The Bishop-Phelps-Bollobás properties in complex Hilbert space

In this paper, we consider theBishop–Phelps–Bollobás point propertyfor variousclasses of operators on complex Hilbert spaces, which is a stronger property thanthe Bishop–Phelps–Bollobás property. We also deal with analogous problem byreplacing the norm of an operator with its numerical radius

Dietary Intake and Serum Levels of Iron in Relation to Oxidative Stress in Breast Cancer Patients

Iron may induce oxidative stress via production of reactive oxygen species, facilitating mammary carcinogenesis. This study investigated the role of iron in relation to oxidative stress as a potential risk factor in the development of breast cancer (BC). BC patients (n = 121) and healthy age-matched controls (n = 149) were entered into the study. Iron and antioxidant vitamins intakes were estimated using a quantitative food frequency questionnaire. Thirty one subjects from each group provided blood samples for measurement of serum iron, plasma malondialdehyde (MDA) and ferric reducing ability of plasma (FRAP). Total and non-heme iron intake of BC patients were lower than those of the controls. However, the serum iron level was significantly higher in BC patients. Plasma MDA levels were also significantly higher in BC patients whereas no significant difference in FRAP values were observed between the two groups. Log-transformed serum iron concentration showed no significant correlation with MDA or FRAP. These results suggest that serum iron overload may be a breast cancer risk factor possibly due to increased oxidative stress

Arithmetic properties of orders in imaginary quadratic fields

Let $K$ be an imaginary quadratic field. For an order $\mathcal{O}$ in $K$ and a positive integer $N$, let $K_{\mathcal{O},\,N}$ be the ray class field of $\mathcal{O}$ modulo $N\mathcal{O}$. We deal with various subjects related to $K_{\mathcal{O},\,N}$, mainly about Galois representations attached to elliptic curves with complex multiplication, form class groups and $L$-functions for orders

Disturbance of greedy publishing to academia

Questionable publications have been accused of "greedy" practices; however, their influence on academia has not been gauged. Here, we probe the impact of questionable publications through a systematic and comprehensive analysis with various participants from academia and compare the results with those of their unaccused counterparts using billions of citation records, including liaisons, e.g., journals and publishers, and prosumers, e.g., authors. The analysis reveals that questionable publications embellished their citation scores by attributing publisher-level self-citations to their journals while also controlling the journal-level self-citations to circumvent the evaluation of journal-indexing services. This approach makes it difficult to detect malpractice by conventional journal-level metrics. We propose journal-publisher-hybrid metric that help detect malpractice. We also demonstrate that the questionable publications had a weaker disruptiveness and influence than their counterparts. This indicates the negative effect of suspicious publishers in the academia. The findings provide a basis for actionable policy making against questionable publications.Comment: 16 pages of main text including 4 figures + 32 pages of supplementary information including 30 supplementary figure

Class fields arising from the form class groups of order O and level N

Let $K$ be an imaginary quadratic field and $\mathcal{O}$ be an order in $K$. We construct class fields associated with form class groups which are isomorphic to certain $\mathcal{O}$-ideal class groups in terms of the theory of canonical models due to Shimura. By utilizing these form class groups, we first derive a congruence relation on special values of a modular function of higher level as an analogue of Kronecker's congruence relation. Furthermore, as an application of such class fields, for a positive integer $n$ we examine primes of the form $x^2+ny^2$ with some additional conditions.Comment: 30 page