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A complex matrix A is ray-nonsingular if det(XοA) ≠ 0 for every matrix X with positive entries. It is known that the order of a full ray-nonsingular matrix is at most 5 and examples of full n×n ray-nonsingular matrices for n=2, 3, 4 exist. In this note, we describe a property of a special full 5 × 5 ray-nonsingular matrix, if such matrix exists, using the concept of an isolated set of transversals and we obtain a necessary condition for a complex matrix A to be ray-nonsingular. Moreover we give an example of a full 5 × 5 ray-pattern matrix that satisfies all three of the properties given by Lee et al. [Discrete Math. 216 (2000) 221-233]. The notion of Q-ray nonsingularity is also introduced.... 

In this paper, we analyze a general quasi-static two-dimensional multiple contact problem between two elastically similar half-planes under the constant normal (including applied moments) and oscillatory tangential loading utilizing the classical singular integral equations approach. Boundary conditions at nonsingular edges of discrete contact zones are applied and new side conditions are extracted and named “the consistency conditions” for multiple contacts. These conditions are mandatory for determination of the positions of the nonsingular edges of the contact and stick zones, when the number of them exceeds the number of the discrete contact and stick zones, respectively. Consequently, a... 

In this paper, a new form of generalized nonsingular fast terminal sliding mode control approach is proposed to provide the finite time tracking in connected chain of double integrator nonlinear systems subjected to additive bounded unknown uncertainties, disturbances, and internal interactions. The proposed approach presents an adjustable finite time for achieving the tracking goal which is a summation of two separate tunable times including finite reaching time and finite settling time. Tuning of the total finite time is done by adjusting arbitrary parameters in the control inputs and sliding surfaces. The high frequency switching of the control method is removed by applying a second order... 

Classes of integer ABS methods have recently been introduced for solving linear systems of Diophantine equations. The Smith normal form of a general integermatrix is a diagonal integer matrix, obtained by elementary nonsingular (unimodular) operations. Such a form may conveniently be used in solving integer systems of equations and integer linear programming problems. Here, we present a class of algorithms for computing the Smith normal form of an integer matrix. In doing this, we propose new ideas to develop a new class of extended integer ABS algorithms generating an integer basis for the integer null space of the matrix. Finally, we test our algorithms and report the obtained numerical... 

This paper investigates the finite-Time landing of a spacecraft on a celestial target subjected to disturbances and air drag forces. Based on nonsingular fast terminal sliding mode control, a novel guidance law is designed to accomplish the landing goal within a specified finite time while the upper bound of disturbances is assumed to be known. Finally, a numerical example of the spacecraft landing problem is simulated by applying the proposed scheme. The obtained results illustrate that the designed guidance law can achieve the landing goal in the specified finite time  

This paper introduces a public key scheme based on polar codes to improve the performance of McEliece cryptosystem. By exploiting the interesting properties of polar codes, we put the encryption matrix of the proposed scheme in systematic form. Moreover, the nonsingular matrix is constructed from the generator matrix of used polar code. These proceedings lead to decrease the public and private key lengths compared with the original McEliece public key cryptosystem. We analyze the proposed scheme against known attacks on the public key cryptosystems based on channel coding. Moreover, it benefits from high code rate and proper error correction capability for reliable communication  

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

The two-dimensional contact problem for an elastic body indenting an elastically similar half plane resulting in double contacts is important for various applications. In this paper, a generic quasi-static two-dimensional symmetric double contact problem with nonsingular end points between two elastically similar half planes, under the constant normal and oscillatory tangential loading, is analyzed. The classical singular integral equations approach is utilized to extract the pressure and shear functions in the contact zones; subsequently boundary conditions at end points are applied and a new side condition is derived and titled "the consistency condition" for symmetric double contacts.... 

It is aimed to obtain global finite time stabilization of a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in the presence of bounded disturbances by applying nonsingular terminal sliding mode controllers. The considered nonlinear systems consist of double integrator subsystems which interact with each other. In the proposed methods, new terminal sliding surfaces are introduced along with design of proper control inputs. The terminal sliding surfaces are defined such that the global finite time stability of sliding mode dynamic is attained. The control inputs are designed to steer the states into sliding motion within finite time and retain them on the terminal sliding... 

This paper deals with the robust finite time tracking of desired trajectories for a wide group of robotic manipulators in spite of unknown disturbances, uncertainties, and saturations of actuators while only manipulator's positions are available and its velocities are not measurable physically. A new form of chattering-free second order fast nonsingular terminal sliding mode control scheme is introduced to design input torques for fulfilling the determined tracking objective in the adjustable total finite settling time. The proposed control algorithm is incorporated with two nonlinear observers to estimate disturbances and velocities of joints within finite settling times. The global finite...