LOWER BOUNDS FOR THE BUCKLING PRESSURE OF SPHERICAL SHELLS

Hydrostatic buckling pressure calculations for spherical shell

Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

[EN] In this work, we study the full randomized versions of Airy, Hermite and Laguerre differential equations, which depend on a random variable appearing as an equation coefficient as well as two random initial conditions. In previous contributions, the mean square stochastic solutions to the aforementioned random differential equations were constructed via the Frobenius method, under the assumption of exponential growth of the absolute moments of the equation coefficient, which is equivalent to its essential boundedness. In this paper we aim at relaxing the boundedness hypothesis to allow more general probability distributions for the equation coefficient. We prove that the equations are solvable in the mean square sense when the equation coefficient has finite moment-generating function in a neighborhood of the origin. A thorough discussion of the new hypotheses is included.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P.Calatayud Gregori, J.; Cortés, J.; Jornet Sanz, M. (2020). Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties. Stochastic Analysis and Applications. 38(5):875-885. https://doi.org/10.1080/07362994.2020.1733017S875885385Neckel, T., & Rupp, F. (2013). Random Differential Equations in Scientific Computing. doi:10.2478/9788376560267Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Cortés, J.-C., Jódar, L., Camacho, F., & Villafuerte, L. (2010). Random Airy type differential equations: Mean square exact and numerical solutions. Computers & Mathematics with Applications, 60(5), 1237-1244. doi:10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.-C., & Jódar, L. (2011). Random Hermite differential equations: Mean square power series solutions and statistical properties. Applied Mathematics and Computation, 218(7), 3654-3666. doi:10.1016/j.amc.2011.09.008Calatayud, J., Cortés, J.-C., & Jornet, M. (2019). Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation. Mediterranean Journal of Mathematics, 16(3). doi:10.1007/s00009-019-1338-6Calatayud, J., Cortés, J.-C., Jornet, M., & Villafuerte, L. (2018). Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Advances in Difference Equations, 2018(1). doi:10.1186/s13662-018-1848-8Gregori, J., López, J., & Sanz, M. (2018). Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling. Mathematical and Computational Applications, 23(4), 76. doi:10.3390/mca23040076Calbo, G., Cortés, J.-C., & Jódar, L. (2010). Mean square power series solution of random linear differential equations. Computers & Mathematics with Applications, 59(1), 559-572. doi:10.1016/j.camwa.2009.06.007Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2010). Analytic stochastic process solutions of second-order random differential equations. Applied Mathematics Letters, 23(12), 1421-1424. doi:10.1016/j.aml.2010.07.011CALBO SANJUÁN, G. (s. f.). Mean Square Analytic Solutions of Random Linear Models. doi:10.4995/thesis/10251/8721Jagadeesan, M. (2017). Simple analysis of sparse, sign-consistent JL. arXiv:1708.02966.Lin, G. D. (2017). Recent developments on the moment problem. Journal of Statistical Distributions and Applications, 4(1). doi:10.1186/s40488-017-0059-2Ernst, O. G., Mugler, A., Starkloff, H.-J., & Ullmann, E. (2011). On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 317-339. doi:10.1051/m2an/2011045Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.04

The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems

We study the influence of a DC bias voltage V on quantum interference corrections to the measured differential conductance in metallic mesoscopic wires and rings. The amplitude of both universal conductance fluctuations (UCF) and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger than the Thouless energy. The enhancement persists even in the presence of inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages electron-phonon collisions lead to the amplitude decaying as a power law for the UCF and exponentially for the ABE. We obtain good agreement of the experimental data with a model which takes into account the decrease of the electron phase-coherence length due to electron-electron and electron-phonon scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in Europhysics Letter

Delayed presentation of symptomatic breast cancers in Hong Kong: Experience in a public cancer centre

Objective Delayed presentation is an important obstacle to improving cancer treatment outcomes. We aimed to study the magnitude of this problem in Hong Kong and the factors associated with delayed presentation of patients with symptomatic breast cancers. Design Retrospective study using self-administered questionnaires. Setting Clinical Oncology Department in a regional public hospital in Hong Kong. Patients A total of 158 Chinese women with breast cancer referred to our hospital between October 2006 and December 2007 consented to participate in this study. Among these, 59 (37%) patients were referred after having surgery in private sector. Results The mean total delay (from first symptom to treatment) was 22 weeks. The mean patient delay (from first symptom to first consultation) was 13 weeks, constituting the largest component (60%) of the total delay. After symptom onset, the delay exceeded 12 weeks for consulting a doctor in 29%, and for receipt of treatment in 52% of them. Low family income (<HK$5000 per month; P<0.001) and surgery in public hospitals (P=0.013) were both independent predictors of patient delay. Surgery in public hospitals (P=0.006) and low family income (P=0.005) were the only predictors of doctor/system delay and total delay, respectively. Conclusions Delayed presentation and treatment of symptomatic breast cancer remains an important issue in Hong Kong. Apart from socio-economic factors, limited access to public medical care was likely an important contributing factor in delays related to patients as well as to doctor/system.published_or_final_versio

UK survey of occupational therapist’s and physiotherapist’s experiences and attitudes towards hip replacement precautions and equipment

Background: Total hip replacement (THR) is one of the most common orthopaedic procedures in the United Kingdom (UK). Historically, people following THR have been provided with hip precautions and equipment such as: raised toilet seats and furniture rises, in order to reduce the risks of dislocation post-operation. The purpose of this study was to determine current practices in the provision of these interventions in the UK for people following primary THR. Methods: A 27-question, self-administered online survey was developed and distributed to UK physiotherapists and occupational therapists involved in the management of people following primary THR (target respondents). The survey included questions regarding the current practices in the provision of equipment and hip precautions for THR patients, and physiotherapist’s and occupational therapist’s attitudes towards these practices. The survey was disseminated through print and web-based/social media channels. Results: 170 health professionals (87 physiotherapists and 83 occupational therapists), responded to the survey. Commonly prescribed equipment in respondent’s health trusts were raised toilet seats (95%), toilet frames and rails (88%), furniture raises (79%), helping hands/grabbers (77%), perching stools (75%) and long-handled shoe horns (75%). Hip precautions were routinely prescribed by 97% of respondents. Hip precautions were most frequently taught in a pre-operative group (52% of respondents). Similarly equipment was most frequently provided pre-operatively (61% respondents), and most commonly by occupational therapists (74% respondents). There was variability in the advice provided on the duration of hip precautions and equipment from up to six weeks post-operatively to life-time usage. Conclusions: Current practice on hip precautions and provision of equipment is not full representative of clinician’s perceptions of best care after THR. Future research is warranted to determine whether and to whom hip precautions and equipment should be prescribed post-THR as opposed to the current ‘blanket’ provision of equipment and movement restriction provided in UK practice

Relativistic effects and two-body currents in 2H(e⃗,e′p)n^{2}H(\vec{e},e^{\prime}p)n using out-of-plane detection

Measurements of the ${^2}H(\vec{e},e^{\prime}p)n$ reaction were performed using an 800-MeV polarized electron beam at the MIT-Bates Linear Accelerator and with the out-of-plane magnetic spectrometers (OOPS). The longitudinal-transverse, $f_{LT}$ and $f_{LT}^{\prime}$, and the transverse-transverse, $f_{TT}$, interference responses at a missing momentum of 210 MeV/c were simultaneously extracted in the dip region at Q$^2$=0.15 (GeV/c)$^2$. On comparison to models of deuteron electrodisintegration, the data clearly reveal strong effects of relativity and final-state interactions, and the importance of the two-body meson-exchange currents and isobar configurations. We demonstrate that these effects can be disentangled and studied by extracting the interference response functions using the novel out-of-plane technique.Comment: 4 pages, 4 figures, and submitted to PRL for publicatio

Measurement of the Transverse-Longitudinal Cross Sections in the p (e,e'p)pi0 Reaction in the Delta Region

Accurate measurements of the p(e,e?p)pi0 reaction were performed at Q^2=0.127(GeV/c)^2 in the Delta resonance energy region. The experiments at the MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam with the out of plane magnetic spectrometer system (OOPS). In this paper we report the first simultaneous determination of both the TL and TL? (``fifth" or polarized) cross sections at low Q^{2} where the pion cloud contribution dominates the quadrupole amplitudes (E2 and C2). The real and imaginary parts of the transverse-longitudinal cross section provide both a sensitive determination of the Coulomb quadrupole amplitude and a test of reaction calculations. Comparisons with model calculations are presented. The empirical MAID calculation gives the best overall agreement with this accurate data. The parameters of this model for the values of the resonant multipoles are |M_{1+}(I=3/2)|= (40.9 \pm 0.3)10^{-3}/m_pi, CMR= C2/M1= -6.5 \pm 0.3%, EMR=E2/M1=-2.2 \pm 0.9%, where the errors are due to the experimental uncertainties.Comment: 10 pages, 3 figures, minor corrections and addition

Comparative structural response of two steel bridges constructed 100 years apart

This paper presents a comparative numerical analysis of the structural behaviour and seismic performance of two existing steel bridges, the Infiernillo II Bridge and the Pinhao Bridge, one located in Mexico and the other in Portugal. The two bridges have similar general geometrical characteristics, but were constructed 100 years apart. Three-dimensional structural models of both bridges are developed and analysed for various load cases and several seismic conditions. The results of the comparative analysis between the two bridges are presented in terms of natural frequencies and corresponding vibration modes, maximum stresses in the structural elements and maximum displacements. The study is aimed at determining the influence of a 1 century period in material properties, transverse sections and expected behaviour of two quite similar bridges. In addition, the influence of the bearing conditions in the global response of the Pinhao Bridge was evaluated