The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to...

Elliptic Curve Cryptosystems (ECCs) are utilized as an alternative to traditional publickey cryptosystems, and are more suitable for resource limited environments due to smaller parameter size. In this dissertation we carry out a thorough investigation of side-channel attack aware ECC implementations over finite fields of prime characteristic including the recently introduced Edwards formulatio...

In this paper, a recently proposed evolutionary self-organizing map is extended and applied to visual tracking of objects in video sequences. The proposed approach uses a simple geometric template to track an object executing a smooth movement represented by affine transformations. The template is selected manually in the first frame and consists of a small number of keypoints and the neighborh...

There is a long-standing problem of repeated patterns in correspondence problems, where mismatches frequently occur because inherent ambiguity. The unique position information associated with makes coordinate representations useful supplement to appearance for improving feature correspondences. However, the issue appropriate representation has remained unresolved. In this study, we demonstrate ...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

An extension of a recently proposed evolutionary selforganizing map is introduced and applied to the tracking of objects in video sequences. In the proposed approach, a geometric template consisting of a small number of keypoints is used to track an object that moves smoothly. The coordinates of the keypoints and their neighborhood relations are associated with the coordinates of the nodes of a...

In this paper, a new continuous observer is developed to determine range information (and hence the 3dimensional (3D) coordinates) of an object feature moving with affine motion dynamics (or the more general Riccati motion dynamics) with known motion parameters. The unmeasurable range information is determined from a single camera provided an observability condition is satisfied that has physic...

Public key cryptography is a concept used by many useful functionalities such as digital signature, encryption, key agreements, ... For those needs, elliptic curve cryptography is an attractive solution: for a given level of security, it provides one of the best key sizes and amount of exchanged data. Cryptosystems based on elliptic curve necessitate a costly modular division. Depending on the ...

In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained from the Lagrangian of the system that transforms the system into a partially linear cascade non...

This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient 3P formula in λ-projective coordinates and 5P formula in both affine and λ-projective coordinates. Secondly, extensive experiments have been conducted to test various multi-base scalar multiplication methods (e.g., greedy, ternary/binary, multi...