Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

Inarinsaamen käsitemetaforat

This study discusses the conceptual metaphors of Inari Saami, an endangered, indigenous, Finno-Ugrian language spoken in northern Finland. The research focuses on systematical mappings between source and target domains in conventional Inari Saami metaphors and metonymies. The research material consists of the Inarinsaamen idiomisanakirja [Inari Saami idiom dictionary] which has been compiled by the author in collaboration with an Inari Saami co-author; the Inarilappisches Wörterbuch; Inarinsaamelaista kansantietoutta [Inari Saami folk knowledge]; and Aanaarkiela čájttuzeh [Inari Saami sample texts]. The metaphors and metonymies found in these literary sources are divided into categories on the basis of the target domains and according to the classic model of Lakoff ja Johnson (1980). This method reveals the systematical recurrence of source domains inside each category and thus discovers the systematical patterns of metaphoric mapping, the conceptual metaphors . As a result 44 conceptual metaphors and 16 conceptual metonymies are presented through approximately 500 glossed examples. These findings are discussed against the background of what is known about the cognitive and neural processing of metaphors on the one hand, and what is known about Inari Saami culture on the other. This theoretical framework highlights culture as the underlying force behind conceptual metaphors. The recurring metonymies seem to follow a culturally salient indexicality. For example, the Inari Saami conceptual metonymy TIME IS NATURE reflects the seasonal changes in the year s cycle, which was the salient index of time in traditional Inari Saami culture. The recurring metaphors, for their part, follow a culturally salient iconicity. The conceptual metaphor PRIDE IS ANTLERS is based on an iconicity which is experienced and interpreted by the Inari Saami. A proud person is associated with a reindeer who shows off his impressive antlers. The conceptual metaphor/metonymy seems to be a reflection of culture rather than a cognitive means of understanding an abstract domain in terms of a concrete domain, as hypothesized by certain theoreticians. Repeating this study with other languages may lead to the possibility of typologizing the metaphorical systems of the world s languages and understanding the diversity of metaphor systems in the endangered languages of the world.

Split-Freedom And Mvd-Intersection - A New Characterization Of Multivalued Dependencies Having Conflict-Free Covers

Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [2,12,15,16]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a confiict-free cover. In [8] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of “split-free” sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of “intersection” of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial-time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorthms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs,thereby showing that they are interesting in their own right.

Evaluating business process compliance management frameworks

This research contributes a formal framework to evaluate whether existing CMFs can model and reason about various types of normative requirements. The framework can be used to determine the level of coverage of concepts provided by CMFs, establish mappings between CMF languages and the semantics for the normative concepts and evaluate the suitability of a CMF for issuing a certification of compliance. The developed framework is independent of any specific formalism and it has been formally defined and validated through the examples of such mappings of CMFs.

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

A new analytical approach to optimize a generation schedule

Identification of the optimum generation schedule by various methods of coordinating incremental generation costs and incremental transmission losses has been described previously in the literature. This paper presents an analytical approach which reduces the time-consuming iterative procedure into a mere positive-root determination of a third-order polynomial in λ. This approach includes the effect of transmission losses and is suitable for systems with any number of plants. The validity and effectiveness of this method are demonstrated by analysing a sample system.

Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

A dual-slope analogue-to-digital converter for generating polynomials

A new digital polynomial generator using the principle of dual-slope analogue-to-digital conversion is proposed. Techniques for realizing a wide range of integer as well as fractional coefficients to obtain the desired polynomial have been discussed. The suitability of realizing the proposed polynomial generator in integrated circuit form is also indicated.

Non-linear and linear postulations of technology adoption determinants

Using polynomial regression and response surface analysis to examine the non-linearity between variables, this study demonstrates that better analytical nuances are required to investigate the relationships between constructs when the underlying theories suggest non-linearity. By utilising the Theory of Planned Behaviour (TPB), Ettlie’s adoption stages as well as employing data gathered from 162 owners of Small and Medium-sized Enterprises (SMEs), our findings reveal that subjective norms and attitude have differing influences upon behavioural intention in both the evaluation and trial stages of the adoption.

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.

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.

The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Self-tuning is applied to the control of nonlinear systems represented by the Hammerstein model wherein the nonlinearity is any odd-order polynomial. But control costing is not feasible in general. Initial relay control is employed to contain the deviations.