It has long been conjectured that the crossing numbers of links are additive under the connected sum of links. This is a difficult problem in knot theory and has been open for more than 100 years. In fact, we do not even know that Cr(K1#K2) = Cr(K1) or Cr(K1#K2) = Cr(K2) holds in general, here K1#K2 is the connected sum of K1 and K2 and Cr(K) stands for the crossing number of the link K. The be...

Let S(R) be an o-minimal structure over R, T ⊂ R k1+k2+l a closed definable set, and π1 : R k1+k2+l → R12 , π2 : R k1+k2+l → R, π3 : R k1+k2 → R2 the projection maps as depicted below.

BACKGROUND Understanding how biotoxins kill cells is of prime importance in biomedicine and the food industry. The budding yeast (S. cerevisiae) killers serve as a convenient model to study the activity of biotoxins consistently supplying with significant insights into the basic mechanisms of virus-host cell interactions and toxin entry into eukaryotic target cells. K1 and K2 toxins are active ...

The effects of vitamin K2 on apoptosis in a variety of cancer cells have been well established in previous studies. However, the apoptotic effect of vitamin K2 on bladder cancer cells has not been evaluated. The aim of this study is to examine the apoptotic activity of Vitamin K2 in bladder cancer cells and investigate the underlying mechanism. In this study, Vitamin K2 induced apoptosis in bla...

Let S(R) be an o-minimal structure over R, T ⊂ Rk1+k2+l a closed definable set, and π1 : R k1+k2+l → R12 , π2 : R k1+k2+l → R, π3 : R k1+k2 → R2 the projection maps as depicted below.

Let K be a knot in the 3–sphere S3 , t(K) the tunnel number of K and K1#K2 the connected sum of two knots K1 and K2 , where t(K) is the minimal genus −1 among all Heegaard splittings which contain K as a core of a handle. Concerning the relationship between t(K1)+ t(K2) and t(K1#K2), we showed in Morimoto [2] that there are infinitely many tunnel number two knots K such that t(K#K′) is two agai...

For developing race-specific anthropometry-based total body water (TBW) equations, we measured TBW using bioelectrical impedance analysis (TBW(BIA)) in 2,943 healthy Korean adults. Among them, 2,223 were used as a reference group. Two equations (TBW(K1) and TBW(K2)) were developed based on age, sex, height, and body weight. The adjusted R2 was 0.908 for TBW(K1) and 0.910 for TBW(K2). The remain...

In data mining, association and correlation rules are inferred from data in order to highlight statistical dependencies among attributes. The metrics defined for evaluating these rules can be exploited to score relationships between attributes in Bayesian network learning. In this paper, we propose two novel methods for learning Bayesian networks from data that are based on the K2 learning algo...