The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

the immortality of the rational soul is one of the most important issues of ibn sina’s philosophy and anthropology. he poses many arguments in proving this subject. ibn sina proves the immortality of rational soul by not having relation or position of the intelligible concepts, indefinite power of the rational soul in his actions as well as its needlessness to sensible faculties in some of its ...

The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Although it is situated in the core of many modern physical computations, the Radon transform lacks a coherent discrete definition for 2D discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon t...

Training support vector machines (SVM) with indefinite kernels has recently attracted attention in the machine learning community. This is partly due to the fact that many similarity functions that arise in practice are not symmetric positive semidefinite, i.e. the Mercer condition is not satisfied, or the Mercer condition is difficult to verify. Previous work on training SVM with indefinite ke...

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Generalizing [11] we express universal triple Massey products between line bundles on elliptic curves in terms of Hecke's indefinite theta series. We show that all Hecke's indefinite theta series arise in this way.

A Lorentz surface in an indefinite space form is called parallel if its second fundamental form is parallel. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Parallel Lorentz surfaces i...