Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Perceived self-other differences in persuasibility: the effects of interpersonal and group-based similarity

Two experiments examined the effects of interpersonal and group-based similarity on perceived self-other differences in persuasibility (i.e. on third-person effects, Davison, 1983). Results of Experiment 1 (N=121), based on experimentally-created groups, indicated that third-person perceptions with respect to the impact of televised product ads were accentuated when the comparison was made with interpersonally different others. Contrary to predictions, third-person perceptions were not affected by group-based similarity (i.e. ingroup or outgroup other). Results of Experiment 2 (N = 102), based an an enduring social identity, indicated that both interpersonal and group-based similarity moderated perceptions of the impact on self and other of least-liked product ads. Overall, third-person effects were more pronounced with respect to interpersonally dissimilar others. However, when social identity was salient, information about interpersonal similarity of the target did not affect perceived self-other differences with respect to ingroup targets. Results also highlighted significant differences in third-person perceptions according to the perceiver's affective evaluation of the persuasive message. (C) 1998 John Wiley & Sons, Ltd.

Factors influencing wound healing after surgery for metastatic disease of the spine

Study Design, The study group consisted of 53 patients who underwent 75 operations for spine metastases. Patient and tumor demographic factors, preoperative nutritional status, and perioperative adjunctive therapy were retrospectively reviewed. Objective, To determine the risk factors for wound breakdown and infection in patients undergoing surgery for spinal metastases. Summary of Background Data. Spinal Fusion using spine implants may be associated with an infection rate of 5% or more. Surgery for spine metastases is associated with an infection rate of more than 10%. Factors other than the type of surgery performed may account for the greater infection rate. Methods. Data were obtained by reviewing patient records. Age, sex, and neurologic status of the patient; tumor type and site; and surgical details were noted. Adjunctive treatment with corticosteroids and radiotherapy was recorded, Nutritional status was evaluated by determining serum protein and serum albumin concentrations and by total lymphocyte count. Results. Wound breakdown and Infection occurred in 75 of 75 wounds. No patient or tumor demographic factors other than intraoperative blood loss (P < 0.1) were statistically associated with infection; The correlation between preoperative protein deficiency (P < 0.01) or perioperative corticosteroid administration (P < 0.10) and wound infection was significant. There was no statistical correlation between lymphocyte count or perioperative radiotherapy and wound infection. Conclusions, The results indicate that preoperative protein depletion and perioperative administration of corticosteroids are risk factors for wound infection in patients undergoing surgery for spine metastases, Perioperative correction of nutritional depletion and cessation of steroid therapy may reduce wound complications.

Correlation between carbon isotope discrimination and transpiration efficiency in lines of the C-4 species Sorghum bicolor in the glasshouse and the field

Transpiration efficiency, W, the ratio of plant carbon produced to water transpired and carbon isotope discrimination of leaf dry matter, Delta(d)' were measured together on 30 lines of the C-4 species, Sorghum bicolor in the glasshouse and on eight lines grown in the field. In the glasshouse, the mean W observed was 4.9 mmol C mol(-1) H2O and the range was 0.8 mmol C mol(-1) H2O The mean Delta(d) was 3.0 parts per thousand and the observed range was 0.4 parts per thousand. In the field, the mean W was lower at 2.8 mmol C mol H2O and the mean Delta(d) was 4.6 parts per thousand. Significant positive correlations between W and Delta(d) were observed for plants grown in the glasshouse and in the field. The observed correlations were consistent with theory, opposite to those for C-4 species, and showed that variation in Delta(d) was an integrated measure of long-term variation in the ratio of intercellular to ambient CO2 partial pressure, p(i)/p(a). Detailed gas exchange measurements of carbon isotope discrimination during CO2 uptake, Delta(A) and p(i)/p(a) were made on leaves of eight S. bicolor lines. The observed relationship between Delta(A) and p(i)/p(a) was linear with a negative slope of 3.7 parts per thousand in Delta(A) for a unit change in p(i)/p(a). The slope of this linear relationship between Delta(A) and p(i)/p(a) in C-4 species is dependent on the leakiness of the CO2 concentrating mechanism of the C pathway, We estimated the leakiness (defined as the fraction of CO2 released in the bundle sheath by C-4 acid decarboxylations, which is lost by leakage) to be 0.2. We conclude that, although variation in Delta(d) observed in the 30 lines of S. bicolor is smaller than that commonly observed in C-4 species, it also reflects variation in transpiration efficiency, W. Among the eight lines examined in detail and in the environments used, there was considerable genotype x environment interaction.

Children's understanding of pictorial and mental representations

Two studies demonstrate dissociation between children's understanding of pictorial representations (photos and drawings) and mental representations (beliefs). In Study 1, 37 preschoolers were tested on false belief, appearance-reality, false photo, and false drawing tasks. The false picture tasks were significantly easier, and no correlation was found between children's performances on false belief and false picture tasks. Ln Study 2, 30 children who failed a false belief pretest were randomly assigned to 3 training groups: Belief (trained on false belief tasks), Picture (trained on false picture tasks), or Control (trained on number conservation tasks). Training was conducted in 2 sessions over the course of 2 weeks, tasks were presented and feedback was provided. All children were posttested on theory of mind tasks, false picture tasks, and a number conservation task. The posttest results showed differential patterns of performance, with the Belief group scoring highest on the theory of mind posttests, the Picture group scoring highest on the false picture posttests, and the Control group scoring highest on the number conservation posttest. Results are discussed with respect to competing models of theory of mind development.

Peak bone mineral accrual and age at menarche in adolescent girls: A 6-year longitudinal study

Background and objectives: The greatest increase in bone mineral content occurs during adolescence. The amount of bone accrued may significantly affect bone mineral status in later life. We carried out a longitudinal investigation of the magnitude and timing of peak bone mineral content velocity (PBMCV) in relation to peak height velocity (PHV) and the age at menarche in a group of adolescent girls over a 6-year period. Methods: The 53 girls in this study are a subset of the 115 girls (initially 8 to 16 years) in a g-year longitudinal study of bone mineral accretion. The ages at PBMCV and PHV were determined by using a cubic spline curve fitting procedure. Determinations were based on height (n = 12) and bone (n = 6) measurements over 6 years. Results: The timing of PBMCV and menarche were coincident, preceded approximately 1 year earlier by PHV. Correlation showed a negative relationship between age at menarche and both peak bone mineral accrual (r = -0.42, P

Spider toxins: A new group of potassium channel modulators

Spider toxins that target potassium channels constitute a new class of pharmacological tools that can be used to probe the structure and function of these channels at the molecular level. The limited studies performed to date indicate that these peptide toxins may facilitate the analysis of K+ channels that have proved insensitive to peptide inhibitors isolated from other animal sources. Thus far, two classes of K+ channel-selective spider toxins have been isolated, sequenced, and pharmacologically characterised - the hanatoxins (HaTx) from Grammastola spatulata and heteropodatoxins (HpTx) from Heteropoda venatoria. The hanatoxins block Kv2.1 and Kv4.2 voltage-gated K+ channels. In Kv2.1 K+ channels this occurs as a consequence of a depolarising shift in the voltage dependence of activation and not by occlusion of the channel pore. These toxins show minimal sequence homology with other peptide inhibitors of K+ channels, but they do share some homology with other ion channel toxins from spiders, particularly with regard to the spacing between cysteine residues. We have recently isolated three K+ channel antagonists from the venom of the Australian funnel-web spider Hadronyche versuta; at least two of these toxins are likely to constitute a new class of spider toxins active on K+ channels as they are approximately twice as large as HaTx and HpTx.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.