Природний підхід у концепції індивідуального виховання Герберта Спенсера

During the XIX century the European society had profound changes in the philosophy of life. That was the development of individualism: the new social conditions associated with the Industrial Revolution formed a new type of a personality that outlined his/her contacts with society on the basis of goods and money relations. Focusing on individual cultural goals and radical response to the conditions dictated by public opinion were realized in the works of the English philosopher Herbert Spencer (1820-1903). The pedagogy of H. Spencer consists of the following problems which are: the problem of selfdevelopment of a child; establishment of the successful system of self-education and training which is based on the "natural method of education" [8] and training of parents for their duties; thirdly, changes in educational programmes abandoning old forms of work and study; fourth, teachers and parents have to discover a child in order to contribute to its successful physical and moral development. The famous book by Herbert Spencer "Education: intellectual, moral, and physical" seemed to be the key to the regeneration of society. The author skilfully contrasted natural laws to the necessity to adhere to the old traditional beliefs in education. It is known that Herbert Spencer advised major Japanese diplomats and ministers on general policy and reorganization of education. We may find interesting propositions in the works of Spencer, particularly he writes about the necessity to teach pedagogy at school as future parents should know basic principles of educating and upbringing children. Another interesting thought of H. Spencer is if a child got accustomed to immediate response of the parents to his actions and having become an adult is incapable independently assess the results of his actions. Perhaps the philosopher is right when indicates that the method of education with the help of "natural consequences" teaches the educators to analyze their own motives more seriously. Herbert Spencer followed democratic and progressive views. He singled out the following general tasks of education as full development of a child, specifying the full description of intellectual, moral and physical development. The educational views of H. Spencer and his theoretical and practical contribution to solving the problem of individual education of children in public and family education were systematised and analysed. General tasks of education as full development of a child, specifying the full description of intellectual, moral and physical development were singled out. В статті представлено аналіз педагогічних поглядів англійського філософа Герберта Спенсера та його концепції індивідуального підходу у розумовому, моральному та фізичному вихованні. Було проаналізовано та систематизовано теоретичний та практичний внесок Г. Спенсера у вирішення проблеми індивідуального виховання дітей в рамках громадської та сімейної освіти. В статье представлен анализ педагогических взглядов английского философа Герберта Спенсера и его концепции индивидуального подхода в умственном, нравственном и физическом воспитании. Были проанализированы и систематизированы теоретический и практический вклад Г. Спенсера в решение проблемы индивидуального воспитания детей в рамках общественного и семейного воспитания

On deformation theory of quantum vertex algebras

We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an assocative algebra. We show that this system of equations results from an action principle. This might be the starting point for a perturbative treatment of the deformation problem of quantum vertex algebras. Our action generalizes the action of the Kodaira-Spencer theory of gravity and might therefore also be of relevance for applications in string theory.Comment: 22 page

Algebraic connections on ellipsoid surfaces

This paper is part of a series of papers where the aim is to give explicit formulas for algebraic differential operators on a finitely generated projective module E on a commutative unital ring A. In previous papers on the subject the Kodaira-Spencer map and Kodaira-Spencer class was used to give explicit formulas for flat algebraic connections on a class of maximal Cohen-Macaulay modules on isolated hypersurface singularities. In this paper we give explicit formulas for algebraic connections on a class of finitely generated projective modules on ellipsoid surfaces. The connections we construct are non-flat with trace of curvature equal to zero. We construct these formulas using the fundamental matrix M of the module E. This matrix may in the case when A is a finitely generated algebra over a field be calculated using Groebner bases. We also discuss a possible relationship to algebraic cycles and a problem on existence of holomorphic connections in complex analysis.Comment: Example 2.21 added. A minor correction to Example 3.1

Sociology

Sociology emerged in response to the problem of social order in modern society in the wake of the American and French Revolutions and the rise of industrialism and market capitalism. Sociology had its roots in the theories of August Comte and Herbert Spencer and in empirical work previously conducted by census bureaus, state labor boards, and reform organizations. By the 1880s, sociologists had perceived a threat in the alliance with biology: It undercut the need for a separate discipline and, in Spencer\u27s laissez-faire version, tainted the discipline among social reformers and other constituencies crucial to its success. In Dynamic Sociology, the American Lester Frank Ward addressed both issues. On the surface, American and European sociology during the interwar decades was a study in contrasts. The 1960s spelled the end of \u27modern\u27 sociology. In the United States, Parsons\u27s hegemony and Merton\u27s \u27middle range\u27 compromise gave way to a politically charged humanist/positivist divide

Clausius/Cosserat/Maxwell/Weyl Equations: The Virial Theorem Revisited

In 1870, R. Clausius found the virial theorem which amounts to introduce the trace of the stress tensor when studying the foundations of thermodynamics, as a way to relate the absolute temperature of an ideal gas to the mean kinetic energy of its molecules. In 1901, H. Poincar{\'e} introduced a duality principle in analytical mechanics in order to study lagrangians invariant under the action of a Lie group of transformations. In 1909, the brothers E. and F. Cosserat discovered another approach for studying the same problem though using quite different equations. In 1916, H. Weyl considered again the same problem for the conformal group of transformations, obtaining at the same time the Maxwell equations and an additional specific equation also involving the trace of the impulsion-energy tensor. Finally, having in mind the space-time formulation of electromagnetism and the Maurer-Cartan equations for Lie groups, gauge theory has been created by C.N. Yang and R.L. Mills in 1954 as a way to introduce in physics the differential geometric methods available at that time, independently of any group action, contrary to all the previous approaches. The main purpose of this paper is to revisit the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups, mostly developped by D.C Spencer and coworkers around 1970. In particular, we justify and extend the virial theorem, showing that the Clausius/Cosserat/Maxwell/Weyl equations are nothing else but the formal adjoint of the Spencer operator appearing in the canonical Spencer sequence for the conformal group of space-time and are thus totally dependent on the group action. The duality principle also appeals to the formal adjoint of a linear differential operator used in differential geometry and to the extension modules used in homological algebra.Comment: This paper must be published under the title "From Thermodynamics to Gauge Theory: The Viral Theorem Revisited" as a chapter of a forthcoming book "Gauge Theory and Differential Geometry" published by Nova Editors

Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations

We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-K\"ahler theorem. We consider a linear partial differential operator $P$ given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that $P$ is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor $R$ of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds