Faculty of Computer and Information Systems, Islamic University of Madinah, Saudi Arabiatanweer03@iu.edu.saShamimul QamarComputer Engineering Department, King Khalid University, Abha, Saudi ArabiaAmit DixitDepartment of ECE, Quantum School of Technology, Roorkee, IndiaMohamed BenaidaFaculty of Computer and Information Systems, Islamic University of Madinah, Saudi Arabia

In this paper, we consider a Camassa and Holm-Degasperis and Procesi (CH-DP) equation $u_{t}- c_{0}u_{x}+4uu_{x}-\alpha^2(u_{xxt}+uu_{xxx}+3u_{x}u_{xx})+\gamma u_{xxx}=0$. By using the bifurcation method of dynamical systems, some new explicit compacton and generalized kink wave solutions are presented through some special phase orbits. The results of before references are extended.

We are exploring solitons and other solutions describe new interaction between two solitons besides, new three soliton solutions are generated. we examine the commutative product between multi unknown Lie infinitesimals for the (2+1) dimensional variable-coefficients Bogoyavlensky Konopelchenko (VCBK) equation and this study result some new Lie vectors. The commutative product generates a system of nonlinear ODEs which had been solved manually. Through two stages of Lie symmetry reduction, (VCBK) equation is reduced to non-solvable nonlinear ODEs using various combinations of optimal Lie vectors. Using the Integration method, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solitons and other solutions for (VCBK). Some selected solutions illustrated through three-dimensional plots.

This article is concerned with an initial-boundary value problem (IBVP) for a new phase-field model describing the evolution of structural phase transition in elastically deformable solid materials. The model consists of an elliptic-parabolic system in which the displacement field and the order parameter both satisfy periodic boundary conditions. We prove the existence of global solutions to this IBVP by applying the method of continuation of local solutions and perform numerical simulations to investigate the microstructure evolution of MnNi alloys by using this new phase-field model.

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Heat transfer in a magnetohydrodynamic (MHD) micropolar fluid through a squeezing channel in the presence of viscous dissipation and Joule heating is studied. The analysis is carried out over different water based nanofluids consisting of alumina (Al2O3), titania (TiO2), and magnetite (Fe3O4) nanoparticles. A model with non-linear partial differential equations is converted to a set of non-linear ordinary differential equations by the aid of similarity transformations. The resulting equationsare then numerically solved by Runge–Kutta (RK) method with fourth order approximation followed by shooting method. A comprehensive investigation describing the influences of the physical parameters such as vortex viscosity parameter, ohmic heating parameter, Hartmann number, squeezing parameter and solid volume fraction parameter on the distributions of temperature, velocity and microrotationis are graphically showed. In the absence of squeezing and expanding, it is observed that both water and nanofluid experience same viscous drag. Further, an increase in volume fraction lowers the microrotation, and thereby causing an elevation in the temperature of titania–water nanofluid. This is in contrast to the behaviour of the other nanofluids.

Mammary-like glands (MLG) are normal structures in the vulva which have possible but rare malignant potential.Given this rarity, guidelines for treating MLG adenocarcinoma are lacking. In the current literature, approximately thirty six reported cases of MLG in the vulva exist.

Esophageal perforation is a rare but life-threatening condition1. Early detection and diagnosis are important to ensure good patient outcomes. The case that we present is of a patient that developed spontaneous esophageal perforation following irrigation and drainage of a retropharyngeal abscess.

Chyle leak is serious sequela of head and neck surgery and has been reported after esophageal, parathyroid, and thyroid surgery. However, it has only been reported postoperatively once before after anterior cervical disc fusion (ACDF). This case discusses the formation of a chyloma following an anterior cervical spinal procedure.

Four weeks subsequent to a maxillary molar extraction a prolapse of the antrum lining through the extraction socket occurred. It was managed with a buccal fat pad pedicle graft.

We present 3 cases of Panfacial fractures through which we try to emphasize two important sequencing rules: “Reference point”(the most intact area to determine the starting point for fixation) and the “Confirming points” ( the points which should be checked out to confirm the exact position & orientation).

The objective of the present paper is to investigate the dynamics of Hepatitis B-type virus (HBV) infection through mathematical model. Distinct to the existing mathematical models on HBV, the present model considers the various factors such as immune impairment, the maximum number of T-cells (total carrying capacity), logistic growth term. Besides, for more accuracy, the role of antiretroviral therapies are also involved in the analysis. In addition, time delays are inevitable during the activation of immune response and during the antiretroviral therapy. Considering these factors while formulating the mathematical model which helps to gain insights into the disease progression. With the derived model, the qualitative analysis such as stability analysis, bifurcation analysis and stabilization analysis can be performed to investigate the performance of the model over the period of time. The significance of the model parameters are revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of dataset values that are extracted from the literature the efficiency of the derived theoretical results are explored.

In this article, we consider the zero dissipation limit of the micropolar equations with temperature-dependent viscosity and heat-conduction coefficient. If the given rarefaction wave to the corresponding conservation systems connects to vacuum at one side, we can construct a sequence of solutions to the micropolar equations which converge to the given rarefaction wave with vacuum as the transport coefficients tend to zero. And the uniform convergence rate can be obtained. The key point in our analysis is how to control the degeneracies of the density, the temperature and the temperature-dependent viscosities at the vacuum region in the zero dissipation limit process.

In this paper, quantum version of Montgomery identity by applying $q^{b}$-integral is obtained. By employing the established identity, some new quantum Ostrowski type inequalities are proved. Several special cases of our main results are presented. It is also shown that the results presented in this paper generalize several other well known inequalities given in the existing literature on this subject.

In this study, we present an algorithm in MATLAB to classify $8$ dimensional non-abelian nilsoliton metric Lie algebras with singular Gram matrices. With this algorithm, we can compute Lie brackets, structure constants, index, rank and eigenvalues of the nilsoliton derivation. This paper can be considered as a follow up paper to our previous study \cite{Kad3}. In our previous paper, we defined an algorithm that helps to classify algebras that admit simple derivations and singular Gram matrices $U$. Since the Gram matrices are singular, there exists infinitely many solutions to $Uv=[1]_m$, where the solutions are exactly the structure constants’ squares. In order the algebra to be a Lie algebra, the structure constants has to satisfy the Jacobi identity. In our previous work, we did not present a methodology to classify algebras that satisfy Jacobi identity. But in this paper, we extend the capability in such a way that we are able to create and solve the Jacobi identity/identities with the help of computer algorithms for each index set. Therefore we completely classify all indecomposible nilsolitons in dimension $8$. Several examples are provided for the illustration of the methodology.

In this paper, we introduce an iteration process to approximate a fixed point of a contractive self-mapping. The comparison theorem indicates that our iteration process is faster than the other existing iteration processes in the literature. We also obtain convergence and stability theorems of this iterative process for a contractive self-mapping. Numerical examples show that our iteration process for approximating a fixed point of a contractive self-mapping is faster than the existing methods. Based on this process, we finally present a new modified Newton-Raphson method for finding the roots of a function and generate some nice polynomiographs.

In this paper, we will solve Generalized Korteweg-De Vries equation with Local fractional derivative bylocal fractional homotopy analysis method (LFHAM). The approximate solutions of non-differentiabletype with the generalized functions defined on Cantor sets are analyzed. Further, some examples andspecial cases of main results are also discussed.

An 80-year old gentleman with very severe aplastic anemia was treated with standard combination therapy of equine antithymocyte globulin and cyclosporine A. His death shortly after treatment could be attributed to his advanced age, severe pancytopenia at diagnosis, absence of minor paroxysmal nocturnal hemoglobinuria clone and immunosuppressive therapy-related complications.

Coronavirus disease 2019 (COVID-19) may present with different symptoms and complications. Acrocyanosis and digital necrosis may be associated with COVID-19. We describe two patients with COVID-19 who died with acrocyanosis and digital necrosis at the terminal stage of their illness.

Background: Hybrid coronary revascularization (HCR) constitutes a left internal mammary artery (LIMA) graft to the left anterior descending (LAD) coronary artery, coupled with percutaneous coronary intervention (PCI) for non-LAD lesions. This management strategy is not commonly offered to patients with complex multi-vessel disease. Our objective was to evaluate 8-year survival in patients with triple-vessel disease (TVD) treated by HCR, compared with that of concurrent matched patients managed by traditional coronary artery bypass grafting (CABG) or multi-vessel PCI. Methods: A retrospective review was undertaken of 4805 patients with TVD who presented between January 2009 and December 2016. A cohort of 100 patients who underwent HCR were propensity-matched with patients treated by CABG or multi-vessel PCI. The primary end-point was all-cause mortality at 8 years. Results: Patients with TVD who underwent HCR had similar 8-year mortality (5.0%) as did those with CABG (4.0%) or multi-vessel PCI (9.0%). A composite end-point of death, repeat revascularization, and new myocardial infarction, was not significantly different between patient groups (HCR 21.0% vs. CABG 15.0%, p = 0.36; HCR 21.0% vs. PCI 25.0%, p = 0.60). Despite a higher baseline SYNTAX score, HCR was able to achieve a lower residual SYNTAX score than multi-vessel PCI (p = 0.001). Conclusions: In select patients with TVD, long-term survival and freedom from major adverse cardiovascular events (MACE) after HCR are similar to that seen after traditional CABG or multi-vessel PCI. HCR should be considered for patients with multi-vessel disease, presuming a low residual SYNTAX score can be achieved.

Quantum Fisher information (QFI) and geometric phase have recently been performed different tasks in quantum information technology. We investigate the QFI and entanglement of a three-level atom in $\Lambda $ configuration interacting with a quantized field mode by using linear entropy. We study the dynamical behavior of the geometric phase based on the engineering of a three-level atomic configuration. We analyze the effect of energy dissipation of the dynamical properties of the geometric phase and the QFI as an entanglement quantifier between the three-level atom and field. We explore the correlation between the engineering geometric phase and QFI in the absence and presence of energy dissipation effect. We have found that the $\mathrm{QFI}$ is very sensitive to the effect of the time dependent coupling and energy dissipation.

We consider the reaction-diffusion equation for fractional Dirichlet-to-Neumann operator with subcritical exponent motivated by electrical impedance tomography (EIT) and a need to overcome the Non-locality of a fractional differential equation for modeling anomalous diffusion. We mainly deal with the asymptotic behavior of global solution and the boundedness of global orbit which allows us to show that any global solution is classical solution using Moser iteration technique.

Primary hypothyroidism has been associated with many adverse effects. Its cardiovascular manifestations include reductions in heart rate and contractility with the development of hypertension, angina, heart failure, and pericardial effusion consistent with a hypothyroid heart. Early recognition and treatment can help mitigate these advanced features.

Dobutamine stress echocardiogram (DSE) is routinely used in the clinical assessment of patients with known or suspected coronary artery disease (CAD). DSE can cause serious complications including cerebrovascular accident (CVA). Even though, the incidence of CVA associated with DSE is very low (<0.01%), it can be life-threatening or cause significant morbidity. We present a patient who also developed acute multifocal intracranial (ICH) and subarachnoid hemorrhages (SAH) during the DSE. A 39 years old female, with no prior cardiac history, presented to the outpatient echocardiography lab for DSE. She had blunted heart rate response with increasing dose of dobutamine 30 μg/kg/min and was given one milligram of atropine. The patient complained of frontal headache, nausea, and severe dyspnea. CT head showed acute multifocal bilateral SAH, left frontal and right parieto-occipital ICH. Hypertension is one of the risk factors for ICH and dobutamine infusion can exacerbate severe acute hypertension, which can cause acute intraparenchymal hemorrhage. Even though the risk of ICH associated with DSE is extremely low, there should be increased vigilance if there is development of severe acute hypertension and the operator should keep a low threshold for further evaluation if the patient develops neurological symptoms.