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This article studies the Bowen-Margulis-Sullivan (BMS) measures on non-compact manifolds without conjugate points. The finiteness of this measure on the unit tangent space indicates some important dynamical properties. Under the assumptions of uniform visibility axiom and Axiom 2, we give a criterion when the BMS measure is finite.

The use of the barycentre map between two copies of ℝn , the first one with a metric without conjugate points, the second one with the canonical flat metric, allows to prove in a simplified way the fact that Riemannian tori without conjugate points are flat, as conjectured by Hopf in 1948 and proved definitively by Burago and Ivanov in 1994.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means of subordination, the analytic parts of which are reciprocal starlike (or convex) functions. Further, by combining with the graph of the function, we discuss the bound of the Bloch constant and the norm of the pre-Schwarzian derivative for the classes.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means of subordination, the analytic parts of which are reciprocal starlike (or convex) functions. Further, we discuss the geometric properties of the classes, such as the integral expression, coefficient estimation, distortion theorem, Jacobian estimation, growth estimates, and covering theorem.

A large number of evenly distributed conjugate points (CPs) in entirely overlapping regions of the images are required to achieve successful co-registration between very-high-resolution (VHR) remote sensing images. The CPs are then used to construct a non-linear transformation model that locally warps a sensed image to a reference image’s coordinates. Piecewise linear (PL) transformation is largely exploited for warping VHR images because of its superior performance as compared to the other methods. The PL transformation constructs triangular regions on a sensed image from the CPs by applying the Delaunay algorithm, after which the corresponding triangular regions in a reference image are constructed using the same CPs on the image. Each corresponding region in the sensed image is then locally warped to the regions of the reference image through an affine transformation estimated from the CPs on the triangle vertices. The warping performance of the PL transformation shows reliable results, particularly in regions inside the triangles, i.e., within the convex hulls. However, the regions outside the triangles, which are warped when the extrapolated boundary planes are extended using CPs located close to the regions, incur severe geometric distortion. In this study, we propose an effective approach that focuses on the improvement of the warping performance of the PL transformation over the external area of the triangles. Accordingly, the proposed improved piecewise linear (IPL) transformation uses additional pseudo-CPs intentionally extracted from positions on the boundary of the sensed image. The corresponding pseudo-CPs on the reference image are determined by estimating the affine transformation from CPs located close to the pseudo-CPs. The latter are simultaneously used with the former to construct the triangular regions, which are enlarged accordingly. Experiments on both simulated and real datasets, constructed from Worldview-3 and Kompsat-3A satellite images, were conducted to validate the effectiveness of the proposed IPL transformation. That transformation was shown to outperform the existing linear/non-linear transformation models such as an affine, third and fourth polynomials, local weighted mean, and PL. Moreover, we demonstrated that the IPL transformation improved the warping performance over the PL transformation outside the triangular regions by increasing the correlation coefficient values from 0.259 to 0.304, 0.603 to 0.657, and 0.180 to 0.338 in the first, second, and third real datasets, respectively.

The aim of the present paper is to find the necessary and sufficient conditions for subclasses of starlike functions with respect to symmetric points, starlike functions with respect to conjugate points, starlike functions with respect to symmetric conjugate points associated with Pascal distribution series and inclusion relations for such subclasses in the open unit disk U. Further, we consider an integral operator related to Pascal distribution series. Keywords: Analytic functions, Starlike functions with respect to symmetric points, Starlike functions with respect to conjugate points, Starlike functions with respect to symmetric conjugate points, Pascal distribution series. AMS Subject Classification: 30C45.

We present and investigate two additional subclasses of bi-univalent functions corresponding to symmetric and symmetric conjugate points in the open unit disc employing the Al-Oboudi operator. The initial coefficients of functions assigned to these classes are estimated.

Gastric cancer stem cells (CSCs) are important for the initiation, growth, recurrence, and metastasis of gastric cancer, due to their chemo-resistance and indefinite proliferation. Herein, to eliminate gastric CSCs, we developed novel CSC-targeting glioma-associated oncogene homolog 1 ( ) small interfering RNA (siRNA) nanoparticles that are specifically guided by a di-stearoyl-phosphatidyl-ethanolamine- hyaluronic-acid (DSPE-HA) single-point conjugate, as an intrinsic ligand of the CD44 receptor. We refer to these as targeting Gli1 siRNA nanoparticles. We used the reductive amination reaction method for attaching amine groups of DSPE to aldehydic group of hyaluronic acid (HA) at the reducing end, to synthesize the DSPE-HA single-point conjugate. Next, targeting Gli1 siRNA nanoparticles were prepared using the layer-by-layer assembly method. We characterized the stem cellular features of targeting Gli1 siRNA nanoparticles, including their targeting efficiency, self-renewal capacity, the migration and invasion capacity of gastric CSCs, and the penetration ability of 3D tumor spheroids. Next, we evaluated the therapeutic efficacy of the targeting Gli1 siRNA nanoparticles by using in vivo relapsed tumor models of gastric CSCs. Compared with the multipoint conjugates, DSPE-HA single-point conjugates on the surface of nanoparticles showed significantly higher binding affinities with CD44. The targeting Gli1 siRNA nanoparticles significantly decreased Gli1 protein expression, inhibited CSC tumor spheroid and colony formation, and suppressed cell migration and invasion. Furthermore, in vivo imaging demonstrated that targeting Gli1 siRNA nanoparticles accumulated in tumor tissues, showing significant antitumor recurrence efficacy in vivo. In summary, our targeting Gli1 siRNA nanoparticles significantly inhibited CSC malignancy features by specifically blocking Hedgehog (Hh) signaling both in vitro and in vivo, suggesting that this novel siRNA delivery system that specifically eliminates gastric CSCs provides a promising targeted therapeutic strategy for gastric cancer treatment.

Kompsat-3/3A provides along-track and across-track stereo data for accurate three-dimensional (3D) topographic mapping. Stereo data preprocessing involves conjugate point extraction and acquisition of ground control points (GCPs), rational polynomial coefficient (RPC) bias compensation, and epipolar image resampling. Applications where absolute positional accuracy is not a top priority do not require GCPs, but require precise conjugate points from stereo images for subsequent RPC bias compensation, i.e., relative orientation. Conjugate points are extracted between the original stereo data using image-matching methods by a proper outlier removal process. Inaccurate matching results and potential outliers produce geometric inconsistency in the stereo data. Hence, the reliability of conjugate point extraction must be improved. For this purpose, we proposed to apply the coarse epipolar resampling using raw RPCs before the conjugate point matching. We expect epipolar images with even inaccurate RPCs to show better stereo similarity than the original images, providing better conjugate point extraction. To this end, we carried out the quantitative analysis of the conjugate point extraction performance by comparing the proposed approach using the coarsely epipolar resampled images to the traditional approach using the original stereo images. We tested along-track Kompsat-3 stereo and across-track Kompsat-3A stereo data with four well-known image-matching methods: phase correlation (PC), mutual information (MI), speeded up robust features (SURF), and Harris detector combined with fast retina keypoint (FREAK) descriptor (i.e., Harris). These matching methods were applied to the original stereo images and coarsely resampled epipolar images, and the conjugate point extraction performance was investigated. Experimental results showed that the coarse epipolar image approach was very helpful for accurate conjugate point extraction, realizing highly accurate RPC refinement and sub-pixel y-parallax through fine epipolar image resampling, which was not achievable through the traditional approach. MI and PC provided the most stable results for both along-track and across-track test data with larger patch sizes of more than 400 pixels.

By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class Σ, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients a2 and a3 for the functions in this new subclass of Σ are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries.