Lax Tensors, Killing Tensors and Geometric Duality

The solution of the Lax tensor equations in the case $L_{\alpha\beta\gamma}=-L_{\beta\alpha\gamma}$ was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two dimensional metrics having the symmetric Lax tensor $L_{\alpha\beta\gamma}$. The Lax tensors of the flat space, Rindler system and its dual were found.Comment: 9 pages LATE

A new integrable generalization of the Korteweg - de Vries equation

A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.Comment: 13 pages, 2 figure

Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy

Recently proposed nonholonomic deformation of the KdV equation is solved through inverse scattering method by constructing AKNS-type Lax pair. Exact and explicit N-soliton solutions are found for the basic field and the deforming function showing an unusual accelerated (decelerated) motion. A two-fold integrable hierarchy is revealed, one with usual higher order dispersion and the other with novel higher nonholonomic deformations.Comment: 7 pages, 2 figures, latex. Exact explicit exact N-soliton solutions (through ISM) for KdV field u and deforming function w are included. Version to be published in J. Phys.

Right to development and emotional exhaustion: The case of healthcare institutions in Turkey

Right to development covers economic, social, cultural, and political development. Encouraging its subjects to participate actively in economic, social, cultural, and political development, right to development has significant impact on each person. Although it is wide in scope, person, being the central subject of development, this study focuses on right to development of health care professionals limited to doctors and nurses. This paper assessed right to development of health care staff, considering their work conditions and other demographic characteristics. For the implementation of regulations regarding to right to development, a significant fieldwork covering 20 health care institutions in three cities of Turkey was successfully completed. In this fieldwork, Maslach Burnout Inventory (MBI) was used for data collection. This article assessed emotional exhaustion of 185 health workers via SPSS program. The analyse found that education status and type of health care institution have effect on emotional exhaustion while other demographic characteristics such as work experience, annual income or the city were found non-effective on emotional exhaustion of health care professionals. Considering results of this fieldwork, the correlation of emotional exhaustion with the right to development was discussed. The findings reveal that the fear of aggression, lack of sufficient trainings, defamation or mobbing by senior doctors are potential adverse effects causing emotional exhaustion of health workers. To decrease emotional exhaustion caused by work, institutions are suggested to provide ongoing training or a sustainable method for decrement of patient burden and workload. Last but not least, as a sustainable solution, a national wide precise legal monitoring mechanism covering both public and private, ordinary and university health care institutions is strictly offered to be created for prevention of infringement on right to development of medical staff

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we provide an algebraic construction for the negative even mKdV hierarchy which gives rise to time evolutions associated to even graded Lie algebraic structure. We propose a modification of the dressing method, in order to incorporate a non-trivial vacuum configuration and construct a deformed vertex operator for $\hat{sl}(2)$, that enable us to obtain explicit and systematic solutions for the whole negative even grade equations

Time-dependent recursion operators and symmetries

The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve this problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion operators need modification. A general formula is given for the missing term of the recursion operators. Apart from the recursion operators a method is introduced to calculate the correct symmetries. For illustrations several examples of scalar and coupled system of equations are considered

Analysis of roof live loads in industrial buildings

In design, structural engineers must have a clear understanding of live loads, both qualitatively and statistically. For decades, multiple studies have been published that relate live loads for floor loads in various occupancies such as offices and residences. However, survey data or probabilistic live load models for industrial building roofs are difficult to find. There are recommendations in major standards used in the modern world that give design live load values for roofs based on the accessibility of the rooftops. On the other hand, engineers may not understand the origin of these values. Comparison is made between current U.S standards for roof live loads and standards used in other parts of the world. To ensure that the most accurate live load assessment is implemented in the design, our understanding of live loads should be updated on a regular basis. Furthermore, in the United States, the current roof live load design value is 0.96 kN/m2 (20 psf), which is much greater than the values recommended by European, Australian, and Chinese standards. As a result, determining the source of live load on industrial building roofs is essential. To cover the gap in the literature, this article gives survey methodology and probabilistic studies related to design live load value on roofs. The sensitivity of existing probabilistic models to mean, variance, and time duration was also investigated.This work is part of the research project Roof Live Load Models for Metal Buildings which is sponsored by the Metal Building Manufacturers Association (MBMA) and the Steel Deck Institute (SDI). The authors would like to thank Dr. Zhanjie Li, Associate Professor at Suny Polytechnic, for his help translating the Chinese standards

Algebraic properties of Gardner's deformations for integrable systems

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear

Dynamics and stability of the Godel universe

We use covariant techniques to describe the properties of the Godel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Godel model depends primarily upon the presence of gradients in the centrifugal energy, and secondarily on the equation of state of the fluid. The latter dictates the behaviour of the model when dealing with homogeneous perturbations. The vorticity of the perturbed Godel model is found to evolve as in almost-FRW spacetimes, with some additional directional effects due to shape distortions. We also consider gravitational-wave perturbations by investigating the evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave equation, which argues for the neutral stability of the Godel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Godel cosmologies are also discussed.Comment: Revised version, to match paper published in Class. Quantum Gra