Nonhomogeneous Systems Research Articles

Graph-Based Modeling of Nonhomogeneous One-Dimensional Multibody Systems With Arbitrary Topology

This paper presents a method to study multibody system dynamics based on graph theory. The transfer function between any pair of bodies of nonhomogeneous multibody systems with arbitrary topology can be computed without any matrix inversion. The analysis is limited to one-dimensional topologies for clarity, although it can be extended to systems with higher dimensions. Examples illustrate its application to topologies of increasing complexity.

A novel fluorogenic substrate for the measurement of endothelial lipase activity

Endothelial lipase (EL) is a phospholipase A1 (PLA1) enzyme that hydrolyzes phospholipids at the sn-1 position to produce lysophospholipids and free fatty acids. Measurement of the PLA1 activity of EL is usually accomplished by the use of substrates that are also hydrolyzed by lipases in other subfamilies such as PLA2 enzymes. In order to distinguish PLA1 activity of EL from PLA2 enzymatic activity in cell-based assays, cell supernatants, and other nonhomogeneous systems, a novel fluorogenic substrate with selectivity toward PLA1 hydrolysis was conceived and characterized. This substrate was preferred by PLA1 enzymes, such as EL and hepatic lipase, and was cleaved with much lower efficiency by lipases that exhibit primarily triglyceride lipase activity, such as LPL or a lipase with PLA2 activity. The phospholipase activity detected by the PLA1 substrate could be inhibited with the small molecule esterase inhibitor ebelactone B. Furthermore, the PLA1 substrate was able to detect EL activity in human umbilical vein endothelial cells in a cell-based assay. This substrate is a useful reagent for identifying modulators of PLA1 enzymes, such as EL, and aiding in characterizing their mechanisms of action.

Cauchy and Green matrices type and stability in alternately advanced and delayed differential systems

In this paper, we study differential equations with piecewise constant argument of generalized (DEPCAGs) type, i.e., the argument is a general step function. They are hybrid equations combining properties of continuous and discrete equations. The play of the discrete part is always very important. The explicit solutions of the homogeneous and non-homogeneous linear DEPCAGs systems are obtained. Existence, uniqueness and stability of the solutions of the quasilinear DEPCAGs are under discussion. All previous results are improved. The importance of the advanced and delayed intervals will be clear. Cauchy and Green matrices type are deduced. The integral representation and Gronwall's inequality type obtained can be fruitfully applied to the investigation of stability, oscillations, controllability and many other problems of DEPCAGs.

Global Inverse Optimal Control With Guaranteed Convergence Rates of Input Affine Nonlinear Systems

In earlier works, global inverse optimal controllers were proposed for input affine nonlinear systems with given control Lyapunov functions. However, these controllers do not provide information about the convergence rates. If the systems have local homogeneous approximations, we can employ homogeneous controllers, which locally asymptotically stabilize the origin and specify the convergence rates. However, homogeneous controllers generally do not attain global stability for nonhomogeneous systems. In this paper, we design global inverse optimal controllers with guaranteed local convergence rates by utilizing local homogeneity of input affine nonlinear systems. If we do not consider inverse optimality, we can liberally adjust the sector margins. We also clarify that local convergence rates and sector margins are invariant under coordinate transformations.

Performance of Non-Homogeneous Multi-Agent Systems on a Graph

AbstractThis paper considers distributed control of interconnected multi-agent systems. The dynamics of the individual agents are not required to be homogeneous and the interaction topology is described by an arbitrary directed graph. We derive the sensitivity transfer functions between every pair of agents and we analyze performance of non-homogeneous systems, showing that the low frequency behavior is influenced not only by topology, but also by static gain and poles of the agents.

Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems

The weakly perturbed linear nonhomogeneous impulsive systems in the form , and i ∈ ℤ are considered. Under the assumption that the generating system (for ε = 0) does not have solutions bounded on the entire real axis for some nonhomogeneities and using the Vishik‐Lyusternik method, we establish conditions for the existence of solutions of these systems bounded on the entire real axis in the form of a Laurent series in powers of small parameter ε with finitely many terms with negative powers of ε, and we suggest an algorithm of construction of these solutions.

Stability Analysis of Nonlinear Switched Systems via Reduction Method

AbstractStability of nonlinear switched systems is discussed. A method of constructing the common (scalar and vector) Lyapunov functions is proposed for switched systems whose equations have homogenous right-hand sides and for switched large-scale systems containing homogeneous subsystems. With the aid of homomorphic mapping the problem of stability for nonhomogeneous nonlinear systems is reduced to an auxiliary problem, which is easier to analyze. Matrix homomorphism is used for the purpose of ellipsoidal estimation of nonlinear dynamics of the polynomial class of systems. Certain applications are mentioned.

Matrix computations and polynomial root-finding with preprocessing

Solution of homogeneous linear systems of equations is a basic operation of matrix computations. The customary algorithms rely on pivoting, orthogonalization and SVD, but we employ randomized preprocessing instead. This enables us to accelerate the solution dramatically, both in terms of the estimated arithmetic cost and the observed CPU time. The approach is effective in the cases of both general and structured input matrices and we extend it and its computational advantages to the solution of nonhomogeneous linear systems of equations, matrix eigen-solving, the solution of polynomial and secular equations, and approximation of a matrix by a nearby matrix that has a smaller rank or a fixed structure (e.g., of the Toeplitz or Hankel type). Our analysis and extensive experiments show the power of the presented algorithms.

The decoupling of damped linear systems in configuration and state spaces

It has recently been reported that any viscously damped linear system can be decoupled in the configuration space by a real, nonlinear, time-dependent transformation. The purpose of this rapid communication is to provide a few clarifying remarks about the decoupling operation. It is shown that, for homogeneous systems, the time-dependent configuration-space decoupling transformation is real, linear and time-invariant when cast in state space. In addition, the configuration–space transformation generates a diagonalizing structure-preserving transformation. In non-homogeneous systems, both the configuration and associated state transformations are nonlinear and depend continuously on the excitation. An example is given of a linear system that can be decoupled in configuration but not in state space.

Local Lipschitz regularity for degenerate elliptic systems

We start presenting an L∞-gradient bound for solutions to non-homogeneous p-Laplacean type systems and equations, via suitable non-linear potentials of the right-hand side. Such a bound implies a Lorentz space characterization of Lipschitz regularity of solutions which surprisingly turns out to be independent of p, and that reveals to be the same classical one for the standard Laplacean operator. In turn, the a priori estimates derived imply the existence of locally Lipschitz regular solutions to certain degenerate systems with critical growth of the type arising when considering geometric analysis problems.

Formulae of partial reduction for linear systems of first order operator equations

This paper deals with the reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and first order linear operator equations in two variables, is obtained by using the rational canonical form.

Differential equations with linear algebra

1. First-Order Differential Equations. Differential Equations and Mathematical Model. Integrals as General and Particular Solutions. Direction Fields and Solution Curves. Separable Equations and Applications. Linear First-Order Equations. Substitution Methods and Exact Equations. 2. Mathematical Models and Numerical Methods. Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method. The Runge-Kutta Method. 3. Linear Systems and Matrices. Introduction to Linear Systems. Matrices and Gaussian Elimination. Reduced Row-Echelon Matrices. Matrix Operations. Inverses of Matrices. Determinants. Linear Equations and Curve Fitting. 4. Vector Spaces. The Vector Space R 3. The Vector Space Rn and Subspaces. Linear Combinations and Independence of Vectors. Bases and Dimension for Vector Spaces. General Vector Spaces. 5. Linear Equations of Higher Order. Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Undetermined Coefficients and Variation of Parameters. Forced Oscillations and Resonance. 6. Eigenvalues and Eigenvectors. Introduction to Eigenvalues. Diagonalization of Matrices. Applications Involving Powers of Matrices. 7. Linear Systems of Differential Equations. First-Order Systems and Applications. Matrices and Linear Systems. The Eigenvalue Method for Linear Systems. Second-Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Numerical Methods for Systems. 8. Matrix Exponential Methods. Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems. Spectral Decomposition Methods. 9. Nonlinear Systems and Phenomena. Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. 10. Laplace Transform Methods. Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. 11. Power Series Methods. Introduction and Review of Power Series. Power Series Solutions. Frobenius Series Solutions. Bessel's Equation. References for Further Study. Appendix A: The Existence and Uniqueness of Solutions. Appendix B: Theory of Determinants. Answers to Selected Problems. Index.

Nonhomogeneous random walks systems on ℤ

We consider a random walks system on ℤ in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on ℤ, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to 1 but not fast enough.

Nonhomogeneous random walks systems on ℤ

We consider a random walks system on ℤ in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on ℤ, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to 1 but not fast enough.

Conditionally invariant solutions of the rotating shallow water wave equations

This paper is devoted to the extension of the recently proposed conditional symmetry method to first-order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We perform a systematic analysis of the rank-1 and rank-2 solutions admitted by the shallow water wave equations in (2 + 1) dimensions and construct the corresponding solutions of the rotating shallow water wave equations. These solutions involve in general arbitrary functions depending on Riemann invariants, which allow us to construct new interesting classes of solutions.

Application of five frozen human-pooled serum samples assigned by the International Federation of Clinical Chemistry and Laboratory Medicine reference procedure in a traceability investigation of γ-glutamyltransferase catalytic concentration measurements in China

The in vitro directive of the European Union requires traceability to the international recommended reference procedures. The application of the reference procedures is necessary in order to evaluate the accuracy of gamma-glutamyltransferase (GGT) assays of routine measurement systems in China. Five frozen patient-pooled serum samples were assigned values by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) reference procedure in order to evaluate the traceability of the results of GGT catalytic activity from six homogeneous systems. One of the serum samples was used to calibrate seven non-homogeneous systems. All of the homogeneous systems, except the Dade system (Dade Bering Inc, IL, USA), achieved traceability within the measurement range. The Roche and Hitachi systems were better than the other systems. After calibration, the variance of the non-homogeneous systems decreased dramatically from between 14.50% and 25.23% to between 1.25% and 3.09% and the bias decreased from between -11.4% and -4.1% to between 0.5% and 3.5%. Manufacturers in China should ensure that their calibration systems correspond to the IFCC reference procedures. Fresh frozen pooled patient serum assigned by reference laboratories can be used to calibrate non-homogeneous systems in order to achieve traceability.

A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains

The well-known membrane-plate analogy that relates the natural frequencies when dealing with polygonal homogeneous domains is herein extended to non-homogeneous systems comprised of homogeneous subdomains. The analogy is generalized and demonstrated and it is shown that certain restrictions among the frequency parameters of the membranes and plates arise. Several examples of membranes and plates with interfaces separating areas with different material properties are numerically solved with different approaches. The subdomains are separated by straight, curved, and closed line interfaces. It is shown that the analogy is verified provided that the restrictions are satisfied. The analogy is first demonstrated and presented as a practical methodology to find the natural frequencies of membranes knowing the corresponding ones of the plates or vice versa. Second, the plate and membrane vibration problems, governed by the bi-Laplacian and Laplacian differential operators, respectively, can be solved without distinction, though under certain conditions, i.e., solve one of them and deduce the other using the analogy. Various numerical examples validate the analogy.

Optimal Control for Non-Homogeneous Linear Systems Driven by Fractional Noises

The article considers the problem of optimal control of a non homogeneous linear system driven by fractional noises. Due to the high complexity of the specific problem, we use a scalar valued state variable and also a quadratic objective criterion. The entire analysis could be generalized within a multi dimensional framework. The investigation is restricted within the class of the Markovian controls. Actually, we calculate a sub optimal control for the original problem.

Non-homogeneous Navier-Stokes systems with order-parameter-dependent stresses

We consider the Navier–Stokes system with variable density and variable viscosity coupled to a transport equation for an order-parameter c. Moreover, an extra stress depending on c and ∇c, which describes surface tension like effects, is included in the Navier–Stokes system. Such a system arises, e.g. for certain models of granular flows and as a diffuse interface model for a two-phase flow of viscous incompressible fluids. The so-called density-dependent Navier–Stokes system is also a special case of our system. We prove short-time existence of strong solution in Lq-Sobolev spaces with q>d. We consider the case of a bounded domain and an asymptotically flat layer with a combination of a Dirichlet boundary condition and a free surface boundary condition. The result is based on a maximal regularity result for the linearized system. Copyright © 2010 John Wiley & Sons, Ltd.

Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space

In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in the distribution space; the proposed notion enables us to completely separate the perfect reconstruction property of a wavelet system from its stability property in function spaces. The results in this paper lead to a natural explanation for the oblique extension principle, which has been widely used to construct dual wavelet frames from refinable functions, without any a priori condition on the generating wavelet functions and refinable functions. A nonhomogeneous wavelet system, which is not necessarily derived from refinable functions via a multiresolution analysis, not only has a natural multiresolution-like structure that is closely linked to the fast wavelet transform, but also plays a basic role in understanding many aspects of wavelet theory. To illustrate the flexibility and generality of the approach in this paper, we further extend our results to nonstationary wavelets with real dilation factors and to nonstationary wavelet filter banks having the perfect reconstruction property.