1 Belian categories 3 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Diagram chase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Snake Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Delta functors . . . . . . . . . . . . . . . . . . . . ....

There is a contrast between the two sets of functional equations f0(x + y) = f0(x)f0(y) + f1(x)f1(y), f1(x + y) = f1(x)f0(y) + f0(x)f1(y), and f0(x − y) = f0(x)f0(y)− f1(x)f1(y), f1(x − y) = f1(x)f0(y)− f0(x)f1(y) satisfied by the even and odd components of a solution of f(x + y) = f(x)f(y). J. Schwaiger and, later, W. Förg-Rob and J. Schwaiger considered the extension of these ideas to the cas...

T-cell mediated cytotoxic responses to H-Y antigen require co-recognition of H-Y and H-2 gene products. F1 mael stimulating cells and target cells express H-Y antigen in association with both parental H-2 haplotypes. However, F1 females primed in vivo and challenged in vitro with F1 male cells lyse male target cells of F1 and only one parental H-2 haplotype. Thus, (CBA X B10)F1 females sensitiz...

The striped pattern of fushi tarazu (ftz) expression found in the blastoderm of the Drosophila melanogaster embryo is generated largely through complex interactions between multiple transcription factors that bind to the zebra element of the ftz gene. A motif in the zebra element, the FTZ-F1 recognition element (F1RE), has been shown to bind a transcription factor, FTZ-F1 alpha, that is a membe...

The cancellation level and phase were measured for the (f2-f1) distortion product in six normal-hearing ears as a function of input level (L1,L2) and the frequency separation of the two input signals (f1,f2, where f2 greater than f1). The effects of input level were examined for L1 and L2, varied together (L1 = L2) and separately. Typically, f1 was 1500 Hz while f2/f1 was either 1.16, 1.32, 1.4...

Detailed understanding of the action of biological molecular machines must overcome the challenge of gaining a clear knowledge of the corresponding free-energy landscape. An example for this is the elucidation of the nature of converting chemical energy to torque and work in the rotary molecular motor of F1-ATPase. A major part of the challenge involves understanding the rotary-chemical couplin...

F1-ATPase is the catalytic component of the ATP synthase molecular machine responsible for most of the uphill synthesis of ATP in living systems. The enormous advances in biochemical and structural studies of this machine provide an opportunity for detailed understanding of the nature of its rotary mechanism. However, further quantitative progress in this direction requires development of relia...

The Escherichia coli uncA gene codes for the a subunit of the F1-sector of the membrane proton-ATPase. Mutations in this gene cause loss of ATPase and ATP synthesis activity and, in some instances, derangement of F1 structure. From three mutants (uncA401, uncA453, and uncA447), an F1 of normal size and subunit structure may be purified. In this work, purified soluble F1 from these three mutants...