St. Laurent, Louis; Siegel, Bugsy

Contributions by Howard J. Bromberg to The Forties in America

Continued fractions for some transcendental numbers

We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for n?1. It is shown that the terms of the sequence, and multiples of the ratios of successive terms, appear interlaced in the continued fraction expansion of the sum of the series, which is a transcendental number

Convexity of Quotients of Theta Functions

For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, $\theta_{j}(u|i\pi t)/\theta_{j}(v|i\pi t)$, $j=1, 2, 3, 4$, on $0<t<\infty$ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients $\theta_{2}(u|i\pi t)/\theta_{2}(v|i\pi t)$ and $\theta_{3}(u|i\pi t)/\theta_{3}(v|i\pi t)$ are convex on $0<t<\infty$.Comment: 17 pages, 6 figure

La llegada de la fotografía a la Real Academia de Bellas Artes de San Fernando

The advent of photography in the Nineteenth century was a revolution in the way of seeing and reproducing the Art, an area where lithography recorded in exclusive. In Spain, the request of J. Laurent for taking photographs of the Royal Academy of Fine Arts of San Fernando principal tables, opened the discussion, as in their European counterparts, about the competition of the photography in Art reproduction and consolidated the importance of these new visual libraries created by large photographic companies throughout the century.La aparición de la fotografía en el siglo XIX en el ámbito de las artes supuso una revolución en las formas de mirar y reproducir las obras de arte, lugar en el que antes el grabado gozaba de exclusividad. En España, la petición de J. Laurent para fotografiar los cuadros de la Real Academia de Bellas Artes de san Fernando abrió el debate, al igual que en sus homónimas europeas, sobre la competencia de la fotografía en la reproducción artística y consolidó la importancia de estas nuevas bibliotecas visuales creadas por las grandes firmas fotográficas a lo largo de todo el siglo

Direct sums of trace maps and self-adjoint extensions

We give a simple criterion so that a countable infinite direct sum of trace (evaluation) maps is a trace map. An application to the theory of self-adjoint extensions of direct sums of symmetric operators is provided; this gives an alternative approach to results recently obtained by Malamud-Neidhardt and Kostenko-Malamud using regularized direct sums of boundary triplets.Comment: Final version. To appear in: S. Albeverio (ed.), Singular Perturbation Theory, Analysis, Geometry, and Stochastic, special issue of Arab. J. Math. (Springer

Quantum logic as superbraids of entangled qubit world lines

Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying novel quantum skein relations. If the superbraid is closed (e.g. representing quantum circuits with closed-loop feedback, quantum lattice gas algorithms, loop or vacuum diagrams in quantum field theory), then one can decompose the resulting superlink into an entangled superposition of classical links. In turn, for each member link, one can compute a link invariant, e.g. the Jones polynomial. Thus, a superlink possesses a unique link invariant expressed as an entangled superposition of classical link invariants.Comment: 4 page