The organization of behavior: A neuropsychological theory

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

国際会議開催報告:2013 IEEE International Symposium on Information Theory

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.

https://iopscience.iop.org/article/10.1088/0143-0807/32/2/019/pdf

A Comprehensive Analytical Solution of the Nonlinear Pendulum.

The degrees of freedom (DoF) of the MIMO Y-channel, a multi-way communication network consisting of 3 users and a relay, are characterized for arbitrary number of antennas. The converse is provided by cut-set bounds and novel genie-aided bounds. The achievability is shown by a scheme that uses beamforming to establish network coding on-the-fly at the relay in the uplink, and zero-forcing pre-coding in the downlink. It is shown that the network has min{2M2+2M3, M1+ M2 + M3,2N} DoF, where Mj and N represent the number of antennas at user j and the relay, respectively. Thus, in the extreme case where M1+M2+M3 dominates the DoF expression and is smaller than N, the network has the same DoF as the MAC between the 3 users and the relay. In this case, a decode and forward strategy is optimal. In the other extreme where 2N dominates, the DoF of the network is twice that of the aforementioned MAC, and hence network coding is necessary. As a byproduct of this work, it is shown that channel output feedback from the relay to the users has no impact on the DoF of this channel.

The degrees of freedom of the MIMO Y-channel

Most standard wave digital filters are derived from passive reference circuits, where only parallel and serial connections between one-port elements occur. In this paper, a framework for the automated generation of the wave digital structures is presented, where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its so-called SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with networks containing certain multiport elements. We propose two different novel approaches to finding a valid tree representation from a given reference circuit. The first approach relies on the usage of apt replacement graphs for the multiport elements. The second one is based on searches for circles on suitably constructed graph representations and generates wave digital structures with minimum implementation effort even in presence of nonreciprocal elements. In both approaches, standard separation algorithms with known efficient implementations can be applied.

Generation of wave digital structures for networks containing multiport elements

Summary Methods based on the wave digital concept are suited for the modelling of passive physical systems. The generated wave digital models inhere both a high physical transparency as well as a variety of good numerical properties. However, the wave digital concept is known for linear multistep methods only. In this context, passivity imposes a limited accuracy. To this end, more universal integration methods are considered in this paper: The so-called general linear methods which cover in particular linear multistep methods and Runge-Kutta methods. In order to establish a new theory for these integration methods, a network theoretical approach is used. A new class of Runge-Kutta methods will be derived. The generated algorithmic models inhere the same good properties as wave digital models but their numerical accuracy is increased. A simulation example for a nonlinear physical system will be given.

Passive Integration Methods: Fundamental Theory

As battery capacities become suitable for the mass market, there is an increasing demand on technologies to charge electric vehicles. Wireless charging is regarded as the most promising technique for automatic and convenient charging. Especially in publicly accessible parking spaces, foreign objects are able to enter the large air gap between the charging coils easily. Since the evoked magnetic field does not meet regulations, wireless charging systems are demanded to take further precautions related to the protection of endangered objects. Thus, additional sensors are required to protect primarily living objects by preventing them from being exposed to the magnetic field. In this paper, we propose a new approach for monitoring the air gap under the vehicle underbody using an automotive radar sensor on the vehicle side. The concept feasibility is evaluated with the help of a prototypical implementation. Further, two-dimensional signal processing techniques are applied to meet the requirements of inductive charging systems. Consequently, this paper provides measurement data for relevant use cases frequently discussed in the community of inductive charging.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S2052841817000070

Karlheinz Ochs

Papers

A Comprehensive Analytical Solution of the Nonlinear Pendulum.

The degrees of freedom of the MIMO Y-channel

Generation of wave digital structures for networks containing multiport elements

Passive Integration Methods: Fundamental Theory

Radar-based living object protection for inductive charging of electric vehicles using two-dimensional signal processing