A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

Approximate analysis of coupled non-linear non-conservative systems subjected to step-function excitation

The paper deals with the approximate analysis of non-linear non-conservative systems oftwo degrees of freedom subjected to step-function excitation. The method of averaging of Krylov and Bogoliubov is used to arrive at the approximate equations for amplitude and phase. An example of a spring-mass-damper system is presented to illustrate the method and a comparison with numerical results brings out the validity of the approach.

Information, risk and trust in the food chain : Ex-ante valuation of consumer willingness to pay for beef quality information using the contingent valuation method

The safety of food has become an increasingly interesting issue to consumers and the media. It has also become a source of concern, as the amount of information on the risks related to food safety continues to expand. Today, risk and safety are permanent elements within the concept of food quality. Safety, in particular, is the attribute that consumers find very difficult to assess. The literature in this study consists of three main themes: traceability; consumer behaviour related to both quality and safety issues and perception of risk; and valuation methods. The empirical scope of the study was restricted to beef, because the beef labelling system enables reliable tracing of the origin of beef, as well as attributes related to safety, environmental friendliness and animal welfare. The purpose of this study was to examine what kind of information flows are required to ensure quality and safety in the food chain for beef, and who should produce that information. Studying the willingness to pay of consumers makes it possible to determine whether the consumers consider the quantity of information available on the safety and quality of beef sufficient. One of the main findings of this study was that the majority of Finnish consumers (73%) regard increased quality information as beneficial. These benefits were assessed using the contingent valuation method. The results showed that those who were willing to pay for increased information on the quality and safety of beef would accept an average price increase of 24% per kilogram. The results showed that certain risk factors impact consumer willingness to pay. If the respondents considered genetic modification of food or foodborne zoonotic diseases as harmful or extremely harmful risk factors in food, they were more likely to be willing to pay for quality information. The results produced by the models thus confirmed the premise that certain food-related risks affect willingness to pay for beef quality information. The results also showed that safety-related quality cues are significant to the consumers. In the first place, the consumers would like to receive information on the control of zoonotic diseases that are contagious to humans. Similarly, other process-control related information ranked high among the top responses. Information on any potential genetic modification was also considered important, even though genetic modification was not regarded as a high risk factor.

Identification of a class of non-linear systems

This paper considers the on-line identification of a non-linear system in terms of a Hammerstein model, with a zero-memory non-linear gain followed by a linear system. The linear part is represented by a Laguerre expansion of its impulse response and the non-linear part by a polynomial. The identification procedure involves determination of the coefficients of the Laguerre expansion of correlation functions and an iterative adjustment of the parameters of the non-linear gain by gradient methods. The method is applicable to situations involving a wide class of input signals. Even in the presence of additive correlated noise, satisfactory performance is achieved with the variance of the error converging to a value close to the variance of the noise. Digital computer simulation establishes the practicability of the scheme in different situations.

Linear description of electrical networks for computer analysis

A parentheses-free code is suggested for the description of two-terminal electrical networks for computer analysis.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Effect of vitamin A deprivation on the cholesterol side-chain cleavage enzyme activity of testes and ovaries of rats (Short Communication)

The cholesterol side-chain cleavage enzyme activity is decreased considerably at the mild stage of vitamin A deficiency in rat testes and ovaries and the decrease in activity becomes more pronounced with progress of deficiency. Supplementation of the deficient rats with retinyl acetate, but not retinoic acid, restores the enzyme activity to normal values. The cholesterol side-chain cleavage enzyme of adrenals is not affected by any of the above treatments.

A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Starchy Staples Value Chain Review

PARDI – Pacific Agribusiness Research & Development Initiative

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Antioxidative long chain alkylresorcinols. Synthesis and deuterium labelling of bioactive compounds present in whole grains

The first synthesis of long chain 5-n-alkylresorcinols (C15-C25) in whole grains and whole grain products by a novel modification of Wittig reaction is described. 5-n-Alkylresorcinols are phenolic lipids that have various effects on biological systems, such as antioxidant activity and interaction with biological membranes. These compounds are considered as biomarkers of whole grain intake, which is connected with reduced risk of cardiovascular diseases and certain cancers. Novel hapten derivatives of 5-n-alkylresorcinols, potential compounds for immunoanalytical techniques, are prepared by the same procedure utilizing microwave catalysed aqueous Wittig reaction as the key step. The synthesised analogues are required by various analytical, metabolism and bioactivity investigations. Four alternative strategies for producing deuterium polylabelled 5-n-alkylresorcinols are explored. Ring-labelled D3-alkylresorcinols were synthesized by acidic H/D exchange. Side chain -labelled D4-derivative was prepared by a total synthesis approach utilizing D2 deuterogenation of a D2-alkene derivative, and deuterogenation of alkynes was investigated in another total synthesis approach. An -D3-labelled alkylresorcinol is isotopically pure and completely stable under all relevant conditions encountered during analytical work. The labelling of another phenolic component of whole grains was explored. The preparation of D3-ferulic acid and related compounds by way of selective methylation of the precursors is described. The deuterated compounds are useful as standards in the quantification of these natural products in various substances, such as food and human fluids. The pure 5-n-alkylresorcinol analogues prepared were used in in vitro experiments on alkylresorcinol antioxidant activity and antigenotoxicity. The in vitro experiments show that alkylresorcinols act as antioxidants, especially when incorporated into biological systems, but possess lower activity in chemical tests (FRAP and DPPH assay). Whole grain alkylresorcinols are shown for the first time to have a protective effect against copper induced oxidation of LDL, and H2O2 or genotoxic faecal water induced damage on HT29 cells.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems