on lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres the n dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the n 1 dimensional complex projective space which is isometric to the real grassmann manifold of oriented 2 planes and is a compact hermitian symmetric space of rank 2 in this paper we study geometry of compact lagrangian submanifolds in complex hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres from this viewpoint we provide a classification theorem of compact homogeneous lagrangian submanifolds in complex hyperquadrics by using the moment map technique moreover we determine the hamiltonian stability of compact minimal lagrangian submanifolds embedded in complex hyperquadrics which are obtained as gauss images of isoparametric hypersurfaces in spheres with g 1 2 3 distinct principal curvatures

a geometric approach to the classification of the equilibrium shapes of self gravitating fluids the classification of the equilibrium shapes that a self gravitating fluid can take in a riemannian manifold is a classical problem in mathematical physics in this paper it is proved that the equilibrium shapes are isoparametric submanifolds some geometric properties of them are also obtained e g classification and existence for some riemannian spaces and relationship with the isoperimetric problem and the group of isometries of the manifold our approach to the problem is geometrical and allows to study the equilibrium shapes on general riemannian spaces

focal sets and real hypersurfaces in complex projective space let m be a real submanifold of cpm and let j denote the complex structure we begin by finding a formula for the location of the focal points of m in terms of its second fundamental form this takes a particularly tractable form when m is a complex submanifold or a real hypersurface on which ji is a principal vector for each unit normal to m the rank of the focal map onto a sheet of the focal set of m is also computed in terms of the second fundamental form in the case of a real hypersurface on which je is principal with corresponding principal curvature u if the map onto a sheet of the focal set corresponding to u has constant rank then that sheet is a complex submanifold over which m is a tube of constant radius theorem 1 the other sheets of the focal set of such a hypersurface are given a real manifold structure in theorem 2 these results are then employed as major tools in obtaining two classifications of real hypersurfaces in cpm first there are no totally umbilic real hypersurfaces in cpm but we show theorem 3 let m be a connected real hypersurface in cpm m 3 with at most two distinct principal curvatures at each point then m is an open subset of a geodesic hypersphere secondly we show that there are no einstein real hypersurfaces in cpm and characterize the geodesic hyperspheres and two other classes of hypersurfaces in terms of a slightly less stringent requirement on the ricci tensor in theorem 4 one of the first results in the geometry of submanifolds is that an umbilic hypersurface m in euclidean space must be an open subset of a hyperplane or sphere the proof goes as follows assume that the shape operator is a scalar multiple of the identity a ax and use the codazzi equation to show that x is constant then either x 0 in which case m lies on a hyperplane or the focal points fx x x l x t the unit normal all coincide and m lies on the sphere of radius 1 x centered at the unique focal point this simple idea suggests a plan of attack for classifying hypersurfaces in terms of the nature of the principal curvatures under fairly general conditions the set of focal points corresponding to a principal curvature x can be given a differentiable received by the editors december 19 1980 presented to the society at its annual meeting in san francisco january 10 1981 1980 mathematics subject classificatiom primary 53b25 53c40

isoparametric functions on exotic spheres abstract this paper extends widely the work in 11 existence and non existence results of isoparametric functions on exotic spheres and eells kuiper projective planes are established in particular every homotopy n sphere n 4 carries an isoparametric function with certain metric with 2 points as the focal set in strong contrast to the classification of cohomogeneity one actions on homotopy spheres 26 only exotic kervaire spheres admit cohomogeneity one actions besides the standard spheres as an application we improve a beautiful result of berard bergery 2 see also pp 234 235 of 3

reduction of the n dimensional static vacuum einstein equation and generalized schwarzschild solutions abstract we consider the static vacuum einstein spacetime when the spatial factor is conformal to a n dimensional pseudo euclidean space the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations is completely described we obtain the entire set of solutions of the reduced system where the classical schwarzschild solution arises as a particular solution in addition we show that the riemannian spatial factors associated to these solutions are foliated by parallel hypersurfaces of constant mean curvature

robust pid controller tuning based on the constrained particle swarm optimization this paper proposes a novel tuning strategy for robust proportional integral derivative pid controllers based on the augmented lagrangian particle swarm optimization alpso first the problem of pid controller tuning satisfying multiple h performance criteria is considered which is known to suffer from computational intractability and conservatism when any existing method is adopted in order to give some remedy to such a design problem without using any complicated manipulations the alpso based robust gain tuning scheme for pid controllers is introduced it does not need any conservative assumption unlike the conventional methods and often enables us to find the desired pid gains just by solving the constrained optimization problem in a straightforward way however it is difficult to guarantee its effectiveness in a theoretical way because pso is essentially a stochastic approach therefore it is evaluated by several simulation examples which demonstrate that the proposed approach works well to obtain pid controller parameters satisfying the multiple h performance criteria

moment maps of the spin action and the cartan munzner polynomials of degree four we express all the known cartan munzner polynomials of degree four in terms of the moment map of certain group actions

a jordan algebra approach to the cubic eiconal equation we establish a natural correspondence between the equivalence classes of cubic solutions of a cubic eiconal equation and the isomorphy classes of cubic jordan algebras

isoparametric functions on riemannian manifolds i on etablit les proprietes de base des fonctions transnormales et on demontre le lemme du tube on demontre que soit m une variete de riemann lisse complete connexe et f une fonction transnormale sur m alors a les varietes focales de f sont des sous varietes lisses de m b chaque ensemble de niveau regulier de f est un tube sur d autres des varietes focales

isomorphism theorems on generalized effect algebras based on atoms a well known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub generalized effect algebra and simultaneously a proper order ideal the set theoretic complement of which is its dual poset we show that two non isomorphic generalized effect algebras even finite ones may have isomorphic effect algebraic extensions for archimedean atomic lattice effect algebras we prove isomorphism theorem based on atoms as an application we obtain necessary and sufficient conditions for isomorphism of two prelattice archimedean atomic generalized effect algebras with common or isomorphic effect algebraic extensions

on generalized m quasi einstein manifolds with constant scalar curvature abstract we study generalized m quasi einstein manifolds with constant scalar curvature first we establish a classification of generalized m quasi einstein manifolds with parallel ricci tensor second and particularly if an m quasi einstein manifold possesses constant scalar curvature then we determine the scalar curvature in explicit form and show that which values are attainable by presenting examples

ancient solutions to mean curvature flow for isoparametric submanifolds mean curvature flow for isoparametric submanifolds in euclidean spaces and spheres was studied in liu and terng duke math j 147 1 157 179 2009 in this paper we will show that all these solutions are ancient solutions and study their limits as time goes to negative infinity we also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the chern s conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres

heat flow heat content and the isoparametric property let m be a riemannian manifold and omega a compact domain of m with smooth boundary we study the solution of the heat equation on omega having constant unit initial conditions and dirichlet boundary conditions the purpose of this paper is to study the geometry of domains for which at any fixed value of time the normal derivative of the solution heat flow is a constant function on the boundary we express this fact by saying that such domains have the constant flow property in constant curvature spaces known examples of such domains are given by geodesic balls and more generally by domains whose boundary is connected and isoparametric the question is are they all like that this problem is the analogous for the heat equation of the classical serrin s problem for harmonic domains in this paper we give an affirmative answer to the above question in fact we prove more generally that if a domain in an analytic riemannian manifold has the constant flow property then every component of its boundary is an isoparametric hypersurface for space forms we also relate the order of vanishing of the heat content with fixed boundary data with the constancy of the r mean curvatures of the boundary and with the isoparametric property finally we discuss the constant flow property in relation to other well known overdetermined problems involving the laplace operator like the serrin problem or the schiffer problem

attractors and symmetries of vector fields the inverse problem abstract the inverse problem of constructing dynamical systems x with a prescribed compact attracting set k r n and non trivial dynamics on it is solved the boundaries of the attracting basins corresponding to different connected components of k and the relationship between the symmetries of k x and are also studied

isoparametric foliations and critical sets of eigenfunctions jakobson and nadirashvili j differ geom 53 1 177 182 1999 constructed a sequence of eigenfunctions on t 2 with a bounded number of critical points answering in the negative the question raised by yau problem section seminar on differential geometry princeton university press princeton 1982 which asks that whether the number of the critical points of eigenfunctions for the laplacian increases with the corresponding eigenvalues the present paper finds three interesting eigenfunctions on the minimal isoparametric hypersurface m n in s n 1 1 the corresponding eigenvalues are n 2n and 3n while their critical sets consist of 8 points a submanifold infinite many points and 8 points respectively on one of its focal submanifolds a similar phenomenon occurs

degenerate solutions of a nonlinear elliptic equation on the sphere abstract we consider the equation u u u q on the round sphere s m m 3 with 0 and 1 q m 2 m 2 by studying the local structure of solutions bifurcating from the constant solution we show that for any isoparametric hypersurface m in the sphere there is a value of and a solution of the equation at which the linearized equation has nontrivial solutions at the same time we obtain new solutions of the equation

chaos driven evolutionary algorithms for the task of pid control chaos driven differential evolution algorithm and self organizing migrating algorithm are presented in this paper for the task of pid proportional integral derivative controller optimization the dissipative chaotic lozi map is embedded as a number generator inside de and soma in order to avoid local optima stagnation and embed a superior search strategy three unique pid controller problems are presented and successfully resolved using these new approaches the obtained results compare favorably with published results

some families of isoparametric hypersurfaces and rigidity in a complex hyperbolic space the geometric notion of equivalence for submanifolds in a chosen ambient space is that of congruence in this study a certain type of isoparametric hypersurface of a complex hyperbolic space form is shown to have a rigid immersion by utilizing the congruences of a lorentzian hyperbolic space form that lies as an si fiber bundle over the complex hyperbolic space several families of isoparametric hypersurfaces namely tubes and horospheres are constructed whose immersions are rigid

ricci curvature of double manifolds via isoparametric foliations abstract given a closed manifold m and a vector bundle of rank n over m by gluing two copies of the disc bundle of we can obtain a closed manifold d m the so called double manifold in this paper we firstly prove that each sphere bundle s r of radius r 0 is an isoparametric hypersurface in the total space of equipped with a connection metric and for r 0 small enough the induced metric of s r has positive ricci curvature under the additional assumptions that m has a metric with positive ricci curvature and n 3 as an application if m admits a metric with positive ricci curvature and n 2 then we construct a metric with positive ricci curvature on d m moreover under the same metric d m admits a natural isoparametric foliation for a compact minimal isoparametric hypersurface y n in s n 1 1 which separates s n 1 1 into s n 1 and s n 1 one can get double manifolds d s n 1 and d s n 1 inspired by tang xie and yan s work on scalar curvature of such manifolds with isoparametric foliations cf 25 we study ricci curvature of them with isoparametric foliations in the last part

on chern s conjecture for minimal hypersurfaces and rigidity of self shrinkers using the generalized yau parameter method and the sylvester theory we verify that if m is a compact minimal hypersurface in sn 1 whose squared length of the second fundamental form satisfies 0 a 2 n n22 then a 2 n and m is a clifford torus moreover we prove that if m is a complete self shrinker with polynomial volume growth in rn 1 and if the squared length of the second fundamental form of m satisfies 0 a 2 1 121 then a 2 1 and m is a round sphere or a cylinder our results improve the rigidity theorems due to ding and xin 21 22

low energy nodal solutions to the yamabe equation abstract given an isoparametric function f on the n dimensional sphere we consider the space of functions w f to reduce the yamabe equation on the round sphere into a singular ode on w in the interval 0 of the form w h r sin r w w 4 n 2 w w 0 and boundary conditions w 0 0 w where h is a monotone function with exactly one zero on 0 and 0 is a constant for any positive integer k we obtain a solution with exactly k zeroes yielding solutions to the yamabe equation with exactly k connected isoparametric hypersurfaces as nodal set the idea of the proof is to consider the initial value problems on the singularities and then to solve the corresponding double shooting problem matching the values of w and w at the unique zero of h in particular we obtain solutions with exactly one zero providing solutions of the yamabe equation with low energy

the first eigenvalue of the laplacian of an isoparametric minimal hypersurface in a unit sphere soit m n 1 une variete de riemann connexe compacte a n 1 dimensions sans bord et son laplacien agissant sur des fonctions lisses sur m a un spectre discret 0 0 m 1 m 2 m k m x soit f une immersion minimale de m n 1 dans la sphere unite a n dimensions s n 1 de l espace euclidien on etudie la premiere valeur propre du laplacien d une hypersurface isoparametrique minimale fermee dans s n 1

firefly algorithm approach based on chaotic tinkerbell map applied to multivariable pid controller tuning nowadays a variety of controllers used in process industries are still of the proportional integral derivative pid types pid controllers have the advantage of simple structure good stability and high reliability a relevant issue for pid controllers design is the accurate and efficient tuning of parameters in this context several approaches have been reported in the literature for tuning the parameters of pid controllers using evolutionary algorithms mainly for single input single output systems the systematic design of multi loop or decentralized pid control for multivariable processes to meet certain objectives simultaneously is still a challenging task this paper proposes a new chaotic firefly algorithm approach based on tinkerbell map cfa to tune multi loop pid multivariable controllers the firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies to validate the performance of the proposed pid control design a multi loop multivariable pid structure for a binary distillation column plant wood and berry column model and an industrial scale polymerization reactor are taken simulation results indicate that a suitable set of pid parameters can be calculated by the proposed cfa besides some comparison results of a genetic algorithm a particle swarm optimization approach traditional firefly algorithm modified firefly algorithm and the proposed cfa to tune multi loop pid controllers are presented and discussed

isoparametric hypersurfaces in complex hyperbolic spaces we review some results of an ongoing research on isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in the complex hyperbolic space in order to motivate this topic we recall first the main steps of its long history

continuous lattice effect algebras admitting order continuous states we prove that a necessary and sufficient condition for the existence of a faithful o continuous state on a complete modular atomic effect algebra e is the separability of e moreover we generalize the famous kaplansky theorem about order continuity of complemented complete modular lattices onto complete modular atomic effect algebras some other statements about the algebraic structure of modular effect algebras are shown we prove that every chain and every block in an irreducible complete modular atomic effect algebra is finite moreover every complete atomic modular effect algebra is compactly generated by finite elements

brief paper multivariable pid control with set point weighting via bmi optimisation the paper focuses on the design of multivariable pid controllers with set point weighting the advantage of this pid structure is that the responses of the system to disturbances and to changes in the set point can be adjusted separately the proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback sof problem hence multivariable pid controllers can be designed by solving an optimisation problem with bilinear matrix inequalities bmis the paper addresses the design of both time invariant and gain scheduled robust controllers all of the tuning methods discussed through the paper are based on a pid structure with filtered derivative term thus guaranteeing the well posedness of the closed loop system

a self adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization evolutionary algorithms eas have yielded promising results for solving nonlinear non differentiable and multi modal optimization problems due to its population based nature eas can avoid being trapped in a local optimum and consequently have the ability to find global optimal solutions as a novel evolutionary technique differential evolution de has received increasing attention and wide applications in a variety of fields de algorithm uses an efficient way of self adapting mutation using small populations for function optimization over continuous spaces the potentialities of de are its simple structure easy use convergence property quality of solution and robustness in this paper an effective self adaptive de algorithm based on gaussian probability distribution gamma distribution and chaotic sequence degc for solving continuous global optimization problems is proposed the proposed degc algorithm is tested on several benchmark functions from the usual literature numerical results comparisons with a classical de approach and a self adaptive de approach demonstrate the effectiveness and efficiency of the proposed degc algorithm

gradient map of isoparametric polynomial and its application to ginzburg landau system abstract in this note we study properties of the gradient map of the isoparametric polynomial for a given isoparametric hypersurface in sphere we calculate explicitly the gradient map of its isoparametric polynomial which turns out many interesting phenomenons and applications we find that it should map not only the focal submanifolds to focal submanifolds isoparametric hypersurfaces to isoparametric hypersurfaces but also map isoparametric hypersurfaces to focal submanifolds in particular it turns out to be a homogeneous polynomial automorphism on certain isoparametric hypersurface as an immediate consequence we get the brouwer degree of the gradient map which was firstly obtained by peng and tang with moving frame method following farina s construction another immediate consequence is a counterexample of the brezis question about the symmetry for the ginzburg landau system in dimension 6 which gives a partial answer toward the open problem 2 raised by farina

affine connections on 3 sasakian and manifolds the space of invariant affine connections on every 3 sasakian homogeneous manifold of dimension at least seven is described in particular the subspace of invariant affine metric connections and the subclass with skew torsion are also determined to this aim an explicit construction of all 3 sasakian homogeneous manifolds is exhibited it is shown that the 3 sasakian homogeneous manifolds which admit nontrivial einstein with skew torsion invariant affine connections are those of dimension seven that is mathbb s 7 mathbb r p 7 and the aloff wallach space mathfrak w 7 1 1 on mathbb s 7 and mathbb r p 7 the set of such connections is bijective to two copies of the conformal linear transformation group of the euclidean space while it is strictly bigger on mathfrak w 7 1 1 the set of invariant connections with skew torsion whose ricci tensor satisfies that its eigenspaces are the canonical vertical and horizontal distributions is fully described on 3 sasakian homogeneous manifolds an affine connection satisfying these conditions is distinguished by parallelizing all the reeb vector fields associated with the 3 sasakian structure which is also einstein with skew torsion on the 7 dimensional examples the invariant metric affine connections on 3 sasakian homogeneous manifolds with parallel skew torsion have been found finally some results have been adapted to the non homogeneous setting

isoparametric hypersurfaces with g m 6 2 we prove that isoparametric hypersurfaces with g m 6 2 are homogeneous which answers dorfmeister neher s conjecture armatively and solves yau s problem in the case g 6

isoparametric foliations a problem of eells lemaire and conjectures of leung in this paper two sequences of minimal isoparametric hypersurfaces are constructed via representations of clifford algebras based on these we give estimates on eigenvalues of the laplacian of the focal submanifolds of isoparametric hypersurfaces in unit spheres this improves results of z z tang and w j yan isoparametric foliation and yau conjecture on the first eigenvalue j differential geom 94 2013 521 540 z z tang y q xie and w j yan isoparametric foliation and yau conjecture on the first eigenvalue ii j funct anal 266 2014 6174 6199 eells and lemaire selected topics in harmonic maps c b m s regional conference series in mathematics 50 american mathematical society providence ri 1983 posed a problem to characterize the compact riemannian manifold m for which there is an eigenmap from m to sn as another application of our constructions the focal maps give rise to many examples of eigenmaps from minimal isoparametric hypersurfaces to unit spheres most importantly by investigating the second fundamental forms of focal submanifolds of isoparametric hypersurfaces in unit spheres we provide infinitely many counterexamples to two conjectures of leung minimal submanifolds in a sphere ii bull london math soc 23 1991 387 390 posed in 1991 on minimal submanifolds in unit spheres note that these conjectures of leung have been proved in the case that the normal connection is flat t hasanis and t vlachos ricci curvatures and minimal submanifolds pacific j math 197 2001 13 24

real hypersurfaces in a complex space form with η parallel shape operator in this paper we classify the real hypersurfaces in a non flat complex space form with parallel shape operator

basic decomposition of elements and jauch piron effect algebras we show that every element of a complete atomic effect algebra e has a unique basic decomposition into a sum of a sharp element and unsharp multiples of isotropic atoms of e consequently for such effect algebras we obtain the smearing theorem for states establishing that every order continuous state existing on sharp elements of e can be extended to a state on e for a s complete separable atomic effect algebra e we prove that e is a unital and jauch piron effect algebra if and only if the set s e of all sharp elements of e is a unital jauch piron orthomodular lattice and for finite e s e is a boolean algebra

self organizing genetic algorithm based tuning of pid controllers this paper proposes a self organizing genetic algorithm soga with good global search properties and a high convergence speed first we introduce a new dominant selection operator that enhances the action of the dominant individuals along with a cyclical mutation operator that periodically varies the mutation probability in accordance with evolution generation found in biological evolutionary processes next the soga is constructed using the two operators mentioned above the results of a nonlinear regression analysis demonstrate that the self organizing genetic algorithm is able to avoid premature convergence with a higher convergence speed and also indicate that it possesses self organization properties finally the new algorithm is used to optimize proportional integral derivative pid controller parameters our simulation results indicate that a suitable set of pid parameters can be calculated by the proposed soga

mobius curvature laguerre curvature and dupin hypersurface abstract in this paper we show that a dupin hypersurface with constant mobius curvatures is mobius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere we also show that a dupin hypersurface with constant laguerre curvatures is laguerre equivalent to a flat laguerre isoparametric hypersurface these results solve the major issues related to the conjectures of cecil et al on the classification of dupin hypersurfaces

real hypersurfaces and complex submanifolds in complex projective space let m be a real hypersurface in c j be the complex structure and denote a unit normal vector field on m we show that m is an open subset of a homogeneous hypersurface if and only if m has constant principal curvatures and jt is principal we also obtain a characterization of certain complex submanifolds in a complex projective space specifically c totally geodesic q pl c x p c su 5 s u 2 x 7 3 and so 10 t 5 are the only complex submani folds whose principal curvatures are constant in the sense that they depend neither on the point of the submanifold nor on the normal vector

isoparametric foliation and a problem of besse on generalizations of einstein condition abstract the focal sets of isoparametric hypersurfaces in spheres with g 4 are all willmore submanifolds being minimal but mostly non einstein 25 22 inspired by a gray s view the present paper shows that these focal sets are all a manifolds but rarely ricci parallel except possibly for the only unclassified case as a byproduct it gives infinitely many simply connected examples to the problem 16 56 i of besse concerning generalizations of the einstein condition

real hypersurfaces of complex projective spaces let p denote the complex projective space with fubini study metric of constant holomorphic sectional curvature 4 and suppose m 2 it is well known that there does not exist a totally umbilical real hypersurface m of p c see tashiro and tachibana 7 moreover as a consequence of codazzi equation there does not exist a real hypersurface m of pro c with parallel second fundamental form to get this y maeda 4 estimated the norm of the derivative of the second fundamental form he showed

isoparametric foliation and yau conjecture on the first eigenvalue ii abstract this is a continuation of 23 which investigated the first eigenvalues of minimal isoparametric hypersurfaces with g 4 distinct principal curvatures and focal submanifolds in unit spheres for the focal submanifolds with g 6 the present paper obtains estimates on all the eigenvalues among others giving an affirmative answer in one case to the problem posed in 23 which may be regarded as a generalization of yau s conjecture in two of the four unsettled cases in 23 for focal submanifolds m 1 of ot fkm type we prove the first eigenvalues to be their respective dimensions

differentiable classification of 4 manifolds with singular riemannian foliations in this paper we first prove that any closed simply connected 4 manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4 manifolds mathbb s 4 mathbb cp 2 mathbb s 2 times mathbb s 2 or mathbb cp 2 pm mathbb cp 2 as an application we prove that any closed simply connected 4 manifold admitting a nontrivial singular riemannian foliation is diffeomorphic to a connected sum of copies of standard mathbb s 4 pm mathbb cp 2 and mathbb s 2 times mathbb s 2 a classification of singular riemannian foliations of codimension 1 on all closed simply connected 4 manifolds is obtained as a byproduct in particular there are exactly 3 non homogeneous singular riemannian foliations of codimension 1 complementing the list of cohomogeneity one 4 manifolds

modeling and model predictive control of a nonlinear hydraulic system this paper deals with modeling and control of a hydraulic three tank system a process of creating a computer model in the matlab simulink environment is described and optimal pid proportional integral derivative and model predictive controllers are proposed the modeling starts with the creation of an initial mathematical model based on a first principles approach then the initial model is enhanced to obtain better correspondence with a real time system and parameters of the modified system are identified from measurements the real time system contains nonlinearities which cannot be neglected and therefore are identified and included in the final mathematical model the resulting model is used for a control design as the real time system has long time constants usage of the simulink model dramatically speeds up the design process optimal pid and model predictive controllers mpc are proposed and compared model predictive controllers for both a linearized model and the nonlinear system are proposed the techniques described are not limited to one particular modeling problem but can be used as an illustrative example for the modeling of many technological processes

lattice effect algebras with o continuous faithful valuations we prove that if there exists an order continuous faithful valuation on a lattice effect algebra e then e is modular separable and order continuous it is also shown that such an effect algebra e can be supremum and infimum densely embedded into a complete effect algebra e which is also modular separable and order continuous since the valuation can be extended to a unique order continuous faithful valuation on e

the nef value and defect of homogeneous line bundles formulas for the nef value of a homogeneous line bundle are derived and applied to the classification of homogeneous spaces with positive defect and to the classification of complete homogeneous real hypersurfaces of projective space

a simplified version of mamdani s fuzzy controller the natural logic controller this paper proposes the natural logic controller nlc that it comes through a very important simplification of the mamdani s fuzzy controller mfc allowing easy design for single input single output siso regulation problems usually fuzzy controllers are built with two classical signals of process the error and its rate of change they use a moderate number of fuzzy subsets and fuzzy rules the main features of the nlc approach are that use the minimal fuzzy partition only two fuzzy subsets per variable and it use the minimal fuzzy rule base only two rules the nonlinear resulting fuzzy controller is the simplest one with an analytically well defined input output mapping and accepting a linear approximation at origin it allows easy extension to more than two signals of process some properties of nonlinear mapping of nlc are analyzed and some results are also presents on testing stability when nlc is used on a linear process a special attention is addressed to the two inputs nlc case where stability can be tested using the circle criterion finally two application examples are discussed in details

stationary isothermic surfaces in euclidean 3 space let omega be a domain in mathbb r 3 with partial omega partial mathbb r 3 setminus overline omega where partial omega is unbounded and connected and let u be the solution of the cauchy problem for the heat equation partial t u delta u over mathbb r 3 where the initial data is the characteristic function of the set omega c mathbb r 3 setminus omega we show that if there exists a stationary isothermic surface gamma of u with gamma cap partial omega varnothing then both partial omega and gamma must be either parallel planes or co axial circular cylinders this theorem completes the classification of stationary isothermic surfaces in the case that gamma cap partial omega varnothing and partial omega is unbounded to prove this result we establish a similar theorem for uniformly dense domains in mathbb r 3 a notion that was introduced by magnanini et al trans am math soc 358 4821 4841 2006 in the proof we use methods from the theory of surfaces with constant mean curvature combined with a careful analysis of certain asymptotic expansions and a surprising connection with the theory of transnormal functions

infinite families of harmonic self maps of spheres abstract for each of the spheres s n n 5 we construct a new infinite family of harmonic self maps and prove that their members have brouwer degree 1 or 3 these self maps are obtained by solving a singular boundary value problem as an application we show that for each of the special orthogonal groups so 4 so 5 so 6 and so 7 there exist two infinite families of harmonic self maps