flow in the driven cavity calculated by the lattice boltzmann method the lattice boltzmann method with enhanced collisions and rest particles is used to calculate the flow in a two dimensional lid driven cavity the abilitity of this method to compute the velocity and the pressure of an incompressible fluid in a geometry with dirichlet and neumann boundary conditions is verified by calculating a test problem where the analytical solution is known different parameter configurations have been tested for reynolds numbers from re 10 to re 2000 the vortex structure for a more generalized lid driven cavity problem with a non uniform top speed has been studied for various acpect ratios

fuzzy based linguistic patterns as a tool for the flexible assessment of a priority vector obtained by pairwise comparisons a novel approach to the assessment of a hierarchy vector generated by an expert pairwise comparison matrix is proposed the quality of a given hierarchy is measured using so called linguistic patterns i e specially constructed logical expressions and an expert assessment matrix the idea of this approach is based on a concept proposed previously as a flexible criterion for the domain of facility layout problems the adaptation of the linguistic pattern approach to the assessment of a hierarchy vector also by analogy to the analytic hierarchy process or ahp facilitates evaluations of expert consistency the proposed idea is shown to be less sensitive to potential expert errors than both the classical and fuzzy ahp techniques the proposed approach is described in detail and illustrated with simple examples some features of the proposed approach were studied using computer simulation experiments and the results are reported together with the conclusions obtained

evaluating naval tactical missile systems by fuzzy ahp based on the grade value of membership function abstract many decision making problems which are complicated and fuzzy in nature exist in modern society how to solve them is becoming increasingly important for human society for solving multiple criteria s decision making in a fuzzy environment in this paper we will propose a new algorithm for evaluating naval tactical missile systems by the fuzzy analytical hierarchy process based on grade value of membership function generally we are given scores by experience of experts to represent judgmental objects in this paper from viewpoint of many experts we will build membership functions of judgement criteria for all sub items when the membership function is built we can calculate the grade value by data of missile performance the grade value is called performance score our methods can be summarized in the following 1 1 building membership function of judgement criteria for all sub items it is called fuzzy standard 2 2 calculate the grade of membership function by practical data to represent performance scores 3 3 use fuzzy ahp method and entropy concepts to calculate aggregate weights finally for a simple and efficient computation we have developed a systematic and practical program to calculate all algorithms and apply the new algorithm to a naval tactical missile systems valuation and selection problem

tripled coincidence theorems for contractive type mappings in partially ordered metric spaces abstract in this paper we establish tripled coincidence point theorems for a pair of mappings f x x x x and g x x satisfying a nonlinear contractive condition ordered metric spaces presented theorems extend reveral existing results in the literature v lakshmikantham l ciric coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces nonlinear anal 70 2009 4341 4349 and harjani lopez and sadarangani in article j harjani b lopez k sadarangani fixed point theorems for mixed monotone operators and applications to integral equations nonlinear anal 74 2011 1749 1760

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

improved bounce back methods for no slip walls in lattice boltzmann schemes theory and simulations a detailed analysis is presented for the accuracy of several bounce back methods for imposing no slip walls in lattice boltzmann schemes by solving the lattice bgk bhatnagar gross krook equations analytically in the case of plane poiseuille flow it is found that the volumetric approach by chen et al is first order accurate in space and the method of bouzidi et al second order accurate in space the latter method however is not mass conservative because of errors associated with interpolation of densities residing on grid nodes therefore similar interpolations are applied to chen s volumetric scheme which indeed improves the accuracy in the case of plane poiseuille flow with boundaries parallel to the underlying grid for skew boundaries however it is found that the accuracy remains first order an alternative volumetric approach is proposed with a more accurate description of the geometrical surface this scheme is demonstrated to be second order accurate even in the case of skew channels the scheme is mass conservative in the propagation step because of its volumetric description but still not in the collision step however the deviation in the mass is in general found to be small and proportional to the second order terms in the standard bgk equilibrium distribution consequently the scheme is a priori mass conservative for stokes flow

fuzzy hierarchical analysis the lambda max method abstract we present a new method of finding the fuzzy weights in fuzzy hierarchical analysis which is the direct fuzzification of the max method used by saaty in the analytical hierarchical process an example is presented where there are five criteria and three alternatives

some ordered fixed point results and the property p in 2010 kadelburg et al 7 by providing an example showed that a contraction in an ordered metric space is not necessarily a contraction in the classical sense thus fixed point results in ordered metric spaces are generalizations of ones in metric spaces in a sense in this paper we give some ordered fixed point results for convex contractions and special mappings which satisfy some contraction conditions also we give some results concerning the property p

coupled fixed point theorems for contractions in fuzzy metric spaces in the present work we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces

fuzzy system reliability analysis by interval of confidence abstract the use of fuzzy number over interval of confidence instead of probability and possibilitic considerations for evaluating the range value and interval of the fuzzy reliability is proposed this approach of evaluating fuzzy system reliability by interval arithmetic and cuts has a considerable advantage we can calculate reliability problems easily by the use of derive and mathcad packages through theoretical analysis an illustrative example and computational results we show that the proposed approach is more general and simplified

fuzzy eigenvector method for obtaining normalized fuzzy weights from fuzzy pairwise comparison matrices proper formulas for obtaining the fuzzy maximal eigenvalue and the corresponding fuzzy maximal eigenvector of a fuzzy pairwise comparison matrix are proposed in this paper first the formulas for obtaining the fuzzy maximal eigenvalue of a fuzzy pairwise comparison matrix proposed by csutora buckley 2001 and by ishizaka 2014 are reviewed and the flaws in their formulas regarding the violation of the reciprocity of pairwise comparisons are pointed out new formulas for obtaining the fuzzy maximal eigenvalue preserving the reciprocity of pairwise comparisons are then proposed after a fuzzy extension of saaty s consistency index and consistency ratio is introduced in order to verify an acceptable level of inconsistency of a fuzzy pairwise comparison matrix further the methods for obtaining the fuzzy maximal eigenvector corresponding to the fuzzy maximal eigenvalue of a fuzzy pairwise comparison matrix proposed by wang chin 2006 and by ishizaka 2014 are reviewed the flaws in ishizaka s method are pointed out and wang chin s method is studied and modified in order to preserve the reciprocity of pairwise comparisons the fuzzy maximal eigenvalues and the corresponding fuzzy maximal eigenvectors obtained by the new formulas are confronted with those obtained by methods proposed by csutora buckley 2001 wang chin 2006 and ishizaka 2014 and three numerical examples are given for better illustration a proper fuzzy extension of the maximal eigenvector method is proposed the new fuzzy maximal eigenvalue preserves the reciprocity of pairwise comparisons by employing the reciprocity into the method redundant information is eliminated the elements of the fuzzy maximal eigenvector are normalized fuzzy weights

evaluating attack helicopters by ahp based on linguistic variable weight abstract in this paper we propose a new method for evaluating weapon systems by analytical hierarchy process ahp based on linguistic variable weight many researchers used fuzzy arithmetic operations with weight and attribute of computing performance score to solve fuzzy madm problems such as s m chen evaluating weapon systems using fuzzy arithmetic operations fuzzy sets and systems 77 1996 265 276 chen used a large number of fuzzy arithmetic operations which not only causes information data loss or more fuzziness but also adds to the difficulty and accuracy of decision making therefore we use linguistic variable weight method to solve the above problems and to avoid the mistake of decision making our method possesses intuition in accord with human rethinking model and is close to humanized uncertainty of language expression we use many experts viewpoints to build the membership function in order to calculate the performance score and identify expectation of the decision maker to avoid the constraint of system alternatives and subjective judgements of the decision maker in this paper we also use linguistic variable method to revise the method of c h cheng in proceedings of the fourth national conference on defense management pp 1113 1124 and r r yager fuzzy sets and systems 1 1978 87 95 firstly we measure the importance of relative weight and use it to determine the centralization or dilation power of linguistic hedge when the power of linguistic hedge is determined we can use it to calculate the results of decision making finally we construct a practical example for evaluating attack helicopters to illustrate our proposed method

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

common coupled fixed point theorems in cone metric spaces for w compatible mappings in this paper we introduce the concept of a w compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non empty interior coupled common fixed point theorems for such mappings are also proved our results generalize extend and unify several well known comparable results in the literature results are supported by three examples

multidimensional fixed point theorems under ψ φ contractive conditions in partially ordered complete metric spaces in this paper we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak contractive condition our results generalize extend and unify several classical and very recent related results in the literature see aydi et al 2011 berinde 2010 gnana bhaskar and lakshmikantham 2006 berzig and samet 2012 borcut and berinde 2012 choudhury et al 2011 karapinar and luong 2012 lakshmikantham and iric 2009 luong and thuan 2011 roldan 2012

fixed point theorems for mixed monotone operators and applications to integral equations abstract the purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions we also present an application to integral equations

momentum transfer correction for macroscopic gradient boundary conditions in lattice boltzmann methods the boundary conditions used to represent macroscopic gradient related effects in arbitrary geometries with the lattice boltzmann methods need a trade off between the complexity of the scheme due to the loss of localness and the difficulties for directly applying link based approaches and the accuracy obtained a generalization of the momentum transfer boundary condition is presented in which the arbitrary location of the boundary is addressed with link wise interpolation used for dirichlet conditions and the macroscopic gradient is taken into account with a finite difference scheme this leads to a stable approach for arbitrary geometries that can be used to impose neumann and robin boundary conditions the proposal is validated for stress boundary conditions at walls two dimensional steady and unsteady configurations are used as test case partial slip flow between two infinite plates and the slip flow past a circular cylinder

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

fuzzy hierarchical analysis revisited abstract we present a new method of finding the fuzzy weights in fuzzy hierarchical analysis which is the direct fuzzification of the original method used by saaty in the analytic hierarchy process we test our new procedure in two cases where there are formulas for the crisp weights an example is presented where there are five criteria and three alternatives

evaluating the best main battle tank using fuzzy decision theory with linguistic criteria evaluation abstract to face the reality of practical multiple criteria problems usually possessing characters of fuzziness and to consider group decision making with various subjective objective backgrounds usually participating in decision making process in this paper the experts opinions are described by linguistic terms which can be expressed in trapezoidal or triangular fuzzy numbers to make the consensus of the experts consistent we utilize fuzzy delphi method to adjust the fuzzy rating of every expert to achieve the consensus condition for the aggregate of many experts opinions we take the operation of fuzzy numbers to get the mean of fuzzy rating x ij and the mean of weight w j in multi alternatives and multi attributes cases the fuzzy decision matrix x x ij m n is constructed by the mean of the fuzzy rating x ij then we can derive the aggregate fuzzy numbers by multiplying the fuzzy decision matrix with the corresponding fuzzy attribute weights the final results become a problem of ranking fuzzy numbers we also propose an easy procedure of using fuzzy numbers to rank aggregate fuzzy numbers a i in this way we can obtain the best selection for evaluating system for practical application we propose an algorithm for evaluating the best main battle tank by fuzzy decision theory and compare it with other method

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

fixed point theorems in partially ordered metric spaces and applications abstract we prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order using a weak contractivity type of assumption besides including several recent developments our theorem can be used to investigate a large class of problems as an application we discuss the existence and uniqueness of solution for a periodic boundary value problem

lattice boltzmann modeling with discontinuous collision components hydrodynamic and advection diffusion equations irrespective of the nature of the modeled conservation laws we establish first the microscopic interface continuity conditions for lattice boltzmann lb multiple relaxation time link wise collision operators with discontinuous components equilibrium functions and or relaxation parameters effective macroscopic continuity conditions are derived for a planar implicit interface between two immiscible fluids described by the simple two phase hydrodynamic model and for an implicit interface boundary between two heterogeneous and anisotropic variably saturated soils described by richard s equation comparing the effective macroscopic conditions to the physical ones we show that the range of the accessible parameters is restricted e g a variation of fluid densities or a heterogeneity of the anisotropic soil properties when the interface is explicitly tracked the interface collision components are derived from the leading order continuity conditions among particular interface solutions a harmonic mean value is found to be an exact lb solution both for the interface kinematic viscosity and for the interface vertical hydraulic conductivity function we construct simple problems with the explicit and implicit interfaces matched exactly by the lb hydrodynamic and or advection diffusion schemes with the aid of special solutions for free collision parameters

applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy ahp the lack of consistency in decision making can lead to inconsistent conclusions in fuzzy analytic hierarchy process fuzzy ahp method it is difficult to ensure a consistent pairwise comparison furthermore establishing a pairwise comparison matrix requires nx n 1 2 judgments for a level with n criteria alternatives the number of comparisons increases as the number of criteria increases therefore the decision makers judgments will most likely be inconsistent to alleviate inconsistencies this study applies fuzzy linguistic preference relations fuzzy linprera to construct a pairwise comparison matrix with additive reciprocal property and consistency in this study the fuzzy ahp method is reviewed and then the fuzzy linprera method is proposed finally the presented method is applied to the example addressed by kahraman et al c kahraman d ruan i dogan fuzzy group decision making for facility location selection information sciences 157 2003 135 153 this study reveals that the proposed method yields consistent decision rankings from only n 1 pairwise comparisons which is the same result as in kahraman et al research the presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy ahp method

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

evaluating weapon systems using ranking fuzzy numbers abstract in this paper we will point out that chen s 1996 paper has some errors a weapon system is large and complex it has multi level multi factor and multi hierarchy features chen s method does not normalize each criterion s scores which will make a wrong decision under the following conditions i there are many levels for rank scores ii a criterion has many factors iii the total scores of systems have a larger difference under this criterion and iv one criterion s weight is larger than the other criteria numerical illustration is shown in section 5 therefore chen s method is not a general method for the evaluation of weapon systems after pointing out some errors in chen s paper to overcome these errors we will revise it and propose a general method for the evaluation of weapon systems our method utilizes fuzzy ratio scales 1 3 5 7 9 the goal is normalizing heterogeneity into homogeneity to indicate the relative strength of the factors in the corresponding criteria then we build a judgement matrix through comparison of the total scores of performance and use 1 3 5 7 9 to represent a weight vector among these criteria we will derive the priority among the alternatives by multiplying the fuzzy judgement matrix with the corresponding fuzzy weight vector the final results become a problem of ranking fuzzy numbers many triangular fuzzy numbers can easily rank its ordering by the intuition ranking method lee and li 1988 pointed out that human intuition would favor a fuzzy number with the following characteristics higher mean value and at the same time lower spread if its ordering cannot rank by figures we can use many other methods of ranking fuzzy numbers therefore the best weapon selection can be obtained by ranking fuzzy numbers

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

fuzzy eigenvalues and input output analysis abstract we first generalize the perron frobenius results for nonnegative matrices to nonnegative fuzzy matrices which says that these fuzzy matrices have a dominant nonnegative fuzzy eigenvalue this result is then used to extend leontief s closed input output analysis to fuzzy economies and obtain a fuzzy model of the world s economy

lattice boltzmann modeling of microchannel flow in slip flow regime we present the lattice boltzmann equation lbe with multiple relaxation times mrt to simulate pressure driven gaseous flow in a long microchannel we obtain analytic solutions of the mrt lbe with various boundary conditions for the incompressible poiseuille flow with its walls aligned with a lattice axis the analytical solutions are used to realize the dirichlet boundary conditions in the lbe we use the first order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel we validate the lbe results using the compressible navier stokes ns equations with a first order slip velocity the information preservation direct simulation monte carlo ip dsmc and dsmc methods as expected the lbe results agree very well with ip dsmc and dsmc results in the slip velocity regime but deviate significantly from ip dsmc and dsmc results in the transition flow regime in part due to the inadequacy of the slip velocity model while still agreeing very well with the slip ns results possible extensions of the lbe for transition flows are discussed

evaluating weapon system by analytical hierarchy process based on fuzzy scales abstract in this paper we propose a new algorithm for evaluating weapon systems by analytical hierarchy process ahp based on fuzzy scales which is a multiple criteria decision making approach in a fuzzy environment we use the triangular fuzzy number to build the judgement matrices through the pair wise comparison technique from kaufmann and gupta fuzzy mathematical models in engineering and management science north holland amsterdam 1988 p 1 a 3 1 a 2 1 a 1 only approximates the inverse of triangular fuzzy number a 1 where a a 1 a 2 a 3 which is due to a 1 is maybe no longer a fuzzy number therefore we revise juang and lee s fuzzy number 9 ifes 1991 415 421 more accurately in order to estimate the fuzzy eigenvectors of this matrix we utilize interval arithmetic cuts together with optimism of index in this way performance scores of the alternatives and the weights of the difference attributes can finally be obtained and compared for easy computation we use the mathcad package to calculate all results at last we apply and verify this new algorithm to a weapon system evaluation and selection problem

tripled fixed point theorems for contractive type mappings in partially ordered metric spaces abstract in this paper we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence and existence and uniqueness theorems for contractive type mappings our results generalize and extend recent coupled fixed point theorems established by gnana bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 examples to support our new results are given

slip flow boundary condition for straight walls in the lattice boltzmann model a slip flow boundary condition has been developed in the lattice boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node an analytical expression has been derived to connect the model parameters with the slip velocity for couette and poiseuille flows in the nearly continuum limit the proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the knudsen number computer simulations have been carried out to validate the model the couette and poiseuille flows agree with the analytical results to machine order numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions

posbist reliability behavior of typical systems with two types of failure abstract the posbist reliability theory is based on the possibility assumption and the binary state assumption in this paper we study the posbist reliability behavior in the presence of two failure modes for various classes of typical systems including series systems parallel systems k out of n systems series parallel systems and parallel series systems it is shown that for each typical system the posbist system reliability is bounded by the minimum and the maximum of the posbist component reliabilities

characteristic nonreflecting boundary conditions for open boundaries in lattice boltzmann methods a boundary condition for lattice boltzmann methods based on the movement of information through euler characteristic directions is developed with respect to the similar conditions used in finite difference or finite volume implementations some corrections are needed to compensate the isothermal compressible nature of standard lattice boltzmann methods for fluid flow the results show that the proposed method for inlets and outlets is highly nonreflecting and mass conserving

couple fixed point theorems for nonlinear contractions in cone metric spaces the notion of coupled fixed point is introduced by bhaskar and lakshmikantham 2006 in 13 in this manuscript some results of lakshmikantham and ciric 2009 in 5 are extended to the class of cone metric spaces

kinetic boundary conditions in the lattice boltzmann method derivation of the lattice boltzmann method from the continuous kinetic theory x he and l s luo phys rev e 55 r6333 1997 x shan and x he phys rev lett 80 65 1998 is extended in order to obtain boundary conditions for the method for the model of a diffusively reflecting moving solid wall the boundary condition for the discrete set of velocities is derived and the error of the discretization is estimated numerical results are presented which demonstrate convergence to the hydrodynamic limit in particular the knudsen layer in the kramers problem is reproduced correctly for small knudsen numbers

generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces abstract in this paper we extend the coupled fixed point theorems for mixed monotone operators f x x x obtained in t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 by significantly weakening the contractive condition involved our technique of proof is essentially different and more natural an example as well as an application to periodic bvp is also given in order to illustrate the effectiveness of our generalizations

one point boundary condition for the lattice boltzmann method we propose a correction to the bounce back boundary condition for lattice boltzmann algorithms which improves the accuracy of pressure from zero to first order and the accuracy of velocity from first to second order compared to interpolation based corrections our method has the advantage of being completely local in fact methods using interpolation face difficulties at boundary points where not enough neighboring nodes are available we show that a combination with our method offers a natural solution to this problem

application of fuzzy distributions on project management abstract pert cost which is an extension of pert to include economic considerations brings cost factors into project control decisions however pert cost is usually developed by project managers without enough experience in calculating the critical path of crisp pert cost network we usually suppose that all activity durations follow beta distribution of three time parameters ai mi bi i e the mean and variance of an activity duration are ai 4mi bi 6 bi ai 2 36 respectively basically the activity durations and their distributions are subjectively determined so the beta distribution is not always applicable therefore we propose a fuzzy pert cost that can be applied to a variety of fuzzy distributions of activity durations intuitively the higher the risk level the more uncertainty in time cost is involved in the project from fuzzy set theory it corresponds to lower confident level cut or larger interval value we will use such interval of confidence to represent fuzzy activity durations so that cut can be interpreted as a risk level and the attitude of the decision makers can be expressed by another index of optimism thus the relationships between project time and cost under different risk levels and different degrees of optimism can be obtained the solution procedure will be described in detail in conjunction with an example to illustrate the analysis algorithm and computation of the proposed method we have verified two of the empirical philosophy that for the higher risk level the shorter project time for the optimist 1 could be obtained on the other hand for the lower risk level the shorter project time was obtained for the pessimist 0 we have observed that no matter whatever the risk level is the results of the project time and cost of fuzzy pert cost at 0 5 neither optimistic nor pessimistic are equal to those of the crisp pert cost

common fixed point theorems in fuzzy metric spaces using the clrg property the main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces in the sense of kramosil and michalek satisfying new contractive conditions employing the common limit in the range property our results generalize and extend some recent results contained in jain et al 2012 12 to generalized contractive conditions under some control functions in the process some results about multidimensional common fixed points as coupled tripled quadrupled common fixed point results are derived from our main results

local second order boundary methods for lattice boltzmann models a new way to implement solid obstacles in lattice boltzmann models is presented the unknown populations at the boundary nodes are derived from the locally known populations with the help of a second order chapman enskog expansion and dirichlet boundary conditions with a given momentum steady flows near a flat wall arbitrarily inclined with respect to the lattice links are then obtained with a third order error in particular couette and poiseuille flows are exactly recovered without the knudsen layers produced for inclined walls by the bounce back condition

a coupled coincidence point result in partially ordered metric spaces for compatible mappings abstract in this paper we introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result our work extends the work of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 an example is also given

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

interpolated boundary condition for lattice boltzmann simulations of flows in narrow gaps several different interpolation schemes have been proposed for improving the accuracy of lattice boltzmann simulations in the vicinity of a solid boundary however these methods require at least two or three fluid nodes between nearby solid surfaces a condition that may not be fulfilled in dense suspensions or porous media for example here we propose an interpolation of the equilibrium distribution which leads to a velocity field that is both second order accurate in space and independent of viscosity the equilibrium interpolation rule infers population densities on the boundary itself to reduce the span of nodes needed for interpolation it requires a minimum of one grid spacing between the nodes by contrast the linear interpolation rule requires two fluid nodes in the gap and leads to a viscosity dependent slip velocity while the multireflection rule is viscosity independent but requires a minimum of three fluid nodes

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

a novel immersed boundary velocity correction lattice boltzmann method and its application to simulate flow past a circular cylinder a novel immersed boundary velocity correction lattice boltzmann method is presented and validated in this work by its application to simulate the two dimensional flow over a circular cylinder the present approach is inspired from the conventional immersed boundary method ibm in the conventional ibm the effect of rigid body on the surrounding flow is modeled through a forcing term which is in turn used to correct the surrounding velocity field it was found that this process is actually an iterative procedure trying to satisfy the non slip boundary condition at the solid wall in this work a new concept of immersed boundary velocity correction approach is proposed which directly corrects the velocity to enforce the physical boundary condition the main advantage of the new method is that it is simple in concept and easy for implementation and the convergence of numerical computation is faster and more stable than the conventional ibm one challenging issue of conventional ibm is that some streamlines may pass through the solid body since there is no mechanism to enforce the non slip condition at the boundary as shown in the present numerical results this unphysical phenomenon is avoided in our new method since the non slip condition is enforced the present results for the steady and unsteady flows compare very well with available data in the literature

coupled fixed point theorems for ϕ contractive mixed monotone mappings in partially ordered metric spaces abstract in this paper we extend the coupled fixed point theorems for mixed monotone operators f x x x obtained by bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 and luong and thuan n v luong and n x thuan coupled fixed points in partially ordered metric spaces and application nonlinear anal 74 2011 983 992 by weakening the involved contractive condition an example as well as an application to nonlinear fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations

coupled fixed point theorems for a generalized meir keeler contraction in partially ordered metric spaces abstract let x be a non empty set and f x x x be a given mapping an element x y x x is said to be a coupled fixed point of the mapping f if f x y x and f y x y in this paper we consider the case when x is a complete metric space endowed with a partial order we define generalized meir keeler type functions and we prove some coupled fixed point theorems under a generalized meir keeler contractive condition some applications of our obtained results are given the presented theorems extend and complement the recent fixed point theorems due to bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393

fuzzy mcdm based on ideal and anti ideal concepts this paper presents a novel fuzzy multiple criteria decision making mcdm based on the concepts of ideal and anti ideal points the concepts of fuzzy set theory and hierarchical structure analysis are used to develop a weighted suitability decision matrix to evaluate the weighted suitability of different alternatives versus various criteria the distance of different alternatives versus positive ideal solution and negative ideal solution are then obtained by using the proposed ranking method finally the relative approximation values of various alternatives versus positive ideal solution are ranked to determine the best alternative

a note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces abstract in this paper we have used a method of reducing tripled coincidence and tripled fixed point results in ordered metric spaces to the respective results for mappings with one variable even obtaining in some cases more general theorems our results generalize extend unify enrich and complement recently tripled coincidence point theorems established by berinde and borcut 2011 4 borcut and berinde 2012 7 and borcut 2012 9 also by using our method several coupled coincidence and coupled common fixed point results in ordered metric spaces can be reduced to the coincidence and common fixed point results with one variable

coupled fixed points in partially ordered metric spaces and application abstract in this paper we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces the main results of this paper are generalizations of the main results of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 as an application we discuss the existence and uniqueness for a solution of a nonlinear integral equation

boundary scheme for linear heterogeneous surface reactions in the lattice boltzmann method a boundary scheme is proposed to treat the linear heterogeneous surface reaction i e general robin boundary condition for the lattice boltzmann method lbm in this study the basic idea of the present scheme is to compute the scalar variable gradient in the boundary condition with the moment of the nonequilibrium distribution functions the unknown distribution functions on the boundary can then be obtained on the basis of the given boundary condition for a straight wall where the lattice nodes are located on the boundaries both the scalar variable and its gradient can be expressed in terms of the distribution functions at the boundary node and the scheme is purely local the scheme is also extended to problems with a curved wall in which a linear extrapolation is employed to realize the exact boundary position a common feature of the two schemes lies in the easy treatment of the heterogenous reactions in comparison with existing methods a number of simulations are performed to test the accuracy of the schemes the results show that for flat walls the scheme can achieve second order accuracy while for curved walls the order of the accuracy is between 1 0 and 1 5

coupled common fixed point results in two generalized metric spaces in this paper study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated these results generalize several comparable results from the current literature we also provide illustrative examples in support of our new results