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We prove the existence of the global attractor in
for the weakly damped and forced mKdV on the one-dimensional torus. The existence of global attractor below the energy space has not been known, though the global well-posedness below the energy space has been established. We directly apply the
-method to the damped and forced mKdV, because the Miura transformation does not work for the mKdV with damping and forcing terms. We need to make a close investigation into the trilinear estimates involving resonant frequencies, which are different from the bilinear estimates corresponding to the KdV.
We give the generating function of split
-colour partitions and obtain an analogue of Euler’s identity for split
-colour partitions. We derive a combinatorial relation between the number of restricted split
-colour partitions and the function
. We introduce a new class of split perfect partitions with
copies of each part
and extend the work of Agarwal and Subbarao [‘Some properties of perfect partitions’, Indian J. Pure Appl. Math22(9) (1991), 737–743].
To evaluate the survival outcomes and toxicities experienced by non-metastatic head and neck cancer (HNC) patients receiving modulated radiotherapy (RT).
Materials and methods
A total of 608 HNC patients treated consecutively from March 2010 to December 2014 with common subsites (oral cavity, oropharynx, hypopharynx, larynx and nasopharynx) of HNCs formed the study group. Eligible patients included those treated with radical or postoperative RT between March 2010 and December 2014. More than 90% patients received modulated RT [intensity-modulated radiotherapy (IMRT) or volumetric-modulated arc therapy (VMAT)] with concurrent chemotherapy as per stage guidelines. Demographic parameters and disease-related factors were analysed. Disease-free survival (DFS) was calculated from end date of RT till last follow-up or last date of disease control. Overall survival (OS) was calculated from date of registration to last follow-up date if alive. The primary endpoint was survival. The statistical analyses were performed using SPSS version 20.0 and Kaplan–Meier method was used for calculation survival.
Among the evaluable patients, the median age was 60 years (range: 16–93) with male preponderance (male:female – 513:95). Majority were squamous cell carcinoma 93·4% (568/608). The subsites treated were oral cavity 36·8% (224). oropharynx 26·4% (161), larynx 19·7% (120), hypopharynx 10% (62) and nasopharynx 6·4% (41). RT intent was radical in 63·5% (386) and postoperative in 36·5% (222), with 59·5% (362) receiving concurrent chemotherapy. At last follow-up, 348 (57·2%) patients were alive, 169 (27·7%) patients had succumbed to disease and 120 (24·6%) patients had recurrent disease. Out of 120 recurrent cases loco-regional recurrence, nodal recurrence and distant metastases were seen in 62 (51·7%), 25 (20·8%), 33 (27·5%), respectively. In the entire study cohort at 2 year OS and DFS was 80 and 79% whereas 3 years OS and DFS was 70 and 75%, respectively.
In our study, 2 years and 3 years OS and DFS rates are found comparable to the international data with acceptable toxicity profile with the use of modulated RT. It seems to be possible because of stringent departmental protocols and good medical physics support. Our data re-validates need and benefit of advanced RT techniques like IG-IMRT and VMAT for both postoperative and radical HNC treatment at the cost of minimal long-term side effects. Future stringent follow-up and quality of life issues are being considered in a prospective manner.
In this brief report, computed tomography perfusion (CTP) thresholds predicting follow-up infarction in patients presenting <3 hours from stroke onset and achieving ultra-early reperfusion (<45 minutes from CTP) are reported. CTP thresholds that predict follow-up infarction vary based on time to reperfusion: Tmax >20 to 23 seconds and cerebral blood flow <5 to 7 ml/min−1/(100 g)−1 or relative cerebral blood flow <0.14 to 0.20 optimally predicted the final infarct. These thresholds are stricter than published thresholds.
In the present paper, we have studied self-focusing of Gaussian laser beam in weakly relativistic magnetized cold quantum plasma. When interparticle distance is comparable to the de Broglie wavelength of charged particles, we cannot neglect the quantum contribution of plasma constituents. Therefore, propagation characteristics are studied by taking in to account quantum contribution in the presence of static magnetic field applied along the beam propagation. Our results show that the magnetic field plays a key role in achieving additional focusing, it modifies the quiver motion of electrons by adding cyclotron frequency to the natural frequency of oscillating electrons during laser beam propagation. The results are compared with those of weakly relativistic quantum plasma and weakly relativistic magnetized plasma. The self-focusing is found to be more pronounced when axial magnetic field is increased in the present model. We have setup the non-linear differential equation for the evolution of beam-width parameter by well-known paraxial ray approximation and solved it with the help of computational technique.
Networks influence human behavior and well-being, and, realizing this, individuals make conscious efforts to shape their own networks. Over the past decade, economists have combined these ideas with concepts from game theory, oligopoly, general equilibrium, and information economics to develop a general framework of analysis. The ensuing research has deepened our understanding of classical questions in economics and opened up entirely new lines of enquiry.
Our life takes place at the intersection of the global and the local: we function in a world dominated by large firms and international markets, but we also inhabit small and overlapping neighborhoods of friends and family, colleagues and collaborators. Game theory is well suited for the study of behavior in small exclusive groups while general equilibrium theory provides a sophisticated approach to the understanding of large anonymous systems. Networks offer us a framework that combines local interactions within large interconnected populations. In doing so, they fill an important gap in the toolkit of economists.
The key methodological innovation of the early research on networks in the 1990s was the introduction of graph theory alongside purposeful agents. Two ideas were central: the study of how the network architecture shapes human behavior and the study of how purposeful individuals form links and thereby create networks. Over the past decade, economists have developed models that include networks, alongside the familiar notions of strategy, information, prices and competition. These models are now being applied to address an increasingly ambitious range of questions in economics. I see here a close analogy with the spread of game theory in economics, during the 1980s and 1990s, in one applied field after another.
I begin by developing notation and basic concepts on networks in Section 2. Section 3 outlines a framework that combines individual choice, networks and markets, while Section 4 introduces the elements of an economic theory of network formation.
The rest of the paper is devoted to a discussion of economic applications. There has been very rapid growth in research in this field over the last decade. In my presentation, I will favor lines of work that explicitly combine network ideas with familiar models of markets.
During 2007–2014, India had higher trend inflation and lower trend growth together with fluctuations. Sustaining higher growth requires that inflation comes down. But, optimal policy to address inflation depends on whether the primary cause was excess demand or primary or persistent supply shocks. This chapter first explores this question, and then measures the possible contribution of a wage-price spiral to the persistence in supply shocks. Finally, it analyzes the effect of governance failures on food price inflation.
Data on inflation components show multiple primary supply shocks in the period. Rigorous estimates of the share of aggregate demand and supply shocks in inflation using a Structural Vector Auto Regression (SVAR) model also gives multiple supply shocks. Supply shocks were persistently high only for a brief period over 2010–2011. Demand shocks were often negative. The response of wages to food prices is primarily among mechanisms that propagate the relative price changes that constitute primary supply shocks. The nominal exchange rate also affects food prices and the cost of intermediate imports such as oil.
Growth in real wages for rural unskilled male labourers was often negative before September 2007, but became positive after that. Although the output growth rates fell, real wages rose sharply. Nominal wage growth far exceeded that in the relevant Consumer Price Index (CPI). Real wage growth peaked at 12.5 per cent in 2012 m1. As these affects a majority of the work force, we need to test whether the growth in rural wages was due to the factors specific to that time or to those that are likely to persist. How much did this growth contribute to the persistence of inflation?
In addition to the economic factors, such as large numbers of unskilled labour, social norms influence subsistence wages. Food constitutes a large share of the rural consumption basket; hence, food inflation, above a threshold level, may have raised the socially accepted minimum nominal wage. Increasing national wealth and standard of living also have a demonstration effect. Social programmes initiated by the government, such as Mahatma Gandhi National Rural Employment Guarantee Scheme (MGNREGS) may have reflected, as well as raised, social norms of ‘fair’ wages. Rural nonfarm activities, especially construction and inter-state migration, raised labour demand and bargaining power.
Corporate bond returns exhibit predictability in a manner consistent with efficient pricing. Many equity characteristics, such as accruals, standardized unexpected earnings, and idiosyncratic volatility, do not impact bond returns. Profitability and asset growth are negatively related to corporate bond returns. Because firms that are profitable or have high asset growth (and hence more collateral) should be less risky, with lower required returns, the evidence accords with the risk–reward paradigm. Past equity returns are positively related to bond returns, indicating that equities lead bonds. Cross-sectional bond return predictors generally do not provide materially high Sharpe ratios after accounting for trading costs.
Purpose: We measured anterior cerebral artery (ACA)-middle cerebral artery (MCA) and posterior cerebral artery (PCA)-MCA pial filling on single-phase computed tomography angiograms (sCTAs) in acute ischemic stroke and correlate with the CTA-based Massachusetts General Hospital (MGH) and digital subtraction angiography (DSA)-based American Society of Interventional and Therapeutic Neuroradiology (ASITN) score. Methods: Patients with acute stroke and M1 MCA±intracranial internal carotid artery occlusion on baseline CTA were included. Baseline sCTA was assessed for phase of image acquisition. An evaluator assessed collaterals using the Calgary Collateral (CC) Score (measures pial arterial filling in ACA-MCA and PCA-MCA regions separately), the CTA-based MGH score, and on DSA using the ASITN score. Infarct volumes were measured on 24- to 48-hour magnetic resonance imaging/ computed tomography. Results: Of 106 patients, baseline sCTA was acquired in early arterial phase in 9.9%, peak arterial in 50.7%, equilibrium in 32.4%, early venous in 5.6%, and late venous in 1.4%. Variance in ACA-MCA collaterals explained only 32% of variance in PCA-MCA collaterals on the CC score (Spearman’s correlation coefficient rho [rho]=0.56). Correlation between ACA-MCA collaterals and the MGH score was strong (rho=0.8); correlation between PCA-MCA collaterals and this score was modest (rho=0.54). Correlation between ACA-MCA collaterals and the ASITN score was modest (n=53, rho=0.43); and correlation between PCA-MCA collaterals and ASITN score was poor (rho=0.33). Of the CTA-based scores, the CC Score (Akaike [AIC] 1022) was better at predicting follow-up infarct volumes than was the MGH score (AIC 1029). Conclusion: Collateral assessments in acute ischemic stroke are best done using CTA with temporal resolution and by assessing regional variability. ACA-MCA and MCA-PCA collaterals should be evaluated separately.