An octonion algebra originating in combinatorics

C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of delta-codes (now known as T-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.Comment: 11 pages, A simpler proof of the main theorem, due to Alberto Elduque, is inserted. The paper will appear in the Proc. Amer. Math. So

A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood

An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap- propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated

Evidence for very strong electron-phonon coupling in YBa_{2}Cu_{3}O_{6}

From the observed oxygen-isotope shift of the mid-infrared two-magnon absorption peak of YBa$_{2}$Cu$_{3}$O$_{6}$, we evaluate the oxygen-isotope effect on the in-plane antiferromagnetic exchange energy $J$. The exchange energy $J$ in YBa$_{2}$Cu$_{3}$O$_{6}$ is found to decrease by about 0.9% upon replacing $^{16}$O by $^{18}$O, which is slightly larger than that (0.6%) in La$_{2}$CuO$_{4}$. From the oxygen-isotope effects, we determine the lower limit of the polaron binding energy, which is about 1.7 eV for YBa$_{2}$Cu$_{3}$O$_{6}$ and 1.5 eV for La$_{2}$CuO$_{4}$, in quantitative agreement with angle-resolved photoemission data, optical conductivity data, and the parameter-free theoretical estimate. The large polaron binding energies in the insulating parent compounds suggest that electron-phonon coupling should also be strong in doped superconducting cuprates and may play an essential role in high-temperature superconductivity.Comment: 4 pages, 1 figur

Light Front Quantization with the Light Cone Gauge

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2 + 1 dimensional target space

Comment on "Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation" [arXiv:1004.3100]

Recently, the authors of Ref.1[arXiv:1004.3100] claimed that they have proven the traditional adiabatic condition is a necessary condition. Here, it is claimed that there are some mistakes and an artificial over-strong constraint in [1], making its result inconvincible.Comment: 1 pag

Genetic algorithm and neural network hybrid approach for job-shop scheduling

Copyright @ 1998 ACTA PressThis paper proposes a genetic algorithm (GA) and constraint satisfaction adaptive neural network (CSANN) hybrid approach for job-shop scheduling problems. In the hybrid approach, GA is used to iterate for searching optimal solutions, CSANN is used to obtain feasible solutions during the iteration of genetic algorithm. Simulations have shown the valid performance of the proposed hybrid approach for job-shop scheduling with respect to the quality of solutions and the speed of calculation.This research is supported by the National Nature Science Foundation and National High -Tech Program of P. R. China

Angular momentum I ground state probabilities of boson systems interacting by random interactions

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.Comment: 8 pages and 3 figure

Renormalization Scheme Ambiguities in the Models with More than One Coupling

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group beta-functions are not unique beyond one loop order, that it is not in general possible to eliminate all terms beyond certain order for all these beta-functions, but that for a physical process all contributions beyond one loop order can be subsumed into the beta-functions