Given positive integers m, k and s with m > ks, let Dm,k,s represent the set {1, 2, · · · ,m} − {k, 2k, · · · , sk}. The distance graph G(Z,Dm,k,s) has as vertex set all integers Z and edges connecting i and j whenever |i − j| ∈ Dm,k,s. The chromatic number and the fractional chromatic number of G(Z,Dm,k,s) are denoted by χ(Z,Dm,k,s) and χf (Z,Dm,k,s), respectively. For s = 1, χ(Z,Dm,k,1) was s...

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

In this issue of JEM, Marciniak et al. (https ://doi .org /10 .1084 /jem .20161731) identify a putative novel function of tau protein as a regulator of insulin signaling in the brain. They find that tau deletion impairs hippocampal response to insulin through IRS-1 and PTEN dysregulation and suggest that, in Alzheimer’s disease, impairment of brain insulin signaling might occur via tau loss of ...

and Applied Analysis 3 Table 1: Operations of the two-dimensional differential transform. Original function Transformed function u x, y f x, y ∓ g x, y Uα,β k, h Fα,β k, h ∓G k, h u x, y ξf x, y Uα,β k, h ξFα,β k, h u x, y ∂f x, y /∂x Uα,β k, h k 1 F k 1, h u x, y D ∗x0f x, y , 0 < α ≤ 1 Uα,β k, h Γ α k 1 1 /Γ αk 1 Fα,β k 1, h u x, y D ∗y0f x, y , 0 < α ≤ 1 Uα,β k, h Γ α h 1 1 /Γ αh 1 Fα,β k, h...

We consider the problem of partitioning a set of n numbers into m subsets of cardinality k n m or n m , such that the maximum subset sum is minimal. We prove that the performance ratios of the Differencing Method of Karmarkar and Karp for k 3 4 5 and 6 are precisely 4/3, 19/12, 103/60, and 643/360, respectively, by means of a novel approach in which the ratios are explicitly calculated using mi...

A Competitive spectrophotometric method has been used for the study of complexation between Cu2+, Zn2+ and Cd2+ (M) and 18-crown-6(18C6, B) in methanol using 4-(2-thiazolylazo) resorcinol (TAR, HL) as the colorimetric complexant. Absorption spectra of the species in the M-TAR-18 C6 system at a various concentrations of 18C6 showed no formation of ternary com...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

‎a $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$‎ ‎disjoint collections $t_1$‎, ‎$t_2‎, ‎dots t_{mu}$‎, ‎each of $m$‎ ‎blocks‎, ‎such that for every $t$-subset of $v$-set $v$ the number of‎ ‎blocks containing this t-subset is the same in each $t_i (1leq‎ ‎i leq mu)$‎. ‎in other words any pair of collections ${t_i,t_j}$‎, ‎$1leq i< j leq mu‎$ is a $(v,k,t)$ trade of volume $m$. in th...