Sturm Liouville Problem with Moving Discontinuity Points

In this paper, we present a new discontinuous Sturm Liouville problem with symmetrically located discontinuities which are defined depending on a neighborhood of a midpoint of the interval. Also the problem contains an eigenparameter in one of the boundary conditions and has coupled transmission conditions at the discontinuity points. We investigate the properties of the eigenvalues, obtain asymptotic formulas for the eigenvalues and the corresponding eigenfunctions and construct Green's function of this problem.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1210.4350 by other author

Sampling Theorems for Sturm Liouville Problem with Moving Discontinuity Points

In this paper, we investigate the sampling analysis for a new Sturm-Liouville problem with symmetrically located discontinuities which are defined to depending on a neighborhood of a midpoint of the interval. Also the problem has transmission conditions at these points of discontinuity and includes an eigenparameter in a boundary condition. We establish briefly the needed relations for the derivations of the sampling theorems and construct Green's function for the problem. Then we derive sampling representations for transforms whose kernels are either solutions or Green's functions.Comment: 11 page

GCD matrices, posets, and nonintersecting paths

We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.Comment: 10 pages, see related papers at http://www.math.msu.edu/~saga

Metakritik der Literatur

Metakritik der Literatur. Lob des Theaters

Schopenhauers praktische Kognition: Die Philosophie für die Philosophie.

Schopenhauers Kritik der Dialektik stellt die Methode als äußerst flaches, 2 dimensionales dar; wie gerufen für die bildende Kunst. Hieße der Leitspruch zu Schopenhauers Lebzeit schon "l´art pour l´art", wäre Schopenhauer vielleicht ein Spruch wie "Philosophie für Philosophie" dazu eingefallen

Eigenvalue Problem with Moving Discontinuity Points

In this paper, we present a Sturm Liouville problem which has discontinuities in the neighborhood of the midpoint of an interval. Also the problem contains an eigenparameter in one of the boundary conditions. We derive operator theoretic formulation in suitable Hilbert space, give some properties of the eigenvalues and obtain asymptotic formulas for the eigenvalues and the corresponding eigenfunctions

Source Camera Verification from Strongly Stabilized Videos

Image stabilization performed during imaging and/or post-processing poses one of the most significant challenges to photo-response non-uniformity based source camera attribution from videos. When performed digitally, stabilization involves cropping, warping, and inpainting of video frames to eliminate unwanted camera motion. Hence, successful attribution requires the inversion of these transformations in a blind manner. To address this challenge, we introduce a source camera verification method for videos that takes into account the spatially variant nature of stabilization transformations and assumes a larger degree of freedom in their search. Our method identifies transformations at a sub-frame level, incorporates a number of constraints to validate their correctness, and offers computational flexibility in the search for the correct transformation. The method also adopts a holistic approach in countering disruptive effects of other video generation steps, such as video coding and downsizing, for more reliable attribution. Tests performed on one public and two custom datasets show that the proposed method is able to verify the source of 23-30% of all videos that underwent stronger stabilization, depending on computation load, without a significant impact on false attribution