arXiv subjects

Kevin Yang

Publications and source records attributed to Kevin Yang.

57 records · Page 4Linked to original sources

arXiv2016

Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters

While Random Matrix Theory has successfully modeled many quantities of families of L-functions, it frequently cannot see the family's arithmetic. In some situations this requires an extended theory that inserts arithmetic factors depending on the family, while in other cases these factors result in contributions which vanish in the limit, and are thus not detected. We review the general theory associated to one of the most important statistics, the n-level density of zeros near the central point. According to the Katz-Sarnak density conjecture, to each family of L-functions there is a corresponding symmetry group such that the behavior of zeros near the central point as the conductors tend to infinity agrees with the behavior of eigenvalues near 1 as the matrix size tends to infinity. We show how these calculations are done, emphasizing the techniques, methods and obstructions to improving the results, by considering in full detail a family of Dirichlet characters. We then describe how we may associate a symmetry constant to each family, and how to determine the symmetry group of a compound family in terms of the symmetries of the constituents. These calculations explain the remarkable universality of behavior, where the main terms are independent of the arithmetic (only the first two moments of the Satake parameters contribute in the limit; similar to the Central Limit Theorem, the higher moments are only felt in the rate of convergence). We end by exploring lower order terms in families of elliptic curves. We present evidence supporting a conjecture that the average second moment in one-parameter families without complex multiplication has, when appropriately viewed, a negative bias, and end with a discussion of the consequences of this bias on the distribution of low-lying zeros, in particular relations between such a bias and the observed excess rank in families.

math.NT↗

arXiv2015

Image Reconstruction Image reconstruction by using local inverse for full field of view

The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact inverse from an approximate inverse with a few iterations. The IRM has been used in CT image reconstruction to lower the radiation dose. The IRM utilize the errors between the original measured data and the recalculated data to correct the reconstructed images. However if it is not smooth inside the object, there often is an over-correction along the boundary of the organs in the reconstructed images. The over-correction increase the noises especially on the edges inside the image. One solution to reduce the above mentioned noises is using some kind of filters. Filtering the noise before/after/between the image reconstruction processing. However filtering the noises also means reduce the resolution of the reconstructed images. The filtered image is often applied to the image automation for examples image segmentation or image registration but diagnosis. For diagnosis, doctor would prefer the original images without filtering process. In the time these authors of this manuscript did the work of interior image reconstruction with local inverse method, they noticed that the local inverse method does not only reduced the truncation artifacts but also reduced the artifacts and noise introduced from filtered back-projection method without truncation. This discovery lead them to develop the sub-regional iterative refinement (SIRM) image reconstruction method. The SIRM did good job to reduce the artifacts and noises in the reconstructed images. The SIRM divide the image to many small sub-regions. To each small sub-region the principle of local inverse method is applied.

physics.med-ph↗

arXiv2015

The modified Poynting theorem and the concept of mutual energy

The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the retarded potential and advanced potential, time-offset field. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Mixed mutual energy theorem is derived. We derive the mutual energy from Fourier domain. We obtain the time-reversed mutual energy theorem and the mutual energy theorem. Then we derive the mutual energy theorem in time-domain. The instantaneous modified mutual energy theorem is derived. Applying time-offset transform and time integral to the instantaneous modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are two electromagnetic fields one is retarded potential and one is advanced potential, the convolution reciprocity theorem can be derived. Corresponding to the modified time-correlation mutual energy theorem and the time-convolution reciprocity theorem in Fourier domain, there is the modified mutual energy theorem and the Lorentz reciprocity theorem. Hence all mutual energy theorem and the reciprocity theorems are put in one frame of the concept of the mutual energy. 3 new Complementary theorems are derived. The inner product is introduced for two different electromagnetic fields in both time domain and Fourier domain for the application of the wave expansion.

physics.gen-ph↗