Global Attractivity in a Second-Order Nonlinear Difference Equation

AbstractConsider the difference equation xn+1 = xnƒ(xn−1), n = 0, 1, 2, ..., (1) where the function ƒ satisfies the following conditions:•ƒ ∈ [[0, ∞), (0, ∞)] and ƒ() is nonincreasing in ;•The equation ƒ() = 1 has a unique positive solution;•If denotes the unique positive solution of ƒ() = 1, then [xƒ(x) − x](x − x) > 0 for x ≠ x Then x is a global attractor of all positive solutions of Eq. (1)

Oscillations of delay differential equations

[Mathematical equations cannot be displayed here, refer to PDF

Spectator 1951-12-13

xvii, 369hlm. : ilus. ; tab. 24 cm

A Global Convergence Result with Applications to Periodic Solutions

AbstractWe establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation xn+1=∑i=0mAixn−2i,n=0,1,…,converges to a period two solution

Intraoperative pleural lavage cytology is an independent prognostic indicator for staging non–small cell lung cancer

AbstractObjectivesFor patients undergoing lung resection for cancer, macroscopic evidence of metastasis is clearly associated with adverse prognosis. However, less is known about the significance of tumor cells detected by using tests such as pleural lavage cytology. To ascertain the frequency and quantify the effect of this finding on survival, we performed a prospective study of intraoperative pleural lavage cytology.MethodsPleural lavage cytology consisted of cytologic analysis of 100 mL of saline irrigated over the lung surface immediately after thoracotomy. Patients were excluded if they had an existing effusion, extreme adhesions, or lateral chest wall invasion or if resection was not performed. Survival was calculated by means of Kaplan-Meier analysis and compared by using log-rank tests. Cox regression was used to ascertain independent predictors of prognosis.ResultsFrom 1995 through 2003, we performed pleural lavage cytology on 292 patients undergoing thoracotomy for lung cancer. The mean age was 64 (SD, 10) years, and 196 (67%) patients were men. Of 292 samples, 13 (4.5%) showed evidence of malignant cells. The median time to follow-up was 15 months (interquartile range, 1-40 months), with a median survival of 49 months for patients with negative pleural lavage cytology results and 13 months for patients with positive pleural lavage cytology results (P = .002). Univariate prognostic predictors were positive pleural lavage cytology status (P = .03), stage (P = .03), adenocarcinoma (P = .06), and parietal pleural involvement (P = .01). In the final multivariate model only positive pleural lavage cytology status (P = .006) and stage (P = .03) remained significant.ConclusionsIntraoperative pleural lavage cytology is a simple addition to intrathoracic staging and an independent predictor of prognosis. Positive results potentially affect survival by upstaging patients to stage IIIB or greater

Robust Device-to-Device 5G cellular communication in the post-disaster scenario

The wireless communication is an integral part of the society, however, wireless network infrastructure may not fully function during post-disaster wireless network scenario in which we need wireless services even more than normal circumstances. In such post-disaster scenarios, the base stations (BS) could possibly be dysfunctional or overloaded by an excessive number of user calls or data, whereas user terminals are likely to be partially connected to or fully isolated from the BS radio signals. In this paper, we study the network behavior during the post-disaster when BSs undergo the thinning process due to the damage to the network infrastructure. During network recovery phase, we also study the network performance when new temporary BSs are distributed which will bring the network into BS superposition phase. Furthermore, Device-to-Device (D2D) assisted cellular communication helps to increase the link level network connectivity which is highly appreciated during postdisaster network scenario because the network coverage is more desirable than the network throughout in such cases. We also present the analytical study of D2D and cellular communication and show that it will effectively increase the network coverage which may ultimately save many lives during the golden hours of post-disaster phase