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

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