Logarithmic growth of theL 1-norm of the majorant of partial sums of an orthogonal series

It is proved that for anyN ×N orthogonal matrixA = {a _ij} we have $$\sum\limits_{i = 1}^N {\mathop {\max }\limits_{1 \leqslant n \leqslant N} |\left| {\sum\limits_{j = 1}^n {a_{ij} } } \right|} \geqslant \frac{1}{{30}}N^{1/2} \log N.$$ A multidimensional analog of this result is also established.     

Physical nature of intermolecular interactions within cAMP-dependent protein kinase active site: differential transition state stabilization in phosphoryl transfer reaction

The origin of enzyme catalytic activity may be effectively explored within the nonempirical theory of intermolecular interactions. The knowledge of electrostatic, exchange, delocalization, and correlation components of the transition state and substrates stabilization energy arising from each enzyme active site residue allows to examine the most essential physical effects involved in enzymatic catalysis. Consequently, one can build approximate models of the catalytic activity in a systematic and legitimate manner. Whenever the dominant role of electrostatic interactions is recognized or assumed, the properties of an optimal catalytic environment could be simply generalized and visualized by means of catalytic fields that, in turn, aids the design of new catalysts. Differential transition state stabilization (DTSS) methodology has been applied herein to the phosphoryl transfer reaction catalyzed by cAMP-dependent protein kinase (PKA). The MP2 results correlate well with the available experimental data and theoretical findings indicating that Lys72, Asp166, and the two magnesium ions contribute -22.7, -13.3, -32.4, and -15.2 kcal/mol to differential transition state stabilization, respectively. Although all interaction energy components except that of electron correlation contribution are meaningful, the first-order electrostatic term correlates perfectly with MP2 catalytic activity. Catalytic field technique was also employed to visualize crucial electrostatic features of an ideal catalyst and to compare the latter with the environment provided by PKA active site. The map of regional electronic chemical potential was used to analyze the unfavorable catalytic effect of Lys168. It was found that locally induced polarization of TS atoms thermodynamically destabilizes electrons, pulling them to regions displaying higher electronic chemical potential.     

On Hausdorff dimension of invariant measures arising from non-contractive iterated function systems

Under rather general assumptions we give an upper and lower bound estimate of the Hausdorff dimension of the invariant probability measure for an iterated function systems acting on a Polish space. Received: May 2, 2001; in final form: July 30, 2001?Published online: May 29, 2002     

Equicontinuous families of Markov operators in view of asymptotic stability

The relation between the equicontinuity – the so-called e-property – and the stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its support is non-empty satisfies the e-property.     

On the nontrivial projection problem

The nontrivial projection problem asks whether every finite-dimensional normed space admits a well-bounded projection of nontrivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension) is approximately affinely equivalent to a direct product of two bodies of nontrivial dimensions. We show that this is true “up to a logarithmic factor.”     

Neutral transverse momentum spectra in 60 and 200A·GeV16O+nucleus and proton+nucleus reactions

Transverse momentum (p _T) distributions fo inclusive photons and neutral pions at midrapidity are measured with a lead glass calorimeter in 60 and are measured with a lead glass calorimeter in 60 and 200A·Gev¹⁶O+nucleus and and proton+nucleus reactions. Inclusive photon distributions are compared for central and peripheral reactions. The degree of centrality is determined either from the charged particle multiplicity or from the remaining projectile energy in the forward direction. Deviations from a nucleus+nucleus interaction model based upon linear extrapolation from p+p reactions are observed in central¹⁶O+Au data. The variation of theaverage transverse momentum is investigated as function of centrality. The target-mass and energy dependence of π⁰ p _T distributions are presented. For¹⁶O+Au a change of slope in these distributions is observed atp _t ≈0.8 GeV/c compatible with hydrodynamic expansion models.     

A study of the centrally produced π+π−π0 system formed in the reactionpp→p f (π+π−π0)p s at 300 GeV/c

The reactionpp→p _f (π⁺π^?π⁰)p _s , where the π⁺π^?π⁰ system is centrally produced, has been studied at 300 GeV/c. The π⁺π^?π⁰ mass spectrum shows evidence for the η, ω anda ₂ (1320) as well as an enhancement in thea ₁ (1260) region. A Dalitz plot analysis of the π⁺π^?π⁰ system has been performed. Thea ₁ (1260) parameters coming from the fit of the 1⁺ S wave arem=1208±15 MeV and Γ=430±50 MeV. No evidence is found for theh ₁(1170) orh ₁(1380).     

The production ofJ/ψ in 200 GeV/A oxygen-uranium interactions

The dimuon production in 200 GeV/nucleon oxygen-uranium interactions is studied by the NA 38 Collaboration. The production ofJ/ψ, correlated with the transverse energyET, is investigated and compared to the continuum, as a function of the dimuon massM and transverse momentumPT. A value of 0.64±0.06 is found for the ratio (ψ/Continuum at highET)/(ψ/Continuum at lowET), from which theJ/ψ relative suppression can be extracted. This suppression is enhanced at lowPT.     

Production ofρ +, −, 0 (770),η(550), ω(783) andf 2(1270) mesons in\bar v neon and ν neon charged current interactions

The production of the meson resonances ?(770) (all three charge states), η(550), ω(783) andf ₂(1270) in \(\bar v\) Ne and ν Ne charged current interactions is investigated in a bubble chamber experiment with BEBC at CERN. Except for thef ₂, the main features of resonance production are reasonably well described by the Lund model, although the average resonance multiplicities are overestimated by the model by (67±30)%. The average multiplicities of all resonances, including thef ₂, are well reproduced by a semiempirical model, whose parameters were determined from hadron interaction data.     

An examination of the purported reverse anomeric effect beyond acetylated N-xylosyl- and N-glucosylimidazoles

Syntheses of six new N-(pentopyranosyl)imidazoles have been achieved, and their conformations were observed with and without protonation. A decisive decrease in J(5',4), consistent with stabilization of the 1C4 conformations, was clearly observed for three N-(pentopyranosyl)imidazoles. As well, no reverse anomeric stabilization was observed for N-(2,3,4-tri-O-acetyl-alpha-D-lyxopyranosyl)imidazole upon protonation. It is suggested that the previous observations of the reverse anomeric effect were due to the slight increase in steric bulk of the imidazole aglycone upon protonation, along with favorable dipolar interactions between ring substituents, and not by a reverse of the anomeric effect.