Variations on Hartogs and Henkin-Tumanov Theorems

There are equivalent characterizations for holomorphic functions defined on open sets of $\mathbb C^n$; first of all, they can be represented locally as sums of convergent power series. It is obvious that a holomorphic function of several complex variables is separately holomorphic in each variable. Just separating variables, a lot of the well-known properties of holomorphic functions of one complex variable, as the integral Cauchy formula, have a corresponding version in several complex variables; for separation of variables, we need the function to be continuous. Surprisingly, a function which is separately holomorphic, is indeed C^0 and even C^1 and therefore holomorphic (Hartogs Theorem, 1906). This short note deals with the problem of separate analyticity and extends the discussion to the case of separately CR functions defined on CR manifolds. We present our result of [5] and explain how it is related to the former literature. In particular, we explain its link with former results by Henkin and Tumanov of 1983 and by Hanges and Treves of 1983

The Onset for Compressibility Effects for Aerofoils in Ground Effect

The influence of flow compressibility on a highly-cambered inverted aerofoil in ground effect is presented, based on two-dimensional computational studies. This type of problem has relevance to open-wheel racing cars, where local regions of high-speed subsonic flow form under favourable pressure gradients, even though the maximum freestream Mach number is typically considerably less than Mach 0.3. An important consideration for CFD users in the field is addressed in this paper, the freestream Mach number at which flow compressibility significantly affects aerodynamic performance. More broadly, for aerodynamicists, the consequences of this are also considered. Comparisons between incompressible and compressible CFD siulations are used to identify important changes to the flow characteristics caused by density changes, highlighting the inappropriateness of incompressible simulations of ground effect flows for freestream Mach numbers as low as 0.15

Unravelling Mycosphaerella: do you believe in genera?

Many fungal genera have been defined based on single characters considered to be informative at the generic level. In addition, many unrelated taxa have been aggregated in genera because they shared apparently similar morphological characters arising from adaptation to similar niches and convergent evolution. This problem is aptly illustrated in Mycosphaerella. In its broadest definition, this genus of mainly leaf infecting fungi incorporates more than 30 form genera that share similar phenotypic characters mostly associated with structures produced on plant tissue or in culture. DNA sequence data derived from the LSU gene in the present study distinguish several clades and families in what has hitherto been considered to represent the Mycosphaerellaceae. In some cases, these clades represent recognisable monophyletic lineages linked to well circumscribed anamorphs. This association is complicated, however, by the fact that morphologically similar form genera are scattered throughout the order (Capnodiales), and for some species more than one morph is expressed depending on cultural conditions and media employed for cultivation. The present study shows that Mycosphaerella s.s. should best be limited to taxa with Ramularia anamorphs, with other well defined clades in the Mycosphaerellaceae representing Cercospora, Cercosporella, Dothistroma, Lecanosticta, Phaeophleospora, Polythrincium, Pseudocercospora, Ramulispora, Septoria and Sonderhenia. The genus Teratosphaeria accommodates taxa with Kirramyces anamorphs, while other clades supported in the Teratosphaeriaceae include Baudoinea, Capnobotryella, Devriesia, Penidiella, Phaeothecoidea, Readeriella, Staninwardia and Stenella. The genus Schizothyrium with Zygophiala anamorphs is supported as belonging to the Schizothyriaceae, while Dissoconium and Ramichloridium appear to represent a distinct family. Several clades remain unresolved due to limited sampling. Mycosphaerella, which has hitherto been used as a term of convenience to describe ascomycetes with solitary ascomata, bitunicate asci and 1-septate ascospores, represents numerous genera and several families yet to be defined in future studies

Allelochaeta (Sporocadaceae): Pigmentation lost and gained

The appendaged coelomycete genus Seimatosporium (Sporocadaceae, Sordariomycetes) and some of its purported synonyms Allelochaeta,Diploceras and Vermisporium are re-evaluated. Based on DNA data for five loci (ITS, LSU, rpb2, tub2 and tef1), Seimatosporium is shown to be paraphyletic. The ex-type species of Allelochaeta, Discostromopsis and Vermisporium represent a distinct sister clade to which the oldest name Allelochaeta is applied. These genera were traditionally separated based on a combination of conidial pigmentation, septation, and the nature of their conidial appendages. Allelochaeta is revealed to include taxa with both branched or solitary appendages, that could be cellular or continuous, with conidia being (2–)3(–5)-septate, hyaline, or pigmented, concolourous or versicolourous. This suggests that these characters should be applied at species, and not at the generic level. Conidial pigmentation appears to have been lost or gained several times during the evolution of species within Allelochaeta. In total, 25 new species, 15 new combinations, and 10 new epitypifications are proposed

Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet

We have studied the antiferromagnetic order -- disorder transition occurring at $T=0$ in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane coupling is increased. Quantum Monte Carlo results for the staggered structure factor in combination with finite-size scaling theory give the critical ratio $J_c = 2.51 \pm 0.02$ between the inter-plane and in-plane coupling constants. The critical behavior is consistent with the 3D classical Heisenberg universality class. Results for the uniform magnetic susceptibility and the correlation length at finite temperature are compared with recent predictions for the 2+1-dimensional nonlinear $\sigma$-model. The susceptibility is found to exhibit quantum critical behavior at temperatures significantly higher than the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.

Ising cubes with enhanced surface couplings

Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor interactions and enhanced couplings between surface spins are studied. In particular, at the surface transition, the corner magnetization shows non-universal, coupling-dependent critical behavior in the thermodynamic limit. Results on the critical exponent of the corner magnetization are compared to previous findings on two-dimensional Ising models with three intersecting defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.

Direct observation by resonant tunneling of the B^+ level in a delta-doped silicon barrier

We observe a resonance in the conductance of silicon tunneling devices with a delta-doped barrier. The position of the resonance indicates that it arises from tunneling through the B^+ state of the boron atoms of the delta-layer. Since the emitter Fermi level in our devices is a field-independent reference energy, we are able to directly observe the diamagnetic shift of the B^+ level. This is contrary to the situation in magneto-optical spectroscopy, where the shift is absorbed in the measured ionization energy.Comment: submitted to PR

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe

A Review of Controlling Motivational Strategies from a Self-Determination Theory Perspective: Implications for Sports Coaches

The aim of this paper is to present a preliminary taxonomy of six controlling strategies, primarily based on the parental and educational literatures, which we believe are employed by coaches in sport contexts. Research in the sport and physical education literature has primarily focused on coaches’ autonomysupportive behaviours. Surprisingly, there has been very little research on the use of controlling strategies. A brief overview of the research which delineates each proposed strategy is presented, as are examples of the potential manifestation of the behaviours associated with each strategy in the context of sports coaching. In line with self-determination theory (Deci & Ryan, 1985; Ryan & Deci, 2002), we propose that coach behaviours employed to pressure or control athletes have the potential to thwart athletes’ feelings of autonomy, competence,and relatedness, which, in turn, undermine athletes’ self-determined motivation and contribute to the development of controlled motives. When athletes feel pressured to behave in a certain way, a variety of negative consequences are expected to ensue which are to the detriment of the athletes’ well-being. The purpose of this paper is to raise awareness and interest in the darker side of sport participation and to offer suggestions for future research in this area

Self-Similar Factor Approximants

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are named the self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of the self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions which include a variety of transcendental functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.Comment: 22 pages + 11 ps figure