We discuss construction and applications of instanton-like objects which we call fractional space-like branes. These objects are localised at a fixed point of a time-like (or more generally space-time) orbifold which is a string theoretical toy model of a cosmological singularity. We formulate them in boundary state, adsorption, and fermionisation approaches. 1 Fractional space-like branes in a...

In this paper, we get the time evolution equations of curvature and torsion evolving spacelike curves in Minkowski space. Also, give inextensible evolutions timelike ruled surfaces that are produced by normal binormal vector fields curve derive necessary conditions for an inelastic surface evolution. Then, compute coefficients first second fundamental forms, Gauss mean curvatures special surfac...

In 1946, Paul Erdős posed a problem of determining the largest possible cardinality of an isosceles set, i.e., a set of points in plane or in space, any three of which form an isosceles triangle. Such a question can be asked for any metric space, and an upper bound ( n+2 2 ) for the Euclidean space E was found by Blokhuis [3]. This upper bound is known to be sharp for n = 1, 2, 6, and 8. We wil...

We address the question of which function spaces are invariant under the action of scalar conservation laws in one and several space dimensions. We establish two types of results. The rst result shows that if the initial data is in a rearrangement-invariant function space, then the solution is in the same space for all time. Secondly, we examine which smoothness spaces among the Besov spaces ar...

in this paper, we study fuzzy substructures in connection withhv-structures. the original idea comes from geometry, especially from thetwo dimensional euclidean vector space. using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. we connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as hv-groups...