Ultra-Weak Time Operators of Schroedinger Operators

In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schroedinger operators H with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions $f$ such that $f(H)$ has an ultra-weak time operator is found.Comment: We add Sections 1.1,1.2 and 1.

The effects of non-assertion of patents provisions: R&D incentives in vertical relationships

Using a simple downstream duopoly model with vertical relations and downstream R&D, we investigate the effect of non-assertion of patents (NAP) provisions. A monopoly upstream firm decides whether to employ NAP provisions. If it does so, it freely incorporates the R&D outcomes into its inputs. Incorporation improves the efficiency of the downstream firms' production. We have interpreted the introduction of NAP provisions as a source of technology spillover. Using the technologies of two downstream firms is optimal for the upstream firm if and only if the degree of technology spillover is small. In addition, if the ex ante cost difference between the downstream firms is significant, such technology spillovers erode both the profit of the efficient downstream firm and social welfare. We interpret our result in the context of an actual antitrust case related to this model.

Regulation of hematopoietic stem cell and its interaction with stem cell niche

Hematopoietic stem cells (HSCs) are responsible for Blood cell production throughout the lifetime of individuals. Interaction of HSCs with their particular microenvironments, known as stem cell niches, is critical for maintaining the stem cell properties, including self-renewal capacity and the ability of differentiation into single or multiple lineages. In the niche, the niche cells produce signaling molecules, extracellular matrix, and cell adhesion molecules, and regulate stem cell fates. Recently, long-term bone marrow (BM) repopulating (LTR) HSCs exist frequently in BM trabecular bone surface, and it was clarified that an osteoblast (OB) is a critical component for sustainment of HSCs. HSCs balance quiescence and cell division in the osteoblastic niche and also maintain the potential for long-term hematopoiesis. Especially, the quiescent state in the cell cycle is thought to be indispensable for the maintenance of hematopoietic stem cells (HSCs). We demonstrate that c-Kit+Sca-1+Lineage- (KSL) HSCs expressing the receptor tyrosine kinase Tie2 are quiescent and anti-apoptotic, transplantable and comprise a side-population (SP) of HSCs, which contact closely to Angiopoietin-1 (Ang-1), a ligand for Tie2, expressing osteoblasts in the BM niche. Tie2 and Ang-1 are part of a key signaling interaction between HSC and osteoblasts. Tie2 and Ang-1 are expressed in a complementary pattern, and interaction of Tie2 and Ang-1 induced integrin dependent cell adhesion of HSCs to osteoblasts and extracellular matrix. This signaling pathway regulates functional criteria of HSC in the BM niche, including quiescence, anti-cell death and tight adhesion. These observations led us to a novel model in which Ang-1 produced by osteoblasts activates Tie2 on the HSCs and promote tight adhesion of HSCs to the niche, resulting in quiescence and enhanced survival of HSCs

Hepatitis B Virus e Antigen Physically Associates With Receptor-Interacting Serine/Threonine Protein Kinase 2 and Regulates IL-6 Gene Expression

We previously reported that hepatitis B virus (HBV) e antigen (HBeAg) inhibits production of interleukin 6 by suppressing NF-κB activation. NF-κB is known to be activated through receptor-interacting serine/threonine protein kinase 2 (RIPK2), and we examined the mechanisms of interleukin 6 regulation by HBeAg. HBeAg inhibits RIPK2 expression and interacts with RIPK2, which may represent 2 mechanisms through which HBeAg blocks nucleotide-binding oligomerization domain-containing protein 1 ligand-induced NF-κB activation in HepG2 cells. Our findings identified novel molecular mechanisms whereby HBeAg modulates intracellular signaling pathways by targeting RIPK2, supporting the concept that HBeAg could impair both innate and adaptive immune responses to promote chronic HBV infectio

Factors Associated with Inadequate Tissue Yield in EUS-FNA for Gastric SMT

Aims. Our aim was to identify the factors that made the specimens inadequate and nondiagnostic in endoscopic ultrasound-guided fine-needle aspiration (EUS-FNA) biopsy of suspected submucosal tumors (SMTs). Methods. From August 2001 to October 2009, 47 consecutive patients with subepithelial hypoechoic tumors originating in the fourth sonographic layer of the gastric wall suspected as GIST by standard EUS in Chiba University hospital underwent EUS-FNA for histologic diagnosis. We evaluated patient age, sex, location of lesion, size, pattern of growth in a stomach, and pattern of echography retrospectively. We defined a case of gaining no material or an insufficient material for immunohistological diagnosis as nondiagnostic. Results. The diagnostic yield of EUS-FNA for the diagnosis of gastric SMTs was 74.5%. Multivariate logistic regression analysis identified that age of under 60 years (compared with patients older than 60 years: odds ratio [OR] = 11.91, 95% confidence interval [CI] = 1.761–80.48) and location of SMT at lower third area (compared with upper or middle third area: OR = 10.62, 95% CI = 1.290–87.42) were the predictive factors for inadequate tissue yield in EUS-FNA. Conclusions. The factors associated with inadequate tissue yield in EUS-FNA were younger age and the location of lesion at lower third area in stomach

Strong time operators associated with generalized Hamiltonians

Let the pair of operators, $(H, T)$, satisfy the weak Weyl relation: $Te^{-itH} = e^{-itH}(T + t)$, where $H$ is self-adjoint and $T$ is closed symmetric. Suppose that g is a realvalued Lebesgue measurable function on \RR such that $g \in C^2(R K)$ for some closed subset K \subset \RR with Lebesgue measure zero. Then we can construct a closed symmetric operator $D$ such that $(g(H), D)$ also obeys the weak Weyl relation.Comment: 10 page