Integral method for the development of motor abilities and psycho-physiological functions in children from 2 to 4 years old

The aim of the work: to develop and substantiate the method of integral development of the child on the basis of the integrated application of poems about nature and imitation movements. A greater number of significant differences were found between the test scores of the children of the experimental group compared with the control group after the experimen

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

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

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

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

Projective analysis and preliminary group classification of the nonlinear fin equation ut=(E(u)ux)x+h(x)uu_t=(E(u)u_x)_x + h(x)u

In this paper we investigate for further symmetry properties of the nonlinear fin equations of the general form $u_t=(E(u)u_x)_x + h(x)u$ rather than recent works on these equations. At first, we study the projective (fiber-preserving) symmetry to show that equations of the above class can not be reduced to linear equations. Then we determine an equivalence classification which admits an extension by one dimension of the principal Lie algebra of the equation. The invariant solutions of equivalence transformations and classification of nonlinear fin equations among with additional operators are also given.Comment: 9 page

Realizations of Real Low-Dimensional Lie Algebras

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. Known results on classification of low-dimensional real Lie algebras, their automorphisms, differentiations, ideals, subalgebras and realizations are reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in Appendix are correcte

Implicit trust in clinical decision-making by multidisciplinary teams

In clinical practice, decision-making is not performed by individual knowers but by an assemblage of people and instruments in which no one member has full access to every piece of evidence. This is due to decision making teams consisting of members with different kinds of expertise, as well as to organisational and time constraints. This raises important questions for the epistemology of medicine, which is inherently social in this kind of setting, and implies epistemic dependence on others. Trust in these contexts is a highly complex social practice, involving different forms of relationships between trust and reasons for trust: based on reasons, and not based on reasons; based on reasons that are easily accessible to reflection and others that are not. In this paper, we focus on what it means to have reasons to trust colleagues in an established clinical team, collectively supporting or carrying out every day clinical decision-making. We show two important points about these reasons, firstly, they are not sought or given in advance of a situation of epistemic dependence, but are established within these situations; secondly they are implicit in the sense of being contained or nested within other actions that are not directly about trusting another person. The processes of establishing these reasons are directly about accomplishing a task, and indirectly about trusting someone else’s expertise or competence. These processes establish a space of reasons within which what it means to have reasons for trust, or not, gains a meaning and traction in these team-work settings. Based on a qualitative study of decision-making in image assisted diagnosis and treatment of a complex disease called pulmonary hypertension (PH), we show how an intersubjective framework, or ‘space of reasons’ is established through team members forging together a common way of identifying and dealing with evidence. In dealing with images as a central diagnostic tool, this also involves a common way of looking at the images, a common mode or style of perception. These frameworks are developed through many iterations of adjusting and calibrating interpretations in relation to those of others, establishing what counts as evidence, and ranking different kinds of evidence. Implicit trust is at work throughout this process. Trusting the expertise of others in clinical decision-making teams occurs while the members of the team are busy on other tasks, most importantly, building up a framework of common modes of seeing, and common ways of identifying and assessing evidence emerge. It is only in this way that trusting or mistrusting becomes meaningful in these contexts, and that a framework for epistemic dependence is established

Implicit trust in clinical decision-making by multidisciplinary teams

In clinical practice, decision-making is not performed by individual knowers but by an assemblage of people and instruments in which no one member has full access to every piece of evidence. This is due to decision making teams consisting of members with different kinds of expertise, as well as to organisational and time constraints. This raises important questions for the epistemology of medicine, which is inherently social in this kind of setting, and implies epistemic dependence on others. Trust in these contexts is a highly complex social practice, involving different forms of relationships between trust and reasons for trust: based on reasons, and not based on reasons; based on reasons that are easily accessible to reflection and others that are not. In this paper, we focus on what it means to have reasons to trust colleagues in an established clinical team, collectively supporting or carrying out every day clinical decision-making. We show two important points about these reasons, firstly, they are not sought or given in advance of a situation of epistemic dependence, but are established within these situations; secondly they are implicit in the sense of being contained or nested within other actions that are not directly about trusting another person. The processes of establishing these reasons are directly about accomplishing a task, and indirectly about trusting someone else’s expertise or competence. These processes establish a space of reasons within which what it means to have reasons for trust, or not, gains a meaning and traction in these team-work settings. Based on a qualitative study of decision-making in image assisted diagnosis and treatment of a complex disease called pulmonary hypertension (PH), we show how an intersubjective framework, or ‘space of reasons’ is established through team members forging together a common way of identifying and dealing with evidence. In dealing with images as a central diagnostic tool, this also involves a common way of looking at the images, a common mode or style of perception. These frameworks are developed through many iterations of adjusting and calibrating interpretations in relation to those of others, establishing what counts as evidence, and ranking different kinds of evidence. Implicit trust is at work throughout this process. Trusting the expertise of others in clinical decision-making teams occurs while the members of the team are busy on other tasks, most importantly, building up a framework of common modes of seeing, and common ways of identifying and assessing evidence emerge. It is only in this way that trusting or mistrusting becomes meaningful in these contexts, and that a framework for epistemic dependence is established