But here are four fragments that will possibly play a part in longer work: I begin with sketch of what it is to do legal history today, the wake enormous growth and development field education, over past forty years. continue an extended examination answers Willard Hurst, founder modern discipline history, gave more than fifty-five years ago question, does do. Finally, two final fragments, spin...

The Alladi-Gordon identity ∑j k=0(q i−k+1; q)k [ j k ] q(i−k)(j−k) = 1 plays an important role for the Alladi-Gordon generalization of Schur’s partition theorem. By using Joichi-Stanton’s insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by es...

around the roots of plants, as Nicole van Dam and Harro Bouwmeester report in a review of this fi eld (Trends Plant Sci. (2016) DOI: http://dx.doi. org/10.1016/j.tplants.2016.01.008). Direct investigation of signalling in the rhizosphere is currently focused on communication between plants and their microbial symbionts, as Vittorio Venturi and Christopher Keel report, although the scope could b...

Rapid creation of BAC-based human artifical chromosome vectors by transposition with synthetic alpha-satellite arrays Joydeep Basu, Gregory Stromberg, George Compitello, Huntington F. Willard and Gil Van Bokkelen Nucleic Acids Res. (2005) 33, 587–596. The publishers would like to apologize for an error in one of the labels in Figure 1B. The correct complete figure and its legend are given on th...

exchange-coupled Ni11Co11Fe66Zr7B4Cu1 films for high frequency applications S. D. Yoon, A. K. Baraskar, A. Geiler, A. Yang, C. Pettiford, N. X. Sun, R. Goswami, M. A. Willard, C. Vittoria, and V. G. Harris Center for Microwave Magnetic Materials and Integrated Circuits, Northeastern University, Boston, Massachusetts 02115, USA Department of Electrical and Computer Engineering, Northeastern Univ...

Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann’s zeta function, a variety of physics problems, and in the study of Toeplitz operators. This paper surveys these applications and what is currently known about the patterns.

At a theoretical level, the Trivers-Willard Sex Ratio Hypothesis applies to both avian species and mammals. This article, however, conjectures that at the statistical level, sex ratio effects are likely to produce sharper numerical variations among birds than among mammals. We explain this greater statistical variation should likely have beneficial implications for increasing the efficiency of ...

B asil Gordon, who made major research contributions to number theory, combinatorics, and algebra and who enhanced our understanding of Ramanujan’s remarkable identities, passed away on January 12, 2012, at the age of eighty. Gordon, who was a professor of mathematics at UCLA, was an outstanding teacher at all levels. His legacy will continue, owing to the impact of his fundamental work and to ...