Modified Normalized Least Mean Square (MNLMS) algorithm, which is a sign form of NLMS based on set-membership (SM) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performance of algorithm is compared with MNLMS.

Matrix functions play important roles in various branches of science and engineering. In numerical computations and physical measurements there are several sources of error which significantly affect the main results obtained from solving the problems. This effect also influences the matrix computations. In this paper, we propose some approaches to enclose the matrix functions. We then present some analytical arguments to ensure that the obtained enclosures contain the exact result. Numerical experiments are given to illustrate the performance and effectiveness of the proposed approaches.

This paper studies the effect of flexible linear torso on the dynamics of passive quadruped bounding. A reduced-order passive and conservative model with linear flexible torso and springy legs is introduced. The model features extensive spine deformation during high-speed bounding, resembling those observed in a cheetah. Fixed points corresponding to cyclic bounding motions are found and calculated using numerical return map methodologies. Results show that the corresponding robot gaits and the associated performance resemble those of its natural counterparts.

The main object of this paper is to present several bounding inequalities for the classical Jacobi function of the first kind. A number of closely related inequalities for such other special functions as the classical Laguerre function are also considered.

In this paper, it is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph in-creases at most two. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipartite or weakly chordal graph.

The present paper is devoted to a new critical state based plasticity model able to predict drained and undrained behaviour of granular material. It incorporates a bounding surface plasticity model describing in multilaminate framework to capitalize on advantages of this mathematical framework. Most of the models developed using stress/strain invariants are not capable of identifying the parameters depending on directional effects such as principal stress rotation and fabric, this is mainly because stress/strain invariants are scalar quantities. The principal features of this model can be postulated as considering both inherent and induced anisotropy, principal stress rotation. Since the local instability of saturated sand within post-liquefaction is highly dependent on the residual inherent/induced anisotropy, bedding plane effects and also the stress/strain path the new mode is competent to be employed in this regard. The constitutive equations of the model are derived within the context of non-linear elastic behaviour for the whole medium and plastic sliding of interfaces of predefined planes. As follows, the constitutive equations are described in detail and then the experimental results and sensitive analysis of key material constants are shown which all imply the power of the model in predicting of soil behaviour under any condition in soil structures.

In this paper, the physical optics method is used to study the problem of electromagnetic scattering from Haack series nose cone. First, a meshing scheme is introduced which approximates the curvature of the surface by piecewise linear functions in both axial and rotational directions. This results in planar quadrilateral patches and enables efficient determination of the illuminated region and application of closed-form expression for computing physical optics integral. Then the ray-surface intersections are obtained using the implicit surface equation of Haack series nose cone. The equation obtained by the intersection test does not have analytical solution. Hence, the Steffensen method is applied to solve this equation numerically. To find the initial point for Steffensen method's iterations, a bounding cylinder is used. It provides high precision evaluation of initial point, fast convergence and short computation time. Moreover, if the ray does not intersect the bounding volume, it certainly misses the bounded object and hence does not need to be tested in the Steffensen method. The ray-cylinder intersection test has a simple analytical solution, which results in fast rejection of missed rays. Simulation results demonstrate the proper accuracy and efficiency of the presented algorithms.