In recent decades, the world has experienced several emerging virus outbreaks, among which the most recent compromise the respiratory system and are caused by the SARS-CoV2 coronavirus, H1N1, H5N1 viruses, and the H7N9 virus of the severe acute respiratory syndrome (SARS). In this article, we present epidemiological dynamics based on a SIR-type model with nonlinear incidence rates that reflect the impact of the media and the psychological effects on the spread of the disease. The mathematical model of the problem corresponds to a three-dimensional non-linear ODE system. The Rach-Adomian-Meyers (MDM) decomposition method is used to compute an approximation to the solution of the governing system of non-linear differential equations. The present proposed approach is based on dividing the entire domain into subintervals. In each subinterval, the 12-term MDM solution is sufficient to obtain fairly accurate and convergent results.

Aim of the presented study is to investigate the numerical solution of fifth-order nonlinear Lane-Emden (LE) based singular system at the origin with different shape factors developed on the analogous pattern of standard second order LE equations. The stochastic neuro-evolution computing is exploited for numerical outcomes by using the artificial neural networks (ANNs) for applicable mapping and learning of decision variables with integrated meta-heuristics of genetic algorithms (GAs) for global search aided with the rapid local search of active-set (AS) i.e., ANN-GA-AS algorithm. The designed numerical computing approach ANN-GA-AS implemented effectively for solving fifth-order nonlinear LE singular system and results of statistical assessments further authenticate the accuracy, convergence, and stability.

In this paper, we consider a nonlinear viscoelastic problem with infinite history and a nonlinear feedback localized on the domain and a relaxation function satisfying $$g^{\prime}(t) \le -\xi(t)G(g(t)).$$ We establish explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our results are obtained without imposing any restrictive growth assumption on the damping term and without imposing any assumption on the boundedness of initial data used in many earlier papers in the literature.

In this article, the notion of BL-function on a nonempty set P will be studied and for an arbitrary BL-algebra L and the element l ∈ L, the notions of l-functions and l-subsets will be introduced. Moreover, using these notations, the BL-code CL introduce and some related properties and examples will be provided. Finally, I show that the structure of a BL-algebra and the correspondence BL-code are the same.

In the present article, we implement a new numerical scheme, the quasilinearization semiorthogonal B-spline wavelets method, combining the semiorthogonal B-spline wavelets collocation method with the quasilinearization method, for a class of the multi-term nonlinear fractional order equations. The fractional order equations contain Riemann-Liouville fractional integral operator and Caputo fractional differential operator. The quasilinearization method is firstly utilized to convert the multi-term nonlinear fractional order equation into a multi-term linear fractional order equation, which is solved by means of semiorthogonal B-spline wavelets subsequently. Herein, we investigate the operational matrix and the convergence of the proposed scheme. Several numerical results are given to confirm the accuracy and efficiency of our scheme.

Background: Office based laryngeal procedures have dramatically changed the management of many laryngeal procedures. Such practice offers advantages to patients, surgeons and institutions. From patients perspective it has the benefit of eliminating the risk of general anaesthesia completely, most especially in patients with significant co-morbid conditions, or those in need of repeated procedures as recurrent laryngeal papillomatosis. Moreover, it allows titration of amount of injection required during vocal fold injections as it’s effect on patients voice can be instantly heard and assess during injection. This also minimise the risk of over injection and stridor. In addition, it is cost-effective to institutions and saves theatres’ slots. It also allows patients to return to normal activities sooner compared to surgery under a general anaesthesia. Aim: Review of outpatient based laryngology procedures in Manchester Royal infirmary and determining patients’ tolerance to outpatient procedures using pain score for the nose and throat. Study Design: This is a retrospective study of the outpatient based laryngology procedures under local anesthesia in Manchester Royal Infirmary, Department of Ototrhinolaryngology, Head and Neck Surgery from January 2018 till June 2019. Results: Eighty-eight outpatients procedures recorded during that time period, including trans-nasal laryngoscopy laser vocal fold procedures, biopsies, vocal fold injections augmentation, trans-nasal oesophagoscopy and biopsy, and balloon dilatation. Other procedures recorded were laryngeal EMG and Trans-nasal oesophagoscopy and tracheo-esophageal puncture for speech valve insertion. Average pain scores from all procedures according to pain score from 0-10, revealed average score of 2.71 ±0.87 in the nose and 3.35 ±0.99 in the throat. There were no recorded complications. Conclusion: Laryngeal outpatients procedures are generally safe to perform and well tolerated by patients. In addition to being cost-effective for hospitals and institutions. Keywords: Office based procedures, Trans-nasal laryngoscopy, Balloon dilatation, Vocal fold Injection, Office based laser procedures

Inducible lysine decarboxylases (LDCs) are essential in various cellular processes of microorganisms and plants, especially under acid stress, which induces expression of genes encoding LDCs. In this study, a novel Serratia marcesenes LDC (SmcadA) was successfully expressed in E. coli and structural modeling showed the protein as a decamer with a molecular weight of approximately 75 kDa. Further structural analysis of the protein network interactions showed that specific N-terminal and C-terminal residues with significant node size-degree correlation and high color intensity possessed high values of betweenness, suggesting they played a key role in protein function and activity. Molecular dynamics simulations further revealed that hydrogen bonds were vital interactions for stabilization of cofactor PLP and formation of intermediates, hence improved biocatalysis. Furthermore, mutations coffered structural changes of the protein residues and PLP hence altered the type of interacting residues with the ligand, causing changes in conformation of PLP. Moreover, temperature also induced changes in orientation of cofactor PLP and amino acid residues. This work therefore demonstrates the role of protein-ligand interactions in altering cofactor and binding site residue conformations thus contributing to improved biocatalysis.

Objective: We hypothesized that neuromuscular retraining therapy combined with botulinum toxin injections (NMRT-B) could enhance the effectiveness of treatment for facial problems caused by facial paralysis. Also, we developed a new method to evaluate facial functions in a detailed, accurate, and objective manner. Methods: It has been recommended that patients with one-sided facial paralysis that does not resolve for more than 6 months undergo scheduled treatment with NMRT-B. The patients were scheduled to begin NMRT after 1–2 weeks of botulinum toxin A injection on the affected side and/or on the unaffected side. The second botulinum toxin A injection was conducted at 6 months after the first injection, and NMRT was continued for more than 6 months. And we used a computer-based numeric scoring system alone to confirm facial functions. Results: Most patients with chronic facial paralysis who underwent NMRT-B treatment exhibited better results after 1 year. NMRT-B provided satisfactory control of synkinesis as well as primary movement. Using our method for evaluation of facial asymmetry, the average primary facial function movement score was calculated as 57.3 (0.573), average secondary facial function movement score was 14.2 (0.142), and average final facial function movement score was 43.1 (0.431) before treatment Conclusions: We demonstrated that NMRT-B was effective for patients with synkinesis and facial asymmetry and that the results differed depending on the degree of facial paralysis. We also established a method to evaluate facial paralysis in an objective manner that excludes subjective judgment.

This paper is devoted to invest an optimal investment strategy for a defined-contribution (DC) pension plan under the Ornstein-Uhlenbeck (O-U) process and the loan. By considering risk-free asset, a risky asset driven by O-U process and a loan in the financial market, we firstly set up the dynamic equation and the asset market model which are instrumental in achieving the expected utility of ultimate wealth at retirement. Secondly, the corresponding Hamilton-Jacobi-Bellman(HJB) equation is derived by means of dynamic programming principle. The explicit expression for the optimal investment strategy is obtained by Legendre transform method. Finally, different parameters are selected to simulate the explicit solution and the financial interpretation of the optimal investment strategy is given.

A way to obtain approximate periodic solutions to nonlinear oscillators arising in a micro-electro-mechanical system (MEMS) is presented for the case of zero initial conditions and magnetostatic excitation. The frequency-amplitude relationship is derived by adopting He’s frequency formulation. The obtained analytical results are illustrated graphically. The proposed simple approach gives the fast insight into the dynamics of the singular oscillator and can be useful for design of MEMS devices.

A strategy is devised to make the WENO interpolation in the point values achieve optimal accuracy near the discontinuities. The classical WENO interpolation ensures the optimal accuracy when all stencils are smooth and ENO property when the discontinuity appears. When there exist more than two successive smooth stencils, the maximum theoretical accuracy near discontinuity is also preferred to be obtained. To achieve it, we divide the classical WENO algorithm into several sub-WENO procedures. In each sub-WENO procedure, only two stencils are used and the order of accuracy grows one at most. If both stencils are smooth, then sub-WENO procedure increases the order of accuracy by one. If there is a stencil is smooth and the left one is non-smooth, then algorithm conserves the order of interpolation by corresponding smooth stencil and keeps the ENO property. If both stencils are non-smooth, then the value constructed by sub-WENO procedure will be ignored in the latter procedures. The whole of new WENO algorithm can be expressed as a tree structure. The indicator of smoothness of every medium stencil in the tree structure is defined by the indicators of smoothness of corresponding stencils on the top of tree. Such definition is proved to be capable of obtaining the optimal accuracy and keep the ENO property. And the new WENO algorithm has almost the same computational cost as the classical WENO algorithm.

The present work is concerned with the well-posedness and efficient numerical algorithm for a terminal value problem with a generalized Caputo fractional derivative. We investigate the existence and uniqueness of the solution of the terminal value problem, and consider the continuous dependence of the solutions on the given data. To illustrate our theoretical results, we present a one step algorithm for solving the considered problems. Some numerical examples are shown to illustrate the theoretical results and the efficiency of the numerical method.

In this paper, a novel numerical method for solving the optimal control problems (OCPs) are presented. This method uses Genocchi polynomials. Some properties of Genocchi polynomials are given and the operational matrix of derivative is constructed. This matrix helps us to convert the nonlinear constrained optimal control problem to the nonlinear programming one that can be solved by Maple programming software. The presented method is applied on some numerical examples in order to show its advantages.

In this note, we show that the Hausdorff operator $H_{\Phi}$ is unbounded on a large family of Quasi-Banach spaces, unless $H_{\Phi}$ is a zero operator.

In this paper we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficients in the principle part of the elliptic operator. The objective is to provide a well-posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

In this paper, we study the vaporization process of a polydisperse ensemble of liquid drops on the basis of a nonlinear set of balance and kinetics equations for the particle-radius distribution function and temperature in the gaseous phase. We found an exact parametric solution to this problem using a modified time variable and the Laplace integral transform method. The distribution function of vaporizing drops as well as its moments, the temperature dynamics in gas, and the unvaporized mass of drops are found. The initial particle-radius distribution shifts to smaller particle radii with increasing the vaporization time. As this takes place, the temperature difference between the drops and gas decreases with time. It is shown that the heat of vaporization and initial total number of particles in the system substantially influence the dynamics of a polydisperse ensemble of liquid drops.

For the following wave equations with structural damping and nonlinear memory source terms \[ u_{tt}+(-\Delta)^{\frac{\alpha}{2}}u +(-\Delta)^{\frac{\beta}{2}}u_t =\int_{0}^{t}(t-s)^{\gamma-1} \vert u (s)\vert^{p}\,\text{d}s, \] and \[ u_{tt}+(-\Delta)^{\frac{\alpha}{2}}u +(-\Delta)^{\frac{\beta}{2}}u_t = \int_{0}^{t}(t-s)^{\gamma-1} \vert u_s (s)\vert^{p}\,\text{d}s, \] posed in $(x,t) \in \mathbb{R}^N \times [0,\infty) $, where $u=u(x,t)$ is real-value unknown function, $p>1$, $\alpha,\beta\in (0, 2]$, $\gamma\in (0,1)$, we prove the nonexistence of global solutions. Moreover, we give an upper bound estimate of the life span of solutions.

In this paper, the semi-rational solutions that causes vector rogue waves and breathers can be obtained by using the Darboux dressing transformation. We studied vector rogue waves and the interaction between rogue waves and light-dark solitons, and observed that during the interaction, due to the interference between the light-dark components of the solitons, a respiration-like structures appears. Besides, it can be observed that the rogue waves and soliton merge together. Moreover, the main characteristics of the interactions between the breathers and bright-dark solitons are displayed with some graphics.

Orthogonal experiment design together with the analysis of variance was used to examine the processing parameters (laser power, scan speed, layer thickness and hatch spacing) of selective laser melting (SLM) for superior properties of SLM parts, in which nine groups of specimens of Ti-6Al-4V were fabricated. The porosity for each group was measured and the results clarify that the influence sequence of individual parameter on the porosity is laser power > hatch spacing > layer thickness > scan speed. Ultrasonic fatigue tests (20 kHz) were conducted for the SLMed specimens in high-cycle fatigue (HCF) and very-high-cycle fatigue (VHCF) regimes. The S-N data show that the fatigue strength is greatly affected by the porosity: the group with the smallest porosity percentage having the highest fatigue strength in HCF and VHCF regimes. Moreover, the observations by scanning electron microscopy revealed that fatigue cracks initiate at lack-of-fusion defects in the cases of surface and internal crack initiation.

Objective There are some suggestions that global myocardial strain (GLS) early after ST-elevation myocardial infarction (STEMI) is a predictor of improvement in left ventricular ejection fraction (LVEF) after myocardial infarction. The goal of this study was to evaluate predictive value of GLS in patient with STEMI. Methods The study population consists of 43 patients with acute STEMI and no history of prior coronary intervention treated with primary percutaneous coronary intervention. LVEF and myocardial strain indices were measured 48hours and two months after STEMI by transthoracic echocardiography and speckle tracking method. More than 5% improvement in LV EF was considered significant improvement. Results GLS values were significantly higher in patients with >5% improvement in LVEF 2 months after the STEMI (GLS=15.76% in patients with >5% improvement vs. 11.54% in the other group,P <0.05). ROC analysis suggested GLS values more than 13.5 to be a predictor of significant LVEF improvement 2 month after STEMI. Higher GLS was observed in patients with inferior, posterior and inferoseptal STEMI versus anterior, extensive or anteroseptal STEMI and in patients with right coronary occlusion versus occlusion of the left anterior descending or circumflex arteries. Conclusion We have observed that early longitudinal LV strain after STEMI is a predictor of during first 2 months after STEMI. This is a useful method to predict early LV recovery after STEMI. GLS values more than 13.5%is a significant predictor of significant LVEF improvement.

The artificial simulated rainfall test method is used to deeply analyze the mechanism of the change of sediment concentration on the grassland slope .Under the experimental condition, the results show the following. 1). The addition of root volume can increase the accuracy of the expression of the sediment concentration variability and reduction of sediment concentration by 0.5% and 1.12%, respectively; 2).The relationship between the vegetation characteristics and the sediment concentration on the grassland slope is best expressed by the coverage and root volume; 3).The slope plays a larger role than the rain intensity in the change of sediment concentration on grassland slopes .

Nitrogen use efficiency (NUE) is an important and complex crops trait and its improvement represents a strategy to maintain high yield reducing N-supply. We report the genome-wide transcriptomic analysis of four eggplants contrasting for NUE to identify key genes related to the NUE pathway, after short- and long-term low-N exposure, in both root and shoot. Co-expression Gene Networks (CGN) analysis permitted to identify up-regulated differential expressed genes (DEGs) involved in the light reaction pathway, the biological processes response to inorganic substance, abiotic stimulus and cellular response to nitrogen starvation in high NUE genotypes. Some transcription factor (TF) were up-regulated in the N-use efficient genotypes, in particular, WRKY33 showed a significant up-regulation triggering the higher expression of 21 genes cluster including other TFs, many of which associated to N-metabolism. To validate our results, an independent de novo experiment including two other NUE-contrasting genotypes, at both low and high N supply, was carried out. Interestingly, the high significant WRKY33 expression and its cluster were confirmed in the high NUE genotypes at low-N supply. Moreover, the WRKY33 role was confirmed in Arabidopsis as the 35S::AtWRKY33 over expressing line showed a more competitive root system able to uptake more efficiently N from the soil.

We present comprehensive measurements of the evaporation behaviour, E, of a thinning film during a hydrodynamic-evaporative spincoating experiment. E, ω (rotational speed), and \nu (viscosity) are the main control parameters of the process. The evolution of the entire film thinning process can be described theoretically quite well based on the bulk value of \nu of the deposited liquid and with a process-specific (constant) E. The weighing in values of \nu are easily accessible (calculations, literature values, simple measurements). E is specific for the experimental conditions and values cannot be found in literature. There is also no generally accepted strategy to calculate E in advance. We analyzed our experimental results in view of a theoretical prediction for E, which was presented already some time ago by Bornside, Macosco, and Scriven, but never tested experimentally. We find good agreement between theory and experiment for many solvents and different! Accordingly, this approach permits in advance the calculation of the evolution of the entire hydrodynamic-evaporative film thinning in a spincoating process. In addition, we present a general formula, which allows in the case of spincoating mixtures of volatile solvents and nonvolatile solutes the prediction of the final solute deposit based on literature data only.

Sixty-three patients with LCH (54 adults, 9 children), with unifocal or multifocal bone lesions were treated with indomethacin. All but one patient achieved a response, that was complete in 52% of them. Overall, 5-year reactivation-free survival was 72%, significantly higher in patients treated with indomethacin as first-line (81.7% vs 52.5%; p=0.01); in those who received indomethacin as single agent (80.5% vs 36.5%, p=0.005); and in those with unifocal disease (90.9% vs 48.1%, p=0.003). Our results confirmed the efficacy of indomethacin in bone LCH both as front-line treatment and after reactivations, in localized, or more extended disease, with minimal side effects.