strongest strong cycles and theta fuzzy graphs in this paper new concepts are introduced to enhance the process of block identification in fuzzy graphs since reduction in the strength of the connectedness between two nodes occurs more frequently than total disconnection of a network block identification in fuzzy graph networks is very important a special type of cycle which is called a strongest strong cycle and a new connectivity parameter which is called cycle connectivity are introduced in fuzzy graphs a subclass of fuzzy graphs known as fuzzy graphs is identified in which all the existing characterizations of blocks in graphs are true a set of necessary conditions is obtained for a fuzzy graph to be a block as well as a set of necessary and sufficient conditions for a fuzzy graph to be a block

a matrix approach to latticized linear programming with fuzzy relation inequality constraints this paper investigates the latticized linear programming that is subject to the fuzzy relation inequality fri constraints with the max min composition by using the semi tensor product method and proposes a matrix approach to this problem first the resolution of the fri is studied and it is proved that all the minimal solutions and the unique maximum solution are within the finite parameter set solutions based on this and using the semi tensor product solving fris is converted to solving a set of algebraic inequalities and some new results on the resolution of fris are presented second the latticized linear programming that is subject to the fri constraints is solved by taking the following two key steps 1 the optimal value is obtained by calculating the minimum value of the objective function among all the minimal solutions to the fri constraints and 2 the optimal solution set is obtained by solving the fuzzy relation equation that is generated by letting the objective function equal to the optimal value the study of illustrative examples shows that the new results that are obtained in this paper are very effective in solving the latticized linear programming subject to the fri constraints

hamiltonian formulation of surfaces with constant gaussian curvature dirac s method for constrained hamiltonian systems is used to describe surfaces of constant gaussian curvature a geometrical free energy for which these surfaces are equilibrium states is introduced and interpreted as an action an equilibrium surface can then be generated by the evolution of a closed space curve since the underlying action depends on second derivatives the velocity of the curve and its conjugate momentum must be included in the set of phase space variables furthermore the action is linear in the acceleration of the curve and possesses a local symmetry reparametrization invariance which implies primary constraints in the canonical formalism these constraints are incorporated into the hamiltonian through lagrange multiplier functions that are identified as the components of the acceleration of the curve the formulation leads to four first order partial differential equations one for each canonical variable with the appropriate choice of parametrization only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve to illustrate the formalism several evolutions of pseudospherical surfaces are discussed

hamilton s equations for a fluid membrane consider a homogeneous fluid membrane described by the helfrich canham energy quadratic in the mean curvature of the membrane surface the shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature we introduce a hamiltonian formulation of this equation which dismantles it into a set of coupled first order equations this involves interpreting the helfrich canham energy as an action equilibrium surfaces are generated by the evolution of space curves two features complicate the implementation of a hamiltonian framework i the action involves second derivatives this requires treating the velocity as a phase space variable and the introduction of its conjugate momentum the canonical hamiltonian is constructed on this phase space ii the action possesses a local symmetry reparametrization invariance the two labels we use to parametrize points on the surface are themselves physically irrelevant this symmetry implies primary constraints one for each label that need to be implemented within the hamiltonian the two lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface the conservation of the primary constraints implies two secondary constraints fixing the tangential components of the momentum conjugate to the position hamilton s equations are derived and the appropriate initial conditions on the phase space variables are identified finally it is shown how the shape equation can be reconstructed from these equations

shape equations for axisymmetric vesicles a clarification we derive the shape equations for axisymmetric vesicles and show that they are identical to the general shape equation ou yang zhong can and w helfrich phys rev a 39 5280 1989 specialized to axisymmetry we consider three different topologies an axisymmetric membrane segment suspended between two circular rings and closed vesicles of spherical and toroidal topology we point out that the shape equations are independent of the variational method used

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

balancing torques in membrane mediated interactions exact results and numerical illustrations torques on interfaces can be described by a divergence free tensor which is fully encoded in the geometry this tensor consists of two terms one originating in the couple of the stress the other capturing an intrinsic contribution due to curvature in analogy to the description of forces in terms of a stress tensor the torque on a particle can be expressed as a line integral along a contour surrounding the particle interactions between particles mediated by a fluid membrane are studied within this framework in particular torque balance places a strong constraint on the shape of the membrane symmetric two particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime in particular the problem may be solved exactly in the case of two membrane bound parallel cylinders this apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane mediated interactions

laplace pressure as a surface stress in fluid vesicles consider a surface enclosing a fixed volume described by a free energy depending only on the local geometry for example the canham helfrich energy quadratic in the mean curvature describes a fluid membrane the stress at any point on the surface is determined completely by geometry in equilibrium its divergence is proportional to the laplace pressure normal to the surface maintaining the constraint on the volume it is shown that this source itself can be expressed as the divergence of a position dependent surface stress as a consequence the equilibrium can be described in terms of a conserved effective surface stress various non trivial geometrical consequences of this identification are explored in a cylindrical geometry the cross section can be viewed as a closed planar euler elastic curve with respect to an appropriate centre the effective stress itself vanishes this provides a remarkably simple relationship between the curvature and the position along the loop in two or higher dimensions it is shown that the only geometry consistent with the vanishing of the effective stress is spherical it is argued that the appropriate generalization of the loop result will involve null stresses

interface mediated interactions between particles a geometrical approach particles bound to an interface interact because they deform its shape the stresses that result are fully encoded in the geometry and described by a divergence free surface stress tensor this stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle the resulting expression is exact i e free of any smallness assumptions and independent of the chosen surface parametrization additional surface degrees of freedom such as vector fields describing lipid tilt are readily included in this formalism as an illustration we derive the exact force for several important surface hamiltonians in various symmetric two particle configurations in terms of the midplane geometry its sign is evident in certain interesting limits specializing to the linear regime where the shape can be analytically determined these general expressions yield force distance relations several of which have originally been derived by using an energy based approach

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

how paper folds bending with local constraints a variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry this framework is applied to describe the patterns of a folded sheet of paper the unstretchability of paper implies a constraint on the surface metric bending is penalized by an energy quadratic in mean curvature the local lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet the framework is illustrated by examining the deformation of a flat sheet into a generalized cone

solving fuzzy relational equations via semitensor product the problem of solving max min fuzzy relational equations is investigated first we show that if there is a solution then there is a corresponding solution within the set of parameters briefly the parameter set solution pss then the semitensor product of matrices is used to convert the logical equations into algebraic equations via the vector expression of logical variables under this form every pss can be obtained it is proved that all the solutions can be revealed from their corresponding pss some examples are presented to demonstrate the algorithm to solve fuzzy relational equations

inverted catenoid as a fluid membrane with two points pulled together under inversion in any interior point a catenoid transforms into a deflated compact geometry which touches at two points its poles the catenoid is a minimal surface and as such is an equilibrium shape of a symmetric fluid membrane the conformal symmetry of the hamiltonian implies that inverted minimal surfaces are also equilibrium shapes however they will exhibit curvature singularities at their poles such singularities are the geometrical signature of the external forces required to pull the poles together these forces will set up stresses in the inverted shapes tuning the force corresponds geometrically to the translation of the point of inversion for any fixed surface area there will be a maximum force the associated shape is a symmetric discocyte lowering the external force will induce a transition from the discocyte to a cup shaped stomatocyte

conformally invariant bending energy for hypersurfaces the most general conformally invariant bending energy of a closed four dimensional surface polynomial in the extrinsic curvature and its derivatives is constructed this invariance manifests itself as a set of constraints on the corresponding stress tensor if the topology is fixed there are three independent polynomial invariants two of these are the straightforward quartic analogues of the quadratic willmore energy for a two dimensional surface one is intrinsic the weyl invariant the other extrinsic the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature which is not itself invariant and a quartic in the curvature the four dimensional energy quadratic in extrinsic curvature plays a central role in this construction

fast solving method of fuzzy relational equation and its application to lossy image compression reconstruction a fast solving method of the solution for max continuous t norm composite fuzzy relational equation of the type g i j r sup t spl square a sub i sup t spl square b sub j i 1 2 i j 1 2 j where a sub i spl isin f x x x sub 1 x sub 2 x sub m bj spl isin f y y y sub 1 y sub 2 y sub n r spl isin f x spl times y and spl square max continuous t norm composition is proposed it decreases the computation time ijmn l t p to jm i n l p where l t and p denote the computation time of min t norm and relative pseudocomplement operations respectively by simplifying the conventional reconstruction equation based on the properties of t norm and relative pseudocomplement the method is applied to a lossy image compression and reconstruction problem where it is confirmed that the computation time of the reconstructed image is decreased to 1 335 6 the compression rate being 0 0351 and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization

environmental bias and elastic curves on surfaces the behavior of an elastic curve bound to a surface will reflect the geometry of its environment this may occur in an obvious way the curve may deform freely along directions tangent to the surface but not along the surface normal however even if the energy itself is symmetric in the curve s geodesic and normal curvatures which control these modes very distinct roles are played by the two if the elastic curve binds preferentially on one side or is itself assembled on the surface not only would one expect the bending moduli associated with the two modes to differ binding along specific directions reflected in spontaneous values of these curvatures may be favored the shape equations describing the equilibrium states of a surface curve described by an elastic energy accommodating environmental factors will be identified by adapting the method of lagrange multipliers to the darboux frame associated with the curve the forces transmitted to the surface along the surface normal will be determined features associated with a number of different energies both of physical relevance and of mathematical interest are described the conservation laws associated with trajectories on surface geometries exhibiting continuous symmetries are also examined

membrane geometry with auxiliary variables and quadratic constraints consider a surface described by a hamiltonian which depends only on the metric and extrinsic curvature induced on the surface the metric and the curvature along with the basis vectors which connect them to the embedding functions defining the surface are introduced as auxiliary variables by adding appropriate constraints all of them quadratic the response of the hamiltonian to a deformation in each of the variables is determined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established for the purpose of illustration a fluid membrane described by a hamiltonian quadratic in curvature is considered

lipid membranes with an edge consider an open lipid membrane with a free exposed edge the energy describing this membrane is quadratic in the extrinsic curvature that describing the edge is proportional to its length we determine the boundary conditions satisfied by the equilibria of the membrane on this edge the derivation is free of any assumptions on the symmetry of the membrane geometry with respect to the axially symmetric case there is an additional boundary condition that is identically satisfied in that limit by considering the balance of the forces operating at the edge a physical interpretation for the boundary conditions is provided the effect of the addition of a gaussian rigidity term for the membrane is also considered

fluid membrane tethers minimal surfaces and elastic boundary layers thin cylindrical tethers are common lipid bilayer membrane structures arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the golgi apparatus we study the shape and formation of a tether in terms of the classical soap film problem which is applied to the case of a membrane disk under tension subject to a point force a tether forms from the elastic boundary layer near the point of application of the force for sufficiently large displacement analytic results for various aspects of the membrane shape are given

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

hamilton s equations for a fluid membrane axial symmetry consider a homogeneous fluid membrane or vesicle described by the helfrich canham energy quadratic in the mean curvature when the membrane is axially symmetric this energy can be viewed as an action describing the motion of a particle the contours of equilibrium geometries are identified with particle trajectories a novel hamiltonian formulation of the problem is presented which exhibits the following two features i the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space and ii the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved as a result the phase space involves momenta conjugate not only to the particle position but also to its velocity and there are constraints on the phase space variables this formulation provides the groundwork for a field theoretical generalization to arbitrary configurations with the particle replaced by a loop in space

quasi isolated blocks and brauer s height zero conjecture this paper has two main results firstly we complete the parametrisation of all p blocks of nite quasi simple groups by nding the so called quasi isolated blocks of exceptional groups of lie type for bad primes this relies on the explicit decomposition of lusztig induction from suitable levi subgroups our second major result is the proof of one direction of brauer s long standing height zero conjecture on blocks of nite groups using the

large orbits in coprime actions of solvable groups let g be a solvable group of automorphisms of a finite group k if g and k are coprime then there exists an orbit of g on k of size at least g it is also proved that in a solvable group the largest normal subgroup is the intersection of at most three hall subgroups

on the max contraction powers of a fuzzy matrix abstract in the literature the powers of a fuzzy matrix with max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max min compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the max contraction powers of a fuzzy matrix which is an extension of the max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max arithmetic mean operation we show that the powers of such a fuzzy matrix are always convergent and the limit matrix has the feature that all elements of each column are identical

redefined observability matrix for boolean networks and distinguishable partitions of state space this paper redefines the observability matrix and defines the observability index for boolean networks bns in the new definition a bn is observable if and only if the observability matrix is of full rank the observability matrix is calculated by a simple algorithm and is applied to the problem of distinguishability of partitions a partition of the state space is said to be distinguishable if any two distinct subsets are distinguishable and the finest distinguishable partition fdp is finer than any other distinguishable partition a necessary and sufficient condition is proposed for checking the distinguishability of any given partition and an algorithm is proposed for calculating the fdp the proposed results are illustrated by examples

large varvec p prime orbits for varvec p p nilpotent linear groups let g be a p nilpotent linear group on a finite vector space v of characteristic p suppose that g v is odd let p be a sylow p subgroup of g we show that there exist vectors v 1 and v 2 in v such that c g v 1 cap c g v 2 p a striking conjecture of malle and navarro offers a simple global criterion for the nilpotence in the sense of broue and puig of a p block of a finite group our result implies that this conjecture holds for groups of odd order

3d vesicle dynamics simulations with a linearly triangulated surface simulations of biomembranes have gained an increasing interest in the past years specificities of these membranes propose new challenges for the numerics in particular vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint a method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described this method is coupled with a boundary element method solver for inner and outer fluids to compute vesicle dynamics under external flows the surface incompressibility constraint is satisfied by the construction of a projection operator

general decomposition of fuzzy relations semi tensor product approach abstract this paper focuses on the general decomposition problem of fuzzy relations which can be regarded as an extension of the common one modeled by fuzzy relational equation fre x x r the considered decomposition problem is described by an fre x y r for the purpose of deriving all solutions to the decomposition problem the structure of solutions to the corresponding fre is investigated first and a necessary and sufficient condition for the existence of solutions is obtained then based on semi tensor product stp of matrices an algebraic approach is proposed furthermore all solutions to the general decomposition problem can be computed via the proposed method in order to demonstrate the effectiveness of the presented approach two numerical examples are given

stiffening of fluid membranes due to thermal undulations density matrix renormalization group study it has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations however recent thorough investigation by pinnow and helfrich revealed the significance of measure factors for the partition sum accepting the local curvature as a statistical measure they found that fluid membranes are stiffened macroscopically in order to examine this remarkable idea we performed extensive ab initio simulations for a fluid membrane we set up a transfer matrix that is diagonalized by means of the density matrix renormalization group our method has an advantage in that it allows us to survey various statistical measures as a consequence we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure on the contrary for other measures such as normal displacement and tilt angle we found a clear tendency toward softening

a geometric theory on the elasticity of bio membranes the purpose of this paper is to study the shapes and stabilities of bio membranes within the framework of exterior differential forms after a brief review of the current status of theoretical and experimental studies on the shapes of bio membranes a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers the shape equation and boundary conditions of open lipid bilayers and two component membranes the shape equation and in plane strain equations of cell membranes with cross linking structures and the stabilities of closed lipid bilayers and cell membranes the key point of this scheme is to deal with the variational problems on surfaces embedded in three dimensional euclidean space by using exterior differential forms

the one loop elastic coefficients for the helfrich membrane in higher dimensions using a covariant geometric approach we obtain the effective bending couplings for a two dimensional rigid membrane embedded into a 2 d dimensional euclidean space the hamiltonian for the membrane has three terms the first one is quadratic in its mean extrinsic curvature the second one is proportional to its gaussian curvature and the last one is proportional to its area the results we obtain are in agreement with those finding that thermal fluctuations soften the two dimensional membrane embedded into a three dimensional euclidean space

stability and set stability in distribution of probabilistic boolean networks we propose a new concept stability in distribution sd of a probabilistic boolean network pbn which determines whether the probability distribution converges to the distribution of the target state namely a one point distributed random variable in a pbn stability with probability one stability in the stochastic sense and sd are equivalent the sd is easily generalized to subset stability i e to set stability in distribution ssd we prove that the transition probability from any state to an invariant subset or to a fixed point is nondecreasing in time this monotonicity is an important property in establishing stability criteria and in calculating or estimating the transient period we also obtain a verifiable necessary and sufficient condition for sd of pbns with independently and identically distributed switching we then show that sd problems of pbns with markovian switching and pbn synchronizations can be recast as ssd problems of markov chains after calculating the largest invariant subset of a markov chain in a given set by the newly proposed algorithm we propose a necessary and sufficient condition for ssds of markov chains the proposed method and results are supported by examples

deformation of injected vesicles adhering onto flat rigid substrates this study is concerned with the determination of the mechanical behaviour of closed fluid lipid bilayer membranes vesicles under a uniform hydrostatic pressure pressed against and adhering onto a flat homogeneous rigid substrate assuming that the initial and deformed shapes of the vesicle are axisymmetric a variational statement of the problem is developed on the ground of the so called spontaneous curvature model in this setting the vesicle is regarded as a closed surface in the three dimensional euclidean space and its equilibrium shapes are supposed to provide stationary values of the bending energy functional under the constraint of fixed total area the corresponding euler lagrange equations and natural boundary conditions are derived the work done by the pressure being taken into account and used to determine the forces and moments in the membrane several examples of surfaces representing possible equilibrium shapes of so loaded membranes are determined numerically

smectic blue phases layered systems with high intrinsic curvature we report on a construction for smectic blue phases which have quasi long range smectic translational order as well as three dimensional crystalline order our proposed structures fill space by adding layers on top of a minimal surface introducing either curvature or edge defects as necessary we find that for the right range of material parameters the favorable saddle splay energy of these structures can stabilize them against uniform layered structures we also consider the nature of curvature frustration between mean curvature and saddle splay

area constrained planar elastica we determine the equilibria of a rigid loop in the plane subject to the constraints of fixed length and fixed enclosed area rigidity is characterized by an energy functional quadratic in the curvature of the loop we find that the area constraint gives rise to equilibria with remarkable geometrical properties not only can the euler lagrange equation be integrated to provide a quadrature for the curvature but in addition the embedding itself can be expressed as a local function of the curvature the configuration space is shown to be essentially one dimensional with surprisingly rich structure distinct branches of integer indexed equilibria exhibit self intersections and bifurcations a gallery of plots is provided to highlight these findings perturbations connecting equilibria are shown to satisfy a first order ode which is readily solved we also obtain analytical expressions for the energy as a function of the area in some limiting regimes

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

axially symmetric membranes with polar tethers axially symmetric equilibrium configurations of the conformally invariant willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation not one as would be expected on the basis of axial symmetry modulo a translation along the axis this equation involves a single free parameter c if c 0 a geometry with spherical topology will possess curvature singularities at its poles the physical origin of the singularity is identified by examining the noether charge associated with the translational invariance of the energy it is consistent with an external axial force acting at the poles a one parameter family of exact solutions displaying a discocyte to stomatocyte transition is described

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

folding of the triangular lattice in a discrete three dimensional space density matrix renormalization group study folding of the triangular lattice in a discrete three dimensional space is investigated numerically such discrete folding has come about through theoretical investigation since bowick and co workers introduced it as a simplified model for the crumpling of the phantom polymerized membranes so far it has been analyzed with the hexagon approximation of the cluster variation method cvm however the possible systematic error of the approximation was not fully estimated in fact it has been known that the transfer matrix calculation is limited in the tractable strip widths l ensuremath leqslant 6 aiming to surmount this limitation we utilized the density matrix renormalization group thereby we succeeded in treating strip widths up to l 29 which admit reliable extrapolations to the thermodynamic limit our data indicate an onset of a discontinuous crumpling transition with the latent heat substantially larger than the cvm estimate it is even larger than the latent heat of the planar two dimensional folding as first noticed by the preceding cvm study that is contrary to our naive expectation the discontinuous character of the transition is even promoted by the enlargement of the embedding space dimensions we also calculated the folding entropy which appears to lie within the best analytical bound obtained previously via combinatorics arguments

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

strong coupling expansion analysis of the false vacuum decay rate of the lattice phi4 model in 1 1 dimensions strong coupling expansion is performed for the lattice 4 model in 1 1 dimensions because the strong coupling limit itself is not solvable we employed numerical calculations so as to set up unperturbed eigensystems restricting the number of hilbert space bases we performed linked cluster expansion up to 11th order we carried out an alternative simulation by means of the density matrix renormalization group thereby we confirmed that our series expansion data with a convergence acceleration trick are in good agreement with the simulation result through the analytic continuation to the domain of negative biquadratic interaction we obtain the false vacuum decay rate contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments our series expansion reproduces the instanton theory behaviour for a high potential barrier for a shallow barrier in contrast our result tells us that the relaxation is no longer described by an instanton but the decay rate acquires notable enhancement

stresses in lipid membranes the stresses in a closed lipid membrane described by the helfrich hamiltonian quadratic in th ee xtrinsic curvature are identified using noether s theorem three equations describe the conservation of the stress tensor the norma lp rojection is identified as the shape equation describing equilibrium configurations the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes the corresponding torque tensor is also identified the use of the stress tensor as a basis for perturbation theory is discussed the conservation laws are cast in terms of the forces and torques on closed curves as an application the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along the circles of constant latitude

second variation of the helfrich canham hamiltonian and reparametrization invariance a covariant approach towards a theory of deformations is developed to examine both the first and second variation of the helfrich canham hamiltonian quadratic in extrinsic curvature which describes fluid vesicles at mesoscopic scales deformations are decomposed into tangential and normal components at first order tangential deformations may always be identified with a reparametrization at second order they differ the relationship between tangential deformations and reparametrizations as well as the coupling between tangential and normal deformations is examined at this order for both the metric and the extrinsic curvature tensors expressions for the expansion to second order in deformations of geometrical invariants constructed with these tensors are obtained in particular the expansion of the hamiltonian to this order about an equilibrium is considered our approach applies as well to any geometrical model for membranes

new results on the canham helfrich membrane model via the generalized weierstrass representation the canham helfrich membrane model is discussed by making use of the generalized weierstrass representation formulae for arbitrary surfaces immersed into the three dimensional euclidean space particular solutions of the shape equation are considered and correlators describing thermal fluctuations in the one loop approximation are computed

arithmetic fuzzy models it is well known that a fuzzy rule base can be interpreted in different ways from a logical point of view the conjunctive interpretation is preferred while from a practical point of view the disjunctive interpretation has been dominantly present each of these interpretations results in a specific fuzzy relation that models the fuzzy rule base basic interpolation requirements naturally suggest a corresponding inference mechanism the direct image for the conjunctive interpretation and the subdirect image for the disjunctive interpretation interpolation then corresponds to solvability of some system of fuzzy relational equations in this paper we show that other types of fuzzy relations which are closely related to takagi sugeno t s models are of major interest as well these fuzzy relations are based on addition and multiplication only from which we get the name arithmetic fuzzy models under some mild requirements these fuzzy relations turn out to be solutions of the same systems of fuzzy relational equations the impact of these results is both theoretical and practical there exist simple solutions to systems of fuzzy relational equations other than the extremal solutions that have received all the attention so far which are moreover easy to implement

a surface phase field model for two phase biological membranes we study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases the energy laden phase interfaces may be modeled as curves on the hypersurface representing the membrane sharp interface model the phase field methodology is another powerful tool to model such phase separation phenomena where thin layers describe the interfaces diffuse interface model for both approaches we characterize equilibrium shapes in terms of the euler lagrange equations of the total membrane energy subject to constraints on the area of the two phases and the volume we further show by matching appropriate formal asymptotic expansions that the sharp interface model is obtained from the diffuse interface model as the thickness of the phase interface tends to zero the essential challenge lies in the fact that also the geometry of the membrane is unknown and depends on a small parameter representing the interface thickness

spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous curvature fluid membrane model an analytic solution for the helfrich spontaneous curvature membrane model h naito m okuda and pu yang zhong can phys rev e 48 2304 1993 54 2816 1996 which has the conspicuous feature of representing a circular biconcave shape is studied results show that the solution in fact describes a family of shapes which can be classified as i a flat plane trivial case ii a sphere iii a prolate ellipsoid iv a capped cylinder v an oblate ellipsoid vi a circular biconcave shape vii a self intersecting inverted circular biconcave shape and viii a self intersecting nodoidlike cylinder among the closed shapes ii vii a circular biconcave shape is the one with a minimum of local curvature energy s1063 651x 49 00309 8

set stability and set stabilization of boolean control networks based on invariant subsets this study addresses the set stability of boolean networks bns and set stabilization of boolean control networks bcns set stability determines whether a bn converges to a given subset whereas set stabilizability addresses the issue of whether a bcn can be stabilized to a given subset many problems can be viewed as special cases of set stability and set stabilization including synchronization partial stability and partial stabilization problems the concepts of invariant subset and control invariant subset are introduced then algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed based on the invariant subsets obtained the necessary and sufficient conditions for set stability and set stabilizability are established and formulae are provided to calculate the shortest transient periods for respective initial states a design procedure is proposed for finding all the time optimal set stabilizers finally an example is used to show the application of the proposed results to the synchronization problem of bns

on shell membranes of enneper type generalized dupin cyclides it is demonstrated that a class of generalized dupin cyclides arises naturally out of a classical system of equilibrium equations for shell membranes this class consists of all families of parallel canal surfaces on which the lines of curvature are planar various examples of viable membrane geometries such as particular l minimal surfaces are presented