Piecewise-linearized methods for oscillators with limit cycles

A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.     

Indexing text using the Ziv–Lempel trie

Let a text of u characters over an alphabet of size σ be compressible to n phrases by the LZ78 algorithm. We show how to build a data structure based on the Ziv–Lempel trie, called the LZ-index, that takes 4nlog₂n(1+o(1)) bits of space (that is, 4 times the entropy of the text for ergodic sources) and reports the R occurrences of a pattern of length m in worst case time O(m³logσ+(m+R)logn). We present a practical implementation of the LZ-index, which is faster than current alternatives when we take into consideration the time to report the positions or text contexts of the occurrences found.     

Practical algorithms for transposition-invariant string-matching

We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transposition-invariant text searching using indel distance. These problems have applications in music comparison and retrieval. We introduce two novel techniques to solve these problems efficiently. The first is based on the branch and bound method, the second on bit-parallelism. Our branch and bound algorithm computes the longest common transposition-invariant subsequence (LCTS) in time O((m²+loglogσ)logσ) in the best case and O((m²+logσ)σ) in the worst case, where m and σ, respectively, are the length of the strings and the size of the alphabet. On the other hand, we show that the same problem can be solved by using bit-parallelism and thus obtain a speedup of O(w/logm) over the classical algorithms, where the computer word has w bits. The advantage of this latter algorithm over the present bit-parallel ones is that it allows the use of more complex distances, including general integer weights. Since our branch and bound method is very flexible, it can be further improved by combining it with other efficient algorithms such as our novel bit-parallel algorithm. We experiment on several combination possibilities and discuss which are the best settings for each of those combinations. Our algorithms are easily extended to other musically relevant cases, such as δ-matching and polyphony (where there are several parallel texts to be considered). We also show how our bit-parallel algorithm is adapted to text searching and illustrate its effectiveness in complex cases where the only known competing method is the use of brute force.     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques.     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Comparison of steam pretreatment of eucalyptus,aspen, and spruce wood chips and their enzymatic hydrolysis

Applied Biochemistry and Biotechnology - Enzymatic hydrolysis of SO2-impregnated, steam-explodedEucalyptus viminalis was carried out at increasing substrate concentrations and enzyme loadings. When...     

The diastereoselective synthesis of functionalised isoxazolidines using a Cope elimination/intramolecular nitrone cycloaddition strategy

Functionalised hydroxylamine derivatives of (S)-prolinol prepared by a Cope elimination have been found to undergo oxidation to the nitrone either in the presence of air or a catalytic quantity of TPAP. These undergo intramolecular cycloaddition to give tricyclic isoxazolidines with high diastereoselectivity.