A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.     

Unique cascade ring-opening/cyclization reaction of azlactones and DBU or DBN: Synthesis of new pyrrolam A analogues

1-Azabicyclo[3.3.0]oct-3-en-2-one derivatives were synthesized efficiently through the facile cascade reaction of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) or 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) with arylidene azlactones. This research provides a straightforward procedure for the synthesis of a novel class of multicyclic semi-alkaloids which shows good antimicrobial activity. Under catalyst-free, mild, and solventless condition, a wide range of fused tricyclic derivatives was obtained in high yields.     

Reactions of cisplatin hydrolytes, cis-[Pt(15NH3)2(H2O) 2]2+, with N-acetyl-L-cysteine

The reaction of cis-[Pt(¹⁵NH₃)2(H₂O) ₂] ²⁺ (3) with N-acetylcysteine [H₃accys] was investigated in aqueous solution. In this reaction, the ammine in the platinum complex formed was liberated. A mono-dentate sulfur-boundplatinum(II) product cis-[Pt(¹⁵NH₃)₂(H₂O)(H2accys-S)]⁺ (7) and six-membered che-late ring complex cis-[Pt(¹⁵NH₃)₂ (Haccys-S,O)] (8) were formed in solution. The dinuclear sulfur-bridged complex 9, giving a broad peak in ¹⁵N NMR, was also observed, but only present in very tiny amounts. The mass spectrometry (ES-MS) was undertaken from this re action, and the product detected was only the dinuclear sulfur bridged platinum species and species related to it by ammine loss.     

Enantioselective synthesis of bicylco[3.2.1]octan-8-ones using a tandem Michael-Henry reaction

Bicyclo[3.2.1]octan-8-ones have been prepared from a tandem Michael-Henry reaction between cyclohexane-1,2-diones and nitroalkenes using a quinine-derived thiourea as the catalyst. Although four stereogenic centers were created during the reaction, only two diastereomers were obtained in good diastereoselectivity and high enantioselectivity (92-99% ee). When 3-methylcyclohexane-1,2-dione (R¹=Me) was used as the substrate, only the regioisomeric product of the corresponding thermodynamic enolate was obtained.     

Palladium-catalyzed asymmetric allylic alkylation (AAA) with alkyl sulfones as nucleophiles

An efficient palladium-catalyzed AAA reaction with a simple α-sulfonyl carbon anion as nucleophiles is presented for the first time. Allyl fluorides are used as superior precursors for the generation of π-allyl complexes that upon ionization liberate fluoride anions for activation of silylated nucleophiles. With the unique bidentate diamidophosphite ligand ligated palladium as catalyst, the in situ generated α-sulfonyl carbon anion was quickly captured by the allylic intermediates, affording a series of chiral homo-allylic sulfones with high efficiency and selectivity. This work provides a mild in situ desilylation strategy to reveal nucleophilic carbon centers that could be used to overcome the pK_a limitation of “hard” nucleophiles in enantioselective transformations.

A variety of “hard” α-sulfonyl carbanions of aryl, heteroaryl and alkyl sulfones were successfully employed as nucleophiles in palladium-catalyzed asymmetric allylic alkylation with excellent enantioselectivities.     

Strong and Weak Solutions to Second Order Differential Inclusions Governed by Monotone Operators

In this paper we introduce the concept of a weak solution for second order differential inclusions of the form u″(t) ∈ Au(t) + f(t), where A is a maximal monotone operator in a Hilbert space H. We prove existence and uniqueness of weak solutions to two point boundary value problems associated with such kind of equations. Furthermore, existence of (strong and weak) solutions to the equation above which are bounded on the positive half axis is proved under the optimal condition tf(t) ∈ L ¹(0, ∞; H), thus solving a long-standing open problem (for details, see our comments in Section 3 of the paper). Our treatment regarding weak solutions is similar to the corresponding theory related to the first order differential inclusions of the form f(t) ∈ u′(t) + Au(t) which has already been well developed.     

Row–column interaction models,with an R implementation

We propose a family of models called row–column interaction models (RCIMs) for two-way table responses. RCIMs apply some link function to a parameter (such as the cell mean) to equal a row effect plus a column effect plus an optional interaction modelled as a reduced-rank regression. What sets this work apart from others is that our framework incorporates a very wide range of statistical models, e.g., (1) log-link with Poisson counts is Goodman’s RC model, (2) identity-link with a double exponential distribution is median polish, (3) logit-link with Bernoulli responses is a Rasch model, (4) identity-link with normal errors is two-way ANOVA with one observation per cell but allowing semi-complex modelling of interactions of the form  \(\mathbf{A}\mathbf{C}^T\) , (5) exponential-link with normal responses are quasi-variances. Proposed here also is a least significant difference plot augmentation of quasi-variances. Being a special case of RCIMs, quasi-variances are naturally extended from the \(M=1\) linear/additive predictor  \(\eta \) case (within the exponential family) to the \(M>1\) case (vector generalized linear model families). A rank-1 Goodman’s RC model is also shown to estimate the site scores and optimums of an equal-tolerances Poisson unconstrained quadratic ordination. New functions within the VGAM R package are described with examples. Altogether, RCIMs facilitate the analysis of matrix responses of many data types, therefore are potentially useful to many areas of applied statistics.     

Enhancement of catalytic activity of titanosilicalite-1 - sulfated zirconia combination towards epoxidation of 1-octene with aqueous hydrogen peroxide

Summary Titanosilicalite-1 (TS-1) in combination with sulfated zirconia efficiently catalyzes the epoxidation of 1-octene with aqueous hydrogen peroxide. The presence of both octahedral zirconium and sulfate species in the catalysts enhances the epoxidation rates.     

Nanomolar Determination of Methyldopa in the Presence of Large Amounts of Hydrochlorothiazide Using a Carbon Paste Electrode Modified with Graphene Oxide Nanosheets and 3‐(4′‐Amino‐3′‐hydroxy‐biphenyl‐4‐yl)‐acrylic Acid

A novel electrochemical sensor for sensitive detection of methyldopa at physiological pH was developed by the bulk modification of carbon paste electrode (CPE) with graphene oxide nanosheets and 3‐(4′‐amino‐3′‐hydroxy‐biphenyl‐4‐yl)‐acrylic acid (3,′AA). Applying square wave voltammetry (SWV), in phosphate buffer solution (PBS) of pH 7.0, the oxidation current increased linearly with two concentration intervals of methyldopa, one is 1.0×10^?8–1.0×10^?6 M and the other is 1.0×10^?6–4.5×10^?5 M. The detection limit (3σ) obtained by SWV was 9.0 nM. The modified electrode was successfully applied for simultaneous determination of methyldopa and hydrochlorothiazide. Finally, the proposed method was applied to the determination of methyldopa and hydrochlorothiazide in some real samples.     

Corrosion and biological behavior of nanostructured 316L stainless steel processed by severe plastic deformation

Nanostructured metals have different mechanical, chemical, and physical behaviors in comparison with the microstructured ones. Numerous research studies demonstrated that the biological behavior of nanostructured metallic implants was improved significantly. Concerning the nanostructured metals, decreasing the corrosion rate and the releasing of hazardous ions from metallic implants, and thus increasing the biocompatibility of implants are due to improving the native oxide layer. In the present study, nanostructured 316L stainless steel (biomedical grade) was manufactured via equal channel angular pressing (ECAP) method. To do so, the 316L stainless steel (SS) was exposed to the ECAP operation for eight passes. The impact of the ECAP process on corrosion behavior of SS samples was evaluated through performing the electrochemical polarization corrosion tests in Ringer's solution. Scanning electron microscopy was employed to study the surface morphology of common SS and ECAPed SS sample after the electrochemical polarization tests. Moreover, the biological behavior of the samples was evaluated via cell culture using fibroblast cells. The corrosion test results revealed a substantial decrease of corrosion rate from 3.12 (coarse‐grained sample) to 0.42 μA cm^?2 (for nanostructured). Furthermore, the cell proliferation in the interface of nanostructured sample and cell culture medium enhanced dramatically compared with the coarse‐grained one. The much better biological behavior of nanostructured SS sample in comparison with the coarse‐grained one is mostly due to the significant decrease of corrosion rate on the surface of SS samples, and the presence of much more chrome oxide on the surface of SS sample. Copyright © 2015 John Wiley & Sons, Ltd.