Supersymmetric Biorthogonal Quantum Systems

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.Comment: Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-1

Infinite partition monoids

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$ may be generated by the set $\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set

Protective role of nutraceuticals against myocarditis

Myocarditis is an inflammatory disease of the myocardium that mostly affects young adults. The disease is commonly caused by viral infection, medications, autoimmune disorders, and inflammatory conditions. Nearly 50% of the cases of myocarditis are due to post-viral immune response in a setting of an identifiable or non-identifiable infection. The clinical manifestation is nonspecific ranging from asymptomatic courses to sudden death in infants and young patients. This review describes the properties of phytochemicals as plant-derived active ingredients which can be used in the prevention and treatment of myocarditis and its associated risk factors. Meanwhile, it has illustrated epidemiological analyses, mechanism of action, and the metabolism of phytochemicals in animal and human clinical trials. We also mentioned the precise mechanism of action by which phytochemicals elicit their anti-viral, anti-inflammatory, antioxidant, and immunomodulatory effects and how they regulate signal transduction pathways. Nevertheless, comprehensive clinical trials are required to study the properties of phytochemicals in vivo, in vitro, and in silico for a proper management of myocarditis. Our findings indicate that phytochemicals function as potent adjunctive therapeutic drugs in myocarditis and its related complications

Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Empowering Host Nation Counter-IED and Counter-Insurgency Efforts: Innovative Application of Ordnance Recycling

As the United States works to grow its defense partnership with the Philippines, the country continues to fight instability and insecurity amidst a lengthy battle against insurgent and terrorist groups.[i],[ii],[iii] As the overlap between urban areas and conflict zones increases, and with violent groups’ use of improvised explosive devices (IEDs) against government forces, the danger to civilians escalates.[iv] This paper provides a deeper understanding of how the prevalence of unexploded ordnance (UXO) and the use of IEDs in the Philippines fuel the realities of insurgency and humanitarian danger in the country. Furthermore, using Golden West Humanitarian Foundation’s (GWHF) program in Cambodia as a framework, this paper examines how the innovative application of GWHF’s ordnance recycling technology in the Philippines would impact the host nation’s ability to counter the enduring challenges posed by insurgency groups use of UXO and IEDs. Employing GWHF’s technology in a way that uses deteriorating ordnance stockpiles, surplus ordnance, and explosive remnants of war (ERW) to produce water disruptors for use as a successful, efficient, and affordable method of handling explosive hazards offers a unique approach to supporting the Philippines in its counterinsurgency battle

Stripe phases in the two-dimensional Falicov-Kimball model

The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagrams of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions of the phase diagram.Comment: (5 pages, 3 figures

Biorthogonal Quantum Systems

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+\nu)^2+\sum_{k>0}\mu_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.Comment: 34 pages, 5 eps figures; references added and other changes made to conform to journal versio

Statin therapy in chronic viral hepatitis: a systematic review and meta-analysis of nine studies with 195,602 participants

Background: Conflicting data suggest that statins could cause chronic liver disease in certain group of patients, while improving prognosis in those with chronic viral hepatitis (CVH). Purpose: To quantify the potential protective role of statins on some main liver-related health outcomes in clinical studies on CVH patients.Data Sources: The search strategy was explored by a medical librarian using bibliographic databases, from January 2015 to April 2020.Data synthesis: The results showed no significant difference in the risk of mortality between statin users and non-users in the overall analysis. However, the risk of mortality significantly reduced by 39% in statin users who were followed for more than three years. Moreover, the risk of HCC, fibrosis, and cirrhosis in those on statins decreased by 53%, 45% and 41%, respectively. Although ALT and AST reduced slightly following statin therapy, this reduction was not statistically significant. Limitations: A significant heterogeneity among studies was observed, resulting from differences in clinical characteristics between statin users and non-users, study designs, population samples, diseases stage, comorbidities, and confounding covariates. Conclusion: Not only long-term treatment with statins seems to be safe in patients affected by hepatitis, but also it significantly improves their prognosis

Casimir Effect in E3E^3 closed spaces

As it is well known the topology of space is not totally determined by Einstein's equations. It is considered a massless scalar quantum field in a static Euclidean space of dimension 3. The expectation value for the energy density in all compact orientable Euclidean 3-spaces are obtained in this work as a finite summation of Epstein type zeta functions. The Casimir energy density for these particular manifolds is independent of the type of coupling with curvature. A numerical plot of the result inside each Dirichlet region is obtained.Comment: Version accepted for publication. The most general coupling with curvature is chose

The Role of Protein SUMOylation in the Pathogenesis of Atherosclerosis

Atherosclerosis is a progressive, inflammatory cardiovascular disorder characterized by the development of lipid-filled plaques within arteries. Endothelial cell dysfunction in the walls of blood vessels results in an increase in vascular permeability, alteration of the components of the extracellular matrix, and retention of LDL in the sub-endothelial space, thereby accelerating plaque formation. Epigenetic modification by SUMOylation can influence the surface interactions of target proteins and affect cellular functionality, thereby regulating multiple cellular processes. Small ubiquitin-like modifier (SUMO) can modulate NFκB and other proteins such as p53, KLF, and ERK5, which have critical roles in atherogenesis. Furthermore, SUMO regulates leukocyte recruitment and cytokine release and the expression of adherence molecules. In this review, we discuss the regulation by SUMO and SUMOylation modifications of proteins and pathways involved in atherosclerosis