Case Ofn Research Articles

Degeneration of Riemann surfaces and intermediate polarization of the moduli space of flat connections

We construct a family of polarizations of the moduli space of flatSU(n)-connections on a closed 2-manifold of genusg(≧ 2). These are generalizations of various polarizations known until now. That is, our family of polarizations includes Weitsman's real polarizations in the case ofn=2 [17], as well as the Kahler polarizations which are well known since [2] and [18]. Our construction is based on an original formulation of degeneration of Riemann surfaces. The relation between our polarizations and the complex structures of the moduli spaces of parabolic bundles are also studied.

1 The epidemiology of Hodgkin's disease

Much of the epidemiological heterogeneity of HD incidence reflects the behaviour of the NS subtype, at least in the USA. Incidence variation across races (except Asians) and time periods is most marked in this subtype. In young adults with HD, there is compelling evidence for social class modification of risk consistent with an infectious aetiology; limited data suggest that this effect occurs within the NS subtype, but considerable evidence indicates that it does not primarily involve EBV infection. Findings from familial aggregation studies and HLA associations point to inherited susceptibility to this subtype. Despite little sex difference for NS in young adulthood in the latest incidence data, parity nevertheless appears to be protective against this subtype for women. Therefore, the greater increase for females than males in the incidence of young-adult NS in recent years may reflect the impact of population trends towards later childbearing and lower parity. This change, as well as the concomitant smaller family sizes and growing affluence, could explain part of the burgeoning incidence of NS in young adults in the USA. These observations suggest that NS in young adults constitutes a separate disease, probably of infectious origin. The incongruous occurrence of this subtype in older adults, and the presence of EBV in some NS cases, could reflect heterogeneity within NS, for example, representing features of the cellular phase of NS (Cozen et al, 1992; Medeiros and Greiner, 1995). For the non-NS subtypes, many of the factors that predict risk of NS may also be relevant. Patterns of social class determinants in children and older adults, the age groups at risk for MC, support involvement of an infectious precursor given intense exposure, and EBV is a likely candidate, based on its high prevalence in these groups. However, little aetiological research has been directed explicitly at the non-NS subtypes. Considerable effort has gone into exploring an infectious aetiology of HD. Recently, this line of investigation has moved beyond social class determinants to molecular epidemiological studies of EBV and, to a lesser degree, other potentially involved viruses. The roles of genetic susceptibility and sex hormones also represent promising areas for exploration, particularly in their possible interaction with infectious agents and other environmental factors. Ultimately, clearer epidemiological understanding of HD will be aided by more precise classification of this disease at the molecular level.

Effect of weak uniaxial loads on creep strain rate in high-porosity MgO compacts during early sintering stages

Creep phenomena accompanying the early stage of sintering of high-porosity MgO powder compacts were investigated with regard to the dependence of creep rate on the applied stress. This dependence was found to be non-linear, obeying a power law with an exponentn <1, in contrast with the behaviour of dense compacts which exhibit linear Nabarro-Herring creep under the same type of loading. The nature of the creep exponent, expected to be in relation to mechanisms of particle disconnection and rearrangement, frequently observed in a high-porosity compact during the early stage of neck formation, has been explored using an appropriate physico-mathematical model. The relevant point concerning high-porosity compacts is that, owing to the loosely packed microstructure, the necks must resist not only normal forces, but also bending moments. It is the action of such bending moments which is supposed to drive the particles rearrangement. In this framework, the nature of the creep exponent appears to be related mainly to the green density, but it is substantially constant with densification. The predictions of the model explain the experimental results forn <1 (high-porosity green compacts), with a smooth transition to the case ofn=1 (low-porosity green compacts).

On inequalities for norms of intermediate derivatives on a finite interval

For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality $$\left\| {f^{(n - 2)} } \right\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_\infty + \left\| {f^{(n)} } \right\|_\infty /2$$ holds with the exact constant 4n−2(n−1)!.

A note on the Dirichlet problem for the Stokes system in Lipschitz domains

We study the L p {L^p} Dirichlet problem for the Stokes system in Lipschitz domains. Optimal estimates are obtained when the dimension n = 3 n = 3 . In the case of n ≥ 4 n \geq 4 , we establish a weak estimate of solutions for certain range of p.

Some probabilistic properties of the nearest adjoining order method and its extensions

In this paper, some probabilistic properties of the nearest adjoining order (NAO) method are presented. They have been obtained under weaker assumptions than those commonly used, i.e. it is not assumed that comparisons are not independent and that probability of comparison errors are known. The results presented comprise the evaluation of the probability of obtaining an errorless solution with the use of the NAO method; asymptotic properties of this solution derived under the assumption that comparisons of different pairs (i.e. pairsx i ,x j andx r ,x r fori ≠r,s andj ≠r,s) are not correlated — for the case of one expert. An extension of results for the case ofN > 1 independent experts is also presented. This extension is accomplished by including an additional step — the aggregation of comparisons made by all experts for each pair of objects. Two ways of such an aggregation are analyzed: the averaging of experts' opinions and the majority principle. In the latter case, the result of the comparison is the same as the opinion of the majority of experts. The results obtained indicate an exponential convergence of the probability of the NAO solution to an errorless one in both cases. However, an application of the majority principle leads to a minimization problem, which is the same as in the case ofN = 1 and is much simpler than that corresponding to averaging of comparisons.

Various classical limits, centre of mass and coherent states

Two simple measuring processes with various classical limits are discussed using coherent states of the centre of mass ofN particles acting as a detector. the large-N and small-ħ limits are two typical ones. The small-ħ limit corresponds to a large external electric field or large-time limit in our models. It is shown that in the large-N limit all polynomials in averaged operators of the particles are classical, while in the small-ħ limit all polynomials in position and momentum operators of all particles are classical. In the latter case, the number of particlesN does not play an essential role at all, so that we can takeN=1. That is, it is possible to construct a detector consisting of a single particle. We also show that in the case ofN harmonic oscillators they will disturb the measuring process.

Intra- and interspecific copulations in the two congeneric green stink bugs,Nezara antennata andN. viridula (Heteroptera, Pentatomidae), with reference to postcopulatory changes in the spermatheca

Intra- and interspecific copulations betweenNezara antennata andN. viridula were investigated, with reference to postcopulatory changes in the spermatheca. The duration of copulation was significantly shorter in the case ofN. viridula males andN. antennata females than it was in the other 3 combinations. Both sperm and pulpy substance were transferred into the spermatheca during the intraspecific copulation of each species. No sperm was found in the spermatheca after interspecific copulation. However, the pulpy substance was found in the dilated portion of spermathecal ducts of someN. viridula females copulated with anN. antennata male, whereas no such substance was found in the case of theN. antennata females copulated with anN. viridula male. Most of the pulpy substance appeared to have been absorbed from the spermatheca within a 5-day period after the copulation. This absorption was observed for theN. viridula females copulated with anN. antennata male, as well as for the females of each of the species copulated with a conspecific male. It was suggested that this pulpy substance was a male-derived nutrient.

Multiple-parameter Lie transform

A method is developed to construct a Lie transform in the multiple-parameter case; a generalization of Deprit's, Henrard's, and Varadi's methods. The details of the theoretical developments are given for the case of three different parameters. A simple approach is suggested to reduce the case ofn parameters to that of the one parameter case.

Fishes ofNeoclinus from Okinawa with notes on the traits of their habitats

All the fish specimens ofNeoclinus bryope species complex collected from Okinawa Island including the 2 specimens already reported asN. bryope are referable toN. okazakii. Neoclinus nudus, hitherto known only from Taiwan, is newly recorded from Okinawa Island. These two species are redescribed on the basis of the specimens from Okinawa Island. The specimens from Okinawa are compared with those from Shirahama in the case ofN. okazakii and with specimens from Taiwan as well asN. lacunicola andN. toshimaensis specimens from Shirahama in the case ofN. nudus. The habitats ofN. okazakii andN. nudus are clearly separated in the waters of Heshikiya, Okinawa Island and the habitat of either species is rather particular in that it is exceptionally unoccupied by blenniids which are flourishing in the coastal waters of the Okinawa Islands.

2-D SIMD algorithms in the perfect shuffle networks

This paper studies a set of basic algorithms for SIMD Perfect Shuffle networks. These algorithms where studied in several papers, but for the 1-D case, where the size of the problem N is the same as the number of processors P . For the 2-D case of N = L * P , studied by [GK-80] and [Kr-81], we improve several algorithms, achieving run time Ο( L + log P ) rather than Ο( L * log P ), as N exceeds P . We give non-trivial algorithms for the following 2-D operations: Row-Reduction, Parallel-Prefix, Transpose, Smoothing and Cartesian-Product.

Chromatographic behaviour (GC and HPLC) of 1,n-bis(alkylthio)alkanes

The retention behaviour of 1,n-bis(alkylthio)alkanes (39 compounds, R1-S-(CH2)n-S-R2) was characterized by gas chromatography on a SE 54 capillary column and by high pressure liquid chromatography on a ODS phase. Generally, the retention times depend both on the number of methylene groups (n) between the two sulphur atoms and on the alkyl groups R1 and R2. Substitution of n-alkyl groups R by e.g.,i-propyl ort-butyl leads to a decrease in the retention times. This can be explained by the weaker attachement of bulky alkyl groups to the ODS phase (HPLC) and lower boiling points (GC), respectively. A linear correlation was found between boiling points and retention data (Kovats indices) in GC. In HPLC the retention increments of the methylene groups — (CH2)n — between the two sulphur atoms are lower in the case ofn=2–4 than forn>4, which can be related to a sulphur-sulphur interaction.

Estimating true scores in kinship data.

Estimated true scores are occasionally used to provide an estimate of scores which would be obtained if measurement error could be removed from fallible measures. When one knows only a test's relibility and an observed score for each subject, true scores are estimated by regressing observed scores toward the group mean. When relatives' observed scores are also available, estimates of true scores can be improved by using the additional information. Observed scores of subjects and relatives can be used as predictors of subjects' true scores in a multiple regression. The resulting formula is presented for the case in which only one relative's score per subject is known. Estimation of true scores for the general case ofN relatives per subject is also discussed.

Average-case results on heapsort

A new algorithm for rearranging a heap is presented and analysed in the average case. The average case upper bound for deleting the maximum element of a random heap is improved, and is shown to be less than [logn]+0.299+M(n) comparisons, *) whereM(n) is between 0 and 1. It is also shown that a heap can be constructed using 1.650n+O(logn) comparisons with this algorithm, the best result for any algorithm which does not use any extra space. The expected time to sortn elements is argued to be less thann logn+0.670n+O(logn), while simulation result points at an average case ofn log n+0.4n which will make it the fastest in-place sorting algorithm. The same technique is used to show that the average number of comparisons when deleting the maximum element of a heap using Williams' algorithm for rearrangement is 2([logn]−1.299+L(n)) whereL(n) also is between 0 and 1, and the average cost for Floyd-Williams Heapsort is at least 2nlogn−3.27n, counting only comparisons. An analysis of the number of interchanges when deleting the maximum element of a random heap, which is the same for both algorithms, is also presented.

Further results on correlation functions of de Bruijn sequences

In this paper we develop some bounds for the correlation functions of sequences with period 2n and specific linear complexities. These bounds are also applicable to the correlation functions of de Bruijn sequences with spann and specific linear complexities. It is interesting that a conjecture of Chan, Games and Key's for the case ofn=2m can be proved easily by using the results developed here. Their conjecture asserts that there are no de Bruijn sequences with spann and linear complexity 2n−1+n+1. The comjecture was proved by Games by a different method.

Asymptotically anti-de Sitter spaces

Asymptotically anti-de Sitter spaces are defined by boundary conditions on the gravitational field which obey the following criteria: (i) they are O(3, 2) invariant; (ii) they make the O(3, 2) surface integral charges finite; (iii) they include the Kerr-anti-de Sitter metric. An explicit expression of the O(3, 2) charges in terms of the canonical variables is given. These charges are shown to close in the Dirac brackets according to the anti-de Sitter algebra. The results are extended to the case ofN=1 supergravity. The coupling to gravity of a third-rank, completely antisymmetric, abelian gauge field is also considered. That coupling makes it possible to vary the cosmological constant and to compare the various anti-de Sitter spaces which are shown to have the same energy.

Field and electroantennogram responses to sex pheromone optical isomers by monophagous jack pine sawflies (Hymenoptera: Diprionidae)

Several species of monophagous jack pine sawflies (Hymenoptera: Diprionidae) were tested in the field and by electroantennograms (EAG) for activity toward the optical isomers of a pine sawfly sex pheromone, the acetate and propionate esters of 3,7-dimethylpentadecan-2-ol.Neodiprion rugifrons andNeodiprion dubiosus were attracted to a mixture of the propionate esters of the 2S,3R,7R and 2S,3R,7S isomers, whereasNeodiprion swainei was attracted to the 2S,3S,7S propionate isomer. Samples containing the 2S,3R,7S propionate isomer elicited the strongest EAG responses in these three species andNeodiprion nigroscutum. The 2S,3S,7S propionate isomer was equally active (EAG) in the case ofN. swainei.

The Lagrangian planetary equations for secular perturbations

For the case ofn planets, we derive Lagrange's secular planetary equations in terms of the Poincare canonical variables, using the Jacobi-Radau set of origins, and referring to a common fixed plane.

Electrochemical reactions with protonations at equilibrium Part VIII. The 2 e, 2 H+ reaction (nine-member square scheme) for a surface or for a heterogeneous reaction in the absence of disproportionation and dimerization reactions

A theoretical study of the 2 e, 2H+ reaction (nine-member square scheme) is presented for a surface reaction (adsorbed species, Langmuir isotherm or monolayer-modified electrode), or for a heterogeneous electrochemical reaction with protonations taking place in solution near the electrode. The thermodynamic equilibrium diagrams are first examined. In the absence of dimerization, four types of diagrams (NN, SS, NS and SN) are possible, according to the order of the pKa's. The conditions for a direct apparent 2 e, 2H+ reaction are established; the limits pHs (low pH) and pHt (high pH) of the region in which it occurs are calculated. The radical formed after a 1 e, 1H+ reaction (AH in the case of a process AAH2) tends to exist in a broader potential range for the SS than for the NN type, the NS and SN cases being intermediate. The kinetic behaviour of the system is investigated by assuming that the symmetry factors of the electrochemical reactions are equal to 0.5, that the protonations are at equilibrium and that the radicals do not dimerize. The hypothesis is also made that the disproportionation reactions can be neglected; this hypothesis is discussed. In these conditions, when a direct 2 e, 2H+ reaction occurs, the system behaves as a simple reaction with two successive one-electron exchanges. Two apparent rate constants, which depend on the electrochemical rate constants, on the pKa's, on the pH and on the difference between the redox potentials can be defined. Both the protonations and the occurrence of a direct 2 e process cause a decrease, which can reach several orders of magnitude, in the apparent rate constants. The graphs of the logarithm of the rate constants as a function of pH are V-shaped, with slopes of ±0.5. The reaction sequence (order of addition of the electrons and protons) is discussed; for a reduction it is H+ eH+ e near pHs and eH+ eH+ near pH1 for all types. Between these sequences, the succession is eH+ H+ e for the NN case, H+ eeH+ for the SS case, and either or both for the NS and SN cases.

Electrochemical reactions with protonations at equilibrium: Part VIII. The 2 e, 2H + reaction (nine-member square scheme) for a surface or for a heterogeneous reaction in the absence of disproportionation and dimerization reactions

A theoretical study of the 2 e, 2H + reaction (nine-member square scheme) is presented for a surface reaction (adsorbed species, Langmuir isotherm or monolayer-modified electrode), or for a heterogeneous electrochemical reaction with protonations taking place in solution near the electrode. The thermodynamic equilibrium diagrams are first examined. In the absence of dimerization, four types of diagrams (NN, SS, NS and SN) are possible, according to the order of the p K a 's. The conditions for a direct apparent 2 e, 2H + reaction are established; the limits pH s (low pH) and pH t (high pH) of the region in which it occurs are calculated. The radical formed after a 1 e, 1H + reaction (AH in the case of a process AAH 2) tends to exist in a broader potential range for the SS than for the NN type, the NS and SN cases being intermediate. The kinetic behaviour of the system is investigated by assuming that the symmetry factors of the electrochemical reactions are equal to 0.5, that the protonations are at equilibrium and that the radicals do not dimerize. The hypothesis is also made that the disproportionation reactions can be neglected; this hypothesis is discussed. In these conditions, when a direct 2 e, 2H + reaction occurs, the system behaves as a simple reaction with two successive one-electron exchanges. Two apparent rate constants, which depend on the electrochemical rate constants, on the p K a 's, on the pH and on the difference between the redox potentials can be defined. Both the protonations and the occurrence of a direct 2 e process cause a decrease, which can reach several orders of magnitude, in the apparent rate constants. The graphs of the logarithm of the rate constants as a function of pH are V-shaped, with slopes of ±0.5. The reaction sequence (order of addition of the electrons and protons) is discussed; for a reduction it is H + eH + e near pH s and eH + eH + near pH 1 for all types. Between these sequences, the succession is eH + H + e for the NN case, H + eeH + for the SS case, and either or both for the NS and SN cases.