderón, and the "complex" interpolation spaces of M. Schechter are all generalized interpolation spaces. Furthermore, we prove that each of the interpolation theorems established respectively for the abovementioned interpolation spaces is indeed a special case of our generalized interpolation theorem.In §111 of this paper we use the generalized interpolation space concept to state and prove a "generalized" duality theorem. The very elegant duality theorems proved by Calderón, Lions-Peetre and Schechter, respectively, are shown to be special cases of our generalized duality theorem. Of special interest here is the isolation by the general theorem of the need in each of the separate theorems for certain "base" spaces to be duals of others.At the close of §11 of this paper we employ our generalized interpolation theorem "structure" to construct new interpolation spaces which are neither complex nor mean spaces.
The tendency to adopt a fatalistic view of American race relations is an easy posture to assume-especially in light of the contradictory realities of maintaining race as real and its obvious utter worthlessness as a scientific concept. The IQ controversy is a prime example of this problematic. Although most competent social scientists concur in the belief that race is not a valid scientific concept; and, more specifically that IQ tests are culturally biased, and, as a consequence, do not provide irrefutable proof that some so-called racial groups are superior to others in intelligence, there exist some influential neo-racists social scientists who maintain that IQ tests are valid indicators of the intellectual abilities of the so-called races.Nevertheless, some social scientists who hold that race, although not a valid scientific concept, is real-that is, real in its consequences-argue, as did Robert E. Park in (1939, The nature of race relations. In Race and Culture. New York: The Free), that immigration and education, will change the social habits and mores of peoples, resulting in the increasing confusion of race and class.
A tubo-ovarian abscess (TOA) is a relatively rare medical complication that results from an untreated/unrecognized ascending pelvic infection of the female genital tract. In a right-sided TOA, this clinical entity may mimic appendicitis on computed tomography (CT). In addition, both disease processes can present with pelvic pain, leukocytosis and fever. We present the case of a 47-year-old female with mid right-sided abdominal pain that was diagnosed on CT scan with an appendiceal abscess. She underwent CT-guided percutaneous drainage with interventional radiology. On Day 8, a CT limited study involving a contrast injection was performed to evaluate for abscess resolution. The contrast within the drain filled the fallopian tube, endometrial cavity and contralateral fallopian tube. These findings demonstrated that the initial diagnosis actually represented a TOA. To the authors’ knowledge, this is the only reported case involving a TOA secondary to Streptococcus agalactiae (GBS) mimicking an appendicitis with abscess formation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.