Numerical Solutions to Some Families of Fractional Order Differential Equations by Laguerre Polynomials

This article is devoted to compute numerical solutions of some classes and families of fractional order differential equations (FODEs). For the required numerical analysis, we utilize Laguerre polynomials and establish some operational matrices regarding to fractional order derivatives and integrals without discretizing the data. Further corresponding to boundary value problems (BVPs), we establish a new operational matrix which is used to compute numerical solutions of boundary value problems (BVPs) of FODEs. Based on these operational matrices (OMs), we convert the proposed (FODEs) or their system to corresponding algebraic equation of Sylvester type or system of Sylvester type. The resulting algebraic equations are solved by MATLAB® using Gauss elimination method for the unknown coefficient matrix. To demonstrate the suggested scheme for numerical solution, many suitable examples are provided

The role of indoleamine 2,3-dioxygenase 1 in early-onset post-stroke depression

BackgroundThe immune-inflammatory response has been widely considered to be involved in the pathogenesis of post-stroke depression (PSD), but there is ambiguity about the mechanism underlying such association.MethodsAccording to Diagnostic and Statistical Manual of Mental Disorders (5th edition), depressive symptoms were assessed at 2 weeks after stroke onset. 15 single nucleotide polymorphisms (SNPs) in genes of indoleamine 2,3-dioxygenase (IDO, including IDO1 and IDO2) and its inducers (including pro-inflammatory cytokines interferon [IFN]-γ, tumor necrosis factor [TNF]-α, interleukin [IL]-1β, IL-2 and IL-6) were genotyped using SNPscan™ technology, and serum IDO1 levels were detected by double-antibody sandwich enzyme-linked immune-sorbent assay.ResultsFifty-nine patients (31.72%) were diagnosed with depression at 2 weeks after stroke onset (early-onset PSD). The IDO1 rs9657182 T/T genotype was independently associated with early-onset PSD (adjusted odds ratio [OR] = 3.008, 95% confidence interval [CI] 1.157-7.822, p = 0.024) and the frequency of rs9657182 T allele was significantly higher in patients with PSD than that in patients with non-PSD (χ2 = 4.355, p = 0.037), but these results did not reach the Bonferroni significance threshold (p > 0.003). Serum IDO1 levels were also independently linked to early-onset PSD (adjusted OR = 1.071, 95% CI 1.002-1.145, p = 0.044) and patients with PSD had higher serum IDO1 levels than patients with non-PSD in the presence of the rs9657182 T allele but not homozygous C allele (t = -2.046, p = 0.043). Stroke patients with the TNF-α rs361525 G/G genotype had higher serum IDO1 levels compared to those with the G/A genotype (Z = -2.451, p = 0.014).ConclusionsOur findings provided evidence that IDO1 gene polymorphisms and protein levels were involved in the development of early-onset PSD and TNF-α polymorphism was associated with IDO1 levels, supporting that IDO1 which underlie strongly regulation by cytokines may be a specific pathway for the involvement of immune-inflammatory mechanism in the pathophysiology of PSD

In-situ secondary growth of nanocube-based Prussian-blue film as an ultrasensitive biosensor

A regular nanostructure has been widely confirmed to result ina marked improvement in material performance in biosensing applications. In the present study, a regular nanostructured Prussian blue (PB) film with two heterogeneous crystal layers was synthesized in-situ using a secondary growth method. A PB seed layer was first controlled to form uniform cube-like crystal nuclei through an ultrasonic reaction with a single reactant. Then, well-defined 100 nm PB nanocubes were further crystallized on this seed layer using a self-assembly approach. In order to accelerate the electron transfer rate during the enzyme reaction for glucose detection, the graphene was used as the main cross-linker to immobilize glucose oxidase on the PB film. The as-prepared biosensor exhibited high electrocatalysis and electron conductivity for the detection of trace glucose with a sensitivity of 141.5 µA mM-1 cm-2, as well as excellent anti-interference ability in the presence of ascorbic acid and uric acid under a low operation potential of -0.05 V

An 18.9-minute Blue Large-Amplitude Pulsator Crossing the 'Hertzsprung Gap' of Hot Subdwarfs

Blue large-amplitude pulsators (BLAPs) represent a new and rare class of hot pulsating stars with unusually large amplitudes and short periods. Up to now, only 24 confirmed BLAPs have been identified from more than one billion monitored stars, including a group with pulsation period longer than $\sim 20$ min (classical BLAPs, hereafter) and the other group with pulsation period below $\sim 8$ min. The evolutionary path that could give rise to such kinds of stellar configurations is unclear. Here we report on a comprehensive study of the peculiar BLAP discovered by the Tsinghua University - Ma Huateng Telescopes for Survey (TMTS), TMTS J035143.63+584504.2 (TMTS-BLAP-1). This new BLAP has an 18.9 min pulsation period and is similar to the BLAPs with a low surface gravity and an extended helium-enriched envelope, suggesting that it is a low-gravity BLAP at the shortest-period end. In particular, the long-term monitoring data reveal that this pulsating star has an unusually large rate of period change, P_dot/P=2.2e-6/yr. Such a significant and positive value challenges its origins from both helium-core pre-white-dwarfs and core helium-burning subdwarfs, but is consistent with that derived from shell helium-burning subdwarfs. The particular pulsation period and unusual rate of period change indicate that TMTS-BLAP-1 is at a short-lived (~10^6 yr) phase of shell-helium ignition before the stable shell-helium burning; in other words, TMTS-BLAP-1 is going through a "Hertzsprung gap" of hot subdwarfs.Comment: 26 pages, 12 figures, 4 tables, published on Nature Astronomy, URL: https://www.nature.com/articles/s41550-022-01783-

Associations of vitamin D-related single nucleotide polymorphisms with post-stroke depression among ischemic stroke population

ObjectiveTo investigate the relationship between single nucleotide polymorphisms (SNPs) related to vitamin D (VitD) metabolism and post-stroke depression (PSD) in patients with ischemic stroke.MethodsA total of 210 patients with ischemic stroke were enrolled at the Department of Neurology in Xiangya Hospital, Central South University, from July 2019 to August 2021. SNPs in the VitD metabolic pathway (VDR, CYP2R1, CYP24A1, and CYP27B1) were genotyped using the SNPscan™ multiplex SNP typing kit. Demographic and clinical data were collected using a standardized questionnaire. Multiple genetic models including dominant, recessive, and over-dominant models were utilized to analyze the associations between SNPs and PSD.ResultsIn the dominant, recessive, and over-dominant models, no significant association was observed between the selected SNPs in the CYP24A1 and CYP2R1 genes and PSD. However, univariate and multivariate logistic regression analysis revealed that the CYP27B1 rs10877012 G/G genotype was associated with a decreased risk of PSD (OR: 0.41, 95% CI: 0.18–0.92, p = 0.030 and OR: 0.42, 95% CI: 0.18–0.98, p = 0.040, respectively). Furthermore, haplotype association analysis indicated that rs11568820-rs1544410-rs2228570-rs7975232-rs731236 CCGAA haplotype in the VDR gene was associated with a reduced risk of PSD (OR: 0.14, 95% CI: 0.03–0.65, p = 0.010), whereas no significant association was observed between haplotypes in the CYP2R1 and CYP24A1 genes and PSD.ConclusionOur findings suggest that the polymorphisms of VitD metabolic pathway genes VDR and CYP27B1 may be associated with PSD in patients with ischemic stroke

Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses

Abstract In this paper, we mainly consider the existence and finite-time stability of solutions for a kind of ψ-Hilfer fractional differential equations involving time-varying delays and non-instantaneous impulses. By Schauder’s fixed point theorem, the contraction mapping principle and the Lagrange mean-value theorem, we present new constructive results as regards existence and uniqueness of solutions. In addition, under some new criteria and by applying the generalized Gronwall inequality, we deduce that the solutions of the addressed equation have finite-time stability. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results

Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results

Ulam–Hyers Stability of Caputo-Type Fractional Stochastic Differential Equations with Time Delays

In this paper, we study a class of Caputo-type fractional stochastic differential equations (FSDEs) with time delays. Under some new criteria, we get the existence and uniqueness of solutions to FSDEs by Carathe´odory approximation. Furthermore, with the help of Ho¨lder’s inequality, Jensen’s inequality, Ito^ isometry, and Gronwall’s inequality, the Ulam–Hyers stability of the considered system is investigated by using Lipschitz condition and non-Lipschitz condition, respectively. As an application, we give two representative examples to show the validity of our theories