In fuzzy logic, where members of a set might be linguistic terms, the degree of reflexivity might be in unit interval [0,1] instead of {0,1}. This behaviour of a fuzzy set plays an important role especially in the field of inclusion and similarity measure. This paper is aimed at discovering the relations between the parameters of Lukasiewicz transitive members of a family of cardinality-based fuzzy measure.

The authors of this article deal with a first order non-linear Volterra integro-differential equation (NVIDE). To this end, the conditions are obtained which are sufficient for stability (S), boundedness (B), and for every solution x of (NVIDE) is integrable. For properties of solutions of (NVIDE) considered three new theorems on (S), (B) and integrability properties of solutions are proved. The methods of the proofs involve constructing of a suitable Lyapunov functional (LF) which gives meaningful results for the problems to be investigated. The conditions to be given involve nonlinear improvement and extensions of those conditions found in the literature. An example is provided to illustrate the effectiveness of the proposed results. The results obtained are new and complements that found in the literature.

The soft category theory offers a way to study soft theories developed so far more generally. The main purpose of this paper is to introduce the basic algebraic operations in soft categories, and for that we introduce some algebraic operations, like intersection and union, in categories. Also, the notion of composition of soft functors is introduced to form category of all soft categories.

In this paper, we introduced a new flexible extension of the Generalized Half-Normal lifetime model as well as a new log-location regression model based on the proposed model. Some useful characterization results are presented and some mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters by means of a graphical Monte Carlo simulation study. We show that the new log-location regression lifetime model can be very useful in analysing real data and provide more realistic fits than other regression models. Index plot of the modified deviance residual and Q-Q plot for modified deviance residual are presented to illustrate that our new model is more appropriate to HIV data set than other competitive models like log-odd log-logistic generalized half-normal regression model and log-generalized half-normal regression model. The sensitivity analysis is used via the index plot of generalized cook distance to discover the possible influential observations.

The aim of this work is to present the construction and use of Surrogate Reservoir Models capable of accurately predicting cumulative oil production for every well stimulated with cyclic steam injection at any given time in a heavy oil reservoir in Mexico considering uncertain variables. The central composite experimental design technique was selected to capture the maximum amount of information from the model response with a minimum number of reservoir models simulations. Four input uncertain variables (the dead oil viscosity with temperature, the reservoir pressure, the reservoir permeability and oil sand thickness hydraulically connected to the well) were selected as the ones with more impact on the initial hot oil production rate according to an analytical production prediction model. Twenty five runs were designed and performed with the STARS simulator for each well type on the reservoir model. The results show that the use of Surrogate Reservoir Models is a fast viable alternative to perform probabilistic production forecasting of the reservoir.

Milaszewicz, (Milaszewic J.P, Linear Algebra. Appl. 93,1987, 161-170) presented new preconditioner for linear system in order to improve the convergence rates of Jacobi and Gauss-Seidel iterative methods. Li et al., (Li Y., Li C., Wu S., Appl. Math. Comput. 186, 2007, 379-388) applied this preconditioner and provided convergence theorem for modified AOR method. Yun and Kim (Yun J.H., Kim S.W., Appl. Math. Comput. 201, 2008, 56-64) pointed out some errors in Li et al. theorem and provided some correct results for convergence of the preconditioned AOR method. In this paper, we analyze their convergence properly and propose a new theorem for irreducible modified AOR method. In particular, based on directed graph, we prove that the convergence theorem of Li et al. is true, without any additional assumptions.

Mimetic finite difference (MFD) approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP). In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC) with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD) stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.