We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove th...

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

Humans use multiple mental models of the world to reason efficiently at different levels of abstraction. Current geographic information systems (GIS) normally use only a single model or representation of the world. If only a single level of abstraction is supported, the utility of the system is limited. Future GIS should support multiple representations at different levels of abstraction, so th...

We present a method of proving existence of center manifolds within specified domains. The method is based on a combination of topological tools, normal forms, and rigorous computer-assisted computations. We apply our method to obtain a proof of a center manifold in an explicit region around the equilibrium point L1 in the Earth–Sun planar restricted circular three-body problem.

In this paper we first characterize all quasi–homogeneous but non–homogeneous planar polynomial differential systems of degree five, and then among which we classify all the ones having a center at the origin. Finally we present the topological phase portrait of the systems having a center at the origin.

In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes the topological category (local max, min, slope, saddle) of the gray level landscape around the center region. Given a 2D grayscale image I, our goal is to obtain a simplified image which can be seen as “minimal” representation in terms of topological characterization of I....