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Davidov J.,Bulgarian Academy of Science | Davidov J.,Higher School of Civil Engineering
International Journal of Geometric Methods in Modern Physics | Year: 2014

Every almost Hermitian structure (g, J) on a four-manifold M determines a hypersurface ΣJ in the (positive) twistor space of (M, g) consisting of the complex structures anti-commuting with J. In this paper, we find the conditions under which ΣJ is minimal with respect to a natural Riemannian metric on the twistor space in the cases when J is integrable or symplectic. Several examples illustrating the obtained results are also discussed. © 2014 World Scientific Publishing Company. Source


Davidov J.,Bulgarian Academy of Science | Davidov J.,Higher School of Civil Engineering | Grantcharov G.,Florida International University | Mushkarov O.,Bulgarian Academy of Science | Yotov M.,Florida International University
Communications in Mathematical Physics | Year: 2011

In this paper we consider pseudo-bihermitian structures - pairs of complex structures compatible with a pseudo-Riemannian metric. We establish relations of these structures with generalized (pseudo-) Kähler geometry and holomorphic Poisson structures similar to that in the positive definite case. We provide a list of compact complex surfaces which could admit pseudo-bihermitian structures and give examples of such structures on some of them. We also consider a naturally defined null plane distribution on a generalized pseudo-Kähler 4-manifold and show that under a mild restriction it determines an Engel structure. © 2011 Springer-Verlag. Source


Ganchev G.,Bulgarian Academy of Science | Milousheva V.,Bulgarian Academy of Science | Milousheva V.,Higher School of Civil Engineering
International Journal of Geometric Methods in Modern Physics | Year: 2013

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their basic invariants. We find all marginally trapped meridian surfaces of parabolic type and give a geometric construction of these surfaces. © World Scientific Publishing Company. Source


Ganchev G.,Bulgarian Academy of Science | Milousheva V.,Bulgarian Academy of Science | Milousheva V.,Higher School of Civil Engineering
Journal of Mathematical Physics | Year: 2012

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the derivative formulas for this frame field we obtain seven invariant functions. Our main theorem states that these seven invariants determine the surface up to a motion in Minkowski space. We introduce meridian surfaces as one-parameter systems of meridians of a rotational hypersurface in the four-dimensional Minkowski space. We find all marginally trapped meridian surfaces. © 2012 American Institute of Physics. Source


Partov D.,Higher School of Civil Engineering | Kantchev V.,HSCE L.Karavelov
Central European Journal of Engineering | Year: 2011

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann - Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete Ec(t) is assumed to be constant in time 't'. The obtained results from the both models are compared. © Versita sp. z o.o. Source

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