Criterion for the LpL^{p}-dissipativity of second order differential operators with complex coefficients

We prove that the algebraic condition $|p-2| |< {\mathscr Im}{\mathscr A}\xi,\xi>| \leq 2 \sqrt{p-1}$ (for any $\xi\in\mathbb{R}^{n}$) is necessary and sufficient for the $L^{p}$-dissipativity of the Dirichlet problem for the differential operator $\nabla^{t}({\mathscr A}\nabla)$, where ${\mathscr A}$ is a matrix whose entries are complex measures and whose imaginary part is symmetric. This result is new even for smooth coefficients, when it implies a criterion for the $L^{p}$-contractivity of the corresponding semigroup. We consider also the operator $\nabla^{t}({\mathscr A}\nabla)+{\bf b}\nabla +a$, where the coefficients are smooth and ${\mathscr Im}{\mathscr A}$ may be not symmetric. We show that the previous algebraic condition is necessary and sufficient for the $L^{p}$-quasi-dissipativity of this operator. The same condition is necessary and sufficient for the $L^{p}$-quasi-contractivity of the corresponding semigroup. We give a necessary and sufficient condition for the $L^{p}$-dissipativity in $\mathbb{R}^{n}$ of the operator $\nabla^{t}({\mathscr A}\nabla)+{\bf b}\nabla +a$ with constant coefficients.Comment: 37 pages, LaTeX, no figure

Construction of Slepian-Wolf Source Code and Broadcast Channel Code Based on Hash Property

The aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble of functions. Since an ensemble of sparse matrices has a strong hash property, codes using sparse matrices can realize the achievable rate region. Furthermore, extensions to the multiple source coding and multiple output broadcast channel coding are investigated.Comment: The proofs of Lemmas 4 and 9 are revised. Some proofs are simplified. Some typos are fixed. A part of this paper has been published in Proceedings of 2010 IEEE International Symposium on Information Theory (ISIT2010) and Proceedings of 7th Asia-Europe Workshop "CONCEPTS in INFORMATION THEORY" (AEW7), 2011, 39 page

Sum rule for a difference of proton and neutron total photoproduction cross-sections

Starting from very high energy inelastic electron-nucleon scattering with a production of a hadronic state $X$ to be moved closely to the direction of the initial nucleon, then utilizing analytic properties of parts of forward virtual Compton scattering amplitudes on proton and neutron, one obtains the relation between nucleon form factors and a difference of proton and neutron differential electroproduction cross-sections. In particular, for the case of small transferred momenta, one finally derives sum rule, relating Dirac proton mean square radius and anomalous magnetic moments of proton and neutron to the integral over a difference of the total proton and neutron photoproduction cross-sections.Comment: LaTeX2e, 7 pages, 1 eps figure (revised version

Do Phillips curves conditionally help to forecast inflation?

The Phillips curve has long been used as a foundation for forecasting inflation. Yet numerous studies indicate that over the past 20 years or so, inflation forecasts based on the Phillips curve generally do not predict inflation any better than a univariate forecasting model. In this paper, the authors take a deeper look at the forecasting ability of Phillips curves from both an unconditional and a conditional view. Namely, they use the test results developed by Giacomini and White (2006) to examine the forecasting ability of Phillips curve models. The authors' main results indicate that forecasts from their Phillips curve models are unconditionally inferior to those of their univariate forecasting models and sometimes the difference is statistically significant. However, the authors do find that conditioning on various measures of the state of the economy does at times improve the performance of the Phillips curve model in a statistically significant way. Of interest is that improvement is more likely to occur at longer forecasting horizons and over the sample period 1984Q1—2010Q3. Strikingly, the improvement is asymmetric — Phillips curve forecasts tend to be more accurate when the economy is weak and less accurate when the economy is strong. It, therefore, appears that forecasters should not fully discount the inflation forecasts of Phillips curve-based models when the economy is weak.Phillips curve ; Unemployment

Intestinal blood flow in patients with chronic heart failure: A link with bacterial growth, gastrointestinal symptoms, and cachexia

Background: Blood flow in the intestinal arteries is reduced in patients with stable heart failure (HF) and relates to gastrointestinal (GI) symptoms and cardiac cachexia. Objectives: The aims of this study were to measure arterial intestinal blood flow and assess its role in juxtamucosal bacterial growth, GI symptoms, and cachexia in patients with HF. Methods: A total of 65 patients and 25 controls were investigated. Twelve patients were cachectic. Intestinal blood flow and bowel wall thickness were measured using ultrasound. GI symptoms were documented. Bacteria in stool and juxtamucosal bacteria on biopsies taken during sigmoidoscopy were studied in a subgroup by fluorescence in situ hybridization. Serum lipopolysaccharide antibodies were measured. Results: Patients showed 30% to 43% reduced mean systolic blood flow in the superior and inferior mesenteric arteries and celiac trunk (CT) compared with controls (p < 0.007 for all). Cachectic patients had the lowest blood flow (p < 0.002). Lower blood flow in the superior mesenteric artery and CT was correlated with HF severity (p < 0.04 for all). Patients had more feelings of repletion, flatulence, intestinal murmurs, and burping (p < 0.04). Burping and nausea or vomiting were most severe in patients with cachexia (p < 0.05). Patients with lower CT blood flow had more abdominal discomfort and immunoglobulin A–antilipopolysaccharide (r = 0.76, p < 0.02). Antilipopolysaccharide response was correlated with increased growth of juxtamucosal but not stool bacteria. Patients with intestinal murmurs had greater bowel wall thickness of the sigmoid and descending colon, suggestive of edema contributing to GI symptoms (p < 0.05). In multivariate regression analysis, lower blood flow in the superior mesenteric artery, CT (p < 0.04), and inferior mesenteric artery (p = 0.056) was correlated with the presence of cardiac cachexia. Conclusions: Intestinal blood flow is reduced in patients with HF. This may contribute to juxtamucosal bacterial growth and GI symptoms in patients with advanced HF complicated by cachexia