An iterative Wiener filtering method based on the gravity gradient invariants

How to deal with colored noises of GOCE （Gravity field and steady - state Ocean Circulation Explorer） satellite has been the key to data processing. This paper focused on colored noises of GOCE gradient data and the frequency spectrum analysis. According to the analysis results, gravity field model of the optima] degrees 90-240 is given, which is recovered by COCE gradient data. This paper presents an iterative Wiener filtering method based on the gravity gradient invariants. By this method a degree-220 model was calculated from GOCE SGG （Satellite Gravity Gradient） data. The degrees above 90 of ITG2010 were taken as the prior gravity field model, replacing the low degree gravity field model calculated by GOCE orbit data. GOCE gradient colored noises was processed by Wiener filtering. Finally by Wiener filtering iterative calculation, the gravity field model was restored by space-wise harmonic analysis method. The results show that the model＇s accuracy matched well with the ESA＇s （European Space Agency） results by using the same data,

Signed Tilings by Ribbon L n-Ominoes, n Even, via Gröbner Bases

Let Tn be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T+n be Tn with an extra 2 x 2 square. We investigate signed tilings of rectangles by Tn and T+n . We show that a rectangle has a signed tiling by Tn if and only if both sides of the rectangle are even and one of them is divisible by n, or if one of the sides is odd and the other side is divisible by . We also show that a rectangle has a signed tiling by T+n, n≥6 even, if and only if both sides of the rectangle are even, or if one of the sides is odd and the other side is divisible by . Our proofs are based on the exhibition of explicit GrÖbner bases for the ideals generated by polynomials associated to the tiling sets. In particular, we show that some of the regular tiling results in Nitica, V. (2015) Every tiling of the first quadrant by ribbon L n-ominoes follows the rectangular pattern. Open Journal of Discrete Mathematics, 5, 11-25, cannot be obtained from coloring invariants.

Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner Bases

We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.

Image matching algorithm based on SIFT using color and exposure information

Image matching based on scale invariant feature transform（SIFT） is one of the most popular image matching algorithms, which exhibits high robustness and accuracy. Grayscale images rather than color images are generally used to get SIFT descriptors in order to reduce the complexity. The regions which have a similar grayscale level but different hues tend to produce wrong matching results in this case. Therefore, the loss of color information may result in decreasing of matching ratio. An image matching algorithm based on SIFT is proposed, which adds a color offset and an exposure offset when converting color images to grayscale images in order to enhance the matching ratio. Experimental results show that the proposed algorithm can effectively differentiate the regions with different colors but the similar grayscale level, and increase the matching ratio of image matching based on SIFT. Furthermore, it does not introduce much complexity than the traditional SIFT.

New structures for colored HOMFLY-PT invariants

In this paper,we present several new structures for the colored HOMFLY-PT(Hoste-Ocneanu-Millet-Freyd-Lickorish-Yetter-Przytycki-Traczyk)invariants of framed links.First,we prove the strong integrality property for the normalized colored HOMFLY-PT invariants by purely using the HOMFLY-PT skein theory developed by Morton and his collaborators.By this strong integrality property,we immediately obtain several symmetric properties for the full colored HOMFLY-PT invariants of links.Then we apply our results to refine the mathematical structures appearing in the Labastida-Mari?o-Ooguri-Vafa(LMOV)integrality conjecture for framed links.As another application of the strong integrality,we obtain that the q=1 and a=1 specializations of the normalized colored HOMFLY-PT invariant are well-defined link polynomials.We find that a conjectural formula for the colored Alexander polynomial which is the a=1 specialization of the normalized colored HOMFLY-PT invariant implies that a special case of the LMOV conjecture for framed knots holds.