angle variable holonomy in adiabatic excursion of an integrable hamiltonian if an integrable classical hamiltonian h describing bound motion depends on parameters which are changed very slowly then the adiabatic theorem states that the action variables i of the motion are conserved here the fate of the angle variables is analysed because of the unavoidable arbitrariness in their definition angle variables belonging to distinct initial and final hamiltonians cannot generally be compared however they can be compared if the hamiltonian is taken on a closed excursion in parameter space so that initial and final hamiltonians are the same the result shows that the angle variable change arising from such an excursion is not merely the time integral of the instantaneous frequency omega dh di but differs from it by a definite extra angle which depends only on the circuit in parameter space not on the duration of the process the 2 form which describes this angle variable holonomy is calculated

characterizations of uni nullnorms with continuous archimedean underlying t norms and t conorms abstract a uni nullnorm is a special case of 2 uninorms obtained by letting a uninorm and a nullnorm share the same underlying t conorm in this paper we give complete descriptions of uni nullnorms with continuous archimedean underlying t norms and t conorms

classical adiabatic angles and quantal adiabatic phase a semiclassical connection is established between quantal and classical properties of a system whose hamiltonian is slowly cycled by varying its parameters round a circuit the quantal property is a geometrical phase shift gamma n associated with an eigenstate with quantum numbers n nl the classical property is a shift delta theta l i in the lth angle variable for motion round a phase space torus with actions i il the connection is delta theta l delta gamma delta nl two applications are worked out in detail the generalised harmonic oscillator with quadratic hamiltonian whose parameters are the coefficients of q2 qp and p2 and the rotated rotator consisting of a particle sliding freely round a non circular hoop slowly turned round once in its own plane

characterization of idempotent n uninorms abstract the structure of idempotent n uninorms is studied we show that each idempotent 2 uninorm can be expressed as an ordinal sum of an idempotent uninorm possibly also of a countable number of idempotent semigroups with operations min and max and a 2 uninorm from class 1 possibly restricted to open or half open unit square similar results are shown also for idempotent n uninorms further it is shown that idempotent n uninorms are in one to one correspondence with special lower semi lattices defined on the unit interval the z ordinal sum construction for partially ordered semigroups is also defined

modularity conditions between overlap grouping function and uni nullnorm or null uninorm abstract overlap and grouping functions as two kinds of special continuous commutative aggregation functions have wide applications in image processing and classification modularity conditions between the class of overlap grouping functions satisfying o 1 e e g 0 e e and special classes of uninorms and those of another special class of overlap grouping functions over nullnorms have been studied in 49 in this paper we extend these results to any overlap grouping function moreover we study the modularity conditions between overlap grouping functions and uni nullnorms null uninorms which are the generalization of uninorms nullnorms

existence condition of positive definite solutions for algebraic matrix riccati equations abstract algebraic matrix riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time invariant systems a necessary and sufficient condition is established for the existence of unique positive definite solutions and the asymptotically stable closed loop system the condition is stated in terms of the detectability and stabilizability of certain matrix pairs as was the case for the non negative definite solution simple examples are included to illustrate the new results against the existing ones

berry s phase and hannay s angle from quantum canonical transformations using an action angle coherent states formalism introduced by the authors in a preceding paper it is shown that berry s phase and hannay s angle can both be derived from the same quantum unitary transformation their relationship is easily established in this framework

distributivity and conditional distributivity for uni nullnorms abstract the distributivity and conditional distributivity of a uninorm over a continuous t conorm is an open problem posed by klement in the linz seminar 2000 closing session after this the study of distributivity and conditional distributivity between two aggregation operators become specially interesting in this work we continue investigating the same topic for uni nullnorms then the full characterization of all pairs f g satisfying distributivity and conditional distributivity is given where f is a uni nullnorm g is a t norm or a t conorm or a uninorm from u min and u max

hannay s angle and berry s phase for su 1 1 systems the classical and quantum systems related to the group su 1 1 are considered the hannay angle is calculated and its relation to berry s phase established

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

exact evolution of the generalized damped harmonic oscillator in this paper we use the algebraic and the invariant method to study the time dependent damped harmonic oscillator from classical and quantum points of view the solution of the classical equation of motion and the wavefunction solving the time dependent schrodinger equation are found explicitly we show that the original time dependent quantum mechanical problem is completely related to the well known time independent harmonic oscillator in addition we elucidate the intimate connection between the damped harmonic oscillator dho and the generalized harmonic oscillator gho more importantly the evolution of the states of the dho cannot be cyclic in contradistinction with the states of the gho explicit expressions for both the dynamical and the geometric angles and phases are deduced in the adiabatic limit the coherent states describing the invariant angle variables of the classical dho are constructed they allow us to recover the classical evolution and invariant from the quantum evolution

the connection whose holonomy is the classical adiabatic angles of hannay and berry and its generalization to the non integrable case we show how averaging defines an ehresmann connection whose holonomy is the classical adiabatic angles which hannay defined for families of completely integrable systems the averaging formula we obtain for the connection only requires that the family of hamiltonians has a continuous symmetry group this allows us to extend the notion of the hannay angles to families of non integrable systems with symmetry we state three geometric axioms satisfied by the connection these axioms uniquely determine the connection thus enabling us to find new formulas for the connection and its curvature two examples are given

berry s transport and minimization of averaged distances in this paper we consider the metric approach to the berry s transport geometrical part of the adiabatic evolution of any pure or mixed state for possibly degenerate hamiltonians we emphasize that explicit formulae for the transport of such states need the introduction of an averaging procedure in analogy with the classical case this quantum averaging involves multiplying each energy eigenstate by a different phase and then integrating over these phases we show in particular how the transport of non stationary pure states rays and density matrices arise from the minimization of hilbert fubini study and bures averaged distances respectively

berry s phase hannay s angle and coherent states through the use of coherent states describing the action angle variables the authors establish a strict parallelism between berry s phase and hannay s angle in particular they define a geometrical transport for classical tori which leads to hannay s angle as in the case of berry s phase the transport can be associated with the minimization of a distance

maslov s complex germ method and berry s phase in the adiabatic approximation the connection of the beny phase with the quasi classical trajectory coherent slates of the schrirdinger type equation with the arbitrary scalar pseudo differential operator and the dirac equation in the external penodic electromagnetic field is studied

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

uni nullnorms on bounded lattices abstract in this paper we study uni nullnorms with both neutral elements and zero elements on bounded lattices in order to illustrate the existence of uni nullnorms on bounded lattices we present two construction methods for obtaining such a uni nullnorm also we show two additional methods for the construction of idempotent nullnorms on bounded lattices which are generalizations of the one proposed by cayli and karacal furthermore we discuss the presence of idempotent uni nullnorms on bounded lattices and propose two construction methods to obtain an idempotent uni nullnorm on any bounded lattice

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

periodic solutions of matrix riccati equations in discrete time invariant systems the well known matrix riccati equations arising in optimal filtering as well as control problems for discrete time invariant systems are considered in this paper existence conditions are established both for general periodic solutions and for non negative definite periodic solutions it is shown that a pair of complex conjugate eigenvalues or a pair of real eigenvalues in a certain symplectic matrix produce periodic solutions furthermore algorithms are obtained to derive such periodic solutions using the symplectic matrix which require slight additional computations to deriving steady state solutions finally numerical examples which possess periodic solutions are presented