An Accurate Method for Solving Riccati Equation with Fractional Variable-Order

Abstract The article proposes a mathematical model based on the fractional Riccati equation to describe the dynamics of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. The model fractional Riccati equation is an equation with variable coefficients and a derivative of a fractional variable order of the Gerasimov-Caputo type. The solution to the model Riccati equation is given using the modified Newton method. The obtained model curves are compared with the experimental data of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. It is shown that with a suitable choice of parameters in the mathematical model, the calculated curves give results close to real experimental data.

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Application of the Riccati hereditary mathematical model to the study of the dynamics of radon accumulation in the storage chamber

EPJ Web of Conferences ◽

10.1051/epjconf/202125403001 ◽

2021 ◽

Vol 254 ◽

pp. 03001

Author(s):

Dmitryi Tverdyi ◽

Roman Parovik ◽

Evgeniy Makarov ◽

Pavel Firstov ◽

Nazira Alimova

Keyword(s):

Mathematical Model ◽

Riccati Equation ◽

Model Equation ◽

Real Data ◽

Accurate Description ◽

Variable Order ◽

Accumulation Process ◽

Storage Chamber ◽

Real Curves ◽

Hereditary Properties

The article proposes a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates. The model equation is the fractional Riccati equation with a derivative of a fractional variable order of the Gerasimov-Caputo type, taking into account heredity, as well as taking into account nonlinearity, which is responsible for the mechanisms of radon entry into the chamber. The obtained model curves of the accumulation process are compared with real data. It is shown that the model described in the work gives a better agreement between the model and real curves of radon accumulation and can be used for a more accurate description of the processes occurring in the chamber.

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Hereditary Riccati Equation with Fractional Derivative of Variable Order

Journal of Mathematical Sciences ◽

10.1007/s10958-021-05254-0 ◽

2021 ◽

Vol 253 (4) ◽

pp. 564-572

Author(s):

D. A. Tvyordyj

Keyword(s):

Fractional Derivative ◽

Riccati Equation ◽

Variable Order

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Application of Lattice Imaging Techniques to Amorphous Films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100113664 ◽

1975 ◽

Vol 33 ◽

pp. 8-9

Author(s):

S. R. Herd ◽

P. Chaudhari

Keyword(s):

Nearest Neighbor ◽

Random Network ◽

Imaging Techniques ◽

Network Models ◽

Accurate Method ◽

Direct Transmission ◽

Lattice Imaging ◽

Transmission Electron ◽

Lattice Planes ◽

Nearest Neighbor Distances

Electron diffraction and direct transmission have been used extensively to study the local atomic arrangement in amorphous solids and in particular Ge. Nearest neighbor distances had been calculated from E.D. profiles and the results have been interpreted in terms of the microcrystalline or the random network models. Direct transmission electron microscopy appears the most direct and accurate method to resolve this issue since the spacial resolution of the better instruments are of the order of 3Å. In particular the tilted beam interference method is used regularly to show fringes corresponding to 1.5 to 3Å lattice planes in crystals as resolution tests.

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The effect of temperature on high-resolution TEM image contrast

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100139573 ◽

1995 ◽

Vol 53 ◽

pp. 640-641

Author(s):

T. Geipel ◽

W. Mader ◽

P. Pirouz

Keyword(s):

Form Factor ◽

Inelastic Scattering ◽

Accurate Method ◽

Waller Factor ◽

Effect Of Temperature ◽

Specimen Thickness ◽

Influence Of Temperature ◽

Debye Waller Factor ◽

Influence Of Temperature On ◽

Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

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Improving diagnosis of acute appendicitis with atypical findings by Tc-99m HMPAO leukocyte scan

Nuklearmedizin ◽

10.1055/s-0038-1623994 ◽

2002 ◽

Vol 41 (01) ◽

pp. 37-41 ◽

Cited By ~ 3

Author(s):

S. Shung-Shung ◽

S. Yu-Chien ◽

Y. Mei-Due ◽

W. Hwei-Chung ◽

A. Kao

Keyword(s):

Acute Appendicitis ◽

False Positive ◽

False Positive Rate ◽

Accurate Method ◽

Clinical Findings ◽

Pathological Findings ◽

Lower Quadrant ◽

Predictive Values ◽

Positive Rate

Summary Aim: Even with careful observation, the overall false-positive rate of laparotomy remains 10-15% when acute appendicitis was suspected. Therefore, the clinical efficacy of Tc-99m HMPAO labeled leukocyte (TC-WBC) scan for the diagnosis of acute appendicitis in patients presenting with atypical clinical findings is assessed. Patients and Methods: Eighty patients presenting with acute abdominal pain and possible acute appendicitis but atypical findings were included in this study. After intravenous injection of TC-WBC, serial anterior abdominal/pelvic images at 30, 60, 120 and 240 min with 800k counts were obtained with a gamma camera. Any abnormal localization of radioactivity in the right lower quadrant of the abdomen, equal to or greater than bone marrow activity, was considered as a positive scan. Results: 36 out of 49 patients showing positive TC-WBC scans received appendectomy. They all proved to have positive pathological findings. Five positive TC-WBC were not related to acute appendicitis, because of other pathological lesions. Eight patients were not operated and clinical follow-up after one month revealed no acute abdominal condition. Three of 31 patients with negative TC-WBC scans received appendectomy. They also presented positive pathological findings. The remaining 28 patients did not receive operations and revealed no evidence of appendicitis after at least one month of follow-up. The overall sensitivity, specificity, accuracy, positive and negative predictive values for TC-WBC scan to diagnose acute appendicitis were 92, 78, 86, 82, and 90%, respectively. Conclusion: TC-WBC scan provides a rapid and highly accurate method for the diagnosis of acute appendicitis in patients with equivocal clinical examination. It proved useful in reducing the false-positive rate of laparotomy and shortens the time necessary for clinical observation.

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Detection of Mycobacterium tuberculosis in smear negative sputum by PCR

Bangladesh Journal of Medical Microbiology ◽

10.3329/bjmm.v6i2.19368 ◽

2012 ◽

Vol 6 (2) ◽

pp. 2-6 ◽

Cited By ~ 1

Author(s):

Mohammad Jobayer ◽

SM Shamsuzzaman ◽

Kazi Zulfiquer Mamun

Keyword(s):

Mycobacterium Tuberculosis ◽

Pulmonary Tuberculosis ◽

Accurate Method ◽

Major Health Problem ◽

Major Health ◽

Tuberculosis Patients ◽

Diagnostic Potential ◽

Total Death ◽

Smear Negative ◽

Negative Sputum

Pulmonary tuberculosis is a major health problem in Bangladesh that is responsible for about 7% of total death in a year. This study was conducted to isolate and identify Mycobacterium tuberculosis from sputum and to evaluate the efficacy of PCR as a modern diagnostic tool, for diagnosis of pulmonary tuberculosis, especially in the smear negative cases. One hundred and fifty suspected pulmonary TB patients (male/ female: 97/53) were included in this study. Single morning sputum was collected from each patient and diagnostic potential of PCR was compared with staining and culture. Twenty five (16.7%) sputum were positive by ZN stained smear. Among 125 smear negative samples, 13 (10.4%) yielded growth in culture in LJ media and 21 (16.8%) samples were positive by PCR. The sensitivity and specificity of PCR in smear negative cases was 100% and 92.9% respectively. Mean detection time in PCR was 24 hours. PCR detected M. tuberculosis in 21 smear negative and 9 culture negative samples. For diagnosis of tuberculosis in smear negative cases, PCR directly from sputum was a very sensitive and accurate method. In conclusion, PCR may be done, especially in clinically suspected pulmonary tuberculosis patients who remain negative by conventional methods.DOI: http://dx.doi.org/10.3329/bjmm.v6i2.19368 Bangladesh J Med Microbiol 2012; 06(02): 2-6

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