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...

We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE under the hypothesis of the GilletWaldhausen theorem. More generally we show that K1(C(E)) of the category of bounded complexes in E always coincides with K1(DE).

The Kaposi's sarcoma-associated herpesvirus (KSHV) K1 gene encodes a polypeptide bearing an immunoreceptor tyrosine-based activation motif (ITAM) that is constitutively active for ITAM-based signal transduction. Although ectopic overexpression of K1 in cultured fibroblasts can lead to growth transformation, in vivo this gene is primarily expressed in lymphoid cells undergoing lytic infection. H...

In a recent work, the combinatorial interpretation of the polynomial α(n; k1, k2, . . . , kn) counting the number of Monotone Triangles with bottom row k1 < k2 < · · · < kn was extended to weakly decreasing sequences k1 ≥ k2 ≥ · · · ≥ kn. In this case the evaluation of the polynomial is equal to a signed enumeration of objects called Decreasing Monotone Triangles. In this paper we define Genera...

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.

We introduce a new invariant for C?-algebras of stable rank one that merges the Cuntz semigroup information together with K1-group information. This semigroup, termed Cu1-semigroup, is constructed as equivalence classes pairs consisting positive element in stabilization given C?-algebra unitary unitization hereditary subalgebra generated by element. show Cu1-semigroup well-defined continuous fu...

Using a magnetic Frederiks transition technique, we measure the temperature and concentration dependences of splay K1, twist K2, and bend K3 elastic constants for the lyotropic chromonic liquid crystal sunset yellow formed through noncovalent reversible aggregation of organic molecules in water. K1 and K3 are comparable to each other and are an order of magnitude higher than K2. At higher conce...

This paperwork gives an overview of NVIDIA’s Jetson TK1 Development Kit and its Tegra K1 architecture (32-bit version). We also compare some critical metrics between the Kepler GPU in Tegra K1 and that used in high-end systems, and highlighed that Tegra K1 is more power efficient. Furthermore, we conducted an experiment which shows how Tegra K1 performed compared with Tesla K40C in a specific a...