A direct method for solving the generalized sine-Gordon equation II

The generalized sine-Gordon (sG) equation $u_{tx}=(1+\nu\partial_x^2)\sin\,u$ was derived as an integrable generalization of the sG equation. In a previous paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is referred to as I, we developed a systematic method for solving the generalized sG equation with $\nu=-1$. Here, we address the equation with $\nu=1$. By solving the equation analytically, we find that the structure of solutions differs substantially from that of the former equation. In particular, we show that the equation exhibits kink and breather solutions and does not admit multi-valued solutions like loop solitons as obtained in I. We also demonstrate that the equation reduces to the short pulse and sG equations in appropriate scaling limits. The limiting forms of the multisoliton solutions are also presented. Last, we provide a recipe for deriving an infinite number of conservation laws by using a novel B\"acklund transformation connecting solutions of the sG and generalized sG equations.Comment: To appear in J. Phys. A: Math. Theor. The first part of this paper has been published in J. Phys. A: Math. Theor. 43 (2010) 10520

Methane Emission From Digestion of Palm Oil Mill Effluent (POME) in a Thermophilic Anaerobic Reactor

As the issue of global warming draws increasing concern, many studies to reduce CO2 and CH4 gases (greenhouse gases, GHG) have been implemented in several countries, including in Indonesia. Considering that Indonesia has a huge numbers of palm oil mills, no doubt if their waste water treatment as one of the major sources in GHG. This paper presents the results from a research project between Metawater Co., Ltd.-Japan and University of Sumatera Utara-Indonesia. The objective of the research is to study the methane emission of thermophilic fermentation in the treatment of palm oil mill effluent (POME) on a laboratory scale. Anaerobic digestion was performed in two-litre water jacketed biodigester type continuous stirred tank reactor (CSTR) and operated at a thermophilic temperature (55 oC). As raw material, a real liquid waste (POME) from palm oil mill was used. Fresh POME was obtained from seeding pond of PTPN II waste water treatment facility which has concentration of 39.7 g of VS/L and COD value of 59,000 mg/L. To gain precise results, complete recording and reliable equipment of reactor was employed. As the experimental results, for hydraulic retention time (HRT) 8 days, VS decomposition rate of 63.5% and gas generation of 6.05-9.82 L/day were obtained, while for HRT 6 and 4 days, VS decomposition rate of 61.2, 53.3% and gas generation of 6.93-8.94 and 13.95-16.14 L/day were obtained respectively. Keywords—methane (CH4), palm oil mill effluent (POME), anaerobic digestion, thermophilic, green house gases (GHG

On the thermal sunset diagram for scalar field theories

We study the so-called `` sunset diagram'', which is one of two-loop self-energy diagrams, for scalar field theories at finite temperature. For this purpose, we first find the complete expression of the bubble diagram, the one-loop subdiagram of the sunset diagram, for arbitrary momentum. We calculate the temperature independent part and dependent part of the sunset diagram separately. For the former, we obtain the discontinuous part first and the finite continuous part next using a twice-subtracted dispersion relation. For the latter, we express it as a one-dimensional integral in terms of the bubble diagram. We also study the structure of the discontinuous part of the sunset diagram. Physical processes, which are responsible for it, are identified. Processes due to the scattering with particles in the heat bath exist only at finite temperature and generate discontinuity for arbitrary momentum, which is a remarkable feature of the two-loop diagrams at finite temperature. As an application of our result, we study the effect of the diagram on the spectral function of the sigma meson at finite temperature in the linear sigma model, which was obtained at one-loop order previously. At high temperature where the decay $\sigma\to\pi\pi$ is forbidden, sigma acquires a finite width of the order of $10 {\rm MeV}$ while within the one-loop calculation its width vanishes. At low temperature, the spectrum does not deviate much from that at one-loop order. Possible consequences with including other two-loop diagrams are discussed.Comment: 30 page

A direct method of solution for the Fokas-Lenells derivative nonlinear Schr\"odinger equation: I. Bright soliton solutions

We develop a direct method of solution for finding the bright $N$-soliton solution of the Fokas-Lenells derivative nonlinear Schr\"odinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.Comment: To appear in J. Phys. A: Math. Theor. 45(2012) Ma

IPAD: Stable Interpretable Forecasting with Knockoffs Inference

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Cand\`{e}s, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods

Measurements of short-lived cosmogenic nuclides in rain samples

金沢大学自然計測応用研究センター自然計測研究部門金沢大学理学部Extremely low activity levels of cosmic ray induced nuclides have been measured in freshly precipitated rainwater by quick chemical separation coupled with ultra low background gamma-spectrometry. The nuclides detected were 38S (T1/2 = 2.83 h)-38Cl (37.2 m), 39Cl (55.6 m), 24Na (14.96 h), 28Mg (20.9 h), 7Be (53.3 d) and 22Na (2.602 y). The number of atoms in rain water were evaluated to be ranging from 400-1900 l-1 for 39Cl (n = 6, mean: 1200), 30-1500 l-1 for 24Na (n = 16, mean: 520), 80-600 l-1 for 28Mg (n = 13, mean: 260), 1·106-4·107 l-17Be (n = 16, mean: 7·106) and 2·10 3-1·105 l-1 for 22Na (n = 9, mean: 2·104). Measurements of activity levels and activity ratios of short-lived cosmic-ray induced short-lived nuclides will open new method to understand atmospheric processes occurred at the altitude of rain cloud. © 2006 Akadémiai Kiadó

Mass transportation monitored by trace level radioactivity

金沢大学大学院自然科学研究科場所：金沢大学自然科学研究科図書館棟1階，講演会場：図書館棟1階　大会議室，ポスター会場：図書館棟1階12会議室,主催・共催：文部科学省２１世紀COE「環日本海域の環境計測と長期・短期変動予測」， 大気環境学会， 金沢大学工学

Mass transportation monitored by trace level radioactivity

金沢大学大学院自然科学研究科場所：金沢大学自然科学研究科図書館棟1階，講演会場：図書館棟1階　大会議室，ポスター会場：図書館棟1階12会議室,主催・共催：文部科学省２１世紀COE「環日本海域の環境計測と長期・短期変動予測」， 大気環境学会， 金沢大学工学

Moderately differentiated colorectal adenocarcinoma as a lymph node metastatic phenotype: comparison with well differentiated counterparts

<p>Abstract</p> <p>Background</p> <p>The differences between the metastatic property of moderately (Mod) and well (Wel) differentiated colorectal adenocarcinoma remain unclear. Since Mod is unable to form complete acini, therefore an epithelial-mesenchymal transition (EMT) can occur in that structure. Herein, we hypothesized that Mod metastasizes more easily than the Wel counterparts.</p> <p>Methods</p> <p>The medical records of 283 consecutive patients with Mod (n = 71) or Wel (n = 212) who underwent surgery were reviewed between January 1, 2001, and December 31, 2003, for actual 5-year overall survival. We examined the differences between the clinicopathological characteristics of the Mod and the Wel groups.</p> <p>Results</p> <p>The lymph node involvement (<it>p </it>< 0.0001), lymphatic permeation, venous permeation, depth of invasion, liver metastasis, and carcinomatous peritonitis were significantly higher in the Mod group in comparison to the Wel group. The independent risk factors by a logistic regression analysis for lymph node involvement were as follows: lymphatic permeation, liver metastasis, and Mod (<it>p </it>= 0.0291, Relative Risk of 1.991: 95% Confidence Interval: 1.073-3.697). A Kaplan-Meier survival curve showed that Mod had a trend towards a poor survival (<it>p </it>= 0.0517).</p> <p>Conclusion</p> <p>Mod metastasizes to the lymph nodes more easily in comparison to Wel. Therefore, patients with Mod may be considered the existence of lymph node involvement.</p