Diameter two properties and the Radon-Nikod\'ym property in Orlicz spaces

Some necessary and sufficient conditions are found for Banach function lattices to have the Radon-Nikod\'ym property. Consequently it is shown that an Orlicz space $L_\varphi$ over a non-atomic $\sigma$-finite measure space $(\Omega, \Sigma,\mu)$, not necessarily separable, has the Radon-Nikod\'ym property if and only if $\varphi$ is an $N$-function at infinity and satisfies the appropriate $\Delta_2$ condition. For an Orlicz sequence space $\ell_\varphi$, it has the Radon-Nikod\'ym property if and only if $\varphi$ satisfies condition $\Delta_2^0$. In the second part the relationships between uniformly $\ell_1^2$ points of the unit sphere of a Banach space and the diameter of the slices are studied. Using these results, a quick proof is given that an Orlicz space $L_\varphi$ has the Daugavet property only if $\varphi$ is linear, so when $L_\varphi$ is isometric to $L_1$. The other consequence is that the Orlicz spaces equipped with the Orlicz norm generated by $N$-functions never have local diameter two property, while it is well-known that when equipped with the Luxemburg norm, it may have that property. Finally, it is shown that the local diameter two property, the diameter two property, the strong diameter two property are equivalent in function and sequence Orlicz spaces with the Luxemburg norm under appropriate conditions on $\varphi$

Daugavet and diameter two properties in Orlicz-Lorentz spaces

In this article, we study the diameter two properties (D2Ps), the diametral diameter two properties (diametral D2Ps), and the Daugavet property in Orlicz-Lorentz spaces equipped with the Luxemburg norm. First, we characterize the Radon-Nikod\'ym property of Orlicz-Lorentz spaces in full generality by considering all finite real-valued Orlicz functions. To show this, the fundamental functions of their K\"othe dual spaces defined by extended real-valued Orlicz functions are computed. We also show that if an Orlicz function does not satisfy the appropriate $\Delta_2$-condition, the Orlicz-Lorentz space and its order-continuous subspace have the strong diameter two property. Consequently, given that an Orlicz function is an N-function at infinity, the same condition characterizes the diameter two properties of Orlicz-Lorentz spaces as well as the octahedralities of their K\"othe dual spaces. The Orlicz-Lorentz function spaces with the Daugavet property and the diametral D2Ps are isometrically isomorphic to $L_1$ when the weight function is regular. In the process, we observe that every locally uniformly nonsquare point is not a $\Delta$-point. This fact provides another class of real Banach spaces without $\Delta$-points. As another application, it is shown that for Orlicz-Lorentz spaces equipped with the Luxemburg norm defined by an N-function at infinity, their K\"othe dual spaces do not have the local diameter two property, and so as other (diametral) diameter two properties and the Daugavet property.Comment: 19 page

A method of measuring the amplitude-modulated vacuum field near a conducting mirror

Electromagnetic fields of the vacuum mode near a conducting mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence from the mirror. Therefore if we combine this spatially amplitude-modulated vacuum field mode and intense coherent light with a beam splitter, we may detect this fluctuation of the vacuum mode in a homodyne detection scheme. It will give a new method to produce squeezed states of light with a single mirror placed close to an unused port of a beam splitter. We show that the amplitude fluctuation of the combined light can be reduced by a factor of 2 below that of the coherent light. We also discuss the limitations due to the finite line width of the laser and the effective absorption length of the photodiodes

Important predictor of mortality in patients with end-stage liver disease

Prognosis is an essential part of the baseline assessment of any disease. For predicting prognosis of end-stage liver disease, many prognostic models were proposed. Child-Pugh score has been the reference for assessing the prognosis of cirrhosis for about three decades in end-stage liver disease. Despite of several limitations, recent large systematic review showed that Child-Pugh score was still robust predictors and it's components (bilirubin, albumin and prothrombin time) were followed by Child-Pugh score. Recently, Model for end-stage liver disease (MELD) score emerged as a "modern" alternative to Child-Pugh score. The MELD score has been an important role to accurately predict the severity of liver disease and effectively assess the risk of mortality. Due to several weakness of MELD score, new modified MELD scores (MELD-Na, Delta MELD) have been developed and validated. This review summarizes the current knowledge about the prognostic factors in end-stage liver disease, focusing on the role of Child-Pugh and MELD score

A Score-Based Evaluation Model for Rehabilitation of Existing Pumped Storage Hydropower Plant Construction

As the proportion of new and renewable energy increases, power control demands are becoming more frequent due to variability in power generation. As a complementary means against this, the pumped storage hydropower plants (PSHP) are attracting attention as energy storage systems (ESS), but it has high construction costs. Therefore, this study aims to improve the economic feasibility by developing the evaluation model of the existing infrastructure into an upper/lower dam suitable for PSHP. The concept of upper dam capacity is newly defined, and the evaluation index is constructed using normalization. A new evaluation system is presented for five factors: environment, stability, energy, capacity, and economy. Finally, it is tested in the pilot area in Korea. Several candidates, including the PSHP in operation, are found to have been distributed with higher scores. These results will help to satisfy the selection of candidates during the preliminary feasibility study phase, and programming them will enable more accurate and rapid assessment

Fingerprints of Multiple Electron Scatterings in Single-Layer Graphene

The electrons in graphene exhibit unusual behaviours, which can be described by massless Dirac quasiparticles. Understanding electron scattering in graphene has been of significant importance for its future application in electronic devices because electron scattering determines electrical properties such as resistivity and electron transport. There are two types of electron scatterings in graphene: intervalley scattering and intravalley scattering. In single-layer graphene, to date, it has been difficult to observe intravalley scattering because of the suppression of backscattering resulting from the chiral nature of the electrons in graphene. Here, we report the multiple electron scattering behaviours in single-layer graphene on a metallic substrate. By applying one- and two-dimensional Fourier transforms to maps of the local density of states, we can distinguish individual scattering processes from complex interference patterns. These techniques enable us to provide direct evidence of intravalley scattering, revealing a linear dispersion relation with a Fermi velocity of ???7.4 ?? 105 m/s.open

Homocysteine-induced peripheral microcirculation dysfunction in zebrafish and its attenuation by L-arginine

Elevated blood homocysteine (Hcy) level is frequently observed in aged individuals and those with age-related vascular diseases. However, its effect on peripheral microcirculation is still not fully understood. Using in vivo zebrafish model, the degree of Hcy-induced peripheral microcirculation dysfunction is assessed in this study with a proposed dimensionless velocity parameter (V) over bar (CV)/(V) over bar (PCV), where (V) over bar (CV) and (V) over bar (PCV) represent the peripheral microcirculation perfusion and the systemic perfusion levels, respectively. The ratio of the peripheral microcirculation perfusion to the systemic perfusion is largely decreased due to peripheral accumulation of neutrophils, while the systemic perfusion is relatively preserved by increased blood supply from subintestinal vein. Pretreatment with L-arginine attenuates the effects of Hcy on peripheral microcirculation and reduces the peripheral accumulation of neutrophils. Given its convenience, high reproducibility of the observation site, non-invasiveness, and the ease of drug treatment, the present zebrafish model with the proposed parameters will be used as a useful drug screening platform for investigating the pathophysiology of Hcy-induced microvascular diseases.111Ysciescopu