Search

Stored-product insects frequently infest packaged food, causing significant monetary losses to both the food industry and consumers worldwide. This work compared the resistance of 9 new monolayer and multilayer food-packaging films to infestation by 4 key insect food pests (Sitophilus granarius, Rhyzopertha dominica, Oryzaephilus surinamensis and Plodia interpunctella). A series of laboratory tests were conducted over 3 months to determine the package penetration by the stored-product insects. The tested pest species differed in their chewing capacity and in the size of their entrance hole (P. interpunctella larvae, 15 ± 17 mm2 penetrated area/hole; S. granarius, 6 ± 5 mm2; R. dominica, 6 ± 2 mm2; and O. surinamensis, unable to penetrate). The insects also caused mechanical weakening of the film surface by creating multiple small superficial holes covering a 10–20× larger area of the film surface than the penetrated area. For insect invaders (S. granarius, R. dominica, and P. interpunctella), porous paper and an unprinted polyethylene monolayer (40 μm thick) provided the least mechanical resistance, while the highest level of mechanical resistance was recorded for 50-μm-thick polypropylene/metalized-polypropylene. The most innovative findings of this study were that the unprinted parts of the polypropylene monofilm were less protective against R. dominica penetration than the printed parts and that duplex and triplex films were more resistant to insect feeding and penetration than single-layer films, irrespective of their thickness. Some multilayer films showed (in our experimental settings and for the packaging machines used) low resistance to O. surinamensis invasion through crevices caused by sealing imperfections. The results of this study are discussed in the context of film application to protect packaged foods against insect contamination.

Inverting a nonlinear operator is usually a difficult problem. Consequently, approximation methods are useful. In this paper, we study the relationship between the set of approximate inverses of a given operator N and the invertibility of N.

Necessary and sufficient conditions for the invertibility of a (not necessarily linear) operatorN between normed linear spaces are given. It is shown thatN is invertible precisely if a certain operator associated withN is a contraction.

The objective of this paper is to present certain conditions guaranteeing invertibility of a nonlinear operator between normed linear spaces. The idea is to approximate the given operator by an invertible, possibly linear operator, and reduce the problem to the contraction mapping principle. Several theorems of this kind are given, which appear as generalizations of some early results by I.W. Sandberg, and estimates for an “approximate inverse” are established. Finally, introducing certain “invertibility indices,” further sufficient and necessary conditions for invertibility are given.

In the stability and sensitivity theory of general, nonlinear input-output systems we encounter a certain inequality concerning solely the nominal system that plays a central role in the whole theory. In particular, this “central inequality,” combined with other assumptions, implies (a) stability of the nominal system, (b) robustness, and (c) insensitivity of the input-output system. This paper presents conditions equivalent to this central inequality, and a further result on the stability-robustness problem.

Let {S(A):A ∈A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D i, of inputs into the space of outputs ¯H 0, the problem we consider is to find, for a given ɛ>0, a “parameter”A e∈A such that the transmission operatorR(A e) ofS(A e) furnishes a nearly best (or ɛ-best) approximation toQ from allR(A),A ∈A. Here the “distance” betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ∈ ¯D i. In Theorems 2 through 5 we show that ifS(A) is “normal” (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA e∈A reduces to minimizing a certain continuous functional on a compact subset ofR n, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.

We consider a general nonlinear input-output system governed by operator equations that relate the system's input, state, and output, all of which are in extended spaces. It is assumed that the system variables are separated. Our results give conditions under which the stability of the nominal system is robust; i.e., it is not destroyed by any sufficiently small admissible perturbation of the system. Theorem 1 deals with the case when by stability we mean theincremental stability. Theorem 3 concerns the*-stability; i.e., the case when the stability is essentially the boundedness of the transmission operator. Moreover, in Theorem 2 it is shown that, under certain conditions, the incremental stability of the nominal system implies insensitivity. Basically, our results show that if the operators describing the nominal system are well behaved, and the transition from the nominal system to the perturbed system is not abrupt, then the nominal system stability is robust. The applications of the results are illustrated by several examples.

We construct a general model of a nonlinear input-output system consisting of finitely many blocks whose variables are in extended spaces. This model encompasses all configurations used in control which have several feedback and feedforward loops. We show that such a system is essentially the traditional MI-MO feedback system. Moreover, assuming that one block of the system is a plant affected by perturbations, we derive conditions guaranteeing linear insensitivity and/or robust stability of the whole system. In particular, we consider systems whose variables are continuous, vector-valued functions on [0, ?), and whose blocks are described by nonlinear Volterra operators. The applications of the results are illustrated by several examples of feedback-feedforward systems.

We study the behavior of a Hilbert network (i.e., a finite or countably infinite network whose variables are in a Hilbert space and in which the associated total energy is finite) whose elements are affected by perturbations. More specifically, we will give estimates for a change of the current distribution caused by (a) perturbations of the elements of the nominal network when the voltage sources are fixed, and (b) a change of voltage sources in a network whose elements are perturbed. The conditions given in our theorems imply insensitivity and robust stability of the nominal network. The applications of the results are illustrated by an example of an infinite network.

The estimates derived in this paper strengthen the available results on sensitivity and robust stability of input-output systems. Two types of estimates are discussed: the “sensitivity type”, which establishes a bound for the output change when the system is perturbed but the input remains the same, and the “robustness type”, which gives a bound for the output change when the input changes but the perturbation does not. First, estimates for general systems over abstract extended spaces are derived; these results are then applied to (1) two frequently used control configurations, and (2) systems governed by vector integral and differential equations on the time domain [0, ∞). The applications of the estimates are illustrated by several examples.

We consider input-output systems (not necessarily of feedback type) on the time domain [0, ∞) which are governed by nonlinear vector integral or differential equations that relate the input and the output. Assuming that these equations depend on a parameterA, describing perturbations, which is allowed to vary in a vicinity of a nominal valueA0 in a linear space, we study how strongly the output is affected by changes of (a)A0 when the input is fixed (insensitivity), and (b) the input whenA is fixed withAA0 being not too large (robust stability).

This paper is the second part of [6] which is concerned with the sensitivity of general input-output systems over extended spaces. It is assumed that such systems, which need not be of feedback type, are governed by nonlinear operator equations relating the input, the state, and the output. These equations depend on a parameterA that can vary in a neighborhood of a nominal valueA 0. Essentially, a system is called insensitive if any truncation of its output depends continuously onA provided the input is fixed. The theorems derived provide sufficient conditions for insensitivity. A control system of a feedback-feedforward type and a dynamical system described by a linear vector differential equation on [0, ?) are discussed as examples.

We consider general input-output systems governed by nonlinear operator equations that relate the system's input, state, and output. The systems under consideration need not be of a feedback type. Assuming that the governing equations depend on a parameterA in a linear space that is allowed to vary in a vicinity Nr(A0) of a “nominal” valueA0, we study conditions under which the system is stable for each A∈Nr (A0), i.e., when the system is robust. By stability we essentially mean that the input-output map is continuous. Depending on the type of continuity used, two concepts of robustness are introduced. The main theorem shows that a certain generalized monotonicity condition imposed on the nominal system combined with a Lipschitz-like condition imposed on the perturbed system guarantees robustness. Moreover, several particular cases of the governing equations are investigated. As examples, we consider (1) a singular system of nonlinear ordinary differential equations (a semistate equation), (2) a feedback system, and (3) a feedback, feedforward system. At the end of this paper some extensions and modifications of the presented theory are discussed.

A generalized solution of a system of semistate equations is defined via the system of associated integral equations. Two theorems on the existence and uniqueness of a generalized solution are given.

It is well known that if A, B are square matrices of the same order such that I + AB is nonsingular, then I + BA is also nonsingular. In this note we show that this assertion can be generalized for the case that A or B is a (not necessarily linear) operator on a linear space.

The concept of a Hilbert network, introduced in another paper, extends network theory to finite or infinite networks whose elements are described by operators on a Hilbert space. The present work investigates a variety of qualitative properties possessed by such networks. In particular, some operators associated with the entire network, such as the driving-point impedances as well as the admittance operator which relates the branch-voltage vector to the branch-current vector, are shown to be—under suitable conditions—either positive, monotonic, or convex. Also, generalized versions of Jeans’ least power theorem and the Shannon–Hagelbarger theorem are proved. Finally, a bound on the power dissipation is determined.

An approximation theorem for a Hammerstein-type equation in a Hilbert,space is proved. Also, applications to the Ritz–Galerkin method and to construction of an approximating feedback system are discussed.

Although an operational amplifier is a nonlinear device, the existing methods of analysis of circuits with operational amplifiers view it as a linear element which possibly has an infinite gain. As a result, it is not clear to what extent the results thus obtained hold. In this paper we construct a general model of a (nonlinear) circuit containing operational amplifiers. Viewing such a network as an interconnection of a multiport withn operational amplifiers, we give conditions for solvability (i.e., for the existence of an input-output operator), and establish estimates for the error incurred by replacing such a system by an idealized system whose operational amplifiers have infinite gain. In this way we determine ranges for variables within which the traditional linear analysis gives results that fulfill given accuracy requirements.

The paper presents a simple yet quite general method for analyzing the sensitivity of a performance characteristic of a system consisting of linear blocks. The analysis is based on properties of a gradient of an abstract function. Applications in network theory and in the theory of feedback systems are discussed.

In this paper we consider a linearization of a nonlinear monotone Hilbert network in a neighborhood of some operating point. Three theorems are established which give estimates for the difference between the exact and approximate current distribution. Two examples of specific networks are considered.

In this paper feedback systems described by nonlinear (possibly multivalued) monotone operators are considered. We establish conditions for the existence and uniqueness of outputs corresponding to a given pair of inputs, conditions for causality, Lipschitz continuity and stability. Also, feedback systems over an extended Hilbert space are discussed. Finally, linear approximations to a nonlinear feedback system are studied.

In this paper there is constructed a simple model of a general nonlinear network. The network considered consists of at most countably many lumped elements described by (not necessarily linear) operators from a Hilbert space into itself. Several theorems are proved on the existence and uniqueness of the solution of the network. Also, it is shown that, under certain conditions, the solution of an infinite network is a limit of solutions of finite subnetworks.

A local implicit function theorem is proved which assumes certain injectivity rather than differentiability. Moreover, there is given a result on solvability of noncanonic systems of differential equations which arise in optimal control and network theory.

In this paper conditions are given guaranteeing the existence and uniqueness of a current distribution in a Hilbert or algebraic network driven by both EMF and current sources. Moreover, a generalization and converse of Tellegen’s theorem for these networks is discussed.

In the paper a general model of a nonlinear network is constructed. The model considered is a generalization of the Hilbert network introduced in [1]. It is assumed that the generalized Hilbert network consists of at most countably many lumped elements described by nonlinear multivalued operators from a subset of a Hilbert space $\mathcal{H}$ into $\mathcal{H}$. Several theorems are proved on the existence and uniqueness of the solution of the network. Also, conditions are established under which the admittance operator of a generalized Hilbert network is causal.

Necessary and sufficient conditions for a plant and controller are established under which there exists a feedback reducing the incremental sensitivity by a given factor $\lambda < 1$. It is understood that the reduction occurs for all prescribed inputs and plant perturbations.

In this paper we establish conditions for the existence and uniqueness of a regime in a linear (finite or infinite) Hilbert network which contains several nonlinear elements. These conditions are given in terms of the driving point set impedance of the linear network, and the operator describing the nonlinear elements. They are easy to test in specific cases. Two examples illustrating the application are given.

In this paper, solvability and stability of nonlinear, time-varying semistate equations is discussed. It is shown that generalized solutions exist in a vicinity of an equilibrium. Moreover, results on a Liapunov-like (uniform, asymptotic) stability are given.

In this paper we consider linearizations of a nonlinear equation in a Hilbert space which are close, in a certain sense, to an optimal linearization. We focus our attention on equations involving monotone operators, particularly on those with Hammerstein-type operators. Finally, we discuss a construction of a linearizing operator in the case when a Nemytskii operator is involved.

In this paper we give sufficient conditions for solvability of a Hilbert network some elements of which are described by monotone operators defined only on subsets of the underlying Hilbert space. As a special case we consider a finite nonlinear LRC-network, whose inductors are linear, time-varying.

In this paper various conditions guaranteeing the ordinary, uniform, and asymptoticA-stability of semistate equations are given. These results are based on and given in terms of the semi-explicit form of a semistate equation.

This paper contains an abstract treatment of functional equations which involve non-linear causal operators. We consider equations on linear spaces that are certain extensions of Banach or Hilbert spaces. The causality is defined in the traditional way, but by a “past” we mean a set from a given family of subsets of a generalized “time domain.”An operator A is said to have a resolvent operator Q, if for each u from a certain space, the equation $x = A(x,u)$ possesses a unique solution x ; then $x = Qu$. We prove a theorem giving conditions for the existence of Q, and for continuity and boundedness of Q in a certain sense.Further results are obtained for the case $A(x,u) = Bx + u$, i.e., for an equation of Hammerstein’s type. In particular, it is shown that some monotonicity properties of operators involved guarantee the existence and continuity of the resolvent Q. The theory is illustrated by several concrete examples.

This paper presents a theorem stating conditions under which an n-port obtained by series and parallel connections of elementary n-ports is passive, i.e., incapable of. producing energy under any excitation. An electrical n-port built up from purely inductive, resistive and capacitive time-varying n-ports by combining them in series and parallel is a type of the n-port considered.

The paper deals with a qualitative property of linear continuous operators defined on distributions, that is, with a property appearing as a generalization of the traditional causality. The traditional causality of an operator A means that ${\operatorname{supp}}Ax \subset S$ whenever ${\operatorname{supp}}x \subset S$, where A is any interval $[T,\infty )$. Here, causality is defined in the same way, but S is any member from a certain family of subsets of $R^m $, called a scale.A theorem is proved which gives necessary and sufficient conditions for an operator to be causal with respect to a given scale.As an application there is considered a slightly generalized convolution-type operator; it is shown that this operator is causal with respect to a scale which consists of all translations of a fixed cone.

Bounds for the uniform norm of the errors in the second and third derivatives of cubic interpolating splines-on-splines are derived. These bounds encompass the case when approximate rather than exact derivatives are used at the endpoints. Furthermore, it is shown that, for a uniform mesh, spline-on-spline techniques lead to an accuracy of one additional order at the knots. Results of some computational experiments are given.

It is shown that every linear, bounded, strictly causal operator on a resolution space $[H,P^t ]$ is in fact contrastive under a certain inner product which generates a norm equivalent to the original norm on H.