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...

Vitamin K2 is a critical nutrient required for blood clotting that also plays an important role in bone formation. Vitamin K2 supplementation up-regulates the expression of bone markers, increases bone density in vivo, and is used clinically in the management of osteoporosis. The mechanism of vitamin K2 action in bone formation was thought to involve its normal role as an essential cofactor for...

We use an array given in H. Kharaghani, Arrays for orthogonal designs, J. Combin. Designs, 8 (2000), 166-173, to obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; hi, kl, kl, kl, k2, k2, k2, k2), where k1 and k2 must be the sum of two squares. In particular we obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; k, k, k, k, k, k, k, k...

We show that there exist knots K ⊂ S with g(E(K)) = 2 and g(E(K#K#K)) = 6. Together with [5, Theorem 1.5], this proves existence of counterexamples to Morimoto’s Conjecture [10]. This is a special case of [6]. Let Ki (i = 1, 2) be knots in the 3-sphere S, and let K1#K2 be their connected sum. We use the notation t(·), E(·), and g(·) to denote tunnel number, exterior, and Heegaard genus respecti...

Let K1 and K2, respectively, be non empty closed convex subsets of real Hilbert spaces H1 and H2. The Approximation − solvability of a generalized system of nonlinear variational inequality (SNV I) problems based on the convergence of projection methods is discussed. The SNVI problem is stated as follows: find an element (x∗, y∗) ∈ K1 × K2 such that 〈ρS(x∗, y∗), x− x∗〉 ≥ 0, ∀x ∈ K1 and for ρ > ...