Particle collisions in the lower dimensional rotating black hole space-time with the cosmological constant

In this paper, we study the effect of ultra-high energy collisions of two particles with different energies near the horizon of a 2+1 dimensional BTZ black hole (BSW effect). We find that the particle with the critical angular momentum could exist inside the outer horizon of BTZ black hole regardless of the particle energy. Therefore, for the non-extremal BTZ black hole, the BSW process is possible on the inner horizon with the fine tuning of parameters which are characterized by the motion of particle. While for the extremal BTZ black hole, the particle with the critical angular momentum could only exist on the degenerate horizon, and the BSW process could also happen there.Comment: 12 pages,3 figure

Cash flow forecast for South African firms

This paper applies models in the extant literature that have been used to forecast operating cash flows to predict the cash flows of South African firms listed on the Johannesburg Stock Exchange. Out-of-sample performance is examined for each model and compared between them. The reported results show that some accrual terms, i.e. depreciation and changes in inventory do not enhance cash flow prediction for the average South African firm in contrast to the reported results of studies in USA and Australia. Inclusion of more explanatory variables does not necessarily improve the models, according to the out-of-sample results. The paper proposes the application of moving average model in panel data, and vector regressive model for multi-period-ahead prediction of cash flows for South Africa firms

Inverse Projection Representation and Category Contribution Rate for Robust Tumor Recognition

Sparse representation based classification (SRC) methods have achieved remarkable results. SRC, however, still suffer from requiring enough training samples, insufficient use of test samples and instability of representation. In this paper, a stable inverse projection representation based classification (IPRC) is presented to tackle these problems by effectively using test samples. An IPR is firstly proposed and its feasibility and stability are analyzed. A classification criterion named category contribution rate is constructed to match the IPR and complete classification. Moreover, a statistical measure is introduced to quantify the stability of representation-based classification methods. Based on the IPRC technique, a robust tumor recognition framework is presented by interpreting microarray gene expression data, where a two-stage hybrid gene selection method is introduced to select informative genes. Finally, the functional analysis of candidate's pathogenicity-related genes is given. Extensive experiments on six public tumor microarray gene expression datasets demonstrate the proposed technique is competitive with state-of-the-art methods.Comment: 14 pages, 19 figures, 10 table

Similarity signature curves for forming periodic orbits in the Lorenz system

In this paper, we systematically investigate the short periodic orbits of the Lorenz system by the aid of the similarity signature curve, and a novel method to find the short-period orbits of the Lorenz system is proposed. The similarity invariants are derived by the equivariant moving frame theory and then the similarity signature curve occurs along with them. The similarity signature curve of the Lorenz system presents a more regular behavior than the original one. By combining the sliding window method, the quasi-periodic orbits can be detected numerically, all periodic orbits with period $p \leqslant 8$ in the Lorenz system are found, and their period lengths and symbol sequences are calculated