Some Inclusion Properties for Meromorphic Functions Defined by New Generalization of Mittag-Leffler Function

In this paper, the authors introduced a new operator by using a generalized Mittag-Leffler function. Also, the authors defined the meromorphic subclasses associated. Finally calculated inclusion relation

Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well

Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu

We investigate the spectral theory of the invariant Landau Hamiltonian \La^\nu acting on the space ${\mathcal{F}}^\nu_{\Gamma,\chi}$ of $(\Gamma,\chi)$-automotphic functions on \C^n, for given real number $\nu>0$, lattice $\Gamma$ of \C^n and a map $\chi:\Gamma\to U(1)$ such that the triplet $(\nu,\Gamma,\chi)$ satisfies a Riemann-Dirac quantization type condition. More precisely, we show that the eigenspace {\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in {\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f}; \lambda\in\C, is non trivial if and only if $\lambda=l=0,1,2, ...$. In such case, ${\mathcal{E}}^\nu_{\Gamma,\chi}(l)$ is a finite dimensional vector space whose the dimension is given explicitly. We show also that the eigenspace ${\mathcal{E}}^\nu_{\Gamma,\chi}(0)$ associated to the lowest Landau level of \La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n), of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma) e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can realize also as the null space of the differential operator $\sum\limits_{j=1}\limits^n(\frac{-\partial^2}{\partial z_j\partial \bar z_j} + \nu \bar z_j \frac{\partial}{\partial \bar z_j})$ acting on $\mathcal C^\infty$ functions on \C^n satisfying $(*)$.Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of "Journal of Mathematical Physics

A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length

It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as “coherent states” today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originated from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics communit

Open Institute of the African BioGenome Project: Bridging the gap in African biodiversity genomics and bioinformatics

Africa, a continent of 1.3 billion people, had 326 researchers per one million people in 2018 (Schneegans, 2021; UNESCO, 2022), despite the global average for the number of researchers per million people being 1368 (Schneegans, 2021; UNESCO, 2022). Nevertheless, a strong research community is a requirement to advance scientific knowledge and innovation and drive economic growth (Agnew, et al., 2020; Sianes, et al., 2022). This low number of researchers extends to scientific research across Africa and finds resonance with genomic projects such as the African BioGenome Project (Ebenezer, et al., 2022). The African BioGenome project (AfricaBP) plans to sequence 100,000 endemic African species in 10 years (Ebenezer, et al., 2022) with an estimated 203,000 gigabases of DNA sequence. AfricaBP aims to generate these genomes on-the-ground in Africa. However, for AfricaBP to achieve its goals of on-the-ground sequencing and data analysis, there is a need to empower African scientists and institutions to obtain the required skill sets, capacity and infrastructure to generate, analyse, and utilise these sequenced genomes in-country. The Open Institute is the genomics and bioinformatics knowledge exchange programme for the AfricaBP (Figures 1 & 2). It consists of 10 participating institutions including the University of South Africa in South Africa and National Institute of Agricultural Research in Morocco. It aims to: develop biodiversity genomics and bioinformatics curricula targeted at African scientists, promote and develop genomics and bioinformatics tools that will address critical needs relevant to the African terrain such as limited internet access, and advance grassroot knowledge exchange through outreach and public engagement such as quarterly training and workshops