Our motivation is the question how similar the f -colouring problem is to the classic edge-colouring problem, particularly with regard to graph parameters. In 2010, Zhang, Yu, and Liu [9] gave a new description of the f -matching polytope and derived a formula for the fractional f -chromatic index, stating that the fractional f -chromatic index equals the maximum of the fractional maximum f -de...

BACKGROUND In amyotrophic lateral sclerosis (ALS), repeater F waves are increased. Accurate assessment of repeater F waves requires an adequate sample size. METHODS We studied the F waves of left ulnar nerves in ALS patients. Based on the presence or absence of pyramidal signs in the left upper limb, the ALS patients were divided into two groups: One group with pyramidal signs designated as P...

For a graph G = (V,E) and a binary labeling f : V (G) → Z2, let vf (i) = |f−1(i)|. The labling f is said to be friendly if |vf (1)−vf (0)| ≤ 1. Any vertex labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)|. Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly verte...

The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision graph of square grid graph, 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] are also investigated here.

Let G be a nonempty simple graph with vertex set V(G) and an edge E(G). For every injective labeling f:V(G)?Z, there are two induced labelings, namely f+:E(G)?Z defined by f+(uv)=f(u)+f(v), f?:E(G)?Z f?(uv)=|f(u)?f(v)|. The sum index the difference minimum cardinalities of ranges f+ f?, respectively. We provide upper lower bounds on index, determine various families graphs. also interesting con...

Least-squares finite element methods (LSFEMs) for the inviscid Burgers equation are studied. The scalar nonlinear hyperbolic conservation law is reformulated by introducing the flux vector, or the associated flux potential, explicitly as additional dependent variables. This reformulation highlights the smoothness of the flux vector for weak solutions, namely f(u) ∈ H(div,Ω). The standard least-...

In 5] some aspects of object-oriented programming have been reformulated in the higher-order Linear Logic framework, F&O, based on the language Forum 14]. In particular, it has been shown how to logically represent objects encapsulating method deenitions and how to describe metarules deening message passing and self-application, according to diierent computational models. A language based on su...

We show how to reformulate gauge theories coupled to scalar fields in terms of explicitly gauge-invariant variables. We show in the case of scalar QED that the classical theory can be reformulated in this way. We discuss the form of some realistic asymptotic solutions to these equations. The equations of motion are then also reformulated in the non-abelian case.

UNLABELLED This study evaluated changes in abuse exposures, therapeutic error exposures, and diversion into illegal markets associated with brand extended-release oxycodone (ERO) following introduction of reformulated ERO. Original ERO and reformulated ERO street prices also were compared. Data from the Poison Center and Drug Diversion programs of the Researched Abuse, Diversion and Addiction-R...