Ward Identities and High-energy Scattering Amplitudes in String Theory

High-energy limit of stringy Ward identities derived from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string are used to check the consistency of saddle point calculations of high energy scattering amplitudes of Gross and Mende and Gross and Manes. Some inconsistencies of their saddle point calculations are found even for the string-tree scattering amplitudes of the excited string states. We discuss and calculate the missing terms of the calculation by those authors to recover the stringy Ward identities. In addition, based on the tree-level stringy Ward identities, we give the proof of a general formula, which was proposed previously, of all high energy four-point string-tree amplitudes of arbitrary particles in the string spectrum. In this formula all such scattering amplitudes are expressed in terms of those of tachyons as conjectured by Gross. The formula is extremely simple which manifestly demonstrates the universal high energy behavior of the interactions among all string states.Comment: 1 typo, to appear in Nucl. Phys.

Theoretical Basis of Electrocatalysis

In this chapter, we introduce the density functional theory (DFT)-based computational approaches to the study of various electrochemical reactions (hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR)) occurring on heterogeneous catalysis surfaces. A detailed computational approach to the theoretical interpretation of electrochemical reactions and structure-catalytic activity relationships for graphene-based catalysts will be discussed. The electrocatalytic activity of catalysis can be theoretically evaluated by overpotential value determined from free energy diagram (FED) of electrochemical reactions. By comparing electrocatalytic activity of systematically designed graphene-based catalysts, we will discuss the structure-catalytic activity relationships, especially the electronic and geometrical effects of heteroatom dopants

Zero-norm states and stringy symmetries

We identify spacetime symmetry charges of 26D open bosonic string theory from an infinite number of zero-norm states (ZNS) with arbitrary high spin in the old covariant first quantized string spectrum. We give various evidences to support this identification. These include massive sigma-model calculation, Witten string field theory calculation, 2D string theory calculation and, most importantly, three methods of high-energy stringy scattering amplitude calculations. The last calculations explicitly prove Gross's conjectures in 1988 on high energy symmetry of string theory.Comment: 6 pages. Talks presented by Jen-Chi Lee at XXVIII Spanish Relativity Meeting (ERE2005),"A Century of Relativity Physics",Oviedo,Spain,6-10 Sep 2005 and "4th Meeting on constrained Dynamics and Quantum Gravity",Cala Gonone,Sardinia,Italy,12-16 Sep 2005. To appear in the Journal of Physics: Conference Serie

Realization of Woodpile Structure Using Optical Interference Holography

We report the use of a (4+1)-beam optical interference holography technique to fabricate woodpile structures in photo-resists. The configuration consists of 4 linear polarized side beams arranged symmetrically around a circular polarized central beam with all the beams from the same half space, making it easily accessible experimentally. The fabricated woodpile structures are in good agreement with model simulations. Furthermore, woodpiles with the diamond symmetry are also obtained by exploiting the deformations of the photo-resists. Directional bandgaps in the visible range are also observed for the samples with and without the correct stacking of the woodpile structures.Comment: 9 pages and three figure

Biomarkers of progression in diabetic nephropathy: The past, present and future

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Evaluating the Operational Efficiency of Life Insurance Companies in Taiwan– An Application of the Dynamic Network SBM Model

Using a Dynamic Network Slack-based Measurement model (Tone & Tsutsui, 2014), this study evaluated the operational efficiency of life insurance firms in Taiwan from 2006 to 2013. In contrast to previous research, we incorporated assets and liabilities management into the model and compared them against optimal efficiency values in order to determine whether firms are earning maximizing profit while ensuring long-term solvency. The life insurance industry in Taiwan has matured. We found that market competitiveness depends on firms size and business model. Financial holdings companies and large corporations are performing strongly, while small local firms and foreign-owned firms scored poorly in technical efficiency. Economies of scale contribute to the business performance of life insurance firms. Life insurance companies that had merged with or been acquired by financial holdings firms showed notable improvement in efficiency. However, change in term efficiency is a warning signal in long-term business performance of life insurance firms. Lastly, most companies achieved optimal carry-over efficiency, indicating that they place considerable emphasis on managing assets and liabilities in order to ensure future solvency

Linear Relations and their Breakdown in High Energy Massive String Scatterings in Compact Spaces

We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta ((m/R),(1/2)nR), we obtain infinite linear relations among high energy scattering amplitudes of different string states. For some kinematic regimes, we discover that linear relations with N_{R}=N_{L} break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual expoential fall-off behavior at high energies. It is the space-time T-duality symmetry that plays a role here. This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of our previous work on the power-law behavior of high energy string/domain-wall scatterings.Comment: 18 pages, 1 figur

High-energy zero-norm states and symmetries of string theory

High-energy limit of zero-norm states (HZNS) in the old covariant first quantized (OCFQ) spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed angle behavior of four point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, as a consistent sample calculation, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to justify our results.Comment: 10 pages, no figure, modifications of text and reference

Can the giant planets of the Solar System form via pebble accretion in a smooth protoplanetary disc?

Context. Prevailing N-body planet formation models typically start with lunar-mass embryos and show a general trend of rapid migration of massive planetary cores to the inner Solar System in the absence of a migration trap. This setup cannot capture the evolution from a planetesimal to embryo, which is crucial to the final architecture of the system.Aims. We aim to model planet formation with planet migration starting with planetesimals of ~10−6−10−4 M⊕ and reproduce the giant planets of the Solar System.Methods. We simulated a population of 1000–5000 planetesimals in a smooth protoplanetary disc, which was evolved under the effects of their mutual gravity, pebble accretion, gas accretion, and planet migration, employing the parallelized N-body code SyMBAp.Results. We find that the dynamical interactions among growing planetesimals are vigorous and can halt pebble accretion for excited bodies. While a set of results without planet migration produces one to two gas giants and one to two ice giants beyond 6 au, massive planetary cores readily move to the inner Solar System once planet migration is in effect. Conclusions. Dynamical heating is important in a planetesimal disc and the reduced pebble encounter time should be considered in similar models. Planet migration remains a challenge to form cold giant planets in a smooth protoplanetary disc, which suggests an alternative mechanism is required to stop them at wide orbits.<br/