Maximal Green Sequences of Exceptional Finite Mutation Type Quivers

Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-C\'ordova-Vafa in the context of supersymmetric gauge theory. The existence of maximal green sequences for exceptional finite mutation type quivers has been shown by Alim-Cecotti-C\'ordova-Espahbodi-Rastogi-Vafa except for the quiver $X_7$. In this paper we show that the quiver $X_7$ does not have any maximal green sequences. We also generalize the idea of the proof to give sufficient conditions for the non-existence of maximal green sequences for an arbitrary quiver

Seven Hills Winery Brochure 2008

A Seven Hills Winery brochure announces a new label design and three summer wine releases: the 2007 Pinot Gris (Oregon), the 2006 Merlot (Seven Hills Vineyard, Walla Walla Valley), and the 2006 Ciel du Cheval (vintage red wine blend, Red Mountain)

The Evolution of Grain Policy Beyond Europe: Ottoman Grain Administration in the Late Eighteenth Century

During the second half of the eighteenth century, the Ottoman policy-makers adopted a more liberal attitude towards price formation in the Ottoman grain markets. This was accompanied by the fiscal and administrative centralization of the grain trade. These seemingly contradictory policy changes could, in part, be explained in the context of conjectural changes in grain demand and supply, which rendered pre-emptive privileges and price controls less effective. The policy change, however, was not only a practical response to the strains on the pre-existing supply network but also reflected a new concern with the state of agricultural production along with the emergence of emulation as a development strategy.Ottoman economic institutions, grain markets, liberalization

Di-μ-bromido-bis-[(diethyl ether-κO)(2,4,6-trimethylphenyl)magnesium] : the mesityl Grignard reagent

The crystal structure of the title compound, [Mg2Br2(C9H11)2(C4H10O)2], features a centrosymmetric two-centre magnesium complex with half a mol-ecule in the asymmetric unit. The Mg atom is in a considerably distorted Br2CO coordination. Bond lengths and angles are comparable with already published values. The crystal packing is stabilized by C-H⋯π inter-actions linking the complexes into sheets parallel to (0-11)

Biped robot walking control on inclined planes with fuzzy parameter adaptation

The bipedal structure is suitable for a robot functioning in the human environment, and assuming assistive roles. However, the bipedal walk is a poses a difficult control problem. Walking on even floor is not satisfactory for the applicability of a humanoid robot. This paper presents a study on bipedal walk on inclined planes. A Zero Moment Point (ZMP) based reference generation technique is employed. The orientation of the upper body is adjusted online by a fuzzy logic system to adapt to different walking surface slopes. This system uses a sampling time larger than the one of the joint space position controllers. A newly defined measure of the oscillatory behavior of the body pitch angle and the average value of the pelvis pitch angle are used as inputs to the fuzzy adaptation system. A 12-degrees-of-freedom (DOF) biped robot model is used in the full-dynamics 3-D simulations. Simulations are carried out on even floor and inclined planes with different slopes. The results indicate that the fuzzy adaptation algorithms presented are successful in enabling the robot to climb slopes of 5.6 degrees (10 percent)