Abstract: In this paper, stratified median ranked set sampling (SMRSS) method is suggested for estimating the population mean. The SMRSS is compared with simple random sampling (SRS), stratified simple random sampling (SSRS) and stratified ranked set sampling (SRSS). It is shown that SMRSS estimator is an unbiased of the population mean of symmetric distributions and is more efficient than its counterparts using SRS, SSRS and SRSS.

Abstract: This paper describes a method for simulating univariate and multivariate Burr Type III and Type XII distributions with specied correlation matrices. The methodology is based on the derivation of the parametric forms of a pdf and cdf for this family of distributions. The paper shows how shape parameters can be computed for specied values of skew and kurtosis. It is also demonstrated how to compute percentage points and other measures of central tendency such as the mode, median, and trimmed mean. Examples are provided to demonstrate how this Burr family can be used in the context of distribution tting using real data sets. The results of a Monte Carlo simulation are provided to conrm that the proposed method generates distributions with user specied values of skew, kurtosis, and intercorrelation. Tabled values of shape parameters and boundary values of kurtosis are also provided in the appendices for the user. Mathematics Subject Classication: 65C05, 65C10, 65C60

Abstract: Fuzzy set provides a powerful technique to introduce uncertainty into numerical methods. However, the computations of fuzzy sets often face difficult problems. This is due to non-applicability of common existing methods, severe overestimation in computation, or very high computational complexity. This paper proposes a new strategy to introduce uncertainty into Euler’s method. It consists of two parts. First, we propose a new fuzzy version of Euler’s method, which takes into account the dependency problem that arises in the classical Euler’s method. Second, we perform optimisation technique to approximate the solution of differential equations with fuzzy initial values. This combination turns out to be a great tool to tackle uncertainty in any numerical method. One example is provided to show the capability of our proposed methods compared to the conventional fuzzy version of Euler’s method proposed in the literature.

Abstract: In a typical class, we have students at different levels of knowledge, student with different ability to learn the material. In the ideal world, we should devote unlimited individual attention to all the students and make sure that everyone learns all the material. In real life, our resources are finite. Based on this finite amount of resources, what is the best way to distribute efforts between different students?

Abstract: Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion in the case of a product of four Hermite polynomials Hn(x) as n → ∞ is obtained by a discrete analogue of Laplace’s method applied to sums. Mathematics Subject Classification:

Abstract: The deviation in SH-waves’ velocities is expected once the saturation degree in the medium is asymmetrical. Hence, SH-waves’ propagation in the porous medium saturated with asymmetry ∞uid density is studied for the difiusive proflles. SH-waves are propagated in similar directions and also opposite directions with the mediums fall into two distinctive groups: insoluble as well as soluble mediums. In similar direction of propagation, low density ∞uid revokes the difiusive characteristics while high density ∞uid promotes difiusive attribute. However, the difiusive SH-waves are as well found in the medium saturated with low density ∞uid when the ∞uid is asymmetrical in density. In the case of opposite direction of propagation, the recurring SH-waves are found in the medium saturated with low and asymmetry density ∞uid. Mathematics Subject Classiflcation: 86A15, 74J30, 86A17

Abstract: For spatially distributed quantities v(x), there are two main reasons why the measured value is different from the actual value. First, the sensors are imprecise, so the measured value is slightly different from the actual one. Second, sensors have a finite spatial resolution: they do not simply measure the value at a single point, they are “blurred”, i.e., affected by the values of the nearby points as well. It is known that uncertainty can be often described by the Gaussian distribution. This possibility comes from the Central Limit Theorem, according to which the sum of many independent small measurement errors has an approximately Gaussian distribution. In this paper, we show how a similar technique can be applied to spatial resolution: a combination of several independent small blurrings can be described by a Gaussian blurring function. Mathematics Subject Classification: 60F05, 60F99, 86A99, 91C05

Abstract: This paper discusses isoparametric technique for handling curvilinear geometries in high accuracy discontinuous Galerkin (DG) simulations for time-domain Maxwell's equations. With isoparametric elements, numerical fluxes along curved boundaries are computed much more accurately due to the high-order representation of the computational domain. Numerical experiments for 2D propagation problems demonstrate the applicability and benefits of the isoparametric technique for simulations involving curved domains.

Abstract: A unified set of governing linear and nonlinear relations are presented, which contain aerodynamic, structural, material and control inclusive contributions. Qualitative analyses are undertaken to determine the influences of the individual terms in the governing dynamic relations of lifting surface panels exposed to inertia, aerodynamic loads and noise. Panel buckling and flutter are considered as well as piezoelectric and aero-servo controls. Nonlinear results are evaluated and compared to linear solutions. Unfortunately the phase relations between the various components of the plate governing relations are sufficiently complicated to prevent analytical sensitivity comparisons. A limited set of numerical simulations are offered instead. Results are applicable to full scale flight vehicles as well as to UAVs and MAVs.

Abstract: In many practical situations, we have a (partially) ordered set V of different values. For example, we may have the set of all possible values of temperature, or the set of all possible degrees of confidence in a statement. In practice, we are often uncertain about the exact value of the quantity. Due to this uncertainty, at best, we know a set S ⊆ V of possible values of the quantity: e.g., an interval of possible values. For such sets, it is natural to define a relation “possibly larger” S1 ♦ ≤ S2 meaning that v1 ≤ v2 for some v1 ∈ S1 and v2 ∈ S2. In this paper, we prove that an arbitrary reflexive relation can be thus represented. Similar representation theorems are proven for different versions of this relation.

Abstract: Several method of perturbation tests have been proposed for testing nullity of a partial regression coefficient in a linera model. These methods were compared in terms of empirical type 1 error and power by statisticians. One striking result of the simulation based comparison is that the two emerging methods, while previously identified as equivalent formulations of the permutation strategy under the reduced model, did actiually produce quite different results. And one of this methods have almost the best result. Some theoretical justification to the empirical findings is given here. We compared estimators and variances of these two methods analytically in the double regression linear model. Our results give mathematical support to the observation obtained by simulation. Furthermore, for the first time we obtained the expected value of the estimators of the variance by the permutational distribution and we found that one of these estimators is unbias.

Abstract: In this paper a set of formulations of an N-dimensional (ND) autoregressive-moving average (ARMA) model identification method, and a two-dimensional (2D) forgetting factor approach in time-series modelling, is developed. An optimum estimation and prediction approach in healthcare picture smoothing based on a 2D ARMA modelling, has been implemented; and satisfactory results have been obtained. Our approach indicates the desirability of accurate statistical modelling of high-dimensional or periodic digital data.

Abstract: To decrease counting errors, it is often reasonable to arrange the counted objects into rectangles and/or parallelepipeds. In this paper, we describe how to design optimal arrangements of this type. A geometric approach to counting: a description. Once, we went to buy 24 cups of easy-to-prepare “instant lunch” soup. When we counted these cups ourselves, we had to count several times to make sure that we did not make a mistake. A salesperson counted them very easily: she grouped them into a nice parallelepiped of length 4, width 3, and height 2, and then multiplied these three numbers to get 4× 3× 2 = 24. Why it is interesting. Of course, everyone knows that the volume of a parallelepiped is the product of the sides, and that, similarly, the area of a rectangle is the product of its sides. The corresponding geometric “area” approach is one of the main methods of teaching multiplication of integers (and fractions); see, e.g., Chapters 10 and 13 from [5], [1, 2, 3, 4], and references therein. What was interesting is that the salesperson used the same geometric arrangement not for multiplication, but for error-less counting. What we do in this paper. We explain why this geometric approach reduced the errors, and what is the best way to use this approach if we want to decrease counting errors. Main idea. Every time we perform an arithmetic operation, there is a probability that we make a mistake. • When we count a new object – i.e., when we add one to the previous total – we can make a mistake. • When we multiply two numbers, we can make a mistake.

Abstract: Detecting arcing faults is an important but difficult-to-solve practical problem. In this paper, we show how the Minimum Description Length (MDL) Principle can help in solving this problem. Mathematics Subject Classification: 68Q30, 93A

Abstract: In this paper, we provide a game-theory-type explanation for the recently observed paradox: that a soccer ball designed to make the trajectories more predictable and thus, to increase the scoring, has actually led to a significant scoring decrease at the 2010 World Cup. Mathematics Subject Classification: 91A80

Abstract: This article discusses Bayesian and non-Bayesian estimation problem of the unknown parameter for the inverse Rayleigh distribution based on lower record values. Maximum likelihood estimator of the unknown parameters were obtained. Also, Bayes estimator have been developed under squared error and zero one loss functions. These estimators are derived using the informative prior distribution. Bayesian and non Bayesian interval estimation for the inverse Rayleigh parameters are obtained. Furthermore, Bayesian prediction interval of the future record values are discussed and obtained. Finally practical example using simulated record values are given to illustrate the theoretical results of prediction interval.