Discrete Morse theory and a reformulation of the K(π,1)-conjecture

A recent theorem of Dobrinskaya [20 Dobrinskaya, N.È. (2006). Configuration spaces of labeled particles and finite Eilenberg-MacLane complexes. Proc. Steklov Inst. Math. 252(1):30–46.[Crossref] , [Google Scholar]] states that the K(π,1)-conjecture holds for an Artin group G if and only if the canonical map BM→BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of [13 Charney, R., Meier, J., Whittlesey, K. (2004). Bestvina’s normal form complex and the homology of Garside groups. Geom. Dedicata 105:171–188.[Crossref], [Web of Science ®] , [Google Scholar]], and a small chain complex for computing its monoid homology, similar to the one of [44 Squier, C. C. (1994). The homological algebra of Artin groups. Math. Scand. 75(1):5–43.[Crossref], [Web of Science ®] , [Google Scholar]].     

Fragmentation of size-selected Xe clusters: Why does the monomer ion channel dominate the Xen and ionization?

The fragmentation of the small Xe_n n=2−5 clusters following 70 eV electron impact ionization has been investigated in a size selective experiment and simulated using non-adiabatic dynamics. The experimental results show that the clusters strongly fragment to yield monomer Xe⁺ (more than 90%) and dimer Xe₂⁺ fragments (the remaining few percent). Trimer Xe₃⁺ fragments first occur from the neutral pentamers Xe₅ in a very low yield of approximately 0.3%. The present results are compared with the previous ones for Kr and Ar clusters. It is shown that the Xe and Kr clusters exhibit a qualitatively similar behavior with a strong propensity for monomer fragments, while in the Ar case dimers prevail. The theoretical calculations also reveal a strong fragmentation to the dimer and monomer fragments. However, the dimer Rg₂⁺ is predicted to be the major product for all rare gases (Rg ≡ Ar, Kr, Xe). Possible reasons for the discrepancy between theory and experiment are discussed.     

An unprecedented heterotrimetallic Fe/Cu/Co core for mild and highly efficient catalytic oxidation of cycloalkanes by hydrogen peroxide

An unprecedented hexanuclear heterotrimetallic Fe/Cu/Co complex bearing two Cu(mu-O)2Co(mu-O)2Fe cores is easily prepared by self-assembly and acts as a remarkable catalyst for the peroxidative oxidation of cycloalkanes under mild conditions.     

Mechanisms of electron-ion recombination of N2H+/N2D+ and HCO+/DCO+ ions: temperature dependence and isotopic effect

The temperature dependencies of the rate coefficients, alpha(e), for electron-ion dissociative recombination (DR) of N2H+/N2D+ and HCO+/DCO+ ions with electrons have been measured over the range 100-500 K. Also, optical emissions have been detected at approximately 100 K from the N2(B3(pi)g) electronically excited products of N2H+/N2D+ recombination. The measurements were carried out using the classic FALP technique combined with an optical monochromator. For N2H+, there was no variation of alpha(e) with temperature above 200 K, with an average value of alpha(e)(N2H+) = 2.8 x 10(-7) cm3 s(-1). The temperature variation for T approximately 100-300 K observed for alpha(e)(HCO+) is similar to that of N2H+ ions for T approximately 300-500 K. The smaller rate coefficient measured for DCO+ and N2D+ ions shows the influence of an isotope effect. The substantial enhancement of the vibrational level, upsilon' = 6, from the N2B state for N2H+ recombination over N2D+ recombination is consistent with previous result at 300 K and implies the influence of a tunneling mechanism of DR.     

Outer-sphere association of p-sulfonatothiacalix[4]arene and tetrasulfonatomethylated calix[4]resorcinarene with cobalt(III) tris(dipyridyl): the effect on the spectral and electrochemical properties of the latter

According to the 1H NMR and X-ray data, the outer-sphere association of [Co(dipy)3]3+ with cyclophanic anions p-sulfonatothiacalix[4]arene and tetrasulfonatomethylated calix[4]resorcinarene is accompanied by the inclusion of the dipyridyl moiety of the former into the cavities of the cyclophanic anions in aqueous and aqueous-DMSO solutions and in the solid state. The first-step dissociation of p-sulfonatothiacalix[4]arene does not change the inclusion mode, but the increase in DMSO content leads to a shallower inclusion of [Co(dipy)3]3+. The electrochemical property changes of [Co(dipy)3]3+ with both receptors undergoing ion pairing indicate the stabilization of the tris(dipyridyl) cobalt complexes in lower oxidation states. The effect of the cyclophanic anions on the cyclic voltammograms of [Co(dipy)3]3+ correlates with the efficiency of binding of the latter with tetrasulfonatomethylated calix[4]resorcinarene and p-sulfonatothiacalix[4]arene.     

Local theorems for some statistics of integer-valued sequences

Let Js={j₁, ..., j_s} be a collection of nonnegative numbers, j₁+...+j_s=n, j_s1, R(Js) be the set of sequencesf=(f(1), ...,f(n)) in each of which the integer m occurs j_s times. Randomly and equiprobably one chooses a sequence f from R(Js). Let _n,r be the number of r-drops in f; _n be the r-principal index off. Local limit theorems are established in this paper for the random variables _n,r and _n as n .Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 61–66, 1988.     

The electrochemical behaviour of [Co(sep)]3+ bound with p-sulfonatothiacalix[4]arene and tetracarboxy-p-sulfonatocalix[4]arene in correlation with inclusive and non-inclusive binding modes

The comparative study of the ion-pairing of Co(III) sepulchrate ([Co(sep)]³⁺) with p-sulfonatothiacalix[4]arene and p-sulfonatocalix[4]arene tetracarbonic acid by ¹H NMR and pH-metric data in solution and X-ray data in solid state elucidates pH dependent effect of carboxylate groups on the stoichiometry and the mode of the ion pairing. The electrochemical data of [Co(sep)]³⁺ bound with both calix[4]arenes have been analyzed in the correlation with stoichiometry and the mode of their binding. The pH-dependent effect of tetracarboxy-p-sulfonatocalix[4]arene on the electrochemical behavior of [Co(sep)]³⁺ has been found to correlate with the participation of carboxylate groups in the host?Cguest binding.