The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x) − f(y)| : xy∈ E(G)} taken over all proper numberings f of G. The composition of two graphs G and H , written as G[H ], is the graph with vertex set V (G) × V (H) and with (u1; v1) is adjacent to (u2; v2) if either u1 is adjacent to u2 in G or u1 =u2 and v1 is adjacent to v2 in H . In this paper, we investigate the bandwidt...

is a nonzero constant, where A = ( ∂ fi ∂ xj )i,j=1 is the n × n Jacobian matrix of f1, ..., fn. One of the major unsolved problems of mathematics [S] (see also [B, CM, V2]), viz. the Jacobian conjecture, states that the reverse of the above statement also holds, namely, if the Jacobian determinant J(f1, ..., fn) ∈ F , then f1(x1, ..., xn), ..., fn(x1, ..., xn) ∈ F[x1, ..., xn] are generators o...

It is provet d that, given any positive integer k, there exists a self-complementary graph with more than 4 .2 4 k vertices which contains no complete subgraph with k+1 vertices . An application of this result to coding theory is mentioned . A graph will be called s-good if it contains neither a complete subgraph with more than s vertices nor an independent set of more than s vertices . A speci...

1.1. Norms on Vector Spaces. We want to measure the “size” or “length” of a vector. The mathematical device for doing this in called a norm. Here is the definition. Definition 1.1. Let V be a vector space over K. A norm on V is a function ‖·‖ : V → R : v 7→ ‖v‖ that has the following properties. (1) ‖v‖ ≥ 0 for all v ∈ V , and ‖v‖ = 0 if and only if v = 0. (2) If λ ∈ K and v ∈ V , ‖λv‖ = |λ| ‖v...

Treating a boundary value problem in analytical fluid dynamics, translation of 2D steady Navier-Stokes equations to ordinary differential form leads to a second order equation of Riccati type. In the case of a compressible fluid with constant kinematic viscosity along streamlines, it is possible to find an exact solution of the differential problem by rational combination of Airy’s functions an...

A novel pyronaridine-artesunate (PA) combination is being developed as a 3:1 fixed ratio oral combination against P. falciparum and P. vivax malaria. Pyronaridine (PYR) has been used on a limited basis as monotherapy to treat malaria in some provinces in China since 1970, and there are minimal published data on pharmacokinetics of PYR in humans. In this thesis, the population pharmacokinetics (...

Brown has defined generalised Thompson’s groups Fn, Tn, Vn where n is an integer at least 2 and F=F2, T=T2, V=V2 in the 80’s. Burillo, Cleary Stein have found that there a quasi-isometric embedding from Fn to Fm m are positive integers 2. We show Tn T2 for any n≥2 no embeddings n≥3.

Measurements of two-particle angular correlations between an identified strange hadron (KS or Λ/Λ) and a charged particle, emitted in pPb collisions, are presented over a wide range in pseudorapidity and full azimuth. The data, corresponding to an integrated luminosity of approximately 35 nb−1, were collected at a nucleon-nucleon center-of-mass energy ( √ sNN ) of 5.02 TeV with the CMS detector...

Let M be a hyperkähler manifold, and F a torsion-free and reflexive coherent sheaf on M . Assume that F (outside of singularities) admits a connection ∇ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [V2]. Such sheaves are stable and their...

These course notes will explain in details the physics behind rigid-body motion. Previously, we treated bodies as dimensionless “particles”. At time t, they existed in pointwise position x(t) with velocity v(t). Net force F(t) induced acceleration a(t), where F(t) = ma(t), with m as the mass of the particle. For readability, note that we mark vector quantities with bold notation: v ∈ R3 = (v1, ...