The conformal gravity fit to observed galactic rotation curves requires γ>0. On the other hand, the conventional method for light deflection by galaxies gives a negative contribution to the Schwarzschild value for γ>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for γ>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date

After the work of Rindler and Ishak, it is now well established that the bending of light is influenced by the cosmological constant Λ appearing in the Schwarzschild-de Sitter spacetime. We show that their method, when applied to the galactic halo gravity parametrized by a constant γ, yields exactly the same γ− correction to Schwarzschild bending as obtained by standard methods. Different cases are analyzed, which include some corrections to the special cases considered in the original paper by Rindler and Ishak.---------------------

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Motion trajectory contains plentiful motion information of moving objects, for example, human gestures and robot actions. Motion perception and recognition via trajectory are useful for characterizing them and a flexible descriptor of motion trajectory plays important role in motion analysis. However, in the existing tasks, trajectories were mostly used in raw data and effective descriptor is lacking. In this paper, we present a mixed invariant signature descriptor with global invariants for motion perception and recognition. The mixed signature is viewpoint invariant for local and global features. A reliable approximation of the mixed signature is proposed to reduce the noise in high-order derivatives. We use this descriptor for motion trajectory description and explore the motion perception with DTW algorithm for salient motion features. To achieve better accuracy, we modified the CDTW algorithm for trajectory matching in motion recognition. Furthermore, a controllable weight parameter is introduced to adjust the global features for tasks in different circumstances. The conducted experiments validated the proposed method.

The fundamental theorem of algebra determines the number of characteristic roots of an ordinary differential equation of integer order. This may cease to be true for a differential equation of fractional order. The results given in this paper suggest that the number of the characteristic roots of a class of oscillators of fractional order may in general be infinitely great. Further, we infer that it may also be the case for the characteristic roots of a differential equation of fractional order greater than 1. The relationship between the range of the fractional order and the locations of characteristic roots of oscillators in the complex plane is considered.

A concept of total stability for continuous or discrete dynamical systems and a generalized definition of bifurcation are given: it is possible to show the link between an abrupt change of the asymptotic behaviour of a family of flows and the arising of new invariant sets, with determined asymptotic properties. The theoretical results are a contribution to the study of the behaviour of flows near an invariant compact set. They are obtained by means of an extension of Liapunov's direct method. © 1975 Fondazione Annali di Matematica Pura ed Applicata

Digital watermarking is a good tool for healthcare information management systems. The wellknown quantization-index-modulation-QIM-based watermarking has its limitations as the host image will be destroyed; however, the recovery of medical image is essential to avoid misdiagnosis.A transparent yet reversible watermarking algorithm is required for medical image applications. In this paper, we propose a fractional-discrete-cosine-transform-FDCT-based watermarking to exactly reconstruct the host image. Experimental results show that the FDCT-based watermarking is preferable to the QIM-based watermarking for the medical image applications.

Can a very low intensity signal overcome a disturbance, the power density of which is much higher than the signal one, and yield some observable effects? The Johnson noise seems to be a disturbance so high as to cause a negative answer to that question, when one studies the effects on the cell level due to the external ELF fields generated by electric power lines (Adair, 1990, 1991). About this subject, we show that the masking effect due to the Johnson noise, known as “Adair’s constraint” and still present in the scientific debate, can be significantly weakened. The values provided by the Johnson noise formula, that is an approximate expression, can be affected by a significant deviation with respect to the correct ones, depending on the frequency and the kind of the cells, human or not human, that one is dealing with. We will give some examples. Eventually, we remark that the so-called Zhadin effect, although born and studied in a different context, could be viewed as an experimental test that gives an affirmative answer to the initial question, when the signal is an extremely weak electromagnetic field and the disturbance is a Johnson noise.