equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

a reduced order model based preconditioner for the efficient solution of transient diffusion equations this paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive definite linear systems arising from the numerical discretization of transient parabolic and selfadjoint partial differential equations the preconditioners are obtained by nesting appropriate projections of reduced order models into the classical iteration of the preconditioned conjugate gradient pcg the main idea is to employ the reduced order solver to project the residual associated with the conjugate gradient iterations onto the space spanned by the reduced bases this approach is particularly appealing for transient systems where the full model solution has to be computed at each time step in these cases the natural reduced space is the one generated by full model solutions at previous time steps when increasing the size of the projection space the proposed methodology highly reduces the system conditioning number and the number of pcg iterations at every time step the cost of the application of the preconditioner linearly increases with the size of the projection basis and a trade off must be found to effectively reduce the pcg computational cost the quality and efficiency of the proposed approach is finally tested in the solution of groundwater flow models c 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

catchments as simple dynamical systems a case study on methods and data requirements for parameter identification in many rainfall runoff models at least some calibration of model parameters has to take place especially for ungauged or poorly gauged basins this can be problematic because there is little or no data available for calibration a possible solution to overcome the problems caused by data scarcity is to set up a measurement campaign for a limited time period in this study we determine the minimum amount of data required to determine robust parameter values for a simple model with two parameters the model is constructed such that the parameters can be determined not only with automatic calibration but also by recession analysis and a priori from boussinesq theory the model has been applied to a research catchment in switzerland for automatic calibration and recession analysis one season 5 months is found to be sufficient to give robust parameters for simulation of high flows over the full observation period for automatic calibration this should be the season with the highest precipitation for recession analysis the season with least evapotranspiration the boussinesq equation is able to give good parameter estimates for modeling high flows but detailed in situ knowledge of the catchment is required automatic calibration outperforms recession analysis and boussinesq theory by far when it comes to parameter estimation with a focus on prediction of low flows it was shown that a single set of parameters cannot simultaneously describe high and low flows with a reasonable accuracy suggesting that more than two parameters are needed to characterize subsurface properties

particle tracking and the diffusion reaction equation 1 particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems recently a novel ad hoc particle based method was proposed to account for multicomponent reactive transport by benson and meerschaert 2008 this one dimensional particle method has been shown to match theoretical predictions but to date there has been no rigorous demonstration that the particle method actually matches the governing equations for chemical transport we generalize this particle method to two dimensional and three dimensional systems and rigorously demonstrate that this particle method converges to the diffusion reaction equation at the limit of infinitely small time step we also investigate the numerical error associated with the method

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

relationship between the reaction diffusion master equation and particle tracking models the reaction diffusion master equation rdme is a model for chemical systems in which both noise in the chemical reaction process and the diffusion of molecules are important it extends the chemical master equation for well mixed chemical reactions by discretizing space into a collection of voxels in this work we show how the rdme may be rewritten as an equivalent particle tracking model following the motion and interaction of individual molecules on a lattice this new representation can be interpreted as a discrete version of the spatially continuous probability distribution function stochastic reaction diffusion model studied by doi we show how this new representation can be mapped to a quantum field theory complementing the existing work by peliti mapping the rdme and doi mapping his spatially continuous model to quantum field theories the formal continuum limit as the voxel size approaches zero of the particle tracking representation is studied to consider the question of whether the rdme approximates any spatially continuous model

error bound and reduced gradient projection algorithms for convex minimization over a polyhedral set consider the problem of minimizing over a polyhedral set the composition of an affine mapping with a strongly convex differentiable function the polyhedral set is expressed as the intersection of an affine set with a simpler polyhedral set and a new local error bound for this problem based on projecting the reduced gradient associated with the affine set onto the simpler polyhedral set is studied a class of reduced gradient projection algorithms for solving the case where the simpler polyhedral set is a box is proposed and this bound is used to show that algorithms in this class attain a linear rate of convergence included in this class are the gradient projection algorithm of goldstein and levitin and poljak and an algorithm of bertsekas a new algorithm in this class reminiscent of active set algorithms is also proposed some of the results presented here extend to problems where the objective function is extended real valued and to variational inequality problems

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

a particle number conserving lagrangian method for mixing driven reactive transport the purely lagrangian algorithm for chemical reactions introduced by benson and meerschaert 2008 suffers from a low concentration resolution problem we alleviate the problem by redefining the probabilistic collision reaction birth death stochastic process as a mass reduction operation theoretically this corresponds to replacing an on off particle with a large number of subparticles and tracking the number fraction the new particle reaction process maintains the original particle numbers but adjusts each particle s mass upon reaction several simulations show the veracity as well as the gains in low concentration resolution offered by the algorithm we also compare the results to those obtained by a traditional finite difference model with suitably defined initial condition demonstrating that the lagrangian models match these

connecting the dots semi analytical and random walk numerical solutions of the diffusion reaction equation with stochastic initial conditions we study a system with bimolecular irreversible kinetic reaction a b a where the underlying transport of reactants is governed by diffusion and the local reaction term is given by the law of mass action we consider the case where the initial concentrations are given in terms of an average and a white noise perturbation our goal is to solve the diffusion reaction equation which governs the system and we tackle it with both analytical and numerical approaches to obtain an analytical solution we develop the equations of moments and solve them approximately to obtain a numerical solution we develop a grid less monte carlo particle tracking approach where diffusion is modeled by a random walk of the particles and reaction is modeled by annihilation of particles the probability of annihilation is derived analytically from the particles co location probability we rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number this enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

a realization of generalized deformed oscillators with cyclic symmetry the algebra of generalized deformed oscillators that possess cyclic symmetry is studied the general set of multilinear operator relations is presented which characterizes the multilinear part of the algebra of cyclic extended deformed oscillators the realization scheme of generalized deformed oscillators with cyclic symmetry in terms of those without cyclic symmetry is established it is shown that all generalized deformed oscillators with cyclic symmetry constructed by the scheme are actually equivalent in the viewpoint of mathematics though each generalized deformed oscillator admits its own particular cyclic extended counterpart examples are given to illustrate this peculiar realization scheme

convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a hilbert space the projection onto convex sets pocs algorithm in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule has been the most prevalent tool to solve such problems nonetheless pocs has several shortcomings it converges slowly it is ill suited for implementation on parallel processors and it requires the computation of exact projections at each iteration we propose a general parallel projection method emopsp that overcomes these shortcomings at each iteration of emopsp a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation the relaxation parameter may vary over an iteration dependent extrapolated range that extends beyond the interval 0 2 used in conventional projection methods emopsp not only generalizes existing projection based schemes but it also converges very efficiently thanks to its extrapolated relaxations theoretical convergence results are presented as well as numerical simulations

comment on the q deformed fermionic oscillator the q deformed fermionic oscillator is identified with the usual fermionic oscillator by virtue of a simple transformation so the realization of quantum algebra suq 2 can also be constructed from the usual fermionic oscillator

preconditioners for image restoration by reblurring techniques it is well known that iterative algorithms for image deblurring that involve the normal equations show usually a slow convergence a variant of the normal equations which replaces the conjugate transpose a h of the system matrix a with a new matrix is proposed this approach which is linked with regularization preconditioning theory and reblurring processes can be applied to a wide set of iterative methods here we examine landweber steepest descent richardson lucy and image space reconstruction algorithm several computational tests show that this strategy leads to a significant improvement of the convergence speed of the methods moreover it can be naturally combined with other widely used acceleration techniques

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

a kernel based lagrangian method for imperfectly mixed chemical reactions abstract current lagrangian particle tracking algorithms used to simulate diffusion reaction equations must employ a certain number of particles to properly emulate the system dynamics particularly for imperfectly mixed systems the number of particles is tied to the statistics of the initial concentration fields of the system at hand systems with shorter range correlation and or smaller concentration variance require more particles potentially limiting the computational feasibility of the method for the well known problem of bimolecular reaction we show that using kernel based rather than dirac delta particles can significantly reduce the required number of particles we derive the fixed width of a gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and dirac solutions at any specified time we also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval numerical results show that the width of the kernel should be kept below about 12 of the domain size and that the analytic equations used to derive kernel width suffer significantly from the neglect of higher order moments the simulations with a kernel width given by least squares minimization perform better than those made to match at one specific time a heuristic time variable kernel size based on the previous results performs on par with the least squares fixed kernel size

incomplete mixing and reactions in laminar shear flow incomplete mixing of reactive solutes is well known to slow down reaction rates relative to what would be expected from assuming perfect mixing in purely diffusive systems for example it is known that small initial fluctuations in reactant concentrations can lead to reactant segregation which in the long run can reduce global reaction rates due to poor mixing in contrast nonuniform flows can enhance mixing between interacting solutes thus a natural question arises can nonuniform flows sufficiently enhance mixing to restrain incomplete mixing effects and if so under what conditions we address this question by considering a specific and simple case namely a laminar pure shear reactive flow two solution approaches are developed a lagrangian random walk method and a semianalytical solution the results consistently highlight that if shear effects in the system are not sufficiently strong incomplete mixing effects initially similar to purely diffusive systems will occur slowing down the overall reaction rate then at some later time dependent on the strength of the shear the system will return to behaving as if it were well mixed but represented by a reduced effective reaction rate

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

q fermionic operators and quantum exceptional algebras using a q deformation of the usual clifford algebra one constructs a realization of the quantum exceptional algebras e6 e7 e8 and f4 in terms of q fermionic operators

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

exceptional lie algebras in terms of fermionic creation annihilation operators from the embedding e8 d4 d4 defining fermionic operators which transform respectively as the vectorial and spinorial representations of d4 the algebra of e8 is constructed in terms of a bilinear in the fermionic operators then by embeddings the adjoint and fundamental representations of the other exceptional algebras are explicitly written

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

projected randomized kaczmarz methods abstract for a constrained linear ill posed problems the projected algebra reconstruction technique part usually has a faster convergence rate than the projected simultaneous iterative reconstruction technique psirt but can not be applied to the inconsistent case in this work we propose the projected randomized kaczmarz method prk to further accelerate the convergence of part and analyze its convergence with the noise free right hand side we show that the prk method can converge exponentially in expectation to the solution for the consistent system with the noisy right hand side we present some insights into the semiconvergence property of the prk method and propose an extended version of prk prek method to seek the least squares solution we prove that the prek method can converge exponentially in expectation to the least squares solution for the inconsistent systems

q deformed classical lie algebras and their anyonic realization all classical lie algebras can be realized a la schwinger 1965 in terms of fermionic oscillators we show that the same can be done for their q deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice the deformation parameter q is a phase related to the anyonic statistical parameter a crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones the entire procedure works even on one dimensional chains in such a case q can also be real

effect of spatial concentration fluctuations on effective kinetics in diffusion reaction systems 1 the effect of spatial concentration fluctuations on the reaction of two solutes a b c is considered in the absence of fluctuations the concentration of solutes decays as adet bdet t 1 contrary to this experimental and numerical studies suggest that concentrations decay significantly slower existing theory suggests a t d 4 scaling in the asymptotic regime d is the dimensionality of the problem here we study the effect of fluctuations using the classical diffusion reaction equation with random initial conditions initial concentrations of the reactants are treated as correlated random fields we use the method of moment equations to solve the resulting stochastic diffusion reaction equation and obtain a solution for the average concentrations that deviates from t 1 to t d 4 behavior at characteristic transition time t we also derive analytical expressions for t as a function of damkohler number and the coefficient of variation of the initial concentration

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

deformation of lie algebras in a non chevalley basis and embedding of q algebras a deformation scheme for lie algebras in a basis which manifestly exhibits for q 1 the content of a singular subalgebra is presented this scheme allows to build up embedding chains of q algebras which can be physically interesting the case when the rank of the subalgebra is one unit less than the rank of the algebra is studied and explicit constructions of the algebras are given in terms of q bosonic and or q fermionic oscillators

bayesian inversion of mualem van genuchten parameters in a multilayer soil profile a data driven assumption free likelihood function this paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in bayesian inversion of vadose zone hydraulic properties the likelihood function or its analogs objective functions and likelihood measures are commonly assumed to be multivariate gaussian in form however this assumption is not possible to verify without a hierarchical simulation and modeling framework in this paper we present the necessary statistical mechanisms for utilizing the hierarchical framework we apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers the key result of our work is that the goodness of fit validated likelihood function form provides empirical justification for the assumption of multivariate gaussian likelihood functions in past and future inversions at similar sites as an alternative the likelihood function need not be assumed to follow a parametric statistical distribution and can be computed directly using nonparametric methods the nonparametric methods are considerably more computationally demanding and to demonstrate this approach we present a smaller dimension synthetic case study of evaporation from a soil column the main drawback of our work is the increased computational expense of the inversion

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

a lagrangian transport eulerian reaction spatial laters markov model for prediction of effective bimolecular reactive transport prediction of effective transport for mixing driven reactive systems at larger scales requires accurate representation of mixing at small scales which poses a significant upscaling challenge depending on the problem at hand there can be benefits to using a lagrangian framework while in others an eulerian might have advantages here we propose and test a novel hybrid model which attempts to leverage benefits of each specifically our framework provides a lagrangian closure required for a volume averaging procedure of the advection diffusion reaction equation this hybrid model is a lagrangian transport eulerian reaction spatial markov model laters markov model which extends previous implementations of the lagrangian spatial markov model and maps concentrations to an eulerian grid to quantify closure terms required to calculate the volume averaged reaction terms the advantage of this approach is that the spatial markov model is known to provide accurate predictions of transport particularly at preasymptotic early times when assumptions required by traditional volume averaging closures are least likely to hold likewise the eulerian reaction method is efficient because it does not require calculation of distances between particles this manuscript introduces the laters markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2d porous medium

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

on diagonally relaxed orthogonal projection methods we propose and study a block iterative projection method for solving linear equations and or inequalities the method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system and is thus called diagonally relaxed orthogonal projections drop diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block iterative projection algorithms but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections drop has been used by practitioners and in this paper a contribution to its convergence theory is provided the mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of drop

equivalence of deformed fermionic algebras generalized deformations of the fermionic algebra are studied the polynomial representations of these algebras are constructed all the deformation schemes can be realized by the same polynomial basis using the bargmann representation thus proving that all deformed fermionic algebras are isomorphically equivalent to the non deformed fermionic algebra

semiconvergence and relaxation parameters for projected sirt algorithms we give a detailed study of the semiconvergence behavior of projected nonstationary simultaneous iterative reconstruction technique sirt algorithms including the projected landweber algorithm we also consider the use of a relaxation parameter strategy proposed recently for the standard algorithms for controlling the semiconvergence of the projected algorithms we demonstrate the semiconvergence and the performance of our strategies by examples taken from tomographic imaging

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

projected landweber iteration for matrix completion recovering an unknown low rank or approximately low rank matrix from a sampling set of its entries is known as the matrix completion problem in this paper a nonlinear constrained quadratic program problem concerning the matrix completion is obtained a new algorithm named the projected landweber iteration plw is proposed and the convergence is proved strictly numerical results show that the proposed algorithm can be fast and efficient under suitable prior conditions of the unknown low rank matrix

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods a kernel density estimation approach random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems while the number of particles in most realistic applications is in the order of 10 6 10 9 the number of reactive molecules even in diluted systems might be in the order of fractions of the avogadro number thus each particle actually represents a group of potentially reactive molecules the use of a low number of particles may result not only in loss of accuracy but also may lead to an improper reproduction of the mixing process limited by diffusion recent works have used this effect as a proxy to model incomplete mixing in porous media in this work we propose using a kernel density estimation kde of the concentrations that allows getting the expected results for a well mixed solution with a limited number of particles the idea consists of treating each particle as a sample drawn from the pool of molecules that it represents this way the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle rigorously represented by a kernel density function the probability of reaction can be obtained by combining the kernels associated to two potentially reactive particles we demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations fixed particle support from discrete particle distributions and not to the occurrence of true incomplete mixing we further explore the evolution of the kernel size with time linking it to the diffusion process our results show that kdes are powerful tools to improve computational efficiency and robustness in reactive transport simulations and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a limited number of particles

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

from analytical solutions of solute transport equations to multidimensional time domain random walk tdrw algorithms in this study new multi dimensional time domain random walk tdrw algorithms are derived from approximate one dimensional 1 d two dimensional 2 d and three dimensional 3 d analytical solutions of the advection dispersion equation and from exact 1 d 2 d and 3 d analytical solutions of the pure diffusion equation these algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point which may be incomplete due to 2 d or 3 d transverse dispersion or diffusion the method is extended to heterogeneous media represented as a piecewise collection of homogeneous media the particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries the accuracy of the multi dimensional tdrw method is verified against i exact analytical solutions of solute transport in homogeneous media and ii finite difference simulations in a synthetic 2 d heterogeneous medium of simple geometry the results demonstrate that the method is ideally suited to purely diffusive transport and to advection dispersion transport problems dominated by advection conversely the method is not recommended for highly dispersive transport problems because the accuracy of the advection dispersion tdrw algorithms degrades rapidly for a low peclet number consistent with the accuracy limit of the approximate analytical solutions the proposed approach provides a unified methodology for deriving multi dimensional time domain particle equations and may be applicable to other mathematical transport models provided that appropriate analytical solutions are available

schultz matrix iteration based method for stable solution of discrete ill posed problems abstract in this paper we propose an iterative method for solving discrete ill posed problems based on matrix iterations generated by schultz method and known to converge to the moore penrose pseudoinverse of a matrix practically letting the schultz matrix iteration be x k we construct the vector x k x k b where b is a data vector hence by construction the iterates converge to the minimum 2 norm solution of a least squares problem with coefficient matrix a and data vector b we derive theoretical properties of the sequence x k and show that it is quadratically convergent in the case of corrupted data we analyze the semi convergence behavior of the iterates and conclude that the iteration must be truncated to control the propagation of the noise error as a result we derive an error estimate for the case where the truncation parameter is chosen by the discrepancy principle in addition combining a projected approach with the new method we propose variants of the method that are well suited for large scale problems several numerical results are presented to illustrate the effectiveness of the method on well known test problems

reply to comment on generalized commutators and deformation of strong coupling superconductivity by a solomon and r mcdermott for original paper see ibid vol 26 p 4827 1993 we reply to the comment by solomon and mcdermott see ibid vol 27 p 2619 1994 that the q deformed fermionic oscillator is equivalent to the usual fermionic quantum oscillator noting that our many body hamiltonian is truly a deformed model of strong coupling superconductivity

a quasi parafermionic realization of g2 and uq g2 the authors present a construction of the exceptional lie algebra g2 and of corresponding quantum algebra uq g2 using quasi parafermionic creation and annihilation operators and their quantum analogue as a by product a new realization of uq a2 is found

use of an entropy based metric in multiobjective calibration to improve model performance parameter estimation for hydrological models is complicated for many reasons one of which is the arbitrary emphasis placed by most traditional measures of fit on various magnitudes of the model residuals recent research has called for the development of robust diagnostic measures that provide insights into which model structural components and or data may be inadequate in this regard the flow duration curve fdc represents the historical variability of flow and is considered to be an informative signature of catchment behavior here we investigate the potential of using the recently developed conditioned entropy difference metric ced in combination with the kling gupta efficiency kge the ced respects the static information contained in the flow frequency distribution and hence the fdc but does not explicitly characterize temporal dynamics the kge reweights the importance of various hydrograph components correlation bias variability in a way that has been demonstrated to provide better model calibrations than the commonly used nash sutcliffe efficiency while being explicitly time sensitive we employ both measures within a multiobjective calibration framework and achieve better performance over the full range of flows than obtained by single criteria approaches or by the common multiobjective approach that uses log transformed and untransformed data to balance fitting of low and high flow periods the investigation highlights the potential of ced to complement kge and vice versa during model identification it is possible that some of the complementarity is due to ced representing more information from moments 2 than kge or other common metrics we therefore suggest that an interesting way forward would be to extend kge to include higher moments i e use different moments as multiple criteria

even and odd q coherent states and their optical statistics properties the authors construct explicitly even and odd q coherent states qcss which are proved to form a representation of the quantum heisenberg weyl algebra and study their properties it is shown that optical statistics properties of the even and odd qcss are very different they find that an even qcs exhibits squeezing but no antibunching effect and an odd qcs has antibunching effect but no squeezing for all finite q values

improvement of space invariant image deblurring by preconditioned landweber iterations the landweber method is a simple and flexible iterative regularization algorithm whose projected variant provides nonnegative image reconstructions since the method is usually very slow we apply circulant preconditioners exploiting the shift invariance of many deblurring problems in order to accelerate the convergence this way reasonable reconstructions can be obtained within a few iterations the method becomes competitive and more robust than other approaches that although faster sometimes lead to lower accuracy some theoretical analysis of convergence is given together with numerical validations