Herglotz variational problems involving distributed-order fractional derivatives with arbitrary smooth kernels

In this paper, we consider Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function. We prove necessary optimality conditions for the Herglotz fractional variational problem with and without time delay, with higher-order derivatives, and with several independent variables. Since the Herglotz-type variational problem is a generalization of the classical variational problem, our main results generalize several results from the fractional calculus of variations. To illustrate the theoretical developments included in this paper, we provide some examplepublishe

Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels

In this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with arbitrary kernels. After proving a fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary conditions for the fundamental variational problem. Also, fractional variational problems with integral and holonomic constraints are considered. We end with some examples to exemplify our results.publishe

General quantum variational calculus

We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the q- and Hahn-calculuspublishe

Symmetric Differentiation on Time Scales

We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can be symmetric differentiable.Comment: This is a preprint of a paper whose final and definite form will be published in Applied Mathematics Letters. Submitted 30-Jul-2012; revised 07-Sept-2012; accepted 10-Sept-201

Higher-order infinite horizon variational problems in discrete quantum calculus

We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.Comment: Submitted 11-May-2011; revised 16-Sept-2011; accepted 02-Dec-2011; for publication in Computers & Mathematics with Application

COVID-19 in relation to hyperglycemia and diabetes mellitus

Coronavirus disease 2019 (COVID-19), triggered by the severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2), may lead to extrapulmonary manifestations like diabetes mellitus (DM) and hyperglycemia, both predicting a poor prognosis and an increased risk of death. SARS-CoV-2 infects the pancreas through angiotensin-converting enzyme 2 (ACE2), where it is highly expressed compared to other organs, leading to pancreatic damage with subsequent impairment of insulin secretion and development of hyperglycemia even in non-DM patients. Thus, this review aims to provide an overview of the potential link between COVID-19 and hyperglycemia as a risk factor for DM development in relation to DM pharmacotherapy. For that, a systematic search was done in the database of MEDLINE through Scopus, Web of Science, PubMed, Embase, China National Knowledge Infrastructure (CNKI), China Biology Medicine (CBM), and Wanfang Data. Data obtained underline that SARS-CoV-2 infection in DM patients is more severe and associated with poor clinical outcomes due to preexistence of comorbidities and inflammation disorders. SARS-CoV-2 infection impairs glucose homeostasis and metabolism in DM and non-DM patients due to cytokine storm (CS) development, downregulation of ACE2, and direct injury of pancreatic beta-cells. Therefore, the potent anti-inflammatory effect of diabetic pharmacotherapies such as metformin, pioglitazone, sodium-glucose co-transporter-2 inhibitors (SGLT2Is), and dipeptidyl peptidase-4 (DPP4) inhibitors may mitigate COVID-19 severity. In addition, some antidiabetic agents and also insulin may reduce SARS-CoV-2 infectivity and severity through the modulation of the ACE2 receptor expression. The findings presented here illustrate that insulin therapy might seem as more appropriate than other anti-DM pharmacotherapies in the management of COVID-19 patients with DM due to low risk of uncontrolled hyperglycemia and diabetic ketoacidosis (DKA). From these findings, we could not give the final conclusion about the efficacy of diabetic pharmacotherapy in COVID-19; thus, clinical trial and prospective studies are warranted to confirm this finding and concern

The influence of miRNAs on radiotherapy treatment in prostate cancer - A systematic review

In the last years, extensive investigation on miRNomics have shown to have great advantages in cancer personalized medicine regarding diagnosis, treatment and even clinical outcomes. Prostate cancer (PCa) is the second most common male cancer and about 50% of all PCa patients received radiotherapy (RT), despite some of them develop radioresistance. Here, we aim to provide an overview on the mechanisms of miRNA biogenesis and to discuss the functional impact of miRNAs on PCa under radiation response. As main findings, 23 miRNAs were already identified as being involved in genetic regulation of PCa cell response to RT. The mechanisms of radioresistance are still poorly understood, despite it has been suggested that miRNAs play an important role in cell signaling pathways. Identification of miRNAs panel can be thus considered an upcoming and potentially useful strategy in PCa diagnosis, given that radioresistance biomarkers, in both prognosis and therapy still remains a challenge.Fundação para a Ciência e Tecnologia | Ref. SFRH/BD/138271/201

Itaconic acid and its applications for textile, pharma and agro-industrial purposes

Itaconic acid (IA) is a well-known bio-based monounsaturated organic acid (C5H6O4), with a white color and crystalline structure. It is widely used in the agro-based, plastics, textile, paint and pharmaceutical sectors, owing to its flexible structure, due to the presence of functional groups with covalent double bonds. IA is an alternative to the petrochemicals acrylic and methacrylic acids. Commercial manufacturing of IA using Aspergillus terreus is more economically effective and feasible, and the Department of Energy (DOE) of the United States added IA under the “top 12” organic chemicals in 2004. This review provides an overview on the synthesis of IA and improvement of its yield by mutagenesis and metabolic engineering of Aspergillus and other fungal strains, along with its wide applications for food, pharmaceutical and textile purposes

Generalized transversality conditions for the Hahn quantum variational calculus

We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory