The Appell Function F1F_1 and Regge String Scattering Amplitudes

We show that each 26D open bosonic Regge string scattering amplitude (RSSA) can be expressed in terms of one single Appell function $F_1$ in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5,C) dynamical symmetry of $F_1$. In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4-8].Comment: 12 pages,no figur

Direct Extrusion Freeforming of Ceramic Pastes

Microextrusion freeforming of ceramic lattices from high solids ceramic pastes provides multi-scale hierarchical void structures with the advantages of low shrinkage stress and high sintered density. Alumina lattices were directly fabricated using 80-500 Pm diameter filaments. We report here on the implementation of design and fabrication of these scaffolds for band gap materials and micro fluidic devices.Mechanical Engineerin

Quantum replication at the Heisenberg limit

No process in nature can perfectly clone an arbitrary quantum state. But is it possible to engineer processes that replicate quantum information with vanishingly small error? Here we demonstrate the possibility of probabilistic super-replication phenomena where N equally prepared quantum clocks are transformed into a much larger number of M nearly perfect replicas, with an error that rapidly vanishes whenever M is small compared to the square of N. The quadratic replication rate is the ultimate limit imposed by Quantum Mechanics to the proliferation of information and is fundamentally linked with the Heisenberg limit of quantum metrology.Comment: 9 + 16 pages, 2 figures, published versio

The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes

We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10].Comment: 19 pages, no figure. v2: 20 pages, typos corrected and Eqs. added. v3: 24 pages, Examples in sec. II added,"Discussion" added, to be published in Nucl.Phys.