‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

In this paper, acoustic waves radiated from the running vehicles, measured by road-side instrument, are utilized for intelligent classification of vehicle type (truck, tractor and car) based on dimension reduction. To improve the accuracy rate and real-time performance of the system, dimension reduction technique as principal component analysis (PCA) and rough set (RS) are adapted to deal with ...

We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov-Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well-suited for the ...

β8 integrin regulates neurogenesis and neurovascular homeostasis in the adult brain Aaron K. Mobley, Jeremy H. Tchaicha, Jaekyung Shin, Mohammad G. Hossain and Joseph H. McCarty Journal of Cell Science 122, 2322 (2009) doi:10.1242/jcs.055939 There were errors published in J. Cell Sci. 122, 1842-1851. In Fig. 3, panels A and C (rather than A and B) were mistakenly labeled as wild type and panels...

We study the range of a classifiable class A of unital separable simple amenable C∗algebras which satisfy the Universal Coefficient Theorem. The class A contains all unital simple AH-algebras. We show that all unital simple inductive limits of dimension drop circle C∗-algebras are also in the class. This unifies some of the previous known classification results for unital simple amenable C∗-alg...

It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display genomic signature in chaos game representation is obtained by eliminating effects of the finite sequence. The optimal string length is further shown as a sel...

In this contribution I discuss transverse momentum dependent quark distributions and their operator structure. Some of the experimental signatures in particular in Drell-Yan scattering are given.

A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motio...

A new type of fractal measures Xs 1 < s < 2, defined on the subsets of the graph of a continuous function is introduced. The J-dimension defined by this measure is 'closer' to the Hausdorff dimension than the other fractal dimensions in recent literatures. For the Weierstrass type functions defined by W(x) = A-aig(Aix), where A > 1, 0 < a < 1, and g is an almost periodic Lipschitz function of o...

OBJECTIVE Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. RESEARCH DESIGN AND METHODS We conducted a cross-sectional study ...