A filtration of -Catalan numbers

The operator of F. Bergeron, Garsia, Haiman and Tesler [F. Bergeron, A. Garsia, M. Haiman, G. Tesler, Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions, Methods Appl. Anal. 6 (1999) 363–420] acting on the k-Schur functions [L. Lapointe, A. Lascoux, J. Morse, Tableaux atoms and a new Macdonald positivity conjecture, Duke Math. J. 116 (2003) 103–146; L. Lapointe, J. Morse, Schur functions analogs for a filtration of the symmetric functions space, J. Combin. Theory Ser. A 101 (2003) 191–224; L. Lapointe, J. Morse, Tableaux on k+1-cores, reduced words for affine permutations and k-Schur expansion, J. Combin. Theory Ser. A 112 (2005) 44–81] indexed by a single column has a coefficient in the expansion which is an analogue of the (q,t)-Catalan number with a level k. When k divides n we conjecture a representation theoretical model in this case such that the graded dimensions of the module are the coefficients of the (q,t)-Catalan polynomials of level k. When the parameter t is set to 1, the Catalan numbers of level k are shown to count the number of Dyck paths that lie below a certain Dyck path with q counting the area of the path.     

Elektrophorese von Radionukliden

Es werden Möglichkeiten zur raschen Trennung von Gemischen chemisch sehr ähnlicher Elemente durch Zonenelektrophorese bei hohen Spannungen gezeigt. So wird als Beispiel die vollsträndige Trennung der 15 Elemente von Lanthan bis Lutetium durch Zonenhochspannungselektrophorese in α-Hydroxyisobuttersäure auf Celluloseacetatfolien beschrieben. Der Zeitbedar für eine Trennung beträgt 14...20 min. Die Anwendung aur Transuranelemente wird erwähnt. Auch bei den Nukliden natürlicher Zerfallsreihen liefert die Methode gute Ergebnisse. So wurde ein Verfahren zur Auftrennung der Glieder der Actiniumreihe ausgearbeiter, mit dem Verunreinigungen von ²¹⁰Pb in käuflichen ²²⁷Ac nachgewiesen werden konnten. In anderen Mutter-Tochter-Systemen konnten Trennnungen auch bei sehr ungünstigen Mengenverhältnissen von 10⁸: 1 durchgeführt werden. Die Anwendung in der Aktivierungsanalyse wird diskutiert.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

PVTx measurements in the gas phase for binary mixtures of HFC-161 and HFC-227ea

The gaseous PVTx properties of ethyl fluoride (HFC-161) + 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) mixtures were measured at temperatures from 318.180 to 403.205 K and corresponding pressures from 961.3 to 3129.8 kPa using the isochoric method. The uncertainties in the present measurements were estimated to be ±1.5 kPa for pressure and ±6 mK for temperature. On the basis of the experimental PVTx property data, a truncated virial equation of state was developed for the binary HFC-161/227ea system. This equation reproduced the experimental data in the gas phase within ±0.164% in pressure and within ±0.178% in density.     

The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.     

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

Let G be a Lie group which is the union of an ascending sequence G₁⊆G₂⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C^∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.     

HFC-161混合物作为HCFC-22替代制冷剂的实验研究

本文提出了以HFC-161混合物作为HCFC-22的新型替代制冷剂(HFC-161/125/32,15/42.5/42.5wt%),并在设计使用R410A的压缩机性能测试台上,进行了该混合制冷剂与R410A在若干工况下的性能对比实验.实验结果表明,该新制冷剂的COP略高于R410A,而排气温度略低于R410A.与R410A相比,该新制冷剂的蒸发压力和冷凝压力均低约10%,制冷量和压缩机功耗分别下降4.3%和4.8%.该混合制冷剂物性环境性能良好,ODP为零,GWP值小于R410A.可作为HCFC-22的较为理想的替代制冷剂之一.     

Surface tension of pentafluoroethane + 1,1-difluoroethane from (243 to 328) K

The surface tension of the binary refrigerant mixture pentafluoroethane (HFC-125) + 1,1-difluoroethane (HFC-152a) was measured in the temperature range from (243 to 328) K with a differential capillary rise method, for three compositions around the composition of the optimum refrigeration performance (HFC-125 + HFC152a, 15%/85%). The uncertainties of the measurement of the temperature and the surface tension were estimated to be within ±10 mK and ±0.2 mN m⁻¹, respectively. A correlation for the surface tension of the binary refrigerant mixture HFC-152a + HFC-125 was developed as a function of the composition.     

Positive solutions for one-dimensional -Laplacian boundary value problems with sign changing nonlinearity

This paper deals with the existence of positive solutions for the one-dimensional p-Laplacian

subject to the boundary value conditions:

where _p(s)=|s|^p−2s,p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term f is involved with the first-order derivative explicitly and f may change sign.     

On the characterization of strong convergence of an iterative algorithm for a class of multi-valued variational inclusions

This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued variational inclusion problems. Characterization of strong convergence of this iterative method is established. L. C. Ceng’s research partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai. S. Schaible’s research partially supported by the National Science Council of Taiwan. This research was partially supported by the grant NSC 96-2628-E-110-014-MY3.