Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Communication in Smoking Cessation and Self-management : a study at Nurse-led COPD-clinics in Primary Health Care

ABSTRACTThe general aim of this thesis was to investigate behavioral change communication at nurse-led chronic obstructive pulmonary disease (COPD) clinics in primary health care, focusing on communication in self-management and smoking cessation for patients with COPD.Designs: Observational, prospective observational and experimental designs were used.Methods: To explore and describe the structure and content of self-management education and smoking cessation communication, consultations between patients (n=30) and nurses (n=7) were videotaped and analyzed with three instruments: Consulting Map (CM), the Motivational Interviewing Treatment Integrity (MITI) scale and the Client Language Assessment in Motivational Interviewing (CLAMI). To examine the effects of structured self-management education, patients with COPD (n=52) were randomized in an intervention and a control group. Patients’ quality of life (QoL), knowledge about COPD and smoking cessation were examined with a questionnaire on knowledge about COPD and smoking habits and with St. George’s Respiratory Questionnaire, addressing QoL. Results: The findings from the videotaped consultations showed that communication about the reasons for consultation mainly concerned medical and physical problems and (to a certain extent) patients´ perceptions. Two consultations ended with shared understanding, but none of the patients received an individual treatment-plan. In the smoking cessation communication the nurses did only to a small extent evoke patients’ reasons for change, fostered collaboration and supported patients’ autonomy. The nurses provided a lot of information (42%), asked closed (21%) rather than open questions (3%), made simpler (14%) rather than complex (2%) reflections and used MI non-adherent (16%) rather than MI-adherent (5%) behavior. Most of the patients’ utterances in the communication were neutral either toward or away from smoking cessation (59%), utterances about reason (desire, ability and need) were 40%, taking steps 1% and commitment to stop smoking 0%. The number of patients who stopped smoking, and patients’ knowledge about the disease and their QoL, was increased by structured self-management education and smoking cessation in collaboration between the patient, nurse and physician and, when necessary, a physiotherapist, a dietician, an occupational therapist and/or a medical social worker.Conclusion The communication at nurse-led COPD clinics rarely involved the patients in shared understanding and responsibility and concerned patients’ fears, worries and problems only to a limited extent. The results also showed that nurses had difficulties in attaining proficiency in behavioral change communication. Structured self-management education showed positive effects on patients’ perceived QoL, on the number of patients who quit smoking and on patients’ knowledge about COPD.

Pregnancy-related low back pain and pelvic girdle pain approximately 14 months after pregnancy : pain status, self-rated health and family situation

Background: Pelvic girdle pain (PGP) in pregnancy is distinct from pregnancy-related low back pain (PLBP). However, women with combined PLBP and PGP report more serious consequences in terms of health and function. PGP has been estimated to affect about half of pregnant women, where 25% experience serious pain and 8% experience severe disability. To date there are relatively few studies regarding persistent PLBP/PGP postpartum of more than 3 months, thus the main objective was to identify the prevalence of persistent PLBP and PGP as well as the differences over time in regard to pain status, self-rated health (SRH) and family situation at 12 months postpartum. Methods: The study is a 12 month follow-up of a cohort of pregnant women developing PLBP and PGP during pregnancy, and who experienced persistent pain at 6 month follow-up after pregnancy. Women reporting PLBP/PGP (n = 639) during pregnancy were followed up with a second questionnaire at approximately six month after delivery. Women reporting recurrent or persistent LBP/PGP at the second questionnaire (n = 200) were sent a third questionnaire at 12 month postpartum. Results: A total of 176 women responded to the questionnaire. Thirty-four women (19.3%) reported remission of LBP/PGP, whereas 65.3% (n = 115) and 15.3% (n = 27), reported recurrent LBP/PGP or continuous LBP/PGP, respectively. The time between base line and the 12 months follow-up was in actuality 14 months. Women with previous LBP before pregnancy had an increased odds ratio (OR) of reporting 'recurrent pain' (OR = 2.47) or 'continuous pain' (OR = 3.35) postpartum compared to women who reported 'no pain' at the follow-up. Women with 'continuous pain' reported statistically significant higher level of pain at all measure points (0, 6 and 12 months postpartum). Non-responders were found to report a statistically significant less positive scoring regarding relationship satisfaction compared to responders. Conclusions: The results from this study demonstrate that persistent PLBP/PGP is a major individual and public health issue among women 14 months postpartum, negatively affecting their self-reported health. However, the perceived relationship satisfaction seems to be stable between the groups.

Duality between non-commutative Yang-Mills-Chem-Simons and non-Abelian self-dual models

By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the non-commutative Yang-Mills-ChernSimons theory and the non-commutative, non-Abelian self-dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map. (C) 2003 Elsevier B.V. B.V. All rights reserved.

On the mKdV-Liouville hierarchy and its self-similarity reduction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structural, Spectroscopic (NMR, IR, and Raman), and DFT Investigation of the Self-Assembled Nanostructure of Pravastatin-LDH (Layered Double Hydroxides) Systems

Layered double hydroxide (LDH) nanocontainers, suitable as carriers for anionic drugs, were intercalated with Pravastatin drug using magnesium-aluminum and zinc-aluminum in a M-II/Al molar ratio equal 2 and different Al3+/Pravastatin molar ratios. Postsynthesis treatments were used in order to increase the materials crystallinity. Hybrid materials were characterized by a set of physical chemical techniques: chemical elemental analysis, X-ray diffraction (XRD), mass coupled thermal analyses, vibrational infrared and Raman spectroscopies, and solid-state C-13 nuclear magnetic resonance (NMR). Results were interpreted in light of computational density functional theory (DFT) calculations performed for Sodium Pravastatin in order to assign the data obtained for the LDH intercalated materials. XRD peaks of LDH-Pravastatin material and the one-dimensional (1D) electron density map pointed out to a bilayer arrangement of Pravastatin in the interlayer region, where its associated carboxylate and vicinal hydroxyl groups are close to the positive LDH. The structural organization observed for the stacked assembly containing the unsymmetrical and bulky monoanion Pravastatin and LDH seems to be promoted by a self-assembling process, in which local interactions are maximized and chloride ion cointercalation is required. It is observed a high similarity among vibrational and C-13 NMR spectra of Na-Pravastatin and LDH-Pravastatin materials. Those features indicate that the intercalation preserves the drug structural integrity. Spectroscopic techniques corroborate the nature of the guest species and their arrangement between the inorganic layers. Changes related to carboxylate, alcohol, and olefinic moieties are observed in both vibrational Raman and C-13 NMR spectra after the drug intercalation. Thus, Pravastatin ions are forced to be arranged as head to tail through intermolecular hydrogen bonding between adjacent organic species. The thermal decomposition profile of the hybrid samples is distinct of that one observed for Na-Pravastatin salt, however, with no visible increase in the thermal behavior when the organic anion is sequestrated within LDH gap.

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. (C) 2012 Elsevier B.V. All rights reserved.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

The relationship between self-efficacy and resting blood pressure in spousal Alzheimer's caregivers

Objective. To examine whether high levels of self-efficacy for problem-focused coping were significantly related to several resting BP measures in spousal Alzheimer's disease caregivers. Design. Cross-sectional. Methods. Participants included 100 older caregivers (mean age = 73.8 ± 8.14 years) providing in home care for a spouse with Alzheimer's disease. All participants completed a 13-item short form of the Coping Self-Efficacy Scale and underwent an in-home assessment where a visiting nurse took the average of three serial BP readings. Multiple regression was used to examine the relationship between self-efficacy and mean arterial pressure (MAP), systolic BP (SBP), diastolic BP (DBP), and pulse pressure (PP) after controlling for age, gender, smoking history, body mass index, the care recipient's clinical dementia rating, diabetes, alcohol use, and the use of antihypertensive medications. Results. Overall, high levels of self-efficacy for problem-focused coping were associated with lower MAP, SBP, and PP. Self-efficacy for problem-focused coping was marginally associated with resting DBP, but not significant. In addition, we conducted secondary analyses of the other two self-efficacy scales to explore the relationship between each dimension and MAP. We found that there were no significant relationships found between MAP and self-efficacy for stopping unpleasant thoughts/emotions or self-efficacy for getting social support. Conclusions. The present study adds to the current body of literature by illustrating the possibility that higher self-efficacy can have physiological advantages, perhaps by buffering chronic stress's impact on resting BP. Another contribution of the current study is its attempt to understand the role of each individual component of self-efficacy. These findings invite future research to investigate whether caregivers might experience cardiovascular benefits from interventions aimed at enhancing self-efficacy.

The Behavior Rating Inventory Of Executive Function - Self-Report Version (Brief-Sr) And The Delis-Kaplan Executive Function Sys

The assessment of executive functions is an area of study that has seen considerable development in recent years. Despite much research examining the validity of various measures of executive functions from both a direct and indirect format, little evidence exists in the extant literature evaluating the correspondence between these types of measures. The current study examined the extent of correspondence, comprising concurrent validity, between the Delis-Kaplan Executive Function System (D-KEFS) and the Behavior Rating Inventory of Executive Function ¿ Self-Report Version (BRIEF-SR). Participants included 30 undergraduate and high school students 18 years of age. Results indicated mixed evidence of concurrent validity between the two measures of executive functions. The findings obtained suggest both expected significant, negative correlation as well as lack of expected correlation between the measures. Suggestions for future research in the assessment of executive functions are discussed.

Use of nitinol self-expandable stents in 26 dogs with tracheal collapse

A study was designed to describe a novel approach to the treatment of tracheal collapse (TC) in dogs using self-expandable nitinol stents. Medical records were reviewed retrospectively for 26 client owned dogs in which nitinol stents were deployed. The entire length of trachea was supported independently of the extent of TC. Two overlapping stents were used instead of one in cases where one stent was not spanning the entire trachea adequately. The diameter of the cranial radiolucent portion of trachea, just behind the cricoid cartilage, was measured as a specific landmark to select the appropriate size of the stent. Two self-expandable nitinol stents were inserted in 9 of 26 dogs; the trachea in the rest of the cases was supported with only one stent. A follow up tracheoscopy was performed in 10 of 26 cases with recurrent clinical signs. Secondary tracheal stenosis in these cases was caused by stent fracture, granuloma or excessive stent shortening. Additional stents were placed successfully to expand the stenotic lumen. A support of the entire trachea may decrease risk of nitinol fracture at the end of the implant. Long term clinical improvement (25 of 26 dogs, 96 %) is comparable with the results of other studies.

Map of Nördliches Bockkar Kees 1979

A new map of Nördliche Bockkarkees (Glocknergroup, Hohe Tauern, Eastern Alps) has been produced in a scale of I : 10000. As a basis an aerophotogrammetric survey on September 18, 1979 was used. The original photogrammetric stereoplotting was in ascale of I : 5000. The map is printed in four coloures with 10m contourlines. Rapid motion of the glacier tongue and ice avalanches up to several million cubic meters occure on Nördliches Bockkarkees frequently. The position of the glacier is shown three weeks before a glacier avalanche broke off the tongue on October 5./6., 1979. The large-scale map represents a contribution to the investigation of the recurrent ice avalanches at this glacier and is one of the necessary preconditions for further research.

Self-adaptive grids for noise mapping refinement

Noise maps are usually represented as contour or isolines maps describing the sound levels in a region. Using this kind of representation the user can easily find the noise level assigned to every location in the map. But the acoustic calculations behind the map are not performed for every single location on it; they are only performed in a grid of receivers. The results in this calculation grid are interpolated to draw the isolines or contours. Therefore, the resolution of the calculation grid and the way it was created (rectangular, triangulated, random…) have an effect on the resulting map. In this paper we describe a smart iterative procedure to optimize the quality of the map at a really low additional computational cost, using self-adaptive grids for the acoustic calculations. These self-adaptive grids add new receivers to the sampling grid in those locations where they are expected to be more useful, so that the performance at the output of the interpolator is enhanced. Self-adaptive sampling grids can be used for minimizing the overall error of the map (improving its quality), or for reducing calculation times, and can be also applied selectively to target areas or contour lines. This can be done by the user customizing the maximum number of iterations, the number of new receivers for each iteration, the target isolines, the target quality…

Experience-dependent corticofugal adjustment of midbrain frequency map in bat auditory system

Recent studies of corticofugal modulation of auditory information processing indicate that cortical neurons mediate both a highly focused positive feedback to subcortical neurons “matched” in tuning to a particular acoustic parameter and a widespread lateral inhibition to “unmatched” subcortical neurons. This cortical function for the adjustment and improvement of subcortical information processing is called egocentric selection. Egocentric selection enhances the neural representation of frequently occurring signals in the central auditory system. For our present studies performed with the big brown bat (Eptesicus fuscus), we hypothesized that egocentric selection adjusts the frequency map of the inferior colliculus (IC) according to auditory experience based on associative learning. To test this hypothesis, we delivered acoustic stimuli paired with electric leg stimulation to the bat, because such paired stimuli allowed the animal to learn that the acoustic stimulus was behaviorally important and to make behavioral and neural adjustments based on the acquired importance of the acoustic stimulus. We found that acoustic stimulation alone evokes a change in the frequency map of the IC; that this change in the IC becomes greater when the acoustic stimulation is made behaviorally relevant by pairing it with electrical stimulation; that the collicular change is mediated by the corticofugal system; and that the IC itself can sustain the change evoked by the corticofugal system for some time. Our data support the hypothesis.