2,156 research outputs found
Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method
In this paper we study the analytic solutions of Burgers-type nonlinear
fractional equations by means of the Invariant Subspace Method. We first study
a class of nonlinear equations directly related to the time-fractional Burgers
equation. Some generalizations linked to the forced time-fractional Burgers
equations and variable-coefficient diffusion are also considered. Finally we
study a Burgers-type equation involving both space and time-fractional
derivatives
Applied Weaving: Mapping Creativity Into Every Strand of a Curriculum
The purpose of this paper is to explore the value of adding creativity skills into curriculum mapping documents at the elementary and middle school level, with the goal of gaining some clarity regarding the intrinsic value and ubiquity of teaching for creativity. The language for the maps was taken from Weaving Creativity Into Every Strand of Your Curriculum (Burnett & Figliotti, 2015). The maps were developed after observations of and meetings with classroom teachers in order to assure their accuracy and authenticity. Because the intended purpose of a curriculum map is to provide a sweeping view of targeted content and skills, the maps are non-specific by their nature. As a result, a major challenge of this project continues to be how to find ways to make these maps meaningful to the greater community, who is largely unaware of the meaning and value of creativity. For the purposes of this project, creativity skills were added to the curriculum maps of grades five through eight at the Elmwood Franklin School in Buffalo, New York
Nonlinear time-fractional dispersive equations
In this paper we study some cases of time-fractional nonlinear dispersive
equations (NDEs) involving Caputo derivatives, by means of the invariant
subspace method. This method allows to find exact solutions to nonlinear
time-fractional partial differential equations by separating variables. We
first consider a third order time-fractional NDE that admits a four-dimensional
invariant subspace and we find a similarity solution. We also study a fifth
order NDE. In this last case we find a solution involving Mittag-Leffler
functions. We finally observe that the invariant subspace method permits to
find explicit solutions for a wide class of nonlinear dispersive
time-fractional equations.Comment: 14 pages; in press in Communications in Applied and Industrial
Mathematics (2014
Aortic Arch Thrombus and Pulmonary Embolism in a COVID-19 Patient
© 2020 Elsevier Inc. Background: Coronavirus disease 2019 (COVID-19) is associated with endothelial inflammation and a hypercoagulable state resulting in both venous and arterial thromboembolic complications. We present a case of COVID-19-associated aortic thrombus in an otherwise healthy patient. Case Report: A 53-year-old woman with no past medical history presented with a 10-day history of dyspnea, fever, and cough. Her pulse oximetry on room air was 84%. She tested positive for severe acute respiratory syndrome coronavirus 2 infection, and chest radiography revealed moderate patchy bilateral airspace opacities. Serology markers for cytokine storm were significantly elevated, with a serum D-dimer level of 8180 ng/mL (normal \u3c 230 ng/mL). Computed tomography of the chest with i.v. contrast was positive for bilateral ground-glass opacities, scattered filling defects within the bilateral segmental and subsegmental pulmonary arteries, and a large thrombus was present at the aortic arch. The patient was admitted to the intensive care unit and successfully treated with unfractionated heparin, alteplase 50 mg, and argatroban 2 μg/kg/min. Why Should an Emergency Physician Be Aware of This?: Mural aortic thrombus is a rare but serious cause of distal embolism and is typically discovered during an evaluation of cryptogenic arterial embolization to the viscera or extremities. Patients with suspected hypercoagulable states, such as that encountered with COVID-19, should be screened for thromboembolism, and when identified, aggressively anticoagulated
Chemotherapy-Response Monitoring of Breast Cancer Patients Using Quantitative Ultrasound-Based Intra-Tumour Heterogeneities
© 2017 The Author(s). Anti-cancer therapies including chemotherapy aim to induce tumour cell death. Cell death introduces alterations in cell morphology and tissue micro-structures that cause measurable changes in tissue echogenicity. This study investigated the effectiveness of quantitative ultrasound (QUS) parametric imaging to characterize intra-tumour heterogeneity and monitor the pathological response of breast cancer to chemotherapy in a large cohort of patients (n = 100). Results demonstrated that QUS imaging can non-invasively monitor pathological response and outcome of breast cancer patients to chemotherapy early following treatment initiation. Specifically, QUS biomarkers quantifying spatial heterogeneities in size, concentration and spacing of acoustic scatterers could predict treatment responses of patients with cross-validated accuracies of 82 ± 0.7%, 86 ± 0.7% and 85 ± 0.9% and areas under the receiver operating characteristic (ROC) curve of 0.75 ± 0.1, 0.80 ± 0.1 and 0.89 ± 0.1 at 1, 4 and 8 weeks after the start of treatment, respectively. The patients classified as responders and non-responders using QUS biomarkers demonstrated significantly different survivals, in good agreement with clinical and pathological endpoints. The results form a basis for using early predictive information on survival-linked patient response to facilitate adapting standard anti-cancer treatments on an individual patient basis
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Measurement of B(B-->X_s {\gamma}), the B-->X_s {\gamma} photon energy spectrum, and the direct CP asymmetry in B-->X_{s+d} {\gamma} decays
The photon spectrum in B --> X_s {\gamma} decay, where X_s is any strange
hadronic state, is studied using a data sample of (382.8\pm 4.2) \times 10^6
e^+ e^- --> \Upsilon(4S) --> BBbar events collected by the BABAR experiment at
the PEP-II collider. The spectrum is used to measure the branching fraction B(B
--> X_s \gamma) = (3.21 \pm 0.15 \pm 0.29 \pm 0.08)\times 10^{-4} and the
first, second, and third moments = 2.267 \pm 0.019 \pm 0.032 \pm
0.003 GeV,, )^2> = 0.0484 \pm 0.0053 \pm 0.0077 \pm
0.0005 GeV^2, and )^3> = -0.0048 \pm 0.0011 \pm 0.0011
\pm 0.0004 GeV^3, for the range E_\gamma > 1.8 GeV, where E_{\gamma} is the
photon energy in the B-meson rest frame. Results are also presented for
narrower E_{\gamma} ranges. In addition, the direct CP asymmetry A_{CP}(B -->
X_{s+d} \gamma) is measured to be 0.057 \pm 0.063. The spectrum itself is also
unfolded to the B-meson rest frame; that is the frame in which theoretical
predictions for its shape are made.Comment: 37 pages, 19 postscript figures, submitted to Phys. Rev. D. No
analysis or results have changed from previous version. Some changes to
improve clarity based on interactions with Phys. Rev. D referees, including
one new Figure (Fig. 13), and some minor wording/punctuation/spelling
mistakes fixe
Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons
We present improved measurements of CP-violation parameters in the decays
, , and , and of
the branching fractions for and . The
results are obtained with the full data set collected at the
resonance by the BABAR experiment at the PEP-II asymmetric-energy factory
at the SLAC National Accelerator Laboratory, corresponding to
million pairs. We find the CP-violation parameter values and
branching fractions where in each case, the first uncertainties are statistical
and the second are systematic. We observe CP violation with a significance of
6.7 standard deviations for and 6.1 standard deviations for
, including systematic uncertainties. Constraints on the
Unitarity Triangle angle are determined from the isospin relations
among the rates and asymmetries. Considering only the solution
preferred by the Standard Model, we find to be in the range
at the 68% confidence level.Comment: 18 pages, 11 postscript figures, submitted to Phys. Rev.
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Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
A precise measurement of the cross section of the process
from threshold to an energy of 3GeV is obtained
with the initial-state radiation (ISR) method using 232fb of data
collected with the BaBar detector at center-of-mass energies near
10.6GeV. The ISR luminosity is determined from a study of the leptonic process
, which is found to agree with the
next-to-leading-order QED prediction to within 1.1%. The cross section for the
process is obtained with a systematic uncertainty
of 0.5% in the dominant resonance region. The leading-order hadronic
contribution to the muon magnetic anomaly calculated using the measured
cross section from threshold to 1.8GeV is .Comment: 58 pages, 56 figures, to be submitted to Phys. Rev.
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