• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.591-603
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• 2005

A representation for non-commutative Banach algebras is discussed, which generalizes the Gelfand representation for commutative Banach algebras and the Gelfand-Naimark representation for $C^{\ast}$-algebras. Its basic properties are also investigated. In appendix, an example of Banach algebra that is neither semi-simple nor radical is presented.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1133-1138
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• 2008

A general method of detecting outliers based on a change of likelihood by using the influence function is suggested. It can be applied to all kinds of distributions that are specified by parameters. For the multivariate normal case, specific computations are made to get the corresponding conditional influence function. A numerical example is provided for illustration.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.479-485
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• 2003

The influence of observations on the Wilks' lambda test of a linear hypothesis in multivariate regression is investigated using the local influence method. The perturbation scheme of case-weights is considered. A numerical example is given to show the effectiveness of the local influence method in identifying the influential observations.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.541-547
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• 2006

A procedure for investigating the influence of observations in choosing Box-Cox transformation for multivariate data is suggested. It is effective in spotting influential observations. A numerical example is provided for illustration.

• Journal of Engineering Education Research
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• v.21 no.2
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• pp.3-6
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• 2018

A few thermodynamics texts are commonly found to have unrealistic example problems in which the process violates the second law of thermodynamics. This error would result from presentation order in the text which introduces first the first law for cycles, systems, and control volumes and then the second law later. In the presentation order, the example problems deal only with the first law without telling whether the process violates the second law. To correct this erroneous situation, it could be recommended to present the first law and the second law successively so that both laws could be applied simultaneously to the given example problems.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.583-589
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• 2019

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.773-778
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• 2009

Recently, Xue et al. [Computers and Mathematics with Applications 55 (2008) 1215-1224] proposed a formula for the expected value of a function of a fuzzy variable based on the assumption that the fuzzy variable has a continuous membership function. In conclusion, they remained the case where the membership function of the fuzzy variable is discontinuous for the future research, and then expected to get similar results. Thus this note is to propose a new formula for the expected value of a function of a general fuzzy variable which is not restricted on having a continuous membership function. Furthermore, we give an example which cannot be applied to the formula that Xue et al. proposed. We also use the same example given by Xue et al. to show how to apply the new formula.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.137-154
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• 2007

In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.787-796
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• 2005

We generalize a characterization of classical orthogonal polynomials and obtain a two-variable analogue. Also an example is given arising from a second order partial differential equation.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.213-223
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• 2001

The use of fuzzy number over interval of confidence instead of possibilitic consideration for solving fuzzy equation is proposed. This approach of solving fuzzy equation by interval arithmetic and ${\alpha}$-cuts has a considerable advantage. Through theoretical analysis, an illustrative example and computational results, we show that the proposed approach is more general and straight-forword.