computing real solutions of fuzzy polynomial systems abstract this paper presents an efficient algorithm called solvefuzzysystem or sfs for finding real solutions of polynomial systems whose coefficients are symmetrical l r fuzzy numbers with bounded support for which the spread functions l and r are bijective the real solutions of such a system are deduced from solutions of some polynomial systems with real coefficients this algorithm is based on new results that are universal because they are independent from the spread functions these theoretical results include the management of the fuzzy system s solutions signs an implementation in the fuzzy package of the free computer algebra software sagemath and a parallel version of the algorithm are described

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

spatial data fusion for qualitative estimation of fuzzy request zones application on precision viticulture this article deals with a method used to describe and manage spatial knowledge each spatial datum is considered as an information element whose location and value are independently described the method proposed uses the information elements to infer the value of any request zone data can be either qualitative or quantitative our approach is based on a fuzzy granulation of available items of information the fusion of information elements is performed by an aggregation operator based on the choquet integral which analyzes the spatial relevancy of the information elements on the request zone we also describe an application of the method to a precision viticulture data set

operator means of probability measures abstract let p be the complete metric space consisting of positive invertible operators on an infinite dimensional hilbert space with the thompson metric we introduce the notion of operator means of probability measures on p in parallel with kubo and ando s definition of two variable operator means and show that every operator mean is contractive for the wasserstein distance by means of a fixed point method we consider deformation of such operator means and show that the deformation of any operator mean becomes again an operator mean in our sense based on this deformation procedure we prove a number of properties and inequalities for operator means of probability measures

generalization of the analytical inversion method for the solution of the point kinetics equations a method based on the analytical inversion of polynomials of the point kinetics matrix is applied to the solution of the reactor kinetics equations this method permits a fast inversion of polynomials by going temporarily to the complex plane several cases using various options of the method are presented for comparison the method developed was found to be very fast and accurate and has the ability to reproduce all the features of transients including prompt jump the analysis of the assumption of constant parameters reactivity and source during a time step are included it is concluded that the method provides a fast and accurate computational technique for the point kinetics equations with step reactivity

spectral inequalities for matrix exponentials abstract this note generalizes an inequality of bernstein as follows if c is an n n complex matrix and c k is the k th compound of c 1 k n n n k and if the eigenvalues of c k are labeled in order of decreasing magnitude 1 c k 2 c k n c k define the partial trace tr k i c by tr k i c h 1 i h c k i 1 n then for any complex n n matrix a tr k i e a e a tr k i e a a i 1 n with equality if a is normal or k n a spectral inequality of k fan is also generalized through the use of compound matrices

the construction of consistent possibility and necessity measures given a general measure finite or infinite we develop possibility and necessity measures as upper and lower estimators of we provide a method for constructing such fuzzy measures and show that the measure can be approximated with arbitrary closeness using fuzzy measures constructed this way using the extension principle these consistent possibility and necessity measures are used to produce possibility and necessity measures on the range space of a measurable function which are consistent with the measure on the range space induced by the measurable function this induced measure can be approximated with arbitrary closeness by extending consistent possibility and necessity measures constructed on the domain space

the ando hiai inequalities for the solution of the generalized karcher equation and related results abstract in this paper we shall give a concrete relation between the generalized karcher equation and operator means as its solution next we shall show two types of the ando hiai inequalities for the solution of the generalized karcher equation in this discussion we also give a property of relative operator entropy

an improved class of generalized runge kutta methods for stiff problems part ii the separated system case in order to study a generalization of the explicit p stage runge kutta methods we introduce a new family of p stage formulas for the numerical integration of some special systems of odes that provides better order and stability results with the same number of stages in our recent paper entitled an improved class of generalized runge kutta methods for stiff problems part i the scalar case we studied new schemes for the numerical integration of scalar autonomous odes in this second part we will show that it is possible to generalize our grk methods so that they can be applied to some non autonomous scalar odes and systems obtaining linearly implicit a stable and l stable methods these methods do not require jacobian evaluations in their implementation some numerical examples are discussed in order to show the good performance of the new schemes

ando hiai inequality and furuta inequality abstract let a b 0 the positive operators on a hilbert space ando hiai inequality ah and furuta inequality f are given as follows ah a b 0 a b i a r b r i for r 1 and f a b 0 a r 1 r p r b p b a we show these inequalities imply each other

characterizations of jordan isomorphisms of c algebras by weighted geometric mean related operations and quantities abstract in this paper we consider three operations on positive definite cones of c algebras which are related to weighted geometric means and appear in the formulas defining various versions of quantum renyi relative entropy we show how jordan isomorphisms between c algebras can be characterized by the preservation of the norms of products under those operations or by the preservation of the operations themselves we also obtain conditions for the commutativity of the underlying algebras by showing that we have that property if one of the quantities under considerations can be transformed by a surjective map to another different such quantity

a study of rosenbrock type methods of high order this paper deals with the solution of nonlinear stiff ordinary differential equations the methods derived here are of rosenbrock type this has the advantage that they area stable or stiffly stable and nevertheless do not require the solution of nonlinear systems of equations we derive methods of orders 5 and 6 which require one evaluation of the jacobian and onelu decomposition per step we have written programs for these methods which use richardson extrapolation for the step size control and give numerical results

constructing consistent fuzzy surfaces from fuzzy data given fuzzy data describing a three dimensional entity such as terrain we develop methods to construct surfaces that are consistent with the uncertainty in the data and surface model itself in particular surfaces generated from higher cut values of the fuzzy data are contained within the surfaces generated by lower cut values of the fuzzy data moreover the smoothness and continuity conditions of the surface generating method is maintained by each level surface we demonstrate the ideas by developing two and three dimensional surfaces from fuzzy data for cubic splines and digital terrain models generated from triangulation

a fuzzy lagrange interpolation theorem abstract the following problem was posed by l a zadeh suppose we are given n 1 points x0 xn in r and for each of these points a fuzzy value in r rather than a crisp one is it then possible to construct some function on r with range also a collection of fuzzy values which coincides on the given n a points with the given fuzzy values and which fulfills some natural smoothness condition in this paper we shall present a solution to this problem based on the fundamental and well known polynomial interpolation theorm of lagrange

stability of generalized runge kutta methods for stiff kinetics coupled differential equations a stability and efficiency improved class of generalized runge kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and or nonlinear coupled differential equations the determination of the coefficients required by the method is precisely obtained from the so called equations of condition which in turn are derived by an approach based on butcher series since the equations of condition are fewer in number free parameters can be chosen for optimizing any desired feature of the process a further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced in addition the a stability properties of the method are investigated implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback

two classes of internally s stable generalized runge kutta processes which remain consistent with an inaccurate jacobian generalized runge kutta processes for stiff systems of ordinary differential equations usually require an accurate evaluation of a jacobian at every step however it is possible to derive processes which are internally s stable when an accurate jacobian is used but still remain consistent and highly stable if an approximate jacobian is used it is shown that these processes require at least as many function evaluations as an explicit runge kutta process of the same order and second and third order processes are developed a second class of generalized runge kutta is introduced which requires that the jacobian be evaluated accurately less than once every step a third order process of this class is developed and all three methods contain an error estimator similar to those of fehlberg or england

some ways of constructing furuta type inequalities abstract let h be an operator mean associated with an operator monotone function h and let a b be positive operators we investigate the following furuta type inequality for some fixed continuous function h a b 0 a r r x h r b r 1 where x h is the positive solution of h x b 1 the map h r r plays a central role in constructing a furuta type inequality similar to the role of the map p r r 1 p r in the following part of the furuta inequality a b 0 p r 1 b r 2 a p b r 2 1 r p r b p r 1 r p r we obtain this map h r r from the following ando hiai type inequality a b 0 a h b 1 a r h b r 1 r 1

picard s iterative method for nonlinear advection reaction diffusion equations picard s iterative method for the solution of nonlinear advection reaction diffusion equations is formulated and its convergence proved the method is based on the introduction of a complete metric space and makes uses of a contractive mapping and banach s fixed point theory from picard s iterative method the variational iteration method is derived without making any use at all of lagrange multipliers and constrained variations some examples that illustrate the advantages and shortcomings of the iterative procedure presented here are shown

neural network approach to solving fuzzy nonlinear equations using z numbers in this article the fuzzy property is described by means of the z number as the coefficients and variables of the fuzzy equations this alteration for the fuzzy equation is appropriate for system modeling with z number parameters in this article the fuzzy equation with z number coefficients and variables is tended to be used as the models for the uncertain systems the modeling issue related to the uncertain system is to obtain the z number coefficients and variables of the fuzzy equation nevertheless it is extremely hard to get the z number coefficients of the fuzzy equations in this article in order to model the uncertain nonlinear systems a novel structure of the multilayer neural network is utilized in such a manner that it is able to obtain the z number coefficients of the fuzzy equation the suggested technique is validated by some examples with applications

the golden thompson trace inequality is complemented we prove a class of trace inequalities which complements the golden thompson inequality for example tr epa epb 2 p tr ea b holds for all p 0 when a and b are hermitian matrices and denotes the geometric mean we also prove related trace inequalities involving the logarithmic function namely p 1tr x log yp 2xpyp 2 tr x log x log y p 1tr x log xp 2ypxp 2 for all p 0 when x and y are nonnegative matrices these inequalities supply lower and upper bounds on the relative entropy

modeling uncertain data with fuzzy b splines abstract fuzzy numbers are an alternative solution to the problem uncertain data modeling the idea of fuzzy b spline is here introduced its power relies on the possibility of being used as approximating function both for fuzzy and crisp data the fuzzy modeling of large collections of noisy data described in this paper moreover achieves a very high degree of compression with a relatively low computational complexity both for maintenance and interrogation of the model itself an extensive description of the modeling technique is given together with methods for interrogating the model experimental results are shown to prove the effectiveness of the proposed approach

when does ando hiai inequality hold abstract let be in 0 1 and r 0 and stand for the weighted operator geometric mean we consider the following statement a b 0 a b i a r b r i ando and hiai show that if r 1 then this holds in the present paper we first prove the converse of this result namely the above statement holds only if r 1 we next show that for each non negative continuous function f on 0 with f t r and f t r there exist a b 0 such that a b i and f a f b i we also try to find a characterization of a continuous function f satisfying a b 0 a b i f a f b i

solution of the point kinetics equations in the presence of newtonian temperature feedback by pade approximations via the analytical inversion method a method based on the pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity the technique consists of treating explicitly the roots of the inhour formula a significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation which usually would make the pade approximation inaccurate also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the pade approximations results are presented for several cases of pade approximations using various options of the method with different types of reactivity the formalism is applicable equally well to non linear problems where the reactivity depends on the neutron density through temperature feedback it was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases

picard iteration and pade approximations for stiff fractional point kinetics equations a model of stiff point kinetics equations is one of the important models in the nuclear reactor dynamics this model describes the neutron density and the precursor concentrations of delayed neutrons into nuclear reactors in this work a fractional model of the stiff point kinetics equations is studied to describe the neutron density behavior by the fractional order picard iteration and pade approximations are presented to solve the stiff fractional point kinetics equations with multi group of delayed neutrons the validity of the fractional model is tested for different cases of step ramp and sinusoidal reactivities the numerical results of picard iteration and pade approximations are computed for various fractional order the results of pade11 approximation are in good agreement with the results of picard iteration than pade01 approximation in addition the numerical results confirm that the neutron density for a positive negative reactivity is increasing decreasing quicker with decreases the fractional order

picard iteration algorithm combined with gauss seidel technique for initial value problems abstract in this paper we introduce and implement a relatively new improvement for the well known picard s method for studying linear and nonlinear systems of ordinary differential equations in this method the solution takes the form of a rapidly convergent series with easily computable components a mathematica computer algebra system mathematica 5 1 is used to introduce a code which generates the series different illustrative examples have been considered as well as different comparison criterion between the proposed method and modern reliable and conventional methods the deeply mathematical roots of the method fixed point theorem and the correspondence with the theory of algebraic systems makes it is very interesting theoretical considerations are being discussed and convergence of the method is addressed other extensions and applications for further work are mentioned

an application of the fuzzy theory in surface interpolation and surface deformation analysis measurements can be considered to be fuzzy values from mathematical point of view their uncertainty is caused by an incomplete knowledge of absolute truth only value ranges can be proposed in this case in this sense measurements provide some raw material for further researches they can be interpolated over a grid and approximated by an analytical surface additionally it can be necessary to obtain some surface characteristics of higher order based on the grid it is clear that each characteristic which is derived from uncertain measurements is also uncertain in this paper we discuss a method of modelling the propagation of the uncertainty the so called fuzzy propagation of measurements to derived differential geometric characteristics and its application

an improved class of generalized runge kutta methods for stiff problems part i the scalar case a new family of p stage methods for the numerical integration of some scalar equations and systems of odes is proposed these methods can be seen as a generalization of the explicit p stage runge kutta ones while providing better order and stability results we will show in this first part that at the cost of losing linearity in the formulas it is possible to obtain explicit a stable and l stable methods for the numerical integration of scalar autonomous odes scalar autonomous odes are of very little interest in current applications however be begin studying this kind of problems because most of the work can be easily extended to a more general situation in fact we will show in a second part entitled the separated system case that it is possible to generalize our methods so that they can be applied to some non autonomous scalar odes and systems we will obtain linearly implicit l stable methods which do not require jacobian evaluations in both parts some numerical examples are discussed in order to show the good performance of the new schemes

a generalization of araki s log majorization abstract we generalize araki s log majorization to the log convexity theorem for the eigenvalues of a p 1 2 b p a p 1 2 as a function of p 0 where a b are positive semidefinite matrices and are positive linear maps between matrix algebras similar generalizations of the log majorization of ando hiai type for the weighted geometric mean a b are also given including a lemma on general operator means a e of a and a projection e

log majorization and complementary golden thompson type inequalities abstract we obtain a log majorization result for power means of positive semidefinite matrices this implies matrix norm inequalities for unitarily invariant norms which are considered as complementary to the golden thompson one other log majorization results are also obtained we give logarithmic trace inequalities and determinant inequalities as applications of our log majorizations

interpolation of fuzzy data abstract we will consider the interpolation of fuzzy data by a continuous fuzzy valued function and give some numerical methods for calculating the fuzzy interpolant