Abstract: We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension of the sample paths of such processes. Moreover we compare different notions of fractional differentiability and calculate as a second new result

Abstract: An important property of production functions is the concept return to scale (RTS) as found in the literature. There are two common variations RTS in data envelopment analysis (DEA) used, constant return to scale (CRS) and variation return to scale (VRS). The envelopment surface in BCC model is VRS and this is the result of the presence of the convexity constraint in the dual model and, equivalently, the presence of new separate variable, usually called u0, is introduced in the primal model which makes it possible to determine whether operations were led in the areas of constant, increasing and decreasing. In conventional BCC model make an assumption that input-output data and u0 are exact. While accurate measurement in many real applications due to either non-availability of sophisticated measurement tools or qualitative nature of the phenomena may not be possible, consequently, this information can be represented as fuzzy numbers or linguistic terms. In this paper the RTS of efficient decision making units (DMUs) are investigated in BCC model where fuzziness is considered in both inputs and outputs and u0 variable. The proposed models provide the stability of fuzzy u0 as interval region, consequently analyst can easily examine the sensitivity of RTS of efficient DMUs. Using alpha-cut, an alternative approach is suggested to solve the obtained model. To illustrate the proposed method, a numerical example is solved.

Abstract: This paper presents new fifth-order diagonally implicit Runge-Kutta integration formulas for stiff initial value problems, designed to be Lstable method. The stability of the method is analyzed and numerical results are shown to verify the conclusions. Mathematics Subject Classifications: 51N20, 62J05, 70F99

Abstract: In this article, a new class of Runge-Kutta methods for initial value problems y � = f (x,y) are introduced, this method replace evaluations of f with approximations of fand use the harmonic mean in the main formula. If fis approximated to sufficient accuracy from past and current evaluations of f, the resulting multi-step Runge-Kutta method can be considered as replacing functional evaluations with approxima- tions of f � . Here is presented an O(h 3 ) method which requires only two evaluations of f. The stability of the method is analyzed. Numer- ical examples with excellent results are shown to verify that this new method is superior to existing multi-step method like the third order Adams-Bashforth. Mathematics Subject Classifications: 51N20, 62J05, 70F99

Abstract: We give a new proof of the classical Watson theorem for the summation of a 3F2 hypergeometric series of unit argument. The proof relies on the two well-known Gauss summation theorems for the 2F1 function.

Abstract: In recent years, some methods have been proposed in solving performance evaluation issues by using fuzzy set theory. In this paper, an improvised method for performance evaluation under fuzzy environment is presented. Fuzzy linguistic variables are used throughout the process and the aggregated fuzzy numbers which are based on the standard score concept are employed in aggregating the fuzzy assessment of the decision makers. The centroid indices such as distance index, area index, score index and index based on standard deviation are used in calculating the ranking order of the alternatives. A study has been carried out in evaluating lecturers’ teaching performance at one of the public universities in the East Coast of Malaysia. This method is capable to provide consistent, effective and precise results and may also give great satisfaction to all parties involved in the decision-making process. It can also be a valuable tool in solving a variety of decision-making problems.

Abstract: Let A denote the class of analytic functions with the normalization f(0) = f � (0) − 1 = 0 in the open unit disk U = {z : |z| < 1}, set

Abstract: A methodology based on the algorithmic complexity theory has been applied to assess the relative efficiency of the stocks listed on Bovespa. We provide eight alternative listings of the top ten stocks according to their efficiency rates.

Abstract: This paper address the exponential stability for a class of switched systems with mixed time delays. Based on linear matrix inequalities and Lyapunov-Krasovskii functional approach, a geometrically switching rule for the exponential stability of the system is designed. The approach allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. Numerical example to show the effectiveness of the proposed method is given. Mathematics Subject Classification: 34D05, 34D20, 34K20, 34K35

Abstract: We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n 2p , where n is the summation index and p is a positive integer. The possibility is examined of reducing the number of terms below the value Nt � (t/2π) 1/2 in the finite main sum appearing in asymptotic approximations for ζ(s) on the critical line s = 1 + it as t →∞ .I t is shown that the expansion corresponding to quadratic dependence on n (p = 1) is the best possible representation of this type for ζ(s). Mathematics Subject Classification: 11M06, 33B20, 34E05, 41A60

Abstract: In this paper we consider the problem of missing data in a time series analysis. We propose asymmetrical r = s winsorized mean to handle the problem of missing data. Beside that we suggested the Neyman allocation method to choose the values of r and s in asymmetric winsorized mean. We used the a absolute mean error and mean square error to compare the result of estimation missing data with other methods, such as trends, average of the whole data, naive forecast and average bound of the holes and simultaneous filling in the missing data. An example had been presented.

Abstract: Certain types of combinatorial rankings and hierarchies of labeled or unlabeled elements are presented along with their counting formulas. Mathematics Subject Classication: 05A15, 05A18

Abstract: In this paper, we consider a class of continuous nonlinear programs posed in a function space called separated continuous nonlinear programs (SCNP). In first step we transform the constraints of problem to integral constraints. Then by using Riesz representation theorem we reduce the later problem to an infinitedimensional linear programming problem. After that we approximate the later problem to a finite-dimensional linear programming problem. Then by solving this problem, we obtain an approximate solution for original problem in the form piecewise constant function. Finally, we investigate several numerical examples.

Abstract: The results of three-parameter experiments are commonly interpreted by the trilinear equation for eight data in a prismatic array. Ifa center point estimate is available, the eight-and nine-point arrays can be represented by new exponential-type equations. The equations are easy to generate, they are invariant under data translation, and they estimate curvature coefficients.

Abstract: The unit root tests of Perron (1989, Econometrica) were designed to have power against the stationary alternative characterized by a break in the trend function. We show that all versions of Perron’s (1989) tests can be over-sized when there is a break in the innovation variance. We propose modified Perron statistics based on the GLS transformation proposed by Kim, Leybourne, and Newbold (2002, Journal of Econometrics) that maintain size and have power against the trend-break stationary alternative. The modified Perron statistics weakens evidence against the unit root null for the Nelson-Plosser macroeconomic series. Mathematics Subject Classification: 62F03, 62M10, 62P20, 91B84

Abstract: In many practical situations in which the only information we have about the quantity x is that its value is within an interval [x,x], a reasonable estimate for this quantity is the geometric mean of the bounds √ x · x. In this paper, we provide a new justification for this geometric mean heuristic.

Abstract: In the present paper, the authors introduce and study new subclass of normalized analytic univalent function S ∗ (k, β) for some operator on Hilbert space.

Abstract: We revisit the notion of using divergences, or relative-entropies, as measures of the distance between two mixed states, with special em- phasis on power-law entropies. We analyze the Csiszar and Bregman- type q-divergences with reference to i) Werner states, and ii) thermal states obtained using a one-dimensional Heisenberg two-spin chain with a magnetic field B along the z-axis. In both cases, we find that the q-Jensen-Shannon divergence enlarges the range of permissible power- law exponents, as compared to results of previous literature. It is also shown that this divergence-measure serves as a good indicator for crit- ical phenomena in the Heisenberg model.

Abstract: Two classes of univalent functions with respect to k-symmetric points define on the unit disk satisfying the conditions: � ∞ n=1 (nk +1 − α)|ank+1| + � ∞ n=2;nlk+1 n|an |≤ 1 − α, and ∞ � n=1 (nk + 1)(nk +1 − α)|ank+1| + ∞ � n=2;nlk+1 n 2 |an |≤ 1 − α are given. The two inequalities of the functions belonging to these two classes are the starlike and convex functions with respect to k-symmetric points, respectively. Some interesting properties of generalisations of Hadamard product in these classes are given. Mathematics Subject Classification: 30C45, 30C50, 30C55

Abstract: Traditionally, fuzzy logic used non-standard notations like m1/x1 + . . . + mn/xn for a function that attains the value m1 at x1, . . . , and the value mn at xn. In this paper, we provide an algebraic explanation for these notations. Mathematics Subject Classification: 03B52

Abstract: In this paper, the two-dimensional creeping flows outside a circular cylinder induced by source/sink with various boundary conditions is studied. Analytical solutions for the flow field are obtained by straight forward application of the Fourier method. The streamline patterns are sketched for a number of special cases where the boundary conditions is varying from no slip to perfect slip boundary conditions. Some interesting flow patterns are observed in the parameter space which may have potential significance in studies of various flows including flows in journal bearing, mixing flows, etc. We also investigate into the way the streamline topologies change as the parameters are varied.