Computing the eigenvalues and eigenvectors of a fuzzy matrix

Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.

Fractional and time-scales differential equations

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Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed

On new solutions of linear system of first -order fuzzy differential equations with fuzzy coefficient

In this paper, we firstly introduce system of first order fuzzy differential equations. Then, we convert the problem to two crisp systems of first order differential equations. For numerical aspects, we apply exponentially fitted Runge Kutta method to solve the fuzzy problems. We solve some well-known examples in order to demonstrate the applicability and accuracy of results

Imaging data in COVID-19 patients: focused on echocardiographic findings

To assess imaging data in COVID-19 patients and its association with clinical course and survival and 86 consecutive patients (52 males, 34 females, mean age = 58.8 year) with documented COVID-19 infection were included. Seventy-eight patients (91) were in severe stage of the disease. All patients underwent transthoracic echocardiography. Mean LVEF was 48.1 and mean estimated systolic pulmonary artery pressure (sPAP) was 27.9 mmHg. LV diastolic dysfunction was mildly abnormal in 49 patients (57.6) and moderately abnormal in 7 cases (8.2). Pericardial effusion was present in 5/86 (minimal in size in 3 cases and mild- moderate in 2). In 32/86 cases (37.2), the severity of infection progressed from �severe� to �critical�. Eleven patients (12.8) died. sPAP and computed tomography score were associated with disease progression (P value = 0.002, 0.002 respectively). Tricuspid annular plane systolic excursion (TAPSE) was significantly higher in patients with no disease progression compared with those who deteriorated (P value = 0.005). Pericardial effusion (minimal, mild or moderate) was detected more often in progressive disease (P = 0.03). sPAP was significantly lower among survivors (P value = 0.007). Echocardiographic findings (including systolic PAP, TAPSE and pericardial effusion), total CT score may have prognostic and therapeutic implication in COVID-19 patients. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature

Safety and effectiveness of high-dose vitamin C in patients with COVID-19: a randomized open-label clinical trial

Background: Vitamin C is an essential water-soluble nutrient that functions as a key antioxidant and has been proven to be effective for boosting immunity. In this study, we aimed to assess the efficacy of adding high-dose intravenous vitamin C (HDIVC) to the regimens for patients with severe COVID-19 disease. Methods: An open-label, randomized, and controlled trial was conducted on patients with severe COVID-19 infection. The case and control treatment groups each consisted of 30 patients. The control group received lopinavir/ritonavir and hydroxychloroquine and the case group received HDIVC (6 g daily) added to the same regimen. Results: There were no statistically significant differences between two groups with respect to age and gender, laboratory results, and underlying diseases. The mean body temperature was significantly lower in the case group on the 3rd day of hospitalization (p = 0.001). Peripheral capillary oxygen saturations (SpO2) measured at the 3rd day of hospitalization was also higher in the case group receiving HDIVC (p = 0.014). The median length of hospitalization in the case group was significantly longer than the control group (8.5 days vs. 6.5 days) (p = 0.028). There was no significant difference in SpO2 levels at discharge time, the length of intensive care unit (ICU) stay, and mortality between the two groups. Conclusions: We did not find significantly better outcomes in the group who were treated with HDIVC in addition to the main treatment regimen at discharge. Trial registration irct.ir (IRCT20200411047025N1), April 14, 2020 © 2021, The Author(s)

An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems