Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.     

Synthesis and characterization of alt‐bipyridinylene‐phenylene copolymers containing ruthenium(II) complexes

Poly{bis(4,4′‐tert‐butyl‐2,2′‐bipyridine)–(2,2′‐bipyridine‐5,5′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3a ), poly{bis(4,4′‐tert‐butyl‐2,2′‐bipyridine)–(2,2′‐bipyridine‐4,4′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3b ), and poly{bis(2,2′‐bipyridine)–(2,2′‐bipyridine‐5,5′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3c ) were synthesized by the Suzuki coupling reaction. The alternating structure of the copolymers was confirmed by ¹H and ¹³C NMR and elemental analysis. The polymers showed, by ultraviolet–visible, the π–π* absorption of the polymer backbone (320–380 nm) and at a lower energy attributed to the d–π* metal‐to‐ligand charge‐transfer absorption (450 nm for linear 3a and 480 nm for angular 3b ). The polymers were characterized by a monomodal molecular weight distribution. The degree of polymerization was approximately 8 for polymer 3b and 28 for polymer 3d . © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2911–2919, 2004