Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.Comment: 53 page

Solvable Lie algebras are not that hypo

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Group

Sexual activity and risk of HIV infection among patients with schizophrenia

This study sought to determine the frequency and types of sexual behavior among patients with schizophrenia and to assess the behavior with respect to risk of HIV infection. METHOD: Ninety-five inpatients and outpatients with a research diagnosis of schizophrenia underwent a series of face-to-face interviews to determine their sexual activity and correlate it with demographic characteristics, psychopathology, and medication side effects. RESULTS: Forty-four percent of the patients had been sexually active in the preceding 6 months, and 62% of these had had multiple partners. Sexual activity was associated with greater general psychopathology. Having multiple sexual partners was associated with younger age, a lower level of functioning, the presence of delusions, and more positive symptoms. Of the sexually active patients, 12% reported at least one partner who was HIV positive or injected drugs, or both, and 50% had exchanged sex for money or goods. Ten percent of the patients had engaged in homosexual activity in the preceding 6 months and 22% during their lifetime; the frequency was similar among men and women. Consistent condom use was uncommon. CONCLUSIONS: A substantial proportion of schizophrenic patients had recent histories of sexual abstinence, but an almost equal number were sexually active. Sexual activity was usually accompanied by behavior related to HIV risk. Sexual activity and having multiple partners were associated with certain measures of more severe illness. Younger patients were more likely to have multiple partners but were also more likely to use condoms. There is a need for aggressive prevention strategies with this population

Safeguarding children in dentistry: 1. Child protection training, experience and practice of dental professionals with an interest in paediatric dentistry

* Few dental professionals with child protection training have experience of making referrals. * There is a wide gap in practice between recognising signs of child abuse and neglect and responding effectively. * This may indicate missed opportunities to save children from continuing abuse. * There is a need for improved child protection information, support and training for dental professionals. Abstract Following several highly publicised inquiries into the deaths of children from abuse and neglect, there has been much recent interest in the role and responsibility of all health professionals to protect children at risk of maltreatment. The findings of a postal questionnaire, sent in March 2005 to 789 dentists and dental care professionals with an interest in paediatric dentistry working in varied settings in the UK, are presented in a two-part report and discussed in the context of current multi-agency good practice in safeguarding and promoting the welfare of children. This first part explores reported child protection training, experience and practice. There was a significant gap between recognising signs of abuse and responding effectively: 67% of respondents had suspected abuse or neglect of a child patient at some time in their career but only 29% had ever made a child protection referral. The dental profession is alerted to the need to ensure necessary appropriate action to safeguard children is always taken when child abuse or neglect are suspected

High Molecular Weight Hyaluronan Promotes Corneal Nerve Growth in Severe Dry Eyes

The purpose of this study was to investigate the effect of high molecular weight hyaluronan (HMWHA) eye drops on subbasal corneal nerves in patients suffering from severe dry eye disease (DED) and to evaluate the damage of subbasal corneal nerves associated with severe DED. Designed as an international, multicenter study, 16 patients with symptoms of at least an Ocular Surface Disease Index (OSDI) score of 33, and corneal fluorescein staining (CFS) of at least Oxford grade 3, were included and randomized into two study arms. The control group continued to use their individual optimum artificial tears over the study period of eight weeks; in the verum group, the artificial tears were substituted by eye drops containing 0.15% HMWHA. At the baseline visit, and after eight weeks, the subbasal nerve plexus of 16 patients were assessed by confocal laser scanning microscopy (CSLM). The images were submitted to a masked reading center for evaluation. Results showed a significant increase of total nerve fiber lengths (CNFL) in the HMWHA group (p = 0.030) when compared to the control group, where the total subbasal CNFL did not significantly change from baseline to week 8. We concluded that in severe DED patients, HMWHA from topically applied eye drops could cross the epithelial barrier and reach the subbasal nerve plexus, where it exercised a trophic effect

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Developments in Agricultural Soil Quality and Health: Reflections by the Research Committee on Soil Organic Matter Management

The North Central Education and Research Activity Committee (NCERA-59) was formed in 1952 to address how soil organic matter formation and management practices affect soil structure and productivity. It is in this capacity that we comment on the science supporting soil quality and associated soil health assessment for agricultural lands with the goal of hastening progress in this important field. Even though the suite of soil quality indicators being applied by U.S. soil health efforts closely mirrors the “minimum data set” we developed and recommended in the mid-1990s, we question whether the methods or means for their selection and development are sufficient to meet current and emerging soil health challenges. The rush to enshrine a standard suite of dated measures may be incompatible with longer-term goals. Legitimate study of soil health considers soil change accrued over years to decades that influence on- and off-site function. Tailoring of methods to local conditions is needed to effectively apply and interpret indicators for different soil resource regions and land uses. Adherence to a set suite of methods selected by subjective criteria should be avoided, particularly when we do not yet have adequate data or agreed upon interpretive frameworks for many so-called “Tier 1” biological indicators used in soil health assessment. While pooling data collected by producer-groups is one of the most exciting new trends in soil health, standardizing methods to meet broad inventory goals could compromise indicator use for site or application-specific problem solving. Changes in our nation’s research landscape are shifting responsibility for soil stewardship from national and state government backed entities to public-private partnerships. As a result, it is critical to ensure that the data needed to assess soil health are generated by reproducible methods selected through a transparent process, and that data are readily available for public and private sector use. Appropriate methods for engagement need to be applied by public-private research partnerships as they establish and expand coordinated research enterprises that can deliver fact-based interpretation of soil quality indicators within the type of normative soil health framework conceived by USDA over 20 years ago. We look to existing examples as we consider how to put soil health information into the hands of practitioners in a manner that protects soils’ services

Developments in Agricultural Soil Quality and Health: Reflections by the Research Committee on Soil Organic Matter Management

The North Central Education and Research Activity Committee (NCERA-59) was formed in 1952 to address how soil organic matter formation and management practices affect soil structure and productivity. It is in this capacity that we comment on the science supporting soil quality and associated soil health assessment for agricultural lands with the goal of hastening progress in this important field. Even though the suite of soil quality indicators being applied by U.S. soil health efforts closely mirrors the “minimum data set” we developed and recommended in the mid-1990s, we question whether the methods or means for their selection and development are sufficient to meet current and emerging soil health challenges. The rush to enshrine a standard suite of dated measures may be incompatible with longer-term goals. Legitimate study of soil health considers soil change accrued over years to decades that influence on- and off-site function. Tailoring of methods to local conditions is needed to effectively apply and interpret indicators for different soil resource regions and land uses. Adherence to a set suite of methods selected by subjective criteria should be avoided, particularly when we do not yet have adequate data or agreed upon interpretive frameworks for many so-called “Tier 1” biological indicators used in soil health assessment. While pooling data collected by producer-groups is one of the most exciting new trends in soil health, standardizing methods to meet broad inventory goals could compromise indicator use for site or application-specific problem solving. Changes in our nation’s research landscape are shifting responsibility for soil stewardship from national and state government backed entities to public-private partnerships. As a result, it is critical to ensure that the data needed to assess soil health are generated by reproducible methods selected through a transparent process, and that data are readily available for public and private sector use. Appropriate methods for engagement need to be applied by public-private research partnerships as they establish and expand coordinated research enterprises that can deliver fact-based interpretation of soil quality indicators within the type of normative soil health framework conceived by USDA over 20 years ago. We look to existing examples as we consider how to put soil health information into the hands of practitioners in a manner that protects soils’ services

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page