Abstract: Regularity has often been present in the form of regular
polyhedra or tessellations; classical examples are the nine regular
polyhedra consisting of the five Platonic solids (regular convex
polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes
can be seen as regular maps. Maps are cellular embeddings of
graphs (with possibly multiple edges, loops or dangling edges) on
compact connected (closed) surfaces with or without boundary. The
n-dimensional abstract polytopes, particularly the regular ones, have
gained popularity over recent years. The main focus of research
has been their symmetries and regularity. Planification of polyhedra
helps its spatial construction, yet it destroys its symmetries. To our
knowledge there is no “planification” for n-dimensional polytopes.
However we show that it is possible to make a “surfacification”
of the n-dimensional polytope, that is, it is possible to construct a
restrictedly-marked map representation of the abstract polytope on
some surface that describes its combinatorial structures as well as
all of its symmetries. We also show that there are infinitely many
ways to do this; yet there is one that is more natural that describes
reflections on the sides ((n−1)-faces) of n-simplices with reflections
on the sides of n-polygons. We illustrate this construction with the
4-tetrahedron (a regular 4-polytope with automorphism group of size
120) and the 4-cube (a regular 4-polytope with automorphism group
of size 384).
Abstract: In recent years, the social economy is increasingly seen as a viable means to address social problems. Social enterprises, as well as public projects and initiatives targeted to meet social purposes, offer organizational models that assume heterogeneity, flexibility and adaptability to the ‘real world and real problems’. Despite the growing popularity of social initiatives, decision makers still face a paucity in what concerns the available models and tools to adequately assess its sustainability, and its impacts, notably the nature of its contribution to economic growth. This study was carried out at the local level, by analyzing the social impact initiatives and projects promoted by the Municipality of Albergaria-a-Velha (Câmara Municipal de Albergaria-a-Velha -CMA), a municipality of 25,000 inhabitants in the central region of Portugal. This work focuses on the challenges related to the qualifications and employability of citizens, which stands out as one of the key concerns in the Portuguese economy, particularly expressive in the context of small-scale cities and inland territories. The study offers a characterization of the Municipality, its socio-economic structure and challenges, followed by an exploratory analysis of multiple sourced data, collected from the CMA's documental sources as well as from privileged informants. The purpose is to conduct detailed analysis of the CMA's social projects, aimed at characterizing its potential impact for the model of qualifications and employability of the citizens of the Municipality. The study encompasses a discussion of the socio-economic profile of the municipality, notably its asymmetries, the analysis of the social projects and initiatives, as well as of data derived from inquiry actors involved in the implementation of the social projects and its beneficiaries. Finally, the results obtained with the Better Life Index will be included. This study makes it possible to ascertain if what is implicit in the literature goes to the encounter of what one experiences in reality.
Abstract: The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qi, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.
Abstract: A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.
Abstract: In this paper, we have investigated the nonlinear
time-fractional hyperbolic partial differential equation (PDE) for
its symmetries and invariance properties. With the application of
this method, we have tried to reduce it to time-fractional ordinary
differential equation (ODE) which has been further studied for exact
solutions.
Abstract: An experimental study of the turbulent near wake of a rotating circular cylinder was made at a Reynolds number of 2000 for velocity ratios, λ between 0 and 2.7. Particle image velocimetry data are analyzed to study the effects of rotation on the flow structures behind the cylinder. The results indicate that the rotation of the cylinder causes significant changes in the vortex formation. Kármán vortex shedding pattern of alternating vortices gives rise to strong periodic fluctuations of a vortex street for λ < 2.0. Alternate vortex shedding is weak and close to being suppressed at λ = 2.0 resulting a distorted street with vortices of alternating sense subsequently being found on opposite sides. Only part of the circulation is shed due to the interference in the separation point, mixing in the base region, re-attachment, and vortex cut-off phenomenon. Alternating vortex shedding pattern diminishes and completely disappears when the velocity ratio is 2.7. The shed vortices are insignificant in size and forming a single line of vortex street. It is clear that flow asymmetries will deteriorate vortex shedding, and when the asymmetries are large enough, total inhibition of a periodic street occurs.
Abstract: Einstein vacuum equations, that is a system of nonlinear
partial differential equations (PDEs) are derived from Weyl metric
by using relation between Einstein tensor and metric tensor. The
symmetries of Einstein vacuum equations for static axisymmetric
gravitational fields are obtained using the Lie classical method. We
have examined the optimal system of vector fields which is further
used to reduce nonlinear PDE to nonlinear ordinary differential
equation (ODE). Some exact solutions of Einstein vacuum equations
in general relativity are also obtained.
Abstract: In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Abstract: The aim of this paper is to explain what a multienterprise tie is, what evidence its analysis provides and how does the cooperation mechanism influence the establishment of a multienterprise tie. The study focuses on businesses of smaller dimension, geographically dispersed and whose businessmen are learning to cooperate in an international environment. The empirical evidence obtained at this moment permits to conclude the following: The tie is not long-lasting, it has an end; opportunism is an opportunity to learn; the multi-enterprise tie is a space to learn about the cooperation mechanism; the local tie permits a businessman to alternate between competition and cooperation strategies; the disappearance of a tie is an experience of learning for a businessman, diminishing the possibility of failure in the next tie; the cooperation mechanism tends to eliminate hierarchical relations; the multienterprise tie diminishes the asymmetries and permits SME-s to have a better position when they negotiate with large companies; the multi-enterprise tie impacts positively on the local system. The collection of empirical evidence was done trough the following instruments: direct observation in a business encounter to which the businesses attended in 2003 (202 Mexican agro industry SME-s), a survey applied in 2004 (129), a questionnaire applied in 2005 (86 businesses), field visits to the businesses during the period 2006-2008 and; a survey applied by telephone in 2008 (55 Mexican agro industry SME-s).
Abstract: Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.
Abstract: We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.
Abstract: Textures are replications, symmetries and
combinations of various basic patterns, usually with some random
variation one of the gray-level statistics. This article proposes a
new approach to Segment texture images. The proposed approach
proceeds in 2 stages. First, in this method, local texture information
of a pixel is obtained by fuzzy texture unit and global texture
information of an image is obtained by fuzzy texture spectrum.
The purpose of this paper is to demonstrate the usefulness of fuzzy
texture spectrum for texture Segmentation.
The 2nd Stage of the method is devoted to a decision process,
applying a global analysis followed by a fine segmentation,
which is only focused on ambiguous points. The above Proposed
approach was applied to brain image to identify the components
of brain in turn, used to locate the brain tumor and its Growth
rate.