synchronization of arbitrarily switched boolean networks this paper investigates the complete synchronization problem for the drive response switched boolean networks sbns under arbitrary switching signals where the switching signals of the response sbn follow those generated by the drive sbn at each time instant first the definition of complete synchronization is introduced for the drive response sbns under arbitrary switching signals second the concept of switching reachable set starting from a given initial state set is put forward based on it a necessary and sufficient condition is derived for the complete synchronization of the drive response sbns last we give a simple algebraic expression for the switching reachable set in a given number of time steps and two computable algebraic criteria are obtained for the complete synchronization of the sbns a biological example is given to demonstrate the effectiveness of the obtained main results

on an efficient family of derivative free three point methods for solving nonlinear equations abstract new three step derivative free families of three point methods for solving nonlinear equations are presented first a new family without memory of optimal order eight consuming four function evaluations per iteration is proposed by using two weight functions the improvement of the convergence rate of this basic family even up to 50 is obtained without any additional function evaluation using a self accelerating parameter this varying parameter is calculated in each iterative step employing only information from the current and the previous iteration defining in this way a family with memory the self accelerating parameter is calculated applying newton s interpolating polynomials of degree scaling from 1 to 4 the corresponding r orders of convergence are increased from 8 to 10 11 6 4 2 11 66 and 12 providing very high computational efficiency of the proposed methods with memory another convenient fact is that these methods do not use derivatives numerical examples and comparison with the existing three point methods are included to confirm theoretical results

asymptotical stability of probabilistic boolean networks with state delays this paper devotes to establishing a bridge between asymptotical stability of a probabilistic boolean network pbn and a solution to its induced equations which are induced from the pbn s transition matrix by utilizing the semitensor product technique routinely the dynamics of a pbn with coincident state delays can be equivalently converted into that of a higher dimensional pbn without delays subsequently several novel stability criteria are derived from the standpoint of equations solution the most significant finding is that a pbn is globally asymptotically stable at a predesignated one point distribution if and only if a vector obtained by adding 1 at the bottom of this distribution is the unique nonnegative solution to pbn s induced equations moreover the influence of coincident state delays on pbn s asymptotical stability is explicitly analyzed without consideration of the convergence rate consequently such bounded state delays are verified to have no impact on pbn s stability albeit delays are time varying based on this worthwhile observation the time computational complexity of the aforementioned approach can be reduced by removing delays directly furthermore this universal procedure is summarized to reduce the time complexity of some previous results in the literature to a certain extent two examples are employed to demonstrate the feasibility and effectiveness of the obtained theoretical results

synchronization in an array of output coupled boolean networks with time delay this brief presents an analytical study of synchronization in an array of coupled deterministic boolean networks bns with time delay two kinds of models are considered in one model the outputs contain time delay while in another one the outputs do not one restriction in this brief is that the state delay and output delay are restricted to be equal by referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices some necessary and sufficient conditions are derived for the synchronization of delay coupled bns examples including a practical epigenetic example are given for illustration

a class of two point sixth order multiple zero finders of modified double newton type and their dynamics under the assumption of the known multiplicity of zeros of nonlinear equations a class of two point sextic order multiple zero finders and their dynamics are investigated in this paper by means of extensive analysis of modified double newton type of methods with the introduction of a bivariate weight function dependent on function to function and derivative to derivative ratios higher order convergence is obtained additional investigation is carried out for extraneous fixed points of the iterative maps associated with the proposed methods along with a comparison with typically selected cases through a variety of test equations numerical experiments strongly support the theory developed in this paper in addition relevant dynamics of the proposed methods is successfully explored for various polynomials with a number of illustrative basins of attraction

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

a new technique to obtain derivative free optimal iterative methods for solving nonlinear equations abstract a new technique to obtain derivative free methods with optimal order of convergence in the sense of the kung traub conjecture for solving nonlinear smooth equations is described the procedure uses steffensen like methods and pade approximants some numerical examples are provided to show the good performance of the new methods

controllability for a class of linear time varying impulsive systems with time delay in control input in this note the controllability for a class of linear time varying impulsive systems with time delay in control input is studied sufficient and necessary conditions for the controllability of such systems are established specializing the obtained results to the cases of linear time varying impulsive systems and linear time invariant impulsive systems with time delay some simple criteria with respect to coefficient matrices which are less conservative than some existing results are derived it is also shown that the time delay in control input contributes to achieve the controllability of impulsive system even if the system is not controllable two examples are worked out to illustrate our results

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

identifying a probabilistic boolean threshold network from samples this paper studies the problem of exactly identifying the structure of a probabilistic boolean network pbn from a given set of samples where pbns are probabilistic extensions of boolean networks cheng et al studied the problem while focusing on pbns consisting of pairs of and or functions this paper considers pbns consisting of boolean threshold functions while focusing on those threshold functions that have unit coefficients the treatment of boolean threshold functions and triplets and n tuplets of such functions necessitates a deepening of the theoretical analyses it is shown that wide classes of pbns with such threshold functions can be exactly identified from samples under reasonable constraints which include 1 pbns in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2 pbns consisting of pairs of threshold functions with different numbers of input variables it is also shown that the problem of deciding the equivalence of two boolean threshold functions is solvable in pseudopolynomial time but remains co np complete

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

the resolvent algebra a new approach to canonical quantum systems the standard c algebraic version of the algebra of canonical commutation relations the weyl algebra frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as bounded functions of the hamiltonian here a novel c algebra of the canonical commutation relations is presented which does not suffer from such problems it is based on the resolvents of the canonical operators and their algebraic relations the resulting c algebra the resolvent algebra is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple moreover the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems as we demonstrate by several examples

state feedback based output tracking control of probabilistic boolean networks abstract this paper studies the state feedback based output tracking control of probabilistic boolean control networks pbcns by using the semi tensor product of matrices a series of reachable sets with probability 1 is defined inductively for pbcns and some useful properties are obtained for the reachable sets based on the properties of the reachable sets a necessary and sufficient condition is presented for the state feedback based output tracking control of pbcns meanwhile a constructive procedure is proposed to design state feedback laws for pbcns to track a constant reference signal the study of two illustrative examples shows that the obtained new results are very effective

quantum harmonic analysis on phase space relative to an irreducible representation of the canonical commutation relations convolutions between quantum mechanical operators and between functions and operators are defined for which the usual weyl transform acts as a fourier transform basic properties of these operations are developed in close analogy to harmonic analysis on r2n using the quantum version of wiener s approximation theorem a natural one to one correspondence between the closed phase space translation invariant subspaces of classical and quantum observables is established

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

simplified existence and uniqueness conditions for the zeros and the concavity of the f and g functions of improved gauss orbit determination from two position vectors in our first paper we showed how gauss s method for determining the initial position and velocity vectors from two inertial position vectors at two times in an idealized keplerian two body elliptical orbit can be made more robust and efficient by replacing functional iteration with newton raphson iteration to do this we split the orbit determination algorithm into two sub algorithms the x iteration to find the zero of the fixed point function f x when the true anomaly angular difference between the two vectors is large and the y iteration to find the zero of the fixed point function g y when the angular difference is small we derived necessity and sufficiency conditions for the existence and uniqueness of these zeros and conjectured that both functions were concave in this paper we first simplify the necessity and sufficiency conditions we then prove that both f and g are indeed concave existence and uniqueness of the zero of g and its concavity then imply quadratic convergence of the newton raphson iterative sequence from an arbitrary starting point in its domain quadratic convergence to the zero of f x is also the case in its domain except for a small neighborhood of x 1 corresponding to the true anomaly difference angle between the position vectors in a small neighborhood of 180

state space analysis of boolean networks this paper provides a comprehensive framework for the state space approach to boolean networks first it surveys the authors recent work on the topic using semitensor product of matrices and the matrix expression of logic the logical dynamic equations of boolean control networks can be converted into standard discrete time dynamics to use the state space approach the state space and its subspaces of a boolean network have been carefully defined the basis of a subspace has been constructed particularly the regular subspace y friendly subspace and invariant subspace are precisely defined and the verifying algorithms are presented as an application the indistinct rolling gear structure of a boolean network is revealed

brief paper controllability of probabilistic boolean control networks this paper deals with the controllability of probabilistic boolean control networks first a survey on the semi tensor product approach to probabilistic boolean networks is given second the controllability of probabilistic boolean control networks via two kinds inputs is studied finally examples are given to show the efficiency of the obtained results

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

brief paper an integer programming approach to optimal control problems in context sensitive probabilistic boolean networks a boolean network is one of the models of biological networks such as gene regulatory networks and has been extensively studied in particular a probabilistic boolean network pbn is well known as an extension of boolean networks but in the existing methods to solve the optimal control problem of pbns it is necessary to compute the state transition diagram with 2 n nodes for a given pbn with n states to avoid this computation an integer programming based approach is proposed for a context sensitive pbn cs pbn which is a general form of pbns in the proposed method a cs pbn is transformed into a linear system with binary variables and the optimal control problem is reduced to an integer linear programming problem by a numerical example the effectiveness of the proposed method is shown

filtering for nonlinear genetic regulatory networks with stochastic disturbances in this paper the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition the stochastic perturbation is in the form of a scalar brownian motion and the time delays exist in both the translation process and the feedback regulation process the purpose of the addressed filtering problem is to estimate the true concentrations of the mrna and protein specifically we are interested in designing a linear filter such that in the presence of time delays stochastic disturbances as well as sector nonlinearities the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta by using the linear matrix inequality lmi technique sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model and the filter gain is then characterized in terms of the solution to an lmi which can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

a class of steffensen type methods with optimal order of convergence abstract in this paper a family of steffensen type methods of fourth order convergence for solving nonlinear smooth equations is suggested in the proposed methods a linear combination of divided differences is used to get a better approximation to the derivative of the given function each derivative free member of the family requires only three evaluations of the given function per iteration therefore this class of methods has efficiency index equal to 1 587 kung and traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2 d 1 where d is the number of functional evaluations per step the new class of methods agrees with this conjecture for the case d 3 numerical examples are made to show the performance of the presented methods on smooth and nonsmooth equations and to compare with other ones

controllability of probabilistic boolean control networks based on transition probability matrices in this paper we propose a new approach to investigate the controllability and reachability of probabilistic boolean control networks pbcns with forbidden states we first give a simple algebraic formula for the transition probability between two states in a given number of time step while avoiding a set of forbidden states then we construct the controllability matrix based on a new operator and some necessary and sufficient conditions are obtained for the controllability and reachability of pbcns a numerical example is given to illustrate the efficiency of the obtained results

input state incidence matrix of boolean control networks and its applications the input state incidence matrix of a control boolean network is proposed it is shown that this matrix contains complete information of the input state mapping using it an easily verifiable necessary and sufficient condition for the controllability of a boolean control network is obtained the corresponding control which drives a point to a given reachable point is designed moreover certain topological properties such as the fixed points and cycles of a boolean control network are investigated then as another application a sufficient condition for the observability is presented finally the results are extended to mix valued logical control systems

controllability of markovian jump boolean control networks abstract in this paper controllability of markovian jump boolean control networks mjbcns is studied via semi tensor product of matrices first based on the algebraic expression of the considered boolean control networks a necessary and sufficient condition for controllability is presented by iteration equations which however may lead to high dimensional matrices to avoid having such matrices a new matrix is defined and applied to derive another equivalent condition to verify controllability of mjbcns moreover a maximum principle of mjbcns is established to further study the minimal controllable time finally two examples are presented to illustrate the obtained results

on developing a higher order family of double newton methods with a bivariate weighting function a high order family of two point methods costing two derivatives and two functions are developed by introducing a two variable weighting function in the second step of the classical double newton method their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases a variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development in addition this paper investigates the dynamics of rational iterative maps associated with the proposed method and an existing method based on illustrated description of basins of attraction for various polynomials

an optimal family of eighth order simple root finders with weight functions dependent on function to function ratios and their dynamics underlying extraneous fixed points we extend in this paper an optimal family of three step eighth order methods developed by duni etal 2011 with higher order weight functions employed in the second and third sub steps and investigate their dynamics under the relevant extraneous fixed points among which purely imaginary ones are specially treated for the analysis of the rich dynamics their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases a wide variety of relevant numerical examples are illustrated to confirm the underlying theoretical development in addition this paper investigates the dynamics of selected existing optimal eighth order iterative maps with the help of illustrative basins of attraction for various polynomials

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

an obstruction to quantization of the sphere in the standard example of strict deformation quantization of the symplectic sphere s2 the set of allowed values of the quantization parameter is not connected indeed it is almost discrete li recently constructed a class of examples including s2 in which can take any value in an interval but these examples are badly behaved here i identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing s2 is never connected

on robust control invariance of boolean control networks this paper investigates the robust control invariance of boolean control networks bcns via the semi tensor product of matrices firstly based on an algebraic state space representation of bcns two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller secondly by defining a series of suitable sets all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized an illustrative example is presented to demonstrate the obtained new results

synchronization for the realization dependent probabilistic boolean networks this paper investigates the synchronization problem for the realization dependent probabilistic boolean networks pbns coupled unidirectionally in the drive response configuration the realization of the response pbn is assumed to be uniquely determined by the realization signal generated by the drive pbn at each discrete time instant first the drive response pbns are expressed in their algebraic forms based on the semitensor product method and then a necessary and sufficient condition is presented for the synchronization of the pbns second by resorting to a newly defined matrix operator the reachable set from any initial state is expressed by a column vector consequently an easily computable algebraic criterion is derived assuring the synchronization of the drive response pbns finally three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results

dual mean field search for large scale linear and quadratic knapsack problems abstract an implementation of mean field annealing to deal with large scale linear and non linear binary optimization problems is given mean field annealing is based on the analogy between combinatorial optimization and interacting physical systems at thermal equilibrium specifically a mean field approximation of the boltzmann distribution given by a lagrangian that encompass the objective function and the constraints is calculated the original discrete task is in this way transformed into a continuous variational problem in our version of mean field annealing no temperature parameter is used but a good starting point in the dual space is given by a thermodynamic limit argument the method is tested in linear and quadratic knapsack problems with sizes that are considerably larger than those used in previous studies of mean field annealing dual mean field annealing is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms moreover as may be expected for a mean field theory the solutions tend to be more accurate as the number of variables grow

deformation quantization for hilbert space actions rieffel s theory of deformations of c algebras for actions can be extended to actions of infinite dimensional hilbert spaces the ccr algebra over a hilbert space h can be exhibited in this manner as a deformation of a commutative c algebra of almost periodic functions on h

an optimal steffensen type family for solving nonlinear equations abstract in this paper a general family of steffensen type methods with optimal order of convergence for solving nonlinear equations is constructed by using newton s iteration for the direct newtonian interpolation it satisfies the conjecture proposed by kung and traub h t kung j f traub optimal order of one point and multipoint iteration j assoc comput math 21 1974 634 651 that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2 m 1 its error equations and asymptotic convergence constants are obtained finally it is compared with the related methods for solving nonlinear equations in the numerical examples

model construction of boolean network via observed data in this paper a set of data is assumed to be obtained from an experiment that satisfies a boolean dynamic process for instance the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells with the observed datasets several methods to construct the dynamic models for such boolean networks are proposed instead of building the logical dynamics of a boolean network directly its algebraic form is constructed first and then is converted back to the logical form firstly a general construction technique is proposed to reduce the size of required data the model with the known network graph is considered motivated by this the least in degree model is constructed that can reduce the size of required data set tremendously next the uniform network is investigated the number of required data points for identification of such networks is independent of the size of the network finally some principles are proposed for dealing with data with errors

the resolvent algebra ideals and dimension let x be a symplectic space admitting a complex structure and let r x be the corresponding resolvent algebra i e the c algebra generated by the resolvents of selfadjoint operators satisfying canonical commutation relations associated with x in previous work this algebra was shown to provide a convenient framework for the analysis of quantum systems in the present article its mathematical properties are elaborated with emphasis on its ideal structure it is shown that r x is always nuclear and if x is finite dimensional also of type i postliminal in the latter case dim x labels the isomorphism classes of the corresponding resolvent algebras for x of arbitrary dimension principal ideals are identified which are the building blocks for all other ideals the maximal and minimal ideals of the resolvent algebra are also determined

a sixth order family of three point modified newton like multiple root finders and the dynamics behind their extraneous fixed points a class of three point sixth order multiple root finders and the dynamics behind their extraneous fixed points are investigated by extending modified newton like methods with the introduction of the multivariate weight functions in the intermediate steps the multivariate weight functions dependent on function to function ratios play a key role in constructing higher order iterative methods extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials

gauss meets newton again how to make gauss orbit determination from two position vectors more efficient and robust with newton raphson iterations abstract gauss s method for determining the six classical idealized keplerian two body orbital parameters from two position vectors and two times is elegantly formulated it first reduces the three dimensional velocity determination problem to two equation in two variables x y these two equations take the form i x f y l m ii y g x l here l and m are parameters that are functions of the two position vectors and the corresponding time span between them gauss s approach was to form a functional iteration y iteration by substituting i into ii an alternate second functional iteration x iteration is formed by substituting ii into i in either case a further reduction of dimension from two to one is obtained the method first appeared in the early 19th century and is ubiquitous in the astronomy and astro dynamics literature however it could not exploited until the mid 20th century advent of powerful radars these can provide initial elliptical orbital positional observations of such natural space objects as the moon comets asteroids and meteors as well as man made objects such as satellites and ballistic missile in the mid course phase of their trajectories there are however three basic problems with the classical approach 1 it breaks down when the angular difference in true anomaly between the two position vectors grows larger than 4 2 the classical first guess y 0 1 may not lie in the convergence region of the method s functional iteration and 3 the functional iteration when it works is slowly linearly convergent in this paper we show that applying a newton raphson iteration to the fixed point equation that defines the functional iteration in y when the angular spread is sufficiently small or in x when the spread is large together with trivial first guesses solves all three problems at once moreover we prove a theorem on a simple necessary and sufficient condition for the existence of unique solutions and put forth a conjecture on the concavity of the two fixed point equation graphs this newton raphson iteration approach extends the range of algorithm applicability to a true anomaly angular spread close to a basic singularity of the gauss method

higher order derivative free families of chebyshev halley type methods with or without memory for solving nonlinear equations abstract in this paper we present two new derivative free families of chebyshev halley type methods for solving nonlinear equations numerically both families require only three and four functional evaluations to achieve optimal fourth and eighth orders of convergence furthermore accelerations of convergence speed are attained by suitable variation of a free parameter in each iterative step the self accelerating parameter is estimated from the current and previous iteration this self accelerating parameter is calculated using newton s interpolation polynomial of third and fourth degrees consequently the r orders of convergence are increased from 4 to 6 and 8 to 12 respectively without any additional functional evaluation the results require high order derivatives reaching up to the eighth derivative that is why we also present an alternative approach using only the first or at most the fourth derivative we also obtain the radius of convergence and computable error bounds on the distances involved numerical experiments and the comparison of the existing robust methods are included to confirm the theoretical results and high computational efficiency in particular we consider a concrete variety of real life problems coming from different disciplines e g kepler s equation of motion planck s radiation law problem fractional conversion in a chemical reactor the trajectory of an electron in the air gap between two parallel plates van der waal s equation which explains the behavior of a real gas by introducing in the ideal gas equations in order to check the applicability and effectiveness of our proposed methods

state feedback stabilization for probabilistic boolean networks abstract a probabilistic boolean network pbn is a discrete time system composed of a family of boolean networks bns between which the pbn switches in a stochastic fashion studying control related problems in pbns may provide new insights into the intrinsic control in biological systems and enable us to develop strategies for manipulating complex biological systems using exogenous inputs this paper investigates the problem of state feedback stabilization for pbns based on the algebraic representation of logic functions a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a control design method is proposed when the presented condition holds it is shown that the controller designed via the proposed procedure can simultaneously stabilize a collection of pbns that are composed of the same constituent bns

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

quantization and the resolvent algebra abstract we introduce a novel commutative c algebra c r x of functions on a symplectic vector space x admitting a complex structure along with a strict deformation quantization that maps a dense subalgebra of c r x to the resolvent algebra introduced by buchholz and grundling 2 the associated quantization map is a field theoretical weyl quantization compatible with the work of binz honegger and rieckers 1 we also define a berezin type quantization map on all of c r x which continuously and bijectively maps it onto the resolvent algebra the commutative resolvent algebra c r x generally defined on a real inner product space x intimately depends on the finite dimensional subspaces of x we thoroughly analyze the structure of this algebra in the finite dimensional case by giving a characterization of its elements and by computing its gelfand spectrum

constructing a family of optimal eighth order modified newton type multiple zero finders along with the dynamics behind their purely imaginary extraneous fixed points abstract an optimal family of eighth order multiple zero finders and the dynamics behind their basins of attraction are proposed by considering modified newton type methods with multivariate weight functions extensive investigation of purely imaginary extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction numerical experiments strongly support the underlying theory pursued in this paper an exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials

stability and l_1 gain analysis of boolean networks with markovian jump parameters this paper presents some results on stability and l 1 gain analysis of boolean networks with markovian jump parameters a necessary and sufficient condition for global stability of the concerned boolean networks is given in terms of linear programming by utilizing the semi tensor product of matrices and some properties of linear positive systems then the definition of lyapunov function for stochastic boolean networks is presented and lyapunov theorem is derived moreover an l 1 gain problem for stochastic boolean networks with external disturbances is formulated and solved by a sufficient condition examples are shown to illustrate the effectiveness of the obtained results

a class of optimal eighth order derivative free methods for solving the danchick gauss problem abstract a derivative free optimal eighth order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences its performance along with several other derivative free methods is studied on the specific problem of danchick s reformulation of gauss method of preliminary orbit determination numerical experiments show that such derivative free high order methods offer significant advantages over both the classical and danchick s newton approach