fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

symmetry reductions and exact solutions of the 2 1 dimensional jaulent miodek equation by applying the direct symmetry method we obtain the symmetry reductions group invariant solutions and some new exact solutions of the 2 1 dimensional jaulent miodek equation which include jacobi elliptic function solutions airy function solutions trigonometric function solutions hyperbolic function solutions and so on

a note on lo fuzzy nearly compact spaces in this note we define lo fuzzy nc fuzzy sets and introduce the finite intersection property for fuzzy sets in the sense of lowen lo fip for short we give some equivalent characterizations of lo fuzzy nc spaces and lo fuzzy nc fuzzy sets by using lo fip regular open and regular closed fuzzy sets finally we prove that lo fuzzy nearly compactness is preserved under fuzzy almost continuous and almost open mapping

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

fuzzy topology on fuzzy sets product fuzzy topology and fuzzy topological groups the notion of product fuzzy topology in the case of fuzzy topology on fuzzy sets is introduced and the product invariance of fuzzy hausdorffness compactness connectedness are examined the product fuzzy topology is used to define fuzzy group topology on a fuzzy subgroup of a group g and some properties of fuzzy topological groups are obtained

path integral treatment of the hydrogen atom in a curved space of constant curvature ii hyperbolic space for pt i see ibid vol 20 p 6271 the path integral treatment of the hydrogen atom in a hyperbolic space is discussed the authors show by mapping the radial path integral into the su 1 1 group manifold that the system has a dynamical su 1 1 symmetry the energy spectrum and normalised energy eigenfunctions are calculated in the flat space limit the standard hydrogen spectrum and corresponding normalised wavefunctions are regained

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

fuzzy topology on fuzzy sets and tolerance topology in this paper fuzzy topology has been defined on a fuzzy set the notion of quasi coincidence is extended in order to fit this new situation and to generalize the concept of q neighbourhood introduced originally by ming and ming 1980 the generalized q neighbourhood system has been utilized to introduce tolerance topology on a fuzzy set with a fuzzy tolerance relation

application and improvement of a recent approximate analytical solution of richards equation a method for developing wetting front profiles for the one dimensional richards equation is given the method is obtained by simplifying and extending a recent approximate solution and brings together features from several different studies difficulties associated with profile development are discussed by applying the method to several examples providing a deeper understanding of the solutions of richards equation for simplicity we illustrate the improvements for soil water diffusivities and conductivities which have a power law dependence on the water content although they should apply in general and the appropriate generalization is given in the conclusion

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

exact solutions for water infiltration with an arbitrary surface flux or nonlinear solute adsorption several authors have now used the backlund transformation to linearize richard s equation and so obtain analytical solutions for infiltration and redistribution processes for the linearizable class of diffusivities and hydraulic conductivities after transformation a convection diffusion equation is obtained to date all the analytical results making use of the backlund transform have been based on a specified constant flux that is assumed to exist at the surface boundary we generalize the previous work by removing this restriction and obtain a general solution for an arbitrary temporal variation in surface flux the solution contains a function that is specified by a volterra integral equation in practice the volterra equation must be evaluated numerically this task is accomplished using a relatively straightforward algorithm the analytical results for infiltration can be applied to the process of solute transport subject to a nonlinear adsorption isotherm since these two phenomena are equivalent under another mapping our new analytical results therefore also apply to this class of solute transport processes the general form of the adsorption isotherm for which exact results can be obtained is derived this isotherm appears capable of representing a relatively large family of physically relevant cases although this topic remains open for future investigation

semi open sets and semi continuity in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets and fuzzy semi continuous mappings due to azad 1981 have been generalized to fuzzy bitopological spaces and some of their properties are studied

constant rate rainfall infiltration a versatile nonlinear model 1 analytic solution analytic solutions are presented for a nonlinear diffusion convection model describing constant rate rainfall infiltration in uniform soils and other porous materials the model is based on the darcy buckingham approach to unsaturated water flow and assumes simple functional forms for the soil water diffusivity d and hydraulic conductivity k which depend on a single free parameter c and readily measured soil hydraulic properties these d and k yield physically reasonable analytic moisture characteristics the relation between this model and other models which give analytic solutions is explored as c the model reduces to the weakly nonlinear burgers equation which has been applied in certain field situations at the other end of the range as c 1 the model approaches a green ampt like model a wide range of realistic soil hydraulic properties is encompassed by varying the c parameter the general features of the analytic solutions are illustrated for selected c values gradual and steep wetting profiles develop during rainfall aspects seen in the laboratory and field in addition the time dependent surface water content and surface water pressure potential are presented explicitly a simple traveling wave approximation is given which agrees closely with the exact solution at comparatively early infiltration times

multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface the present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi infinite flow domain with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometry the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution can be easily deduced from the general analytical model the model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest new explicit solutions have been obtained for one dimensional infiltration under various prescribed time dependent flux boundary conditions and for two and three dimensional moisture redistribution for constant initial or boundary conditions the multidimensional solution is essentially the product of two or three time dependent terms with each term being a function of only one space variable

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

semi continous and semi closed mappings and semi connectedness in fuzzy setting abstract the aim of the paper is mainly to study and to find different characterizations of semi continuous and semi closed mappings between fuzzy topological spaces the notion of fuzzy semi open sets is used to define fuzzy ti spaces i 0 1 2 and these spaces are investigated under fuzzy semi continuity finally fuzzy semi connectedness is introduced and studied to some extent

fuzzy topology on fuzzy sets fuzzy semicontinuity and fuzzy semiseparation axioms the concept of a fuzzy topology on a fuzzy set was introduced in fuzzy set syst 45 1992 103 the aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined also we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept fuzzy semiconnected and fuzzy semicompact spaces are introduced and some of their properties are discussed

clean two and three dimensional analytical solutions of richards equation for testing numerical solvers 1 this technical note derives clean analytical solutions of richards equation for three dimensional unsaturated groundwater flow clean means that the boundary conditions and steady state solutions are closed form expressions and the transient solutions have relatively simple additional fourier series terms two dimensional versions of these solutions are also given the primary purpose for the solutions is to test linear and nonlinear solvers in finite difference volume element computer programs for accuracy and scalability using architectures ranging from pcs to parallel high performance computers this derivation starts from the quasi linear assumption of relative hydraulic conductivity varying exponentially with pressure head and the separate approximation that relative hydraulic conductivity varies linearly with moisture content this allows a transformation to be used to create a linear partial differential equation separation of variables and fourier series are then used to obtain the final solution physically reasonable material properties are also used a total of four solutions are given in this technical note steady state and transient solutions for two different boundary conditions of the sample problem

coherent states for a polynomial su 1 1 algebra and a conditionally solvable system in a previous paper 2007 j phys a math theor 40 11105 we constructed a class of coherent states for a polynomially deformed su 2 algebra in this paper we first prepare the discrete representations of the nonlinearly deformed su 1 1 algebra then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su 1 1 algebra which contains the barut girardello set and the perelomov set of the su 1 1 coherent states as special cases we also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem

some remarks on lo rs fuzzy compactness abstract in this paper we define lo rs fuzzy compact fuzzy sets we study some properties of lo rs fuzzy compact spaces and lo rs fuzzy compact fuzzy sets we give some characterizations of these notions by fuzzy regularly open sets and fuzzy regularly closed sets we prove that lo rs fuzzy compactness is preserved under a fuzzy almost continuous and fuzzy almost open mapping

fuzzy topology and fuzzy multifunctions the fundamental concept of a fuzzy set was first introduced by zadeh in his classical paper 141 since then work has been done by many authors in several directions which has resulted in the formation of a new mathematical field called fuzzy mathematics the theory of fuzzy topological spaces is a branch of such mathematics chang in 2 was the first to introduce the notion of fuzzy topology several others continued the work in this area for example see 12 131 we remark that general point set topology can be regarded as a special case of fuzzy topology where all membership functions are just characteristic functions in this paper we introduce several fuzzy topological concepts and examine their properties our basic tool in that process is the notion of the fuzzy neighborhood of a point introduced by warren in ill we also introduce the notion of fuzzy multifunctions which we strongly believe will be useful in the study of fuzzy games and general fuzzy optimization problems we study the continuity and measurability properties of these multifunctions also we introduce linear fuzzy multifunctions and study their properties in the light of the recent work of katsaras 5 katsaras and liu s and lowen 9 on fuzzy vector spaces

some results on fuzzy topology on fuzzy sets abstract the object of the present paper is to introduce several fundamental concepts in the context of fuzzy topology on fuzzy sets introduced by chakrabarty and ahsanullah 2 the validity of some standard characterizations of fuzzy continuous proper functions have been examined the concept of hausdorffness regularity normality complete normality compactness connectedness are introduced and some interesting results are obtained

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

some remarks on fuzzy powerset operators fuzzy powerset operators related to morphisms of underlying ground categories of categories of fuzzy topological spaces are considered and some properties of such operators related to isomorphisms fuzzy points and order reversing involutions are verified

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

klauder s coherent states for the radial coulomb problem in a uniformly curved space and their flat space limits first a set of coherent states a la klauder is formally constructed for the coulomb problem in a curved space of constant positive curvature then the flat space limit is taken to reduce the set for the radial coulomb problem to a set of hydrogen atom coherent states corresponding to both the discrete and the continuous portions of the spectrum for a fixed l sector

fuzzy topological properties and hereditariness some known compactness notions and separation axioms already given in chang fuzzy topological spaces are extended to a more general context of categories where i topological spaces on arbitrary i sets are defined the invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated

fisher information delocalization and the semiclassical description of molecular rotation we discuss phase space delocalization for the rigid rotor within a semiclassical context by recourse to the husimi distributions of both the linear and the 3d anisotropic instances the husimi function can be viewed in a variety of ways in particular we obtain it as the expectation value of the density operator in a suitable basis of coherent states our treatment is based upon the concomitant fisher information measures the pertinent wehrl entropy is also investigated in the linear case

a comparison of picard and newton iteration in the numerical solution of multidimensional variably saturated flow problems picard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media the method is simple to code and computationally cheap but has been known to fail or converge slowly the newton method is more complex and expensive on a per iteration basis than picard and as such has not received very much attention its robustness and higher rate of convergence however make it an attractive alternative to the picard method particularly for strongly nonlinear problems in this paper the picard and newton schemes are implemented and compared in one two and three dimensional finite element simulations involving both steady state and transient flow the eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency including problem size spatial and temporal discretization initial solution estimates convergence error norm mass lumping time weighting conductivity and moisture content characteristics boundary conditions seepage faces and the extent of fully saturated zones in the soil previous strategies for enhancing the performance of the picard and newton schemes are revisited and new ones are suggested the strategies include chord slope approximations for the derivatives of the characteristic equations relaxing convergence requirements along seepage faces dynamic time step control nonlinear relaxation and a mixed picard newton approach the tests show that the picard or relaxed picard schemes are often adequate for solving richards equation but that in cases where these fail to converge or converge slowly the newton method should be used the mixed picard newton approach can effectively overcome the newton scheme s sensitivity to initial solution estimates while comparatively poor performance is reported for the various chord slope approximations finally given the reliability and efficiency of current conjugate gradient like methods for solving linear nonsymmetric systems the only real drawback of using newton rather than picard iteration is the algebraic complexity and computational cost of assembling the derivative terms of the jacobian matrix and it is suggested that both methods can be effectively implemented and used in numerical models of richards equation

fuzzy s continuous functions and semilocally connected fuzzy topological spaces abstract the concept of s continuous functions kohli 1978 is translated in fuzzy setting into two concepts fuzzy s continuous functions and fuzzy os continuous functions the concepts of semiconnected functions kohli 1978 and semilocally connected spaces kohli 1978 do the same interactions between those concepts in fuzzy setting and fuzzy continuity chang 1968 are discussed also characterizations of semilocally connected and semilocally o connected fuzzy topological spaces in terms of fuzzy s continuous functions and fuzzy os continuous functions respectively are obtained

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

path integral treatment of the hydrogen atom in a curved space of constant curvature the path integral treatment of the hydrogen atom in a spherical space is discussed the dynamical group su 1 1 of the system is used for path integration by mapping the radial path integral onto the su 1 1 manifold the energy spectrum and the normalised wavefunctions are obtained in the flat space limit the standard hydrogen spectrum and the corresponding normalised energy eigenfunctions are recovered the scattering states are also found in the limit

on fuzzy compactness in this paper we characterize well known fuzzy compactness see 3 4 9 and 10 using the notion of fuzzy upper limit see 5 also we give and study new fuzzy compactness in fuzzy topological spaces

directed family of fuzzy sets and fuzzy perfect maps the present paper deals with the perfect functions in fuzzy setting fuzzy filter bases of fuzzy sets are also studied vis a vis such functions finally certain fuzzy topological properties are taken up for their study with regard to fuzzy perfect functions

on fuzzy t convergences abstract in this paper we introduce and study the notions of fuzzy convergence and weakly convergence on a fuzzy topological space these notions can be considered as generalizations of the convergence defined in georgiou and papadopoulos 1998 also the forementioned convergence does not coincide with the one defined in chen and chenn 1997 the importance of these convergences relies on the fact that they behave equally well as the convergence defined in georgiou and papadopoulos 1998

a perturbative view on the subsurface water pressure response at hillslope scale 1 this work deals with a rearrangement of richards equation to obtain a better understanding of the components of the subsurface water and pressure flows and their interactions in a hillslope the basic idea proposed in this paper is the normalization of the spatial and temporal coordinates according to the physical knowledge of the processes and the geometry of a hillslope the pressure head and all the other quantities contained in richards equation are rescaled to obtain a dimensionless equation the pressure head is also split into an equilibrium component and a transient component and expanded in a perturbation series subsequently richards equation itself is conveniently split into two equations connected by a source sink term results of these manipulations show that for the first order approximation the water and pressure flow is slope normal while slope parallel effects only occur at successive orders integrating the perturbed equation obtained for the long term pressure head component results in the well known boussinesq equation for the water table level further integrations then lead to the hillslope storage boussinesq model and finally to a generalization of the o loughlin formula for the slope parallel long term subsurface flow the introduced source sink term is estimated at the first order of approximation to be proportional to the temporal variation of water pressure head at the bottom of the integration domain the treatment of the equations clarifies some of the mechanisms acting in water pressure redistribution at hillslope scale even without solving the equation

a compactness in bifuzzy topological spaces abstract compact fuzzy topological spaces were first introduced by chang 3 compact fuzzy topological spaces were introduced by gantner et al 4 abd el monsef et al 1 introduced the notion of almost compact fuzzy topological spaces mashbour et al 8 introduced the notion of bifuzzy topological spaces and defined the notion of compactness in those spaces in this paper we obtain some new results about compact bifuzzy topological spaces we introduce and study the notion of pairwise almost compact bifuzzy topological spaces