CLUSTER EXPANSION WITH APPLICATIONS 3 In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so that the left side is roughly proportional to l(x). This suggests to try a(x) = cl(x), and one can then optimize on the v...

June 30, 1986 When Bouroncle and colleagues’ described hairy cell leukaemia as a distinct type of human leukaemia, the methodology for characterising the membrane phenotype of lymphocytes was not yet available. The peculiar morpholo~yofthe hairy cell with its long cytoplasmic villi, well demonstrated by phase contrast microscopy, had some resemblance with that of histiocytes as seen in tissue s...

1 (a) Claim: R[X, Y ] is not a Euclidean domain. Proof: If R[X, Y ] was a Euclidean domain, then it would be a principal ideal domain. But consider I = (x, y) = (x) + (y). I is certainly not a principal ideal, as if it were, there would be some polynomial, g that divides everything in I, so g would divide x, implying that g does not contain any monomials with positive degree in y, and likewise ...

The science of human decision-making has long been a stronghold of psychologists. Among the voices that abound in the literature on how people make choices, one scholarly voice has remained strident through several decades. By studying human behavior through the lens of economics, Princeton University psychologist Daniel Kahneman has shown how inherent biases might influence our choices, overtl...

We study the homotopy types of complements of arrangements of n transverse planes in R, obtaining a complete classification for n ≤ 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the c...

In 1957 Chandler Davis proved a theorem that a rotationally invariant function on symmetric matrices is convex if and only if it is convex on the diagonal matrices. We generalize this result to groups acting nonlinearly on convex subsets of arbitrary vector spaces thereby understanding the abstract mechanism behind the classical theorem. We apply the new theorem to a problem from the mathematic...

Sickle cell anemia has been termed a "molecular disease" because of the demonstration that it is due to a genetically determined abnormality of hemoglobin, consisting of a single amino acid substitution in the t-chains of the globin (1-3). Erythrocytes containing sickle hemoglobin possess the usual biconcave discoid shape when the hemoglobin is combined with oxygen, but when oxygen is removed s...

The monotypic genus Buobellenden Yin & Nomura, 2009 is placed as a junior synonym of Bellenden Chandler, 2001. This act results in Bellenden jingyuanensis (Yin & Nomura), comb. n. (from Buobellenden). A new species, Bellenden siguniang Yin & Jang, sp. n., collected from the alpine area in Sichuan, SW China, is described, illustrated, and distinguished from all congeners. A new illustration of t...

EVEN though social scientists began to discuss the wonders and pitfalls of Italy’s small-scale capitalism only in the late 1970s, the development of specialized clusters of firms constituted one of the basic traits of the country’s heterogeneous economic “miracle” of the 1950s and 1960s, and some of these industrial and artisanal experiences dated back decades and occasionally even centuries. B...

ivision of Cardiothoracic Surgery, University of Florida, Jacksonville, Florida; Division of Cardiovascular & Thoracic Surgery, niversity of Kentucky Chandler Medical Center, Lexington, Kentucky; Department of Surgery, Caritas St. Elizabeth’s Medical enter, Boston, Massachussetts; Duke Clinical Research Institute, Durham, North Carolina; Starr-Wood Cardiac Group of ortland, PC, Portland, Oregon...