Computing Bessel functions of the second kind in extreme parameter regimes

A useful method of computing the integral order Bessel functions of the second kind Y_n(x+iy) when either, the absolute value of the real part, or the imaginary part of the argument z=x+iy is small, is described. This method is based on computing the Bessel functions for extreme parameter regimes when x∼0 (or y∼0) and is useful because a number existing algorithms and methods fail to give correct results for small x or small y. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.     

Linear Algebra Considerations for the Multi-Threaded Simulation of Mechanical Systems

A solution method suitable for the multi-threaded simulation ofmechanical systems represented in Cartesian coordinates isproposed and analyzed. In a state-space framework for thesolution of the Differential Algebraic Equations (DAE) ofMultibody Dynamics, the position/velocity stabilization and theacceleration computation are based on iterative solvers applied toequivalent reduced problems. The most in-depth computationalaspect analyzed is the preconditioning, i.e., the direct solutionof the reduced systems. Provided a topology index reduction is first applied to the model, the effort for the direct solution of the reduced systems is shown to be of order O(N _J ), where N _J is the number of joints in the model. The recurring theme of thepaper is the central role that the topology of the mechanicalsystem plays in the overall performance of the numericalsimulation. Based on the topology of the model, parallelcomputational threads can be established to start in the equationformulation and continue through the iterative numericalalgorithms employed for the numerical solution. Task schedulingthese parallel threads is expected to redeem real-time performancefor certain classes of complex applications.     

A new scheme for the deterministic simulation of PRAMs in VLSI

A deterministic scheme for the simulation of (n, m)-PRAM computation is devised. Each PRAM step is simulated on a bounded degree network consisting of a mesh-of-trees (MT) of siden. The memory is subdivided inn modules, each local to a PRAM processor. The roots of the MT contain these processors and the memory modules, while the otherO(n ²) nodes have the mere capabilities of packet switchers and one-bit comparators. The simulation algorithm makes a crucial use of pipelining on the MT, and attains a time complexity ofO(log² n/log logn). The best previous time bound wasO(log² n) on a different interconnection network withn processors. While the previous simulation schemes use an intermediate MPC model, which is in turn simulated on a bounded degree network, our method performs the simulation directly with a simple algorithm.This work has been supported in part by Ministero della Pubblica Istruzione of Italy under a research grant.     

Characterizing computer input with Fitts’ law parameters—the information and non-information aspects of pointing

Throughput (TP), also known as index of performance or bandwidth in Fitts’ law tasks, has been a fundamental metric in quantifying input system performance. The operational definition of TP is varied in the literature. In part thanks to the common interpretations of International Standard ISO 9241-9, the “Ergonomic requirements for office work with visual display terminals—Part 9: Requirements for non-keyboard input devices”, the measurements of throughput have increasingly converged onto the average ratio of index of difficulty (ID) and trial completion time (MT), i.e. TP=ID/MT. In lieu of the complete Fitts’ law regression results that can only be represented by both slope (b) and intercept (a) (or MT=a+b ID), TP has been used as the sole performance characteristic of input devices, which is problematic. We show that TP defined as ID/MT is an ill-defined concept that may change its value with the set of ID values used for the same input device and cannot be generalized beyond specific experimental target distances and sizes. The greater the absolute value of a is, the more variable TP (=ID/MT) is. ID/MT only equals a constant 1/b when a=0. We suggest that future studies should use the complete Fitts’ law regression characterized by (a, b) parameters to characterize an input system. a reflects the non-informational aspect and b the informational aspect of input performance. For convenience, 1/b can be named as throughput which, unlike ID/MT, is conceptually a true constant.     

On the surface area of the -star graph

We present an explicit formula for the surface area of the (n,k)-star graph, i.e., the number of nodes at a certain distance from the identity node in the graph, by identifying the unique cycle structures associated with the nodes in the graph, deriving a distance expression in terms of such structures between the identity node of the graph and any other node, and enumerating those cycle structures satisfying the distance restriction.The above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group, when the aforementioned distance expression is available.     

Scheduled control for robust attenuation of non-stationary sinusoidal disturbances with measurable frequencies

Attenuation of sinusoidal disturbances with uncertain yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an undisturbed parameter-dependent exogenous system with a skew-symmetric system matrix, obtained in response to nonzero initial conditions. The problem is formulated for a parameter-dependent plant as the synthesis of a parameter-dependent controller in a way to ensure internal stability as well as a desired level of steady-state disturbance attenuation in the face of all admissible parameter variations. The solvability of this problem is first related to the existence of bounded solutions to a matrix differential regulator equation subject to an asymptotic norm constraint. Reformulating this as a parameter-dependent state-feedback like synthesis, based on which suitable solutions to the differential regulator equation can be obtained online, tractable solvability conditions are then provided in the form of parameter-dependent matrix inequalities. Controllers that solve the generalized asymptotic regulation problem are also parameterized in terms of the suitable solutions of the differential regulator equation and some free parameter-dependent matrices that are to be designed off-line to ensure stability. A procedure is then developed to design the free parameters in a way to achieve desirable transient behavior. The use of the developed synthesis procedure is illustrated on a simplified version of the course control problem in ship steering.     

Stability of iterative processes with errors for a system of nonlinear -accretive variational inclusions in Banach spaces

In this paper, by using the concept of (A,η)-accretive mappings and the new resolvent operator technique associated with (A,η)-accretive mappings, we introduce and study a system of general mixed quasivariational inclusions involving (A,η)-accretive mappings in Banach spaces, and construct a new perturbed iterative algorithm with mixed errors for this system of nonlinear (A,η)-accretive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.