High molar mass ethene/1‐olefin copolymers synthesized with acenaphthyl substituted metallocene catalysts

The influence of ligand structure on copolymerization properties of metallocene catalysts was elucidated with three C₁‐symmetric methylalumoxane (MAO) activated zirconocene dichlorides, ethylene(1‐(7, 9)‐diphenylcyclopenta‐[a]‐acenaphthadienyl‐2‐phenyl‐2‐cyclopentadienyl)ZrCl₂ ( 1 ), ethylene(1‐(7, 9)‐diphenylcyclopenta‐[a]‐acenaphthadienyl‐2‐phenyl‐2‐fluorenyl)ZrCl₂ ( 2 ), and ethylene(1‐(9)‐fluorenyl‐(R)1‐phenyl‐2‐(1‐indenyl)ZrCl2 ( 3 ). Polyethenes produced with 1 /MAO had considerable, ca. 10% amount of trans‐vinylene end groups, resulting from the chain end isomerization prior to the chain termination. When ethene was copolymerized with 1‐hexene or 1‐hexadecene using 1 /MAO, molar mass of the copolymers varied from high to moderate (531–116 kg/mol) depending on the comonomer feed. At 50% comonomer feed, ethene/1‐olefin copolymers with high hexene or hexadecene content (around 10%) were achievable. In the series of catalysts, polyethenes with highest molar mass, up to 985 kg/mol, were obtained with sterically most crowded 2 /MAO, but the catalyst was only moderately active to copolymerize higher olefins. Catalyst 3 /MAO produced polyethenes with extremely small amounts of trans‐vinylene end groups and relatively low molar mass 1‐hexene copolymers (from 157 to 38 kg/mol) with similar comonomer content as 1 . These results indicate that the catalyst structure, which favors chain end isomerization, is also capable to produce high molar mass 1‐olefin copolymers with high comonomer content. In addition, an exceptionally strong synergetic effect of the comonomer on the polymerization activity was observed with catalyst 3 /MAO. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 373–382, 2008     

Scheduling a triple round robin tournament with minitournaments for the Finnish national youth ice hockey league

This paper presents a method to schedule a triple round robin tournament, which involves minitournaments, each hosted by one team. A key issue is that at the end of the season the number of home games should be balanced over the teams, despite the fact that in minitournament matches only the host team plays at home. This format is played in the Finnish national ice hockey league for players under the age of 20 years, where the problem is further complicated by many other constraints, for example, preassigned matches resulting from away tours that should limit the distances travelled by the teams. To obtain a schedule for this league, we sequentially solve four distinct combinatorial problems. This method allows us to construct a schedule for the 2009–2010 season, which is superior to the official schedule: it has no hard constraint violations, and outperforms the official schedule on three of five soft constraints.     

An improved model for ground-shielded CMOS test fixtures

An improved model for ground-shielded (GS) test fixtures is proposed. The proposed model provides more accurate device-under-test gap behavioral model than previous test-fixture models and takes into account the impedance of the ground return path. The new model is validated up to 25 GHz by comparing the model simulations with experimental measurements. The proposed model is applied to bulk-silicon- and sapphire-based GS test fixtures with different layouts. Furthermore, a large phase shift in the shield-based test-fixture forward transmission is reported in this study. Based on the results achieved, suggestions for deembedding method selection are given. Test fixtures were fabricated using a 0.35-/spl mu/m CMOS process and 0.5-/spl mu/m silicon-on-sapphire CMOS process.     

Determination of talc in geological samples by infrared spectrometry

Talc is determined by infrared spectrometry in talc ore and mineral mixtures containing clinochlore chlorite, dolomite and magnesite as major minerals. When the Si-O-Si vibration at 668 cm^?1 is used, the calibration graph is linear up to about 0.5 mg of talc. Band overlap from chlorite is corrected by using the ratio of absorbances at 668 and 3620 cm^?1. Talc (?15%) in talc/carbonate/chlorite mixtures and ore was determined with relatively good precision and accuracy (recovery 91.2–97.4%). The sample sizes were 0.5–1 mg for 40–60% talc and 0.5–1.5 mg for 7.5–15% talc. The recoveries were worse (84.0–94.6%) for < 15% talc. The precision for unknown samples of talc ore varied from 1.5 to 4.0% (n=4).     

Current-Mode Temperature Compensated Continuous-Time CMOS Transconductance-C Filter

In this paper a low voltage low power current-mode continuous-timelow-pass filter is presented. The current-integrator is constructedof a multi-output linearized transconductance element drivenby a balanced transimpedance amplifier. A 1 MHz third order ellipticlow pass filter is designed and fabricated with the proposedcurrent-mode integrator. The measurements show capability ofoperation with down to a 3 V supply voltage. The measured currentconsumption is 850 µA at room temperature andthe dynamic range is 66 dB. The distortion of the filter is below50 dBc with peak signal levels up to twice the quiescent currentlevel and with the refined designs even lower distortion is expected.The filter uses a CMOS-current reference for temperature andprocess variation stabilization with a measured corner frequencytemperature coefficient of –100 ppm/K.     

Crossmodal attention effects on brain responses to different stimulus classes

Background  

Attending to a point in space in one modality may facilitate processing to information from the same region in another modality. The involvement of sensory-specific cortical areas in intramodal and crossmodal selective spatial attention can be assessed with event-related brain potentials (ERPs).     

Local equivalence relations

In this paper, we investigate the concept of local equivalence relation, a notion suggested by Grothendieck. A local equivalence relation on a topological space X is a global section of the sheaf of germs of equivalence relations on X. We investigate the extent to which a local equivalence relation can be described by a global one and analogously when can a global equivalence relation be recovered from its associated local one. We also look at the notion of a fiber map, which sheds further light on these concepts. A motivating example is that of a foliation on a manifold.     

Bentley’s conjecture on popularity toplist turnover under random copying

Bentley et al. studied the turnover rate in popularity toplists in a ‘random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ? and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: $\ell \sqrt{\mu}$ . Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.     

Lecture Hall Partitions II

For a non-decreasing integer sequence a=(a₁,...,a_n) we define L_a to be the set of n-tuples of integers = (₁,...,_n) satisfying . This generalizes the so-called lecture hall partitions corresponding to a_i=i and previously studied by the authors and by Andrews. We find sequences a such that the weight generating function for these a-lecture hall partitions has the remarkable form In the limit when n tends to infinity, we obtain a family of identities of the kind the number of partitions of an integer m such that the quotient between consecutive parts is greater than is equal to the number of partitions of m into parts belonging to the set P, for certain real numbers and integer sets P. We then underline the connection between lecture hall partitions and Ehrhart theory and discuss some reciprocity results.