Some identities between partitions and compositions were obtained in the literature. As a natural extension, we introduce and study modulo-p partitions, where p is a positive integer. Moreover, several recurrence relations and some sufficient conditions for the existence of modulo-p partitions are given, respectively. In addition, we obtain some identities of modulo-p partitions. In the end, us...

One of the advantages of the Discrete Wavelet Transform (DWT) compared to Fourier Transform (e.g. Discrete Cosine Transform DCT) is its ability to provide both spatial and frequency localization of image energy. However, WT coefficients, like DCT coefficients, are defined by magnitude as well as sign. While algorithms exist for the coding of wavelet coefficients magnitude, there are no efficien...

Histopathologic Description: Cervical spinal cord: Microscopically, the lesions are characterized by a loss of myelin visible on HE-stained sections where the normally intense eosinophilia of the white matter is lost and the neuropil to has a fine fibrillar meshwork pattern dotted with numerous oligodendrocyte nuclei. With the Luxol fast blue stain, the deep blue color of the white matter is re...

Society is ageing and sadly that ageing leads to a host of issues, not least a society in which the majority are likely to have some loss of strength and dexterity. This can lead to complications in undertaking everyday tasks such as using transport, bathing or even handling and opening food. Packaging has to provide a multitude of services; to protect and preserve the product, to provide infor...

Of the non-ruminant wildlife species known to harbor Mycobacterium avium paratuberculosis (MAP), the rabbit (Oryctolagus cuniculus) is thought to pose the greatest risk of transmission to cattle. We analyzed 80 hunter-harvested wild rabbits from a core study area in southern Spain, and sera from 157 wild rabbits sampled opportunistically on seven additional sites. Gross lesions compatible with ...

In this lecture, I summarize developments presented at the Lepton Photon 2011 conference and give my perspective on the current situation in high-energy physics.

To our knowledge, all prior work in the literature (eg. [Herman & Strohmer 2010; Chi et al. 2011; Rosenbaum et al. 2013; Rudelson & Zhou 2015] among others) only concern themselves with cases 1, 2 and 3. Moreover, for papers that do deal with case 2 and 3, unless s = 0 the existing analysis will be restricted to providing only approximate recovery guarantees. Thus, these methods do not apply di...

Taking bothwhite noise and colored environmental noise into account, a general stochastic logistic model under regime switching is proposed and studied. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence and global attractivity are established. The critical number between weak persistence and extinction is obtained. Moreover, some simulatio...

In this paper, we consider a stochastic Gilpin-Ayala population model with Markovian switching and white noise. All parameters are influenced by stochastic perturbations. We analyze the existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model, which g...