Oscillation theorems for fourth-order quasi-linear delay differential equations

In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $\mathcal{N}_{a}$. As an extension of the approach taken in [1], we establish a new criterion that guarantees that $\mathcal{N}_{a} = \emptyset$. Then, we create a new oscillation criterion

Burnout among surgeons before and during the SARS-CoV-2 pandemic: an international survey

Background: SARS-CoV-2 pandemic has had many significant impacts within the surgical realm, and surgeons have been obligated to reconsider almost every aspect of daily clinical practice. Methods: This is a cross-sectional study reported in compliance with the CHERRIES guidelines and conducted through an online platform from June 14th to July 15th, 2020. The primary outcome was the burden of burnout during the pandemic indicated by the validated Shirom-Melamed Burnout Measure. Results: Nine hundred fifty-four surgeons completed the survey. The median length of practice was 10 years; 78.2% included were male with a median age of 37 years old, 39.5% were consultants, 68.9% were general surgeons, and 55.7% were affiliated with an academic institution. Overall, there was a significant increase in the mean burnout score during the pandemic; longer years of practice and older age were significantly associated with less burnout. There were significant reductions in the median number of outpatient visits, operated cases, on-call hours, emergency visits, and research work, so, 48.2% of respondents felt that the training resources were insufficient. The majority (81.3%) of respondents reported that their hospitals were included in the management of COVID-19, 66.5% felt their roles had been minimized; 41% were asked to assist in non-surgical medical practices, and 37.6% of respondents were included in COVID-19 management. Conclusions: There was a significant burnout among trainees. Almost all aspects of clinical and research activities were affected with a significant reduction in the volume of research, outpatient clinic visits, surgical procedures, on-call hours, and emergency cases hindering the training. Trial registration: The study was registered on clicaltrials.gov "NCT04433286" on 16/06/2020

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Qualitative Study of Solutions of Some Difference Equations

We obtain in this paper the solutions of the following recursive sequences +1=−3/−2(±1±−3), =0,1,…, where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative behavior of the solutions such as the boundedness, the global stability, and the periodicity character of the solutions in each case have been studied. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the obtained results

Global behavior of the solutions of some difference equations

<p>Abstract</p> <p>In this article we study the difference equation</p> <p><display-formula><m:math name="1687-1847-2011-28-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:mi>a</m:mi> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>l</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:mi>b</m:mi> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:mo class="MathClass-bin">-</m:mo> <m:mi>c</m:mi> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>q</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> <m:mo class="MathClass-punc">,</m:mo> <m:mspace width="2.77695pt" class="tmspace"/> <m:mi>n</m:mi> <m:mspace width="2.77695pt" class="tmspace"/> <m:mo class="MathClass-rel">=</m:mo> <m:mn>0</m:mn> <m:mo class="MathClass-punc">,</m:mo> <m:mn>1</m:mn> <m:mo class="MathClass-punc">,</m:mo> <m:mspace width="2.77695pt" class="tmspace"/> <m:mo class="MathClass-op">&#8230;</m:mo> <m:mo class="MathClass-punc">,</m:mo> </m:mrow> </m:math> </display-formula></p> <p>where the initial conditions <it>x</it>_-<it>r</it>, <it>x</it>_{-<it>r</it>+1}, <it>x</it>_{<it>-r</it>+2},..., <it>x</it>₀are arbitrary positive real numbers, <it>r </it>= max{<it>l</it>, <it>k</it>, <it>p</it>, <it>q</it>} is nonnegative integer and <it>a</it>, <it>b</it>, <it>c </it>are positive constants: Also, we study some special cases of this equation.</p