Discrete concavity and the half-plane property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M-concave functions in the literature. In the language of tropical geometry we study the tropicalization of the space of polynomials with the half-plane property, and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's hive theorem which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected

A possible involvement of ion transporter in tumor necrosis factor alpha and cycloheximide-induced apoptosis of endothelial cells.

We examined the tumor necrosis factor alpha (TNFalpha)-induced apoptosis of vascular endothelial cells from the standpoint of ion channels. Cultured vascular endothelial cells from bovine carotid artery were used. Apoptosis was determined by a propidium iodide assay. Treatment of the endothelial cells with TNFalpha and cycloheximide for 6 h induced nuclear fragmentation in a TNFalpha dose-dependent manner (1-10 ng/ml). Concomitant treatment of endothelial cells with TNFalpha at a dose of 10 ng/ml and cycloheximide at a dose of 10 microg/ml elicited endothelial cell apoptosis as high as 23.4+/-4.1% at 6 h after administration. However, 10 ng/ml TNFalpha alone elicited a little apoptosis at 6 h after its administration (% apoptosis=4.1+/-0.8%). Cycloheximide (10 microg/ml) did not induce apoptosis at all. Concomitant treatment of endothelial cells with 1 mmol/l of 4,4-diisothiocyanatostilbene-2,2-disulfonic acid, which is a chloride bicarbonate exchanger blocker, partially inhibited the TNFalpha and cycloheximide-induced endothelial cell apoptosis. On the other hand, endothelial cell apoptosis due to TNFalpha and cycloheximide was completely inhibited by benzyloxycarbonyl-Asp-CH2OC(O)-2,6-dichlorobenzene (50 micromol/l), an inhibitor of caspase. Moreover, pyrrolidine dithiocarbanate, an inhibitor of nuclear factor kappa B (NF-kappaB), also suppressed endothelial cell apoptosis induced by TNFalpha and cycloheximide completely. These findings suggest that the endothelial cell apoptosis induced by TNFalpha and cycloheximide is closely related to not only chloride ions, but also both NF-kappaB and caspase activation. That is to say, there is a possibility that chloride ions or bicarbonate (pH) may play an important role in signal transduction such as NF-kappaB and caspase activation in the apoptosis induced by TNFalpha and cycloheximide

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

A Case of Generalized Acanthosis Nigricans with Positive Lupus Erythematosus-Related Autoantibodies and Antimicrosomal Antibody: Autoimmune Acanthosis Nigricans?

Acanthosis nigricans (AN) is a hyperpigmented keratotic skin lesion known to be associated with malignant disease and endocrinopathy. We report a very rare case of generalized AN with Sjögren's syndrome- and systemic lupus erythematosus-like features but without type B insulin resistance. Neither internal malignancy nor other endocrinological disorders, including glucose intolerance, were detected during a 10-year clinical course with benign diffuse papillomatosis extending from the mucosa of the larynx to the esophagogastric junction. The case was complicated with chronic thyroiditis and interstitial pneumonia, which were not treated with any medication. AN skin lesions and mucosal papillomatosis regressed with oral cyclosporine A, accompanied by the lowering of autoantibody titers. This is the first report of generalized AN involving an area from the mucosa of the larynx to the esophagogastric junction accompanied by autoimmune manifestations which responded to systemic immunosuppressive therapy

Anomalous exothermic and endothermic data observed by Nano-Ni-composite samples

This is an experimental paper summarizing the observations of anomalous data on excess heat, D(H)-loading and abrupt desorption with endothermic heat sink in Ni-nano-composite samples under D(H)-gas charging at both room and elevated temperatures, done by Kobe-Technova group in 2012-2013. Referring to our JCF12 paper (Y. Miyoshi et al., JCF-12-1) on Pd1Ni7/ZrO2 samples, experimental procedure and results reported for Ni/ZrO2, Cu0.21Ni0.21/ZrO2 and Cu0.08Ni0.36/ZrO2 samples (partially reported in our JCF13-15 paper by Sakoh et al.) will be summarized. We have reanalyzed time-dependent data for speculating heat releasing mechanisms during the long (several weeks) lasted phase of D(H)-loading-into-nano-metal. It seems that competing process of D(H)-gas sorption and desorption at the surface of nano-powders would be attributed to the mechanism. Burst-like heat peaks of η-values (in unit of eV per D(H)-take-in/out) were observed with anomalously high values reaching 600 eV/H-sorption, and with smaller [eta]-values for isotopic Dsorption than H-sorption, at 573K. Integrated heat values for several-week runs were reached at the levels of ca. 800eV/atom-Ni for Cu0.08Ni0.36/ZrO2 samples, which were about 10 times larger than those of Ni/ZrO2 samples and about 4 times larger than those of Cu0.21Ni0.21/ZrO2 samples, at temperatures of 523 to 573K

On the validity of the reduced Salpeter equation

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.Comment: Latex (uses epsf macro), 24 pages of text, 12 postscript figures included. Slightly revised version, to appear in Phys. Rev.

On the instantaneous Bethe-Salpeter equation

We present a systematic algebraic and numerical investigation of the instantaneous Bethe-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector types. We explore stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions.Comment: Latex (uses epsf macro), 26 pages of text, 12 postscript figures included

Perturbation theory of bound states and resonances where potentials and propagators have arbitrary energy dependence

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Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections

We estimate the decay rates of $\eta_c\rightarrow 2\gamma$, $\eta_c'\rightarrow 2\gamma$, and $J/\psi\rightarrow e^+ e^-$, $\psi^\prime\rightarrow e^+e^-$, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these $c\bar{c}$ states. We find that the relativistic correction to the ratio $R\equiv \Gamma (\eta_c \rightarrow 2\gamma)/ \Gamma (J/ \psi \rightarrow e^+ e^-)$ is negative and tends to compensate the positive contribution from the QCD radiative correction. Our estimate gives $\Gamma(\eta_c \rightarrow 2\gamma)=(6-7) ~keV$ and $\Gamma(\eta_c^\prime \rightarrow 2\gamma)=2 ~keV$, which are smaller than their nonrelativistic values. The hadronic widths $\Gamma(\eta_c \rightarrow 2g)=(17-23) ~MeV$ and $\Gamma(\eta_c^\prime \rightarrow 2g)=(5-7)~MeV$ are then indicated accordingly to the first order QCD radiative correction, if $\alpha_s(m_c)=0.26-0.29$. The decay widths for $b\bar b$ states are also estimated. We show that when making the assmption that the quarks are on their mass shells our expressions for the decay widths will become identical with that in the NRQCD theory to the next to leading order of $v^2$ and $\alpha_s$.Comment: 14 pages LaTex (2 figures included