Let E be an elliptic curve over the finite field Fq, P a point in E(Fq) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*q , the multiplicative group of nonzero elements of Fq, in the case where n ï q - 1, using GENERALIZED JACOBIAN of E.

In a (t; n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper we propose a veri able (t; n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logarithm problem (ECDLP) by using GENERALIZED JACOBIAN of elliptic curves. The proposed scheme has all the bene ts of Shao and Cao, however, our scheme no need to a secure channel. Furthermore, we exploit the techniques via elliptic curves to perform the scheme. This can be very important, because the hardness of discrete logarithm problem on elliptic curves increases security of the proposed scheme.

In this paper we propose two simultaneous image registration (IR) and super-resolution (SR) methods using a novel approach in calculating the JACOBIAN matrix. SR is the process of fusing several low resolution (LR) images to reconstruct a high resolution (HR) image, however, as an inverse problem, it consists of three principal operations of warping, blurring and down-sampling that should be applied sequentially to the desired HR image to produce the existing LR images. Unlike the previous methods, we neither calculate the JACOBIAN matrix numerically nor derive it by treating the three principal operations separately. We develop a new approach to derive the JACOBIAN matrix analytically from the combination of the three principal operations. In this approach, a Gaussian kernel (as it is more realistic in a wide range of applications) is considered for blurring, which can be adaptively resized for each LR image. The main intended method is established by applying the aforementioned ideas to the joint methods, a class of simultaneous iterative methods in which the incremental values for both registration parameters and HR image are obtained by solving one linear system of equations per iteration. Our second proposed method is formed by applying these ideas to the alternating minimization (AM) methods, a class of simultaneous iterative methods in which the incremental values of registration parameters are obtained after calculating the HR image at each iteration. The results show that our proposed joint and AM methods are superior to the recently proposed methods such as Tian's joint and Hardie's AM methods respectively.

It is well known that, one of the useful and rapid methods for a non-linear system of algebraic equations is Newton's method. Newton's method has at least quadratic convergence when the JACOBIAN is a nonsingular matrix in a neighbor-hood of the solution. In this paper, a di, erential continuation method is presented for solving the nonlinear system of algebraic equations whose JACOBIAN matrix is singular at the solution. For this purpose, at , rst, an auxiliary equation named the homo-topy equation is constructed. Then, by di, erentiating from the homotopy equation, a system of di, erential equations is replaced instead of the target problem and solved. In other words, the solution of the nonlinear system of algebraic equations with sin-gular JACOBIAN is transformed to the solution of a system of di, erential equations. Some numerical tests are presented at the end and the computational e, ciency of the method is described.

Based on the determinant of the JACOBIAN matrix (|𝓙 |) in the power flow (PF) problem, power systems are categorized to well-conditioned, ill-conditioned and unsolvable systems. In this paper, a novel and simple approach based on Newton technique is presented to solve the PF problems in the unsolvable power flow cases in the power systems. The presented method is based on combination of the inverse of JACOBIAN matrix to a nonsingular diagonal matrix. Application of the proposed method causes to change the zero eigenvalues to new values in their neighborhoods. The application of the presented algorithm in various scale power systems (2-bus, 11-bus, 14-bus and 118-bus) indicates that the proposed formulation decreases the computation time and number of iterations in comparison with benchmark methods.

Kinematic performance indices are used to have an evaluation of the potential efficiency of the robots. Some of these items are designing the optimal structure,trajectory planning, programming, and evaluation of behavior of the robot in positioning and orienting withdesired rates or resolution. These indices will be used when the robot has even translational or rotational degrees of freedom (DoF). Due to dimensional incompatibility of the JACOBIAN entries in the complex DoF’s robots with both types of DoF’s, performance indices such as JACOBIAN condition index and associate singular values, are not applicable. In this paper, inhomogeneity of Jacobin matrix has been resolved by introducing a new JACOBIAN matrix which is called Cartesian JACOBIAN Matrix (CJM).Cartesian JACOBIAN Matrix maps Cartesian velocity vector of End-Effector (EE) to the joint space velocity vector. As a case study, the suggested method has been used for a Tricept parallel kinematic manipulator. Moreover, considering Local Conditioning Index (LCI) and associatedsingular values through the workspace have been led to structure optimization of the robot in order to have maximum positioning and orienting rates of EE through the maximum cuboid workspace. The optimization has been performed by Genetic algorithm via GA toolbox of MATLAB 2012 software.

The JACOBIAN-Free Newton-Krylov (JFNK) method has been widely used in solving nonlinear equations arising in many applications. In this paper, the JFNK solver is examined as an alternative to the traditional power iteration method for calculation of the fundamental eigenmode in reactor analysis based on even-parity neutron transport theory. Since the JACOBIAN is not formed the only extra storage required is associated with the workspace of the Krylov solver used at every Newton step. A new nonlinear function is developed for the even-parity neutron transport equation utilized to solve the eigenvalue problem using the JFNK. This Newton-based method is compared with the standard iterative power method for a number of multi-groups, one and two dimensional neutron transport benchmarks. The results show that the proposed algorithm generally ends with fewer iterations and shorter run times than those of the traditional power method.

This paper considers the issue of precise control of robotic manipulators in the presence of dynamic uncertainties along with hard nonlinear perturbation such as friction using Modified Transpose Effective JACOBIAN and model based friction compensator. In order to model friction in robot joints, The LuGre friction model has been used and its unknown parameters have been identified by a bio-inspired optimization algorithm called Cuttlefish. By comparing Cuttlefish with other meta-heuristic algorithms such as Glowworm swarm optimization, its superiorities have been proved. After accurate identification of model parameters and determine frictions function, using Modified Transpose Effective JACOBIAN and model-based friction compensator, a two link planar manipulator has been controlled experimentally. Furthermore in order to compare the controller performance with other methods, the mentioned manipulator has been controlled using computed torque controller and transpose JACOBIAN besides Adaptive Radial Based Function Neural Network friction compensators. Experimental results offer the Modified Transpose effective JACOBIAN control method has privileges for better tracking control with more accuracy and better friction compensating as well as better robustness against dynamic uncertainties with lower computational efforts.

In most of the researches that have been done in the position control of robot manipulator, the assumption is that robot manipulator kinematic or robot JACOBIAN matrix turns out from the joint-space to the task-space. Despite the fact that none of the existing physical parameters in the equations of the robot manipulator cannot be calculated with high precision. In addition, when the robot manipulator picks up an object, uncertainties occur in length, direction and contact point of the end-effector with it. So, it follows that the robot manipulator kinematic is also has the uncertainty and for the various operations that the robot manipulator is responsible, its kinematics be changed too, certainly. To overcome these uncertainties, in this paper, a simple adaptive fuzzy sliding mode control has been presented for tracking the position of the robot manipulator end-effector, in the presence of uncertainties in dynamics, kinematics and JACOBIAN matrix of robot manipulator. In the proposed control, bound of existing uncertainties is set online using an adaptive fuzzy approximator and in the end, controller performance happens in a way that the tracking error of the robot manipulator will converge to zero. In the proposed approximator design, unlike conventional methods, single input-single output fuzzy rules have been used. Thus, in the practical implementation of the proposed control, the need for additional sensors is eliminated and calculations volume of control input decreases too. Mathematical proofs show that the proposed control, is global asymptotic stability. To evaluate the performance of the proposed control, in a few steps, simulations are implemented on a two-link elbow robot manipulator. The simulation results show the favorable performance of the proposed control.

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the GENERALIZED topological spaces and the concept of GENERALIZED continuity and become familiar with weak and strong structures for GENERALIZED topological spaces. Then, introducing the concept of the GENERALIZED embedding and the GENERALIZED injection, we study Császár product of GENERALIZED spaces in the category of GENERALIZED topological spaces. Using by the tools of category theory, we describe the results of classifying on the GENERALIZED injective spaces in which these spaces are characterized as GENERALIZED embedding of Császár product with the product topology of two points Sierpinski space. Finally, the GENERALIZED dual-injection spaces as the objects of a special subcategory of the GENERALIZED topological spaces are studied for which all singlepoint subsets are closed.