Finding minimum clique capacity

Let C be a clique of a graph G. The capacity of C is defined to be (|V (G)\C|+|D|)/2, where D is the set of vertices in V (G)\C that have both a neighbour and a non-neighbour in C. We give a polynomial-time algorithm to find the minimum clique capacity in a graph G. This problem arose in the study [1] of packing vertex-disjoint induced three-vertex paths in a graph with no stable set of size three, which in turn was motivated by Hadwiger’s conjecture.     

MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow

Supercritical fluids (SCF) are useful solvents in green chemistry and oil recovery and are of great current interest in the context of carbon sequestration. Magnetic resonance techniques were applied to study near critical and supercritical dynamics for pump driven flow through a capillary and a packed bed porous media. Velocity maps and displacement propagators measure the dynamics of C(2)F(6) at pressures below, at, and above the critical pressure and at temperatures below and above the critical temperature. Displacement propagators were measured at various displacement observation times to quantify the time evolution of dynamics. In capillary flow, the critical phase transition fluid C(2)F(6) showed increased compressibility compared to the near critical gas and supercritical fluid. These flows exhibit large variations in buoyancy arising from large changes in density due to very small changes in temperature.     

A survey of χ-boundedness

If a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? András Gyárfás made a number of challenging conjectures about this in the early 1980s, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are now.     

Portal, freight and vehicle monitor performance using scintillating glass fiber detectors for the detection of plutonium in the Illicit Trafficking Radiation Assessment Program

Neutron-sensitive scintillating glass fiber sensors provide several advantages over neutron-sensitive gas-tubes for plutonium detection and surveillance. Large area detectors and higher effective neutron capture density provide significant improvements in sensitivity versus cost. The glass sensors offer a wide dynamic counting range, fast response time, no transport hazard, greater operator safety and lower micro-phonic susceptibility relative to conventional ³He and ¹⁰BF₃ sensors. We report on the testing methods used in Illicit Trafficking Radiation Assessment Program and our experience in evaluating the performance of the portal, freight and vehicle monitors for customs applications employing these new sensors. Results of false and real alarm tests and distribution tests are presented and compared to previous Monte Carlo and first principle calculations. These earlier calculations determined the detection limits for neutron glass panels used for continuous monitoring of special nuclear materials. Assumptions used in the model assumed a nominal background count rate for neutrons of 0.010 n·cm^-2·s^-1, an intrinsic neutron efficiency of 20% and an alarm set point of 5.2 sigma representing one false alarm per month. Measured neutron data taken with ²⁵²Cf and several gamma ray sources confirm the calculated data. Calculations assume an unshielded source and are conservative because they do not include environmental improvements in neutron economy. The results demonstrate that these systems are capable of reliably detecting special nuclearmaterials (SNM) and other radionuclides within a few seconds.     

Polymer Science Before and After 1899: Notable Developments During the Lifetime of Maurits Dekker

Several books have been published on the history of Polymer Science [1–5], and most of the post-1899 history parallels the lifetime of Dr. Maurits Dekker, who was born in Holland on March 18, 1899.     

Dipole relaxation, intramolecular mobility, and molecular self-organization in solutions of alternating polymers with phenylazomethine and siloxane fragments

Dielectric relaxation in solutions of polyesters containing flexible siloxane and rigid phenylazomethine fragments of various structures is studied. For these polymers in solution, five relaxation processes that reflect the mobility of certain portions of the macrochain are observed. The kinetic rigidity of the macrochain increases with increasing length of the siloxane spacer. This trend is associated with rearrangement of the electronic structure of silicon atoms and phenyl rings and with ordering of rigid phenylazomethine fragments.     

Ligand exchange processes in some iron-sulphur-carbonyl and -nitrosyl complexes

The complex [Fe₂(SMe)₂(CO)₆] undergoes stepwise exchange with Et₂S₂ to yield successively [Fe₂(SMe)(SEt)(CO)₆] and [Fe₂(SEt)₂(CO)₆]. Carbonyl complexes [Fe₂(SR)₂(CO)₆] are efficiently converted to the nitrosyls [Fe₂(SR)₂(NO)₄] by the action either of NO gas or of methanolic sodium nitrite: the analogous species [Fe₂S₂(CO)₆], [Fe₂S₂(CO)₆]^2?, and [Fe₃S₂(CO)₉] all, with methanolic nitrite, yield [Fe₄S₃(NO)₇]^?. This anion, [Fe₄S₃(NO)₇]^?, reacts with sulphur to give the cubane-like [Fe₄S₄(NO)₄]: the synthesis of its selenium analogue, [Fe₄Se₃(NO)₇]^? is described. The complexes [Fe₂(SR)₂(NO)₄] (R = Me, Et, Prⁿ, Prⁱ, Bu^t, PhCH₂) all consist of two isomers in solution, presumed to have structures of C_2h and C_2v, symmetry: activation parameters for the C_2h?C_2v reaction are reported.