stable particle like solutions to the nonlinear wave equations of three dimensional excitable media so called excitable media support nonlinear waves that propagate as pulses e g the action potential in nerve fibers and heart muscle and the oxidation pulse in certain chemical reactions in two dimensional media the right stimulus will also create rotating vortices which radiate such pulses periodically in every direction their investigation in diverse excitable media has dramatically expanded in the usa and ussr since their discovery in both countries in 1970 in three dimensional media the pivot of the rotating structure is not a point but a curved line generically a closed ring rings linked together and knotted constitute topologically distinctive organizing centers for periodic activity throughout the medium it is of interest to understand how stimuli create organizing centers and how organizing centers persist or decay the numerically discovered stable organizing centers exhibit enough symmetries to encourage mathematical attention this paper illustrates organizing centers by computer g

on institutions for modular coalgebraic specifications abstract we present an algebraic extension of standard coalgebraic specification techniques for state based systems which allows us to integrate constants and n ary operations in a smooth way and which leads to institutions enabling the use of modular specification techniques a sound and complete proof system for first order observational properties of modular specifications is given the framework of structures that we present can be considered as the result of a transformation of concepts of observational logic as in hennicker and bidoit in a haeberer ed algebraic methodology and software technology amast 98 lecture notes in computer science vol 1548 springer berlin 1999 into the coalgebraic world moreover it is shown that the features of structures that make them suitable models for an observational approach to specifications can be categorically expressed by the fact that the operation mapping an structure to its behaviour is a fibred idempotent monad

closure properties for the class of behavioral models hidden k logics can be considered as the underlying logics of program specification they constitute natural generalizations of k deductive systems and encompass deductive systems as well as hidden equational logics and inequational logics in our abstract algebraic approach the data structures are sorted algebras endowed with a designated subset of their visible parts called filter which represents a set of truth values we present a hierarchy of classes of hidden k logics the hidden k logics in each class are characterized by three different kinds of conditions namely properties of their leibniz operators closure properties of the class of their behavioral models and properties of their equivalence systems using equivalence systems we obtain a new and more complete analysis of the axiomatization of the behavioral models this is achieved by means of the leibniz operator and its combinatorial properties

behavioural theories and the proof of behavioural properties abstract behavioural theories are a generalization of first order theories where the equality predicate symbol is interpreted by a behavioural equality of objects and not by their identity in this paper we first consider arbitrary behavioural equalities determined by partial congruence relations and we show how to reduce the behavioural theory of any class of algebras to a subset of the standard theory of some corresponding class of algebras this reduction is the basis of a method for proving behavioural theorems whenever an axiomatization of the behavioural equality is provided then we focus on the important special case of partial observational equalities where two elements are observationally equal if they cannot be distinguished by observable computations over some set of input values we provide general conditions under which an obvious infinite axiomatization of the observational equality can be replaced by a finitary one and we provide methodological guidelines for finding such finitary axiomatizations as a consequence any proof system for first order logic can be used to prove the behavioural validity of first order formulas with respect to a given partial observational equality

topology bounds energy of knots and links in this paper we determine two quantities of geometric and topological character that were left undetermined in two previous results obtained by arnold arnold 1974 in proc summer school in dif

hamiltonians and variational principles for alfven simple waves the evolution equations for the magnetic field induction b with the wave phase for alfven simple waves are expressed as variational principles and in the hamiltonian form the evolution of b with the phase which is a function of the space and time variables depends on the generalized frenet serret equations in which the wave normal n which is a function of the phase is taken to be tangent to a curve x in a 3d cartesian geometry vector space the physical variables the gas density fluid velocity gas pressure and magnetic field induction in the wave depend only on the phase three approaches are developed one approach exploits the fact that the frenet equations may be written as a 3d hamiltonian system which can be described using the nambu bracket it is shown that b as a function of the phase satisfies a modified version of the frenet equations and hence the magnetic field evolution equations can be expressed in the hamiltonian form a second approach develops an euler poincare variational formulation a third approach uses the frenet frame formulation in which the hodograph of b moves on a sphere of constant radius and uses a stereographic projection transformation due to darboux the equations for the projected field components reduce to a complex riccati equation by using a cole hopf transformation the riccati equation reduces to a linear second order differential equation for the new variable a hamiltonian formulation of the second order differential equation then allows the system to be written in the hamiltonian form alignment dynamics equations for alfven simple waves give rise to a complex riccati equation or equivalently to a quaternionic riccati equation which can be mapped onto the riccati equation obtained by stereographic projection

the mathematical structure of rainfall representations 3 some applications of the point process theory to rainfall processes part 3 constitutes the final part of three parts devoted to the mathematical structure of rainfall the objective is to illustrate the scope of the tools developed in part 2 in the mathematical description of rainfall and rainfall driven processes a general overview of the three part series is given in part 1

helicity and the calugareanu invariant the helicity of a localized solenoidal vector field i e the integrated scalar product of the field and its vector potential is known to be a conserved quantity under frozen field distortion of the ambient medium in this paper we present a number of results concerning the helicity of linked and knotted flux tubes particularly as regards the topological interpretation of helicity in terms of the gauss linking number and its limiting form the c lug reanu invariant the helicity of a single knotted flux tube is shown to be intimately related to the c lug reanu invariant and a new and direct derivation of this topological invariant from the invariance of helicity is given helicity is decomposed into writhe and twist contributions the writhe contribution involving the gauss integral for definition see equation 4 8 which admits interpretation in terms of the sum of signed crossings of the knot averaged over all projections part of the twist contribution is shown to be associated with the torsion of the knot and part with what may be described as intrinsic twist of the field lines in the flux tube around the knot see equations 5 13 and 5 15 the generic behaviour associated with the deformation of the knot through a configuration with points of inflexion points at which the curvature vanishes is analysed and the role of the twist parameter is discussed the derivation of the c lug reanu invariant from first principles of fluid mechanics provides a good demonstration of the relevance of fluid dynamical techniques to topological problems

reduction for constrained variational problems on 3 dimensional null curves we consider the optimal control problem for null curves in de sitter 3 space defined by a functional which is linear in the curvature of the trajectory we show how techniques based on the method of moving frames and exterior differential systems coupled with the reduction procedure for systems with a lie group of symmetries lead to the integration by quadratures of the extremals explicit solutions are found in terms of elliptic functions and integrals

cyclic rotations contractibility and gauss bonnet let a rigid object or frame of reference have identical initial and final orientations but be rotated in any way in between with an angular velocity any unit vector carried with the frame passes through a cycle of directions enclosing a solid angle the full relation between these three quantities is shown to be where the turn number n is zero if the sequence of orientations of the frame is contractible and unity if it is non contractible the main derivation uses the calugareanu relation lk w r tw between linking number writhe and twist of a ribbon loop an outline alternative derivation uses the berry phase of a quantum spin finally the result is applied to the standard parallel transport holonomy expressed in the gauss bonnet theorem it is refined to be correct rather than merely

conditional distributions of neyman scott models for storm arrivals and their use in irrigation scheduling count for the widely recognized but often neglected statistical dependence in storm arrivals gabriel and newmann 1957 1962 smith and schreiber 1973 kavvas and delleur 1975 recently authors like kavvas and delleur 1975 and gupta and waymire 1979 have argued that this dependence is due to clustering of rainfall in time and space they suggest modeling storm arrivals with cluster point processes like the neyman scott model this work uses the concept of cluster models for storm arrivals the conditional distribution of the occurrence of future events given a history of the timing of past events is derived for the neyman scott model this new result is then used with a reformulated model of the irrigation scheduling problem now the decision of when and how much to irrigate is based on the time since the last observed storm the effective soil moisture content and the amount of available irrigation water a case study is presented to illustrate the solution significantly there is no important difference between the theoretical net benefits derived from assuming a homogeneous independent poisson model or a dependent neyman scott n s model during the growing season a nonhomogeneous poisson model yields higher theoretical benefits as expected the conditional n s model leads to improved irrigation control as compared to the unconditional n s model from this case study however no definite conclusion can be drawn regarding whether the neyman scott model better represents the process of storm arrivals as opposed to the poisson model however the expected opportunity loss of choosing the wrong model can be significant interesting implications of the results are that data manipulation can have a significant effect on the ultimate model

compatibility of continuous rainfall occurrence models with discrete rainfall observations inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made following the work of i rodriguez iturbe et al 1984 this assertion is tested by examining the compatibility of the neyman scott n s model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day the results suggest that the n s model is inconsistent at different time scales and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought these findings are quite general in that they apply to any model with rainfall deposited instantaneously at times described by a n s process regardless of how the amounts associated with the events are distributed and of the dependence structure of the amounts

isoperimetric problems for the helicity of vector fields and the biot savart and curl operators the helicity of a smooth vector field defined on a domain in three space is the standard measure of the extent to which the field lines wrap and coil around one another it plays important roles in fluid mechanics magnetohydrodynamics and plasma physics the isoperimetric problem in this setting is to maximize helicity among all divergence free vector fields of given energy defined on and tangent to the boundary of all domains of given volume in three space the biot savart operator starts with a divergence free vector field defined on and tangent to the boundary of a domain in three space regards it as a distribution of electric current and computes its magnetic field restricting the magnetic field to the given domain we modify it by subtracting a gradient vector field so as to keep it divergence free while making it tangent to the boundary of the domain the resulting operator when extended to the l2 completion of this family of vector fields is compact and self adjoint and thus has a largest

observational proofs by rewriting observability concepts contribute to a better understanding of software correctness in order to prove observational properties the concept of context induction has been developed by hennicker hennicker formal aspects of computing 3 4 1991 326 345 we propose in this paper to embed context induction in the implicit induction framework of bouhoula and rusinowitch journal of automated reasoning 14 2 1995 189 235 the proof system we obtain applies to conditional specifications it allows for many rewriting techniques and for the refutation of false observational conjectures under reasonable assumptions our method is refutationally complete i e it can refute any conjecture which is not observationally valid moreover this proof system is operational it has been implemented within the spike prover and interesting computer experiments are reported

on the groundstate energy of tight knots new results on the groundstate energy of tight magnetic knots are presented magnetic knots are defined as tubular embeddings of the magnetic field in an ideal perfectly conducting incompressible fluid an orthogonal curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field standard minimization of the magnetic energy is carried out under the usual assumptions of volume and flux preserving flow with the additional constraints that the tube cross section remains circular and that the knot length ropelength is independent from internal field twist framing under these constraints the minimum energy is determined analytically by a new exact expression function of ropelength and framing groundstate energy levels of tight knots are determined from ropelength data obtained by the sono tightening algorithm results for torus knots are compared with previous work and the groundstate energy spectrum of the first prime knots up to 10 crossings is presented and analysed in detail these results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

the jones polynomial for fluid knots from helicity in this paper we prove that under ideal conditions the helicity of fluid knots such as vortex filaments or magnetic flux tubes provides a fundamentally new topological means by which we may associate a topological invariant the jones polynomial that is much stronger than prior interpretations in terms of gauss linking numbers our proof is based on an extension of the kauffman bracket polynomial for unoriented knots explicit calculations of the jones polynomial for the left and right handed trefoil knots and for the whitehead link via the figure of eight knot are presented for illustration this novel approach establishes a topological foundation of classical field theory in general and of mathematical fluid dynamics in particular by opening up new directions of work both in theory and applications

the linking number in systems with periodic boundary conditions periodic boundary conditions pbc are often used for the simulation of complex physical systems using the gauss linking number we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing pbc in the case of closed chains in pbc the periodic linking number is an integer topological invariant that depends on a finite number of components in the periodic system for open chains the periodic linking number is an infinite series that accounts for all the topological interactions in the periodic system in this paper we give a rigorous proof that the periodic linking number is defined for the infinite system i e that it converges for one two and three pbc models it gives a real number that varies continuously with the configuration and gives a global measure of the geometric complexity of the system of chains similarly for a single oriented chain we define the periodic self linking number and prove that it also is defined for open chains in addition we define the cell periodic linking and self linking numbers giving localizations of the periodic linking numbers these can be used to give good estimates of the periodic linking numbers in infinite systems we also define the local periodic linking number associated to chains in the immediate cell neighborhood of a chain in order to study local linking measures in contrast to the global linking measured by the periodic linking numbers finally we study and compare these measures when applied to a pbc model of polyethylene melts

the euler lagrange equation and heat flow for the mobius energy we prove the following results 1 a unique smooth solution exists for a short time for the heat equation associated with the mobius energy of loops in a euclidean space starting with any simple smooth loop 2 a critical loop of the energy is smooth if it has cube integrable curvature combining this with an earlier result of m freedman z wang and the author we show that any local minimizer of the energy must be smooth 3 circles are the only two dimensional critical loops with cube integrable curvature the technique also applies to a family of other knot energies similar problems are open for energies of surfaces or more generally for embedded submanifolds in a fixed riemannian manifold 2000 john wiley sons inc

geometry of călugăreanu s theorem a central result in the space geometry of closed twisted ribbons is clugreanu s theorem also known as white s formula or the clugreanuwhitefuller theorem this enables the integer linking number

irrigation control in the presence of salinity extended linear quadratic approach an intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic elq control the elq control is well suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon a conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration for the intraseasonal model to be effective against perennial salt accumulation in the root zone it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season thus avoiding any significant leaching prior to the next growing season this long term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level the elq control is employed in a case study of expected net benefit maximization over an irrigation season of corn in fort morgan colorado the results in general correspond well with expected irrigation schedules under different conditions and provide valuable information on both short and long term aspects of irrigation control under saline conditions the elq control being an analytic iterative solution scheme with theoretically guaranteed fast convergence has a distinct computational advantage over state of the art procedures

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

intraseasonal water allocation in deficit irrigation this paper is concerned with the optimal temporal allocation of irrigation water taking into consideration the intraseasonal stochastic variation of the crop water requirements and the dynamics of the soil moisture depletion process expressions for the soil moisture transition probabilities over a given time period and the first two moments of associated actual evapotranspiration are derived analytically the conditional probabilities of soil moisture and associated actual evapotranspiration are used within a stochastic dynamic programing dp algorithm with rewards being a function of cost and crop yield the dp algorithm is used to determine optimal control policies at each irrigation decision point conditional on the state of the system soil moisture content both mean and variance of net benefits are computed analytic results are corroborated with a case study example

linking twisting writing and helicity on the 2 sphere and in hyperbolic 3 space in the first paper of this series electrodynamics and the gauss linking integral on the 3 sphere and in hyperbolic 3 space we developed a steady state version of classical electrodynamics in these two spaces including explicit formulas for the vector valued green s operator explicit formulas of biot savart type for the magnetic field and a corresponding ampere s law contained in maxwell s equations and then used these to obtain explicit inte gral formulas for the linking number of two disjoint closed curves in this second paper we obtain integral formulas for twisting writhing and helicity and prove that link twist writhe on the 3 sphere and in hyperbolic 3 space we then use these results to derive upper bounds for the helicity of vector fields and lower bounds for the first eigenvalue of the curl operator on subdomains of these two spaces an announcement of these results and a hint of their proofs can be found in the math arxiv math gt 0406276 while an expanded version of the first paper with full proofs can be found at math gt 0510388

knotted and linked phase singularities in monochromatic waves exact solutions of the helmholtz equation are constructed possessing wavefront dislocation lines phase singularities in the form of knots or links where the wave function vanishes knotted nothings the construction proceeds by making a nongeneric structure with a strength n dislocation loop threaded by a strength m dislocation line and then perturbing this in the resulting unfolded stable structure the dislocation loop becomes an m n torus knot if m and n are coprime and n linked rings or knots if m and n have a common factor n the loop or rings are threaded by an m stranded helix in our explicit implementation the wave is a superposition of bessel beams accessible to experiment paraxially the construction fails

divergence free fields energy and asymptotic crossing number in more than one context the equations of classical physics lead to a closed 2 form co on 3 dimensional space which is a conserved quantity in the sense that it pulls back under time evolution in the physics literature co is written as a divergence free vector field w appendix a describes two settings in which a divergence free w is conserved or frozen one is the magnetic field in ideal magneto hydrodynamics and the other is curl velocity in incompressible inviscid fluid flow if ht denotes the transport diffeomorphisms of a moving fluid in which the field is imbedded with ho id wt denotes the field in the fluid at time t and x0 is the space variable at time t 0 then

the bivector clifford algebra and the geometry of hodge dual operators this article describes features of a natural representation of the clifford algebra of the space of bivectors of a four dimensional vector space the representation space being the vector space plus its dual vectors and covectors are then pure spinors the natural map taking a pure spinor to a totally null 3 bivector is shown to be intertwined with the operation of lowering or raising by a metric with the action of the hodge dual operator new formulae exhibiting a metric in terms of its dial operator are presented as are a few applications

kinematic variational principle for motion of vortex rings abstract we show how the ideas of topology and variational principle opened up by euler facilitate the calculation of motion of vortex rings kelvin benjamin s principle as generalised to three dimensions states that a steady distribution of vorticity relative to a moving frame is the state that maximizes the total kinetic energy under the constraint of constant hydrodynamic impulse on an iso vortical sheet by adapting this principle combined with an asymptotic solution of the euler equations we make an extension of fraenkel saffman s formula for the translation velocity of an axisymmetric vortex ring to third order in a small parameter the ratio of the core radius to the ring radius saffman s formula for a viscous vortex ring is also extended to third order

a special class in vanishing helicity ideal flows the derivation of a lagrangian invariant so called spirality is reviewed through the lagrangian coordinates the value of the spirality is fixed up to a gauge transformation the helicity conservation follows directly from this invariant among all ideal flows with zero helicity in a domain of flow frozen into the fluid motion a special class is introduced this special topological class has the possibility to transform its spirality to be identically zero everywhere in the domain for those simply connected domains of motion a necessary and a sufficient condition is presented for these zero spirality flows

variational problems for plane curves in centro affine geometry in this paper closed extremals of variational problems defined by quadratic polynomials in the centro affine curvature are considered the closure of the trajectories is discussed and the existence of countably many closed critical curves is proven the geometrical properties of closed trajectories are analyzed by numerical methods

the mathematical structure of rainfall representations 2 a review of the theory of point processes part 2 constitutes the second of three parts devoted to the mathematical structure of rainfall an expository yet current treatment of those features of point process theory which are essential to descriptions of the hydrologic processes is developed a general overview of this three part series is given in part 1

the energy spectrum of a twisted flexible string under elastic relaxation a full investigation of the energy spectrum of a twisted flexible string under elastic relaxation is presented and discussed in detail for the first time new polynomial expressions for critical energy states are derived and the whole spectrum of critical states minima maxima and inflexion points of the elastic energy is found and discussed in relation to superhelicity and elastic characteristics of the string the study is carried out in the context of the theory of linear elasticity and the thin rod approximation the relaxation mechanism is studied by using conservation of linking difference by the formula delta lk wr delta tw we show how specific geometric quantities such as pitch angle writhe and twist contributions as well as physical quantities such as torsional and bending energy depend on superhelicity given by the specific linking difference and elastic characteristics of the string given by bending and torsional rigidity these quantities expressed per unit length are examined and compared at each critical energy state starting from a supertwisted configuration we show that the string relaxes by twist reduction through two different intermediate helical states which correspond to different local minima to reach the lowest minimum energy state in a supercoiled configuration the case of a generic kink formation and consequent passage through an inflexional configuration is then examined and new expressions for the energy change in the vicinity of the inflexion point are derived

the mathematical structure of rainfall representations 1 a review of the stochastic rainfall models this is the first of a three part series on the mathematical structure of rainfall models several important attempts at modeling rainfall are reviewed special attention is given to the mathematical structures that arise in the rainfall descriptions a general overview of the three part series is given as preface to this part

proof systems for structured specifications with observability operators abstract an asl like kernel language for structured specifications is presented which contains observability operators for determining the observable behaviour the observational quotient and as a derived operator the observational abstraction of a specification sound and complete infinitary proof systems for first order properties of specifications and for proving implementation relations between specifications are provided the relationships to approaches based on an observational satisfaction relation are discussed

conformal geometry of timelike curves in the 1 2 einstein universe abstract we study the conformal geometry of timelike curves in the 1 2 einstein universe the conformal compactification of minkowski 3 space defined as the quotient of the null cone of r 2 3 by the action by positive scalar multiplications the purpose is to describe local and global conformal invariants of timelike curves and to address the question of existence and properties of closed trajectories for the conformal strain functional some relations between the conformal geometry of timelike curves and the geometry of knots and links in the 3 sphere are discussed

multiple folding and packing in dna modeling in this paper we introduce and analyze a set of equations to study geometric and energetic aspects associated with the kinematics of multiple folding and coiling of closed filaments for dna modeling by these equations we demonstrate that a high degree of coiling may be achieved at relatively low energy costs through appropriate writhe and twist distribution and independently from the number of coils formed for sufficiently high twist we show that coiling is actually favoured by elastic energy relaxation when the deformation energy is due to curvature and the mean twist of the filament we give estimates for the writhing process based purely on curvature information and the number of coils produced we also determine the packing rate associated with filament compaction in the case of a hierarchical helical coiling these results find useful applications in dna biology especially in modeling dna wrapping in proteic regions where there is a strong connection between high coiling efficient compaction and energy localization

generation of ribbons helicoids and complex scherk surfaces in laser matter interactions motivated by a diversity of the shape instability phenomena in condensed matter physics we study the formation of elastic ribbon structures and transformation into helicoidal structures using the multipulse laser matter interaction with the co coated surface a one dimensional high density vortex filament array has been created increasing the number of pulses the oscillatory strain field causes the cascade of the shape transformations into structures of increasing topological complexity vortex filaments into ribbons into ribbon helicoids and tubular ribbon helicoids and then into short ribbon structures with the complex scherk surface being identified the cascade of transformations follows the scenario in which the topological complexity of the new structure increases with the number of pulses thus realizing configurations with more efficient energy relaxation above a critical number of pulses the system is catastrophically disintegrated into small scale wrinkled and crumpled surfaces we show that the critical parameter for the ribbon transformations is the number of laser pulses which is equivalent to some critical oscillatory frequency

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

on behavioural abstraction and behavioural satisfaction in higher order logic abstract the behavioural semantics of specifications with higher order logical formulae as axioms is analyzed a characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability which is due to reichel and was recently generalized to the case of first order logic by bidoit et al is further generalized to this case the fact that higher order logic is powerful enough to express the indistinguishability relation is used to characterize behavioural satisfaction in terms of ordinary satisfaction and to develop new methods for reasoning about specifications under behavioural semantics

local differential geometry of null curves in conformally flat space time the conformally invariant differential geometry of null curves in conformally flat space times is given using the six vector formalism which has generalizations to higher dimensions this is then paralleled by a twistor description with a twofold merit first sometimes the description is easier in twistor terms and sometimes in six vector terms which leads to a mutual enlightenment of both and second the case of null curves in timelike pseudospheres or 2 1 minkowski space could only be treated twistorially making use of an invariant differential found by fubini and cech geometria proiettiva differenziale zanichelli bologna 1926 vol 1 introduction a la geometrie projective differentielle des surfaces gauthier villars paris 1931 the result is the expected one apart from the stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures that when specified in terms of this parameter serve to characterize the curve up to conformal tran

a stochastic cluster model of daily rainfall sequences a two level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension the model is a cluster process of the neyman scott type the model has the rainfall generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level it uses infinite superposition of rainfalls and has a very flexible dependence structure the model is fitted to daily rainfall sequences in indiana after these are stationarized by a transformation the fit of the model is then tested in terms of its correlation and marginal probability characteristics the present form of the neyman scott cluster model is time homogeneous therefore the neyman scott process as presented in this paper may be of practical use only for modeling the stationary rainfall occurrences

how tangled is a tangle abstract new measures of algebraic geometric and topological complexity are introduced and tested to quantify morphological aspects of a generic tangle of filaments the tangle is produced by standard numerical simulation of superfluid helium turbulence which we use as a benchmark for numerical investigation of complex systems we find that the measures used based on crossing number information are good indicators of generic behaviour and detect accurately a tangle s complexity direct measurements of kinetic helicity are found to be in agreement with the other complexity based measures proving that helicity is also a good indicator of structural complexity we find that complexity based measure growth rates are consistently similar to one another the growth rate of kinetic helicity is found to be twice that of energy

writhe and mutual entanglement combine to give the entanglement length we propose a method to estimate n e the entanglement length that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions this estimate uses the writhe of the chains the writhe of the primitive paths and the number of kinks in the chains in a melt an advantage of this method is that it works for both linear and ring chains works under all periodic boundary conditions does not require knowing the contour length of the primitive paths and does not rely on a smooth set of data we apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

the energy and helicity of knotted magnetic flux tubes magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states is considered it is supposed that the magnetic field is confined to a single flux tube which may be knotted a local non orthogonal coordinate system zero framed with respect to the knot is introduced and the field is decomposed into toroidal and poloidal ingredients with respect to this system the helicity of the field is then determined this vanishes for a field that is either purely toroidal or purely poloidal the magnetic energy functional is calculated under the simplifying assumptions that the tube is axially uniform and of circular cross section the case of a tube with helical axis is first considered and new results concerning kink mode instability and associated bifurcations are obtained the case of flux tubes in the form of torus knots is then considered and the ground state energy function m h where h is an internal twist parameter is obtained as expected m h which is a topological invariant of the knot increases with increasing knot complexity the function m h provides an upper bound on the corresponding function m h that applies when the above constraints on tube structure are removed the technique is applicable to any knot admitting a parametric representation on condition that points of vanishing curvature are excluded

universal algebra in higher types abstract we develop the elementary theory of higher order universal algebra using the nonstandard approach to finite type theory introduced by henkin basic results include existence theorems for free and initial higher type algebras a complete higher type equational calculus and characterisation theorems for higher type equational and horn classes

topological invariants in period doubling cascades topological characterization is a useful description of dynamical behaviours as exemplified by templates which synthesize the topological properties of very dissipative chaotic attractors embedded in tri dimensional phase spaces such a description relies on topological invariants such as linking numbers between two periodic orbits which may be viewed as knots these invariants may therefore be used to understand the structure of dynamical behaviours nevertheless as an example the celebrated period doubling cascade is usually investigated by using total twists which are not topological invariants instead we introduce linking numbers between an orbit viewed as the core of a small ribbon and the edges of the ribbon such a linking number which is in fact the calugareanu invariant is related to the total twist number and the number of writhes of the ribbon a second topological invariant called the effective twist number is also introduced and is useful for investigating period doubling cascades in the case of a trivial suspension of a horseshoe map this topological invariant may be predicted from a symbolic dynamics with the aid of framed braid representations