induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

on r l o we prove there exists a somewhat simpler description of l and its fuzzy topology than the one given by hutton 2 and a considerably simpler description of than the one given by rodabaugh 4 as a result of this simplification we are able to give a direct proof of the continuity of an open problem in 4

structures of fuzzy order homomorphisms abstract first the concept of fuzzy order homomorphism is introduced which is a variety of the generalized order homomorphism given in 7 then we show that the fuzzy order homomorphism possesses a nicely local structure furthermore we establish a necessary and sufficient condition under which the fuzz function is a zadeh type function the present condition is simpler than that given in 6 finally for each fuzzy order homomorphism f we yield some characterizations about f 1 1 f which sharpen the corresponding theorem in 6

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

on fuzzy pseudo metric spaces this paper attempts to endow the fuzzy pseudo metric in the sense of george and veeramani with many valued topological structures it is shown that george and veeramani s fuzzy pseudo metric can be characterized by a family of compatible ordinary pseudo metrics called pseudo metric chain in this paper then two kinds of many valued topological structures fuzzifying topology and fuzzifying uniformity are generated by this fuzzy pseudo metric and their properties are also investigated

fuzzifying topological linear spaces abstract in this paper we establish a fundamental framework of fuzzifying topological linear spaces abbreviated to ftls after providing some fuzzy logical notations and some basic properties of fuzzifying topological spaces we define a number of equivalent ftls and discuss some of their basic properties then we deal with the bases for fuzzifying neighborhood systems and particularly verify a characterization of ftls by using the bases of fuzzifying neighborhood systems of original point 0 also we demonstrate two characterizations of t 2 separation axiom after that fuzzy boundedness and fuzzy complete boundedness are defined and some related properties are demonstrated in particular we prove an equivalent characterization of fuzzy boundedness furthermore we study fuzzy compactness in ftls and demonstrate that a subset a is compact if and only if it is completely bounded and any cauchy net s in a converges at some point in a

induced i l fuzzy topological vector spaces abstract in this paper we introduce and study the induced i l fuzzy topological vector spaces the following main result is proved if l x is an l fuzzy topological vector space then i l x i l is an i l fuzzy topological vector space where i l is the fuzzy unit interval and i l is the induced i l fuzzy topology of the l fuzzy topology furthermore we also prove that the induced i l fuzzy topological vector spaces i l x i l preserve the product and quotient space as well

lattice boltzmann method for the convection diffusion equation in curvilinear coordinate systems a lattice boltzmann method for simulating convection and diffusion using a curvilinear grid system is presented the proposed method does not require an interpolation or coarse graining procedure and thus maintains the algorithmic simplicity of the original lattice boltzmann scheme the lattice boltzmann scheme is based on uniformly distributed lattice points in a transformed coordinate system and the apparent anisotropy of diffusion that arises due to the coordinate transformation is properly handled using the multiple relaxation time collision operator an asymptotic analysis of the lattice boltzmann equation shows that the proposed method appropriately reproduces the transformed convection diffusion equation several specific problems are numerically analyzed in order to validate the proposed method including an axially symmetric two dimensional problem in which the diffusion flux at an oblate hemispheroid is simulated using a body fitted orthogonal curvilinear grid system

forty years of hutton fuzzy unit interval this note is a very short history of a specific fuzzy topological space the hutton s fuzzy unit interval 0 1 l which occupies one of the central positions in fuzzy topology on that occasion the superiority of l valued topology over 0 1 valued topology is being discussed we then show how the hutton s concept evolved after obvious identifications we can today say that 0 1 l is the tensor product 0 1 l of the lattices 0 1 and l an account of the consequences of this new view point is hoped to appear thereafter

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

on the l 2 boundedness for the multiple littlewood paley functions with rough kernels abstract in this paper we give a characterization of the l 2 bounds for the littlewood paley functions on product domains as application a new size condition which implies the l 2 boundedness of the multiple parametric marcinkiewicz integrals with rough kernels and is weaker than the previous ones is given

local convexity and local boundedness of induced i l topological vector spaces in this paper we prove that an l topological vector space is locally convex locally bounded iff its induced i l topological vector space is locally convex locally bounded where i l is the l fuzzy unit interval also we give a necessary and sufficient condition for the induced i l topological vector space to be i l fuzzy normable

simulation of micro and nano scale flows via the lattice boltzmann method abstract we use the lattice boltzmann method lbm for analysis of high and moderate knudsen number phenomena simulation results are presented for microscale couette and poiseuille flows the slip velocity nonlinear pressure drop and mass flow rate are compared with previous numerical results and or experimental data the knudsen minimum is successfully predicted for the first time within the lbm framework these results validate the usage of the lbm based commercial arbitrary geometry code powerflow for simulating nanoscale problems

on l fuzzy topological spaces abstract l fuzzy sets and subsequently l fuzzy topological spaces are considered in this paper where l is a complete and completely distributive non atomic boolean algebra a few separation properties as well as subspace l fuzzy topology are defined here in the light of an earlier paper these are more similar to ordinary topological spaces than to fuzzy topological spaces

suitability in fuzzy topological spaces abstract an l fuzzy topological space is said to be suitable if it possesses a nontrivial crisp closed subset basic properties of and sufficient conditions for suitable spaces are derived characterizations of the suitable subspaces of the fuzzy unit interval the fuzzy open unit interval and the fuzzy real line are obtained suitability is l fuzzy productive nondegenerate 1 hausdorff spaces are suitable the fuzzy unit interval the fuzzy open unit interval and the fuzzy real line are not suitable and no suitable subspace of the fuzzy unit interval the fuzzy open unit interval or the fuzzy real line is a fuzzy retract of the fuzzy unit interval the fuzzy open unit interval or the fuzzy real line respectively without restrictions there cannot be a fuzzy extension theorem

i l topological groups and its level l topological groups in this paper we discuss the relationship between an i l topological group and its level l topological groups we supply a method to generate an i l topological group by a co tower of group l topologies and obtain a necessary and sufficient condition for the i l topological group generated by a co tower of group l topologies to be l topologically generated

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

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

on i l topological vector spaces generated by a co tower of l topological vector spaces in this paper a characterization for an i l topological space to be generated by a given co tower of l topological spaces is obtained moreover the relationship between some properties of an i l topological vector space generated by a co tower of l topological vector spaces and the corresponding properties of the given co tower of l topological vector spaces is investigated our results show that if an i l topological vector space generated by a co tower of l topological vector spaces has some properties such as local convexity and local boundedness then all l topological vector spaces in the co tower also have the same properties but the converse is incorrect even in the case of i topological vector space generated by a co tower of classical topological vector spaces finally we supply a necessary and sufficient condition for an i l topological vector space generated by a co tower of l topological vector spaces with some properties such as local convexity and local boundedness to have such properties too

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

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

some questions in fuzzy topology the purpose of this paper is to discuss some basic questions related mainly to hutton s l fuzzy unit interval some of those questions are stated here for the first time while some of them are long standing related results are surveyed in some cases

efficient kinetic method for fluid simulation beyond the navier stokes equation we present a further theoretical extension to the kinetic theory based formulation of the lattice boltzmann method of shan j fluid mech 550 413 2006 in addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate gauss hermite quadrature in the original formulation a regularization procedure is introduced in this paper this procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the galerkin sense using this formulation we construct a specific lattice boltzmann model that accurately incorporates up to third order hydrodynamic moments numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice boltzmann models so that fluid flows at finite knudsen number kn can be more quantitatively simulated results from force driven poiseuille flow simulations predict the knudsen s minimum and the asymptotic behavior of flow flux at large kn

l fuzzy normal spaces and tietze extension theorem abstract in this paper we prove a characterization theorem for normal l fuzzy topological spaces l is an infinitely distributive lattice with an order reversing involution in the particular case l 0 1 this theorem reduces to a known result of kat tov fund math 38 1951 85 91 and tong duke math j 19 1952 289 292 as an important application we obtain a fuzzy version of tietze extension theorem this yields an affirmative answer to a question raised in a series of papers by rodabaugh fuzzy sets and systems 11 1983 163 183

higher separation axioms in l topologically generated i l topological spaces the main result of this paper is a theorem about inserting a pair of semicontinuous l real valued functions which extends the insertion theorem of kubiak comment math univ carolinae 34 1993 357 362 from l 0 1 to an arbitrary meet continuous lattice l endowed with an order reversing involution with this result it is shown that the normality type separation axioms in top l are preserved by the functor which takes an l topological space x to the i l topological space l x obtained by providing the set x with the i l topology consisting of all lower semicontinuous functions from x to i l the same is proved for the case of the regularity axiom

i l topological vector spaces and its level topological spaces in this paper the relationship between i l topological vector spaces and its level topological spaces is discussed the main result of this paper is to give a method which generates an i l topological vector space by a co tower of vector l topologies this result is a generalization of previous results published in this journal by the same authors

linear stability and isotropy properties of athermal regularized lattice boltzmann methods the present work proposes a general methodology to study stability and isotropy properties of lattice boltzmann lb schemes as a first investigation such a methodology is applied to better understand these properties in the context of regularized approaches to this extent linear stability analyses of two dimensional models are proposed the standard bhatnagar gross krook collision model the original precollision regularization and the recursive regularized model where off equilibrium distributions are partially computed thanks to a recursive formula a systematic identification of the physical content carried by each lb mode is done by analyzing the eigenvectors of the linear systems stability results are then numerically confirmed by performing simulations of shear and acoustic waves this work allows drawing fair conclusions on the stability properties of each model in particular among the aforementioned models recursive regularization turns out to be the most stable one for the d2q9 lattice especially in the zero viscosity limit two major properties shared by every regularized model are highlighted 1 a mode filtering property and 2 an incorrect and broadly anisotropic dissipation rate of the modes carrying physical waves in under resolved conditions the first property is the main source of increased stability especially for the recursive regularization it is a direct consequence of the reconstruction of off equilibrium populations before each collision process decreasing the rank of the system of discrete equations the second property seems to be related to numerical errors directly induced by the equilibration of high order moments in such a case this property is likely to occur with any collision model that follows such a stabilization methodology

l p bounds for marcinkiewicz integrals associated to surfaces of revolution abstract in this paper we prove the l p boundedness of some marcinkiewicz integral operators along surfaces of revolution some size conditions implying the l p r n 1 boundedness of these operators for some fixed 1 p are obtained

survey of local connectedness axioms and their properties in l topological spaces based on the notions of fuzzy connectedness defined by lu and li fuzzy connectedness new definitions and comparisons fuzzy sets and systems 157 2006 1928 1940 some new fuzzy local connectedness such as local connectedness local ultra f 1 connectedness local strong f 1 connectedness local ultra f 2 connectedness local strong f 2 connectedness ultra f 1 local connectedness strong f 1 local connectedness ultra f 2 local connectedness and strong f 2 local connectedness of l topological spaces or l cotopological spaces are defined in this paper apart from maintaining some frequently used properties that classical local connected topological spaces possess l topological spaces or l cotopological spaces which satisfy our new fuzzy local connectedness axioms also have some interesting properties for example local connectedness local ultra f 1 connectedness local ultra f 2 connectedness local strong f 1 connectedness and local strong f 2 connectedness are all i l inducible if l is a complete and meet continuous demorgan algebra they are l extension of local connectedness of topological spaces under some moderate restrictions to l it is proved that all l intervals are locally connected if copr l is a generating set of l some categorical results reflecting the differences between classical topology and l topology are obtained the relationships between these notions of connectedness are also investigated in detail

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

kinetic lattice boltzmann method for microscale gas flows issues on boundary condition relaxation time and regularization it is well known that the navier stokes equations cannot adequately describe gas flows in the transition and free molecular regimes in these regimes the boltzmann equation be of kinetic theory is invoked to govern the flows however this equation cannot be solved easily either by analytical techniques or by numerical methods hence in order to efficiently maneuver around this equation for modeling microscale gas flows a kinetic lattice boltzmann method lbm has been introduced in recent years this method is regarded as a numerical approach for solving the be in discrete velocity space with gauss hermite quadrature in this paper a systematic description of the kinetic lbm including the lattice boltzmann equation the diffuse scattering boundary condition for gas surface interactions and definition of the relaxation time is provided to capture the nonlinear effects due to the high order moments and wall boundaries an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work guo et al j appl phys 99 074903 2006 shan et al j fluid mech 550 413 2006 the capability of the kinetic lbm of simulating microscale gas flows is illustrated based on the numerical investigations of micro couette and force driven poiseuille flows

evaluation of a lattice boltzmann method in a complex nanoflow in order to establish a cost effective strategy to simulate complex flows in continuum to slip and transitional regimes the present study assesses the performance of a lattice boltzmann method lbm formerly discussed by the present authors group niu et al phys rev e 76 036711 2007 this lbm is based on a diffuse scattering wall boundary condition a regularization procedure and an effective relaxation time associated with the knudsen number the present assessment is on its regularization procedure and third order truncated system based on the two dimensional twenty one discrete velocity d2q21 model for the cartesian lattices the test flow cases are force driven poiseuille flows the couette flows and a flow around a square cylinder situated in a nanochannel for producing the reference data of the square cylinder flow the molecular dynamics simulation using lennard jones potential is also performed although the flow profiles and the slip velocities of the poiseuille flows and the couette flows are more accurately predicted by the third order truncated system the general velocity profiles around the square cylinder are also well predicted by the second order truncated system based on the two dimensional nine discrete velocity d2q9 model it is also confirmed that without the regularization process the entire flow field prediction suffers unphysical momentum oscillations around the square cylinder