Maximum Independent Sets in Subcubic Graphs: New Results

The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We present a polynomial-time solution in a subclass of subcubic graphs generalizing several previously known results

Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror

A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the "mimimum noise" model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version, except for the reference styl

A note on Makeev's conjectures

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively

Flow patterns and heat transfer for flow boiling in small to micro diameter tubes

An overview of the recent developments in the study of flow patterns and boiling heat transfer in small to micro diameter tubes is presented. The latest results of a long-term study of flow boiling of R134a in five vertical stainless steel tubes of internal diameter 4.26, 2.88, 2.01, 1.1 and 0.52 mm are then discussed. During these experiments, the mass flux was varied from 100 to 700 kg/m2s and the heat flux from as low as 1.6 to 135 kW/m2. Five different pressures were studied, namely 6, 8, 10, 12 and 14 bar. The flow regimes were observed at a glass section located directly at the exit of the heated test section. The range of diameters was chosen to investigate thresholds for macro, small or micro tube characteristics. The heat transfer coefficients in tubes ranging from 4.26 mm down to 1.1 mm increased with heat flux and system pressure, but did not change with vapour quality for low quality values. At higher quality, the heat transfer coefficients decreased with quality, indicating local dryout. There was no significant difference between the characteristics and magnitude of the heat transfer coefficients in the 4.26 mm and 2.88 mm tubes but the coefficients in the 2.01 and 1.1 mm tube higher. The heat transfer results suggested that a tube size of about 2 mm might be considered as a critical diameter to distinguish small and conventional tubes, This is consistent with an earlier study of flow patterns, in which confined bubble flow was observed only in the 2.01 and 1.1 mm tubes. Further differences have now been observed in the 0.52 mm tube: ring flow appeared over a significant range of quality/heat flux and dispersed flow was not observed. The heat transfer characteristics were also different from those in the larger tubes. The data fell into two groups that exhibited different influences of heat flux below and above a heat flux threshold. These differences, both in flow patterns and heat transfer, indicate a possible second change from small to micro behaviour at diameters less than 1 mm for R134a

Bayesian approach to Spatio-temporally Consistent Simulation of Daily Monsoon Rainfall over India

Simulation of rainfall over a region for long time-sequences can be very useful for planning and policy-making, especially in India where the economy is heavily reliant on monsoon rainfall. However, such simulations should be able to preserve the known spatial and temporal characteristics of rainfall over India. General Circulation Models (GCMs) are unable to do so, and various rainfall generators designed by hydrologists using stochastic processes like Gaussian Processes are also difficult to apply over the vast and highly diverse landscape of India. In this paper, we explore a series of Bayesian models based on conditional distributions of latent variables that describe weather conditions at specific locations and over the whole country. During parameter estimation from observed data, we use spatio-temporal smoothing using Markov Random Field so that the parameters learnt are spatially and temporally coherent. Also, we use a nonparametric spatial clustering based on Chinese Restaurant Process to identify homogeneous regions, which are utilized by some of the proposed models to improve spatial correlations of the simulated rainfall. The models are able to simulate daily rainfall across India for years, and can also utilize contextual information for conditional simulation. We use two datasets of different spatial resolutions over India, and focus on the period 2000-2015. We propose a large number of metrics to study the spatio-temporal properties of the simulations by the models, and compare them with the observed data to evaluate the strengths and weaknesses of the models

Developments in Rare Kaon Decay Physics

We review the current status of the field of rare kaon decays. The study of rare kaon decays has played a key role in the development of the standard model, and the field continues to have significant impact. The two areas of greatest import are the search for physics beyond the standard model and the determination of fundamental standard-model parameters. Due to the exquisite sensitivity of rare kaon decay experiments, searches for new physics can probe very high mass scales. Studies of the k->pnn modes in particular, where the first event has recently been seen, will permit tests of the standard-model picture of quark mixing and CP violation.Comment: One major revision to the text is the branching ratio of KL->ppg, based on a new result from KTeV. Several references were updated, with minor modifications to the text. A total of 48 pages, with 28 figures, in LaTeX; to be published in the Annual Review of Nuclear and Particle Science, Vol. 50, December 200

A Rare Case of Isolated torsion of Haematosalphinx Presenting as Acute Abdomen During Pregnancy

Isolated fallopian tubal torsion is a rare non obstetric cause for pain abdomen during pregnancy.We report a case of a 34 year old second gravida who presented with history of amennorrhoe of 7 months, colicky pain in the left iliac fossa , with 2 episodes of vomiting. A Trans vaginal scan revealed a left ovarian cyst. An emergency laparotomy was performed for suspected torsion or haemorrhage into an ovarian cyst. Surprisingly ovaries were normal and a congested and necrotic left tubal torsion with a tubal collection (haematosalphinx) was identified and a salpingectomy was then performed. The differential diagnosis is discussed and the literature is reviewed as it is a very rare clinical entity

Successful Pregnancy Outcome In Maternal Crigler Najjar Syndrome Type II.

Estimated incidence of Crigler-Najjar syndrome(CNS) is 1 case per 1,000,000 births(1 million). The overall prevalence of CN syndrome is unknown, with only several hundred people reported to have this disease. It is interestingly very rare to encounter a pregnant adult women with congenital jaundice. Pregnancy in CN type II patients is a diagnostic and a therapeutic challenge because of the high risk of bilirubin encephalopathy with serious neurological damage as life-threatening complications for the fetus. To date 8 pregnancy outcome have been reported from 5 women and we report the6 woman with a successful 9 th pregnancy outcome. We have discussed detail history, presentation and management during pregnancy and care of the new born