deterministic fuzzy time series model for forecasting enrollments the fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data there have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead however the issues of controlling uncertainty in forecasting effectively partitioning intervals and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated this paper proposes a novel deterministic forecasting model to manage these crucial issues in addition an important parameter the maximum length of subsequence in a fuzzy time series resulting in a certain state is deterministically quantified experimental results using the university of alabama s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy robustness and reliability moreover the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results

effective lengths of intervals to improve forecasting in fuzzy time series abstract length of intervals affects forecasting results in fuzzy time series unfortunately the issue of how to determine effective lengths of intervals has not been touched in previous studies this study proposes distribution and average based length to approach this issue distribution based length is the largest length smaller than at least half the first differences of data average based length is set to one half the average of the first differences of data empirical analyses show that distribution and average based lengths are simple to calculate and can greatly improve forecasting results in particular they are superior to the randomly chosen lengths used in previous studies

fuzzy stochastic fuzzy time series and its models in this paper as an extension of the concept of time series we will present the definition and models of fuzzy stochastic fuzzy time series fsfts both of whose values and probabilities with which the fsfts assumes its values are fuzzy sets and which may not be modeled properly by the concept of time series to investigate fsfts the definition of fuzzy valued probability distributions is considered and discussed when the fsfts is time invariant several preliminary conclusions are derived

the q deformed boson realization of representation of quantum universal enveloping algebras for q a root of unity ii the subalgebra chain of uq cl for pt i see ibid vol 24 p 3265 1991 applying the method of the q deformed boson realization for the quantum group to the case where q is a root of unity the authors establish a set of standard basis for the representation space of the quantum universal enveloping algebra uq cl associated with a typical subalgebra chain of uq cl on this basis they systematically obtain irreducible and indecomposable representations of uq cl and its subalgebras they discuss uq c2 in detail

fuzzy arima model for forecasting the foreign exchange market considering the time series arima p d q model and fuzzy regression model this paper develops a fuzzy arima farima model and applies it to forecasting the exchange rate of nt dollars to us dollars this model includes interval models with interval parameters and the possibility distribution of future values is provided by farima this model makes it possible for decision makers to forecast the best and worst possible situations based on fewer observations than the arima model c 2001 elsevier science b v all rights reserved

taiex forecasting based on fuzzy time series and fuzzy variation groups in this paper we present a new method to forecast the daily taiwan stock exchange capitalization weighted stock index taiex based on fuzzy time series and fuzzy variation groups where the main input factor is the previous day s taiex and the secondary factor is either the dow jones the nasdaq the m 1b or their combination first the proposed method fuzzifies the historical training data of the taiex into fuzzy sets to form fuzzy logical relationships second it groups the fuzzy logical relationships into fuzzy logical relationship groups flrgs based on the fuzzy variations of the secondary factor third it evaluates the leverage of the fuzzy variations between the main factor and the secondary factor to construct fuzzy variation groups fourth it gets the statistics of the fuzzy variations appearing in each fuzzy variation group fifth it calculates the weights of the statistics of the fuzzy variations appearing in each fuzzy variation group respectively finally based on the weights of the statistics of the fuzzy variations appearing in the fuzzy variation groups and the flrgs it performs the forecasting of the daily taiex because the proposed method uses both fuzzy variation groups and flrgs to analyze in detail the historical training data it gets higher forecasting accuracy rates to forecast the taiex than the existing methods

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

on convergence in the methods of strat and of smith for shape from shading we study the convergence of two iterative shape from shading methods the methods of strat and of smith we try to determine the spectral radius of the jacobian matrix of each iteration at any possible fixed point we show that the method of strat diverges for any image containing at least four pixels forming a square any reflectance map and any relative weight between the irradiance term and the integrability term an example is provided in which divergence occurs after a large number of iterations even if the reconstructed surface approaches the real surface after only a few iterations we show then by a similar way that the method of smith diverges for any image containing at least nine pixels forming a square any reflectance map and any relative weight between the irradiance term and the smoothing term

a new fuzzy time series model of fuzzy number observations fuzzy time series 4 has been proposed to model dynamic processes whose observations are fuzzy sets or linguistic values and some applications have been made with satisfactory results 5 6 in this paper a new fuzzy time series model is proposed by means of defining some new operations on fuzzy numbers the proposed model is in the form of two theorems that relate the current value of a fuzzy time series with its past

branching processes in the annni model the mean field equations of the simple cubic annni model are studied on finite lattices the results are consistent with the sequence of distinct commensurate phases 2k 13 k 1 2 3 springing from the multiphase point found using low temperature series expansions moreover evidence for new structure combination branching processes is presented which generate phases of type 2l3 m 2l 13 n or 23l m 23l 1 n where l m and n are integers

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

fuzzy decision support system for demand forecasting with a learning mechanism in this paper a new decision support system for demand forecasting dss df is presented a demand forecast is generated in dss df by combining four forecasts values two of them are obtained independently one by a customer and the other by a market expert they represent subjective judgments on future demand given as linguistic values such as demand is around a certain value or demand is not lower than a certain value etc two additional forecasts are crisp values obtained using conventional statistical methods one using time series analysis based on decomposition tsad and the other using an auto regressive integrated moving average arma model the combination of these four forecast values into one improved forecast is made by applying fuzzy if then rules a modified mamdani style inference is used which enables reasoning with fuzzy inputs a new learning mechanism is developed and incorporated into the dss df to adapt the rule bases that combine the individual forecasted values the rule bases are adapted taking into consideration the performance of each of the forecast methods recorded in the past the application of dss df is demonstrated by an illustrative example the forecasts obtained by dss df are compared with results procured by applying the conventional tsad and arma methods separately the results obtained are encouraging and indicate that combining forecasts obtained by different methods may be beneficial

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

the interpretation of line drawings with contrast failure and shadows in line drawings derived from real images lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources this paper shows that it is the presence of shadows rather than contrast failure that renders the line drawing labelling problem np complete however shadows are a valuable visual cue since their presence is formally shown to reduce the average ambiguity of drawings this is especially true when constraints concerning shadow formation are employed to differentiate shadow and non shadow lines the extended junction constraint concerning straight lines colinear with junctions compensates the loss of information caused by contrast failure in fact we observe the contrast failure paradox a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure it is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing this paper shows that these coplanarity constraints are robust to the presence of contrast failure

singular indecomposable representations of sl 2 c and relativistic wave equations a detailed summary is given of the structure of singular indecomposable representations of si 2 as developed by gel fand and ponomarev usp mat nauk 23 3 1968 translated in russ math surveys 23 1 1968 a variety of four vector operators is constructed acting within direct sums of such representations including some with nonsingular 0 associated wave equations of gel fand yaglom type are considered that admit timelike solutions and lead to mass spin spectra of the majorana type a subclass of these equations is characterized in an invariant way by obtaining basis independent expressions for the commutator and anticommutator of and a brief discussion is given of possible applications to physics of these equations and of others in which nilpotent scalar operators appear

handling forecasting problems based on two factors high order fuzzy time series in our daily life people often use forecasting techniques to predict weather economy population growth stock etc however in the real world an event can be affected by many factors therefore if we consider more factors for prediction then we can get better forecasting results in recent years many researchers used fuzzy time series to handle prediction problems in this paper we present a new method to predict temperature and the taiwan futures exchange taifex based on the two factors high order fuzzy time series the proposed method constructs two factors high order fuzzy logical relationships based on the historical data to increase the forecasting accuracy rate the proposed method gets a higher forecasting accuracy rate than the existing methods

linear constraints for the interpretation of line drawings of curved objects abstract drawings of curved objects often contain many linear features straight lines colinear or coplanar points parallel lines and vanishing points these linear features give rise to linear constraints on the 3d position of scene points the resulting problem can be solved by standard linear programming techniques an important characteristic of this approach is that instead of making a strong assumption such as all surfaces are planar only a very weak assumption which disallows coincidences and highly improbable objects needs to be made to be able to deduce planarity the linear constraints combined with junction labelling constraints are a powerful means of discriminating between possible and impossible line drawings they provide an important tool for the machine reconstruction of a 3d scene from a human entered line drawing

taiex forecasting based on fuzzy time series particle swarm optimization techniques and support vector machines in this paper a new method for forecasting the taiex is presented based on fuzzy time series particle swarm optimization techniques and support vector machines the proposed method to forecast the taiex is based on the slope of one day variation of the taiex and the slope of two days average variation of the taiex because the slope of two days average variation of the taiex is smoother than the slope of one day variation of the taiex it is chosen to define the universe of discourse the particle swarm optimization techniques are used to get optimal intervals in the universe of discourse the support vector machine is used to classify the training data set the first feature and the second feature of the support vector machine are the slope of one day variation and the slope of two days average variation of the taiex respectively the experimental results show that the proposed method outperforms the existing methods for forecasting the taiex

a deformed quantum su 2 superalgebra a quantum q deformation of the su 2 superalgebra is obtained which contains as an even part the quantum suq 2 algebra the finite dimensional irreducible representations of the deformed quantum superalgebra are found

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

tensorial structure of a q deformed sp 4 r superalgebra a supersymmetric quantum algebra is generated by irreducible tensor operators with respect to the algebra suq 2 the even generators are realized as tensor products of q boson creation and annihilation operators transforming as suq 2 spinors and acting as odd generators in this way the transformation properties of all the algebra s generators with respect to the q deformed algebra of the angular momentum are simultaneously preserved which is important in view of future applications in physics in the limit q to 1 the classical lie superalgebra sp 4 r or the algebra osp 1 mod 4 is recovered

algebra representations on eigenfunctions of the rosen morse potential the bound state eigenfunctions of the rosen morse n rosen and p m morse phys rev 42 210 1932 potential are investigated using ladder operators that give a representation of the algebra a1 the representations are generally infinite dimensional and indecomposable the representation space containing unbounded functions as well as the normalizable eigenfunctions operators giving eigenfunctions of a potential with different strength are also found giving a representation of d2 the a1 or su2 representations are identified in terms of a classification proposed by sannikov s s sannikov yad fiz 6 1294 1967 sov j nucl phys 6 939 1968 and the connection with representations obtained by gruber and klimyk b gruber and a u klimyk j math phys 19 2009 1978 25 755 1984 is given the evaluation of matrix elements is considered

fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification the method can generate clustering based intervals the method can predict the fuzzy trend of forecasted data in advance the afs classification is exploited to yield the semantic interpretation of each fuzzy trend with the proposed method the horizon of prediction can be as long as desired the method has both good interpretability and superior accuracy in spite of the impressive diversity of models of fuzzy forecasting there is still a burning need to arrive at models that are both accurate and highly interpretable this study proposes a new fuzzy forecasting model designed with the use of the two key techniques namely clustering and axiomatic fuzzy set afs classification first clustering algorithm is utilized to generate clustering based intervals second the fuzzy trend labeled training data set is constructed based on fuzzy logic relationships and fuzzy trends of historical samples then the afs classification is exploited to yield the semantic interpretation of each fuzzy trend the main novelty is that the proposed model not only predicts the value but can also capture the trend prevailing in the time series and obtain its semantic interpretation the taiwan stock exchange capitalization weighted stock index taiex inventory demand and spanish electricity prices are used in a series of experiments the results show that the proposed model has both good interpretability and accuracy

forecasting enrollments with fuzzy time series part ii abstract there have been a good many methods to forecast university enrollments in the literature however none of them could be applied when the historical data are linguistic values fuzzy time series is an effective tool to deal with such problems in this paper as an application of fuzzy time series in educational research the forecast of the enrollments of the university of alabama is carried out in so doing a fuzzy time series model is developed using historical data a complete procedure is proposed which includes fuzzifying the historical data developing a fuzzy time series model and calculating and interpreting the outputs to evaluate the forecasting model the robustness of the fuzzy time series model is tested advantages and problems of the forecasting method are also discussed

a multiresolution approach for shape from shading coupling deterministic and stochastic optimization shape from shading is an ill posed inverse problem for which there is no completely satisfactory solution in the existing literature in this paper we address shape from shading as an energy minimization problem we first show that the deterministic approach provides efficient algorithms in terms of cpu time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima we derive an alternative stochastic approach using simulated annealing the obtained results strongly outperform the results of the deterministic approach the shortcoming is an extreme slowness of the optimization therefore we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework

linear time algorithms for testing the realisability of line drawings of curved objects this paper shows that the semantic labelling of line drawings of curved objects with piecewise c 3 surfaces is solvable in linear time this result is robust to changes in the assumptions on object shape when all vanishing points are known a different linear time algorithm exists to solve the labelling problem furthermore in both cases all legally labelled line drawings of curved objects are shown to be physically realisable however when some but not all of the vanishing points are known when the drawing is an orthographic projection of a scene containing parallel lines or when we wish to minimise the number of phantom junctions the labelling problem becomes np hard the introduction of collinearity constraints also renders the labelling problem np complete except in the case when all vanishing points are known 1999 elsevier science b v all rights reserved

a type 2 fuzzy time series model for stock index forecasting abstract most conventional fuzzy time series models type 1 models utilize only one variable in forecasting furthermore only part of the observations in relation to that variable are used to utilize more of that variable s observations in forecasting this study proposes the use of a type 2 fuzzy time series model in such a type 2 model extra observations are used to enrich or to refine the fuzzy relationships obtained from type 1 models and then to improve forecasting performance the taiwan stock index the taiex is used as the forecasting target the study period extends over the 2000 2003 period the taiex from january to october in each year is used for the estimation while that covering november and december is used for forecasting the empirical analyses show that type 2 model outperforms type 1 model

differential realizations boson fermion realizations of the spl 2 1 superalgebra and its representations differential realizations of the spl 2 1 superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson fermion realizations are studied the new indecomposable and irreducible representations of the spl 2 1 superalgebra are given on subspaces and quotient spaces of the universal enveloping algebra of heisenberg weyl superalgebra all the finite dimensional irreducible representations of the spl 2 1 superalgebra are naturally obtained as special cases

weighted fuzzy time series models for taiex forecasting abstract this study proposes weighted models to tackle two issues in fuzzy time series forecasting namely recurrence and weighting it is argued that recurrent fuzzy relationships which were simply ignored in previous studies should be considered in forecasting it is also recommended that different weights be assigned to various fuzzy relationships in previous studies these fuzzy relationships were treated as if they were equally important which might not have properly reflected the importance of each individual fuzzy relationship in forecasting the weighted models are compared with the local regression models in which weight functions also play an important role both models are different by nature but certain theoretical backgrounds in local regression models are adopted by using the taiwan stock index as the forecasting target the empirical results show that the weighted model outperforms one of the conventional fuzzy time series models

fuzzy seasonality forecasting abstract in this paper a fuzzy forecasting technique for seasonality in the time series data is presented using the following procedure first with the fuzzy regression analysis the fuzzy trend of a time series is analyzed then the fuzzy seasonality is defined by realizing the membership grades of the seasons to the fuzzy regression model both making fuzzy forecast and crisp forecast are investigated seasonal fuzziness and trends are analyzed the method is applied to the sales forecasting problem of a food distribution company

deterministic vector long term forecasting for fuzzy time series in the last decade fuzzy time series have received more attention due their ability to deal with the vagueness and incompleteness inherent in time series data although various improvements such as high order models have been developed to enhance the forecasting performance of fuzzy time series their forecasting capability is mostly limited to short term time spans and the forecasting of a single future value in one step this paper presents a new method to overcome this shortcoming called deterministic vector long term forecasting dvl the proposed method built on the basis of our previous deterministic forecasting method that does not require the overhead of determining the order number as in other high order models utilizes a vector quantization technique to support forecasting if there are no matching historical patterns which is usually the case with long term forecasting the vector forecasting method is further realized by seamlessly integrating it with the sliding window scheme finally the forecasting effectiveness and stability of dvl are validated and compared by performing monte carlo simulations on real world data sets

fuzzy time series forecasting based on fuzzy logical relationships and similarity measures in this paper we propose a new fuzzy time series forecasting method for forecasting the taiwan stock exchange capitalization weighted stock index taiex based on fuzzy time series fuzzy logical relationships particle swarm optimization techniques the k means clustering algorithm and similarity measures between the subscript of the fuzzy set of the fuzzified historical testing datum on the previous trading day and the subscripts of the fuzzy sets appearing in the current states of the fuzzy logical relationships in the chosen fuzzy logical relationship group the particle swarm optimization techniques are used to get the optimal partition of the intervals in the universe of discourse the k means clustering algorithm is used to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups the experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods the advantages of the proposed fuzzy forecasting method is that it uses the particle swarm optimization techniques to get the optimal partition of the intervals in the universe of discourse and uses the k means clustering algorithm to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups for increasing the forecasting accuracy rates

on induced scalar products and unitarization infinitesimal unitarity of representations of the simple real lie algebras su 2 su 1 1 and so 4 is discussed with respect to scalar products induced by sesquilinear forms on their universal enveloping algebras sesquilinear forms are explicitly calculated the verma modules their irreducible quotients their irreducible submodules and their infinitesimal unitarizability are discussed

a q deformed osp 1 2 superalgebra and its two component coherent state representations a q deformed osp 1 2 superalgebra is defined by the use of a pair of q boson annihilation and creation operators a kind of two component coherent state representation of the q deformed superalgebra is found and a q differential realization of the q deformed osp 1 2 superalgebra is obtained

new inhomogeneous boson realizations and inhomogeneous differential realizations of lie algebras the inhomogeneous boson realizations ihbr and the corresponding inhomogeneous differential realizations ihdr of lie algebras which play an important role in the search of quasi exactly solvable problems qesp of quantum mechanics are studied all possible ihdr of semisimple lie algebras can be obtained in this way as examples the ihbr and the corresponding ihdr of lie algebras su 2 and su 3 are studied in detail

a fuzzy seasonal arima model for forecasting this paper proposes a fuzzy seasonal arima fsarima forecasting model which combines the advantages of the seasonal time series arima sarima model and the fuzzy regression model it is used to forecast two seasonal time series data of the total production value of the taiwan machinery industry and the soft drink time series the intention of this paper is to provide business which are affected by diversified management with a new method to conduct short term forecasting this model includes both interval models with interval parameters and the possible distribution of future value based on the results of practical application it can be shown that this model makes good forecasts and is realistic furthermore this model makes it possible for decision makers to forecast the best and worst estimates based on fewer observations than the sarima model

shape from recognition a novel approach for 3 d face shape recovery in this paper we develop a novel framework for robust recovery of three dimensional 3 d surfaces of faces from single images the underlying principle is shape from recognition i e the idea that pre recognizing face parts can constrain the space of possible solutions to the image irradiance equation thus allowing robust recovery of the 3 d structure of a specific part parts of faces like nose lips and eyes are recognized and localized using robust expansion matching filter templates under varying pose and illumination specialized backpropagation based neural networks are then employed to recover the 3 d shape of particular face parts representation using principal components allows to efficiently encode classes of objects such as nose lips etc the specialized networks are designed and trained to map the principal component coefficients of the part images to another set of principal component coefficients that represent the corresponding 3 d surface shapes to achieve robustness to viewing conditions the network is trained with a wide range of illumination and viewing directions a method for merging recovered 3 d surface regions by minimizing the sum squared error in overlapping areas is also derived quantitative analysis of the reconstruction of the surface parts in varying illumination and pose show relatively small errors indicating that the method is robust and accurate several examples showing recovery of the complete face also illustrate the efficacy of the approach

indecomposable generalisations of the standard angular momentum representations of so 3 indecomposable representations of the lie algebra of the rotation group so 3 are studied on the heisenberg weyl basis which is the basis for a subspace of a quotient space of the space of the universal enveloping algebra of the heisenberg weyl algebra the author obtains an infinite dimensional indecomposable representation which induces the finite dimensional representation on certain quotient spaces and subduces the infinite dimensional indecomposable representations on invariant subspaces the standard angular momentum representations of so 3 are given as special cases

indecomposable representations of the nonlinear lie algebras on the two state heisenberg weyl basis the indecomposable representations of the nonlinear lie algebras of vector type r 0 1 one of which is generated by two angular momentum operators j0 j2 and any component of an irreducible tensor operator of rank 1 t 1 0 1 of an so 3 group are studied in detail we give the explicit expressions for the infinite dimensional indecomposable representations of r which further subduce the infinite dimensional indecomposable representations on the invariant subspaces and induce the finite dimensional or infinite dimensional indecomposable irreducible representations on the quotient spaces as special cases the standard angular momentum representations of r are given also

inhomogeneous differential realization boson fermion realization of lie superalgebras and their indecomposable representations an inhomogeneous differential realization ihdr of lie superalgebras which plays an important role in the search for quasi exactly solvable problems qesp of quantum mechanics is studied the corresponding inhomogeneous boson fermion realization ihbfr of lie superalgebras is obtained by making use of the ihbfr a new kind of indecomposable and irreducible representations of lie superalgebras is studied on the universal enveloping algebra of heisenberg weyl superalgebra and on its subspaces and quotient spaces the finite dimensional representations of lie superalgebras are naturally obtained on the subspaces of fock space as examples the ihdr of lie superalgebra spl m 1 is given and the indecomposable and irreducible representations of lie superalgebra su 2 1 are studied in detail

some properties of defuzzification neural networks abstract fuzzy systems have gained more and more attention from researchers and practitioners of various fields in such systems the output represented by a fuzzy set sometimes needs to be transformed into a scalar value and this task is known as the defuzzification process several analytic methods have been proposed for this problem but lately the neural network approach has been used for this purpose when employed as defuzzifiers a neural network is called a defuzzification neural network in this paper some preliminary results on properties of such defuzzification networks will be reported

on the decomposition problem of fuzzy sets in this paper we consider an important problem that is frequently encountered and yet almost universally ignored both in the application and in the theoretic studies of fuzzy sets we refer to this problem as the decomposition of fuzzy sets in nearly all applications of fuzzy sets theory e g fuzzy decision making fuzzy control fuzzy forecasting etc the output is in general a fuzzy set this is then defuzzified before it is applied although defuzzification may be necessary if a crisp quantity is definitely needed when a fuzzy output is appropriate desired or required in an application then the defuzzification step becomes unnecessary yet in this case one finds that it is some times difficult to correctly interpret a fuzzy quantity or identify the true meaning of this fuzzy output using a family of predefined fuzzy sets thus how to match the fuzzy output and the predefined fuzzy sets is the problem of concern in this paper to address this problem we first present and review some definitions and then proceed with an investigation of the preliminary properties of these concepts complementing them with illustrative examples finally we propose some algorithms for the solution of this problem

a new hybrid artificial neural networks and fuzzy regression model for time series forecasting quantitative methods have nowadays become very important tools for forecasting purposes in financial markets as for improved decisions and investments forecasting accuracy is one of the most important factors involved in selecting a forecasting method hence never has research directed at improving upon the effectiveness of time series models stopped artificial neural networks anns are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy however anns need a large amount of historical data in order to yield accurate results in a real world situation and in financial markets specifically the environment is full of uncertainties and changes occur rapidly thus future situations must be usually forecasted using the scant data made available over a short span of time therefore forecasting in these situations requires methods that work efficiently with incomplete data although fuzzy forecasting methods are suitable for incomplete data situations their performance is not always satisfactory in this paper based on the basic concepts of anns and fuzzy regression models a new hybrid method is proposed that yields more accurate results with incomplete data sets in our proposed model the advantages of anns and fuzzy regression are combined to overcome the limitations in both anns and fuzzy regression models the empirical results of financial market forecasting indicate that the proposed model can be an effective way of improving forecasting accuracy

a simple method of forecasting based on fuzzy time series in fuzzy time series forecasting various methods have been developed to establish the fuzzy relations on time series data having linguistic values for forecasting the future values however the major problem in fuzzy time series forecasting is the accuracy in the forecasted values the present paper proposes a new method of fuzzy time series forecasting based on difference parameters the proposed method is a simplified computational approach for the forecasting the method has been implemented on the historical enrollment data of university of alabama adapted by song and chissom and the forecasted values have been compared with the results of the existing methods to show is superiority further the proposed method has also been implemented on a real life problem of crop production forecast of wheat crop and the results have been compared with other methods

a note on fuzzy time series model recently song et al fuzzy sets and systems 73 1995 341 348 proposed a homogeneous fuzzy time series model to model dynamic process whose observations are fuzzy sets or linguistic values by means of defining some new operations on fuzzy numbers in this paper we considered expanding the results to the nonhomogeneous fuzzy time series and the general fuzzy time series by using the weakest t norm based algebraic fuzzy operations and solved the open problem suggested by song et al in their conclusion of the paper

a refined fuzzy time series model for forecasting abstract fuzzy time series models have been used to model observations where each one of them contains multiple values the formulation of fuzzy relationships and the lengths of intervals are considered to be two of the critical factors that affect forecasting results unfortunately the lengths of the intervals were determined during the early stages of forecasting in these models and they thus often failed to reflect the distribution of observations this study therefore proposes a refined fuzzy time series model to further refine the lengths of intervals this model can refine the lengths of intervals during the formulation of fuzzy relationships and hence capture the fuzzy relationships more appropriately as a result the forecasting results can be improved both the stock index and enrollment are used as the targets in the empirical analysis

adaptive expectation based multi attribute fts model for forecasting taiex in recent years there have been many time series methods proposed for forecasting enrollments weather the economy population growth and stock price etc however traditional time series such as arima expressed by mathematic equations are unable to be easily understood for stock investors besides fuzzy time series can produce fuzzy rules based on linguistic value which is more reasonable than mathematic equations for investors furthermore from the literature reviews two shortcomings are found in fuzzy time series methods 1 they lack persuasiveness in determining the universe of discourse and the linguistic length of intervals and 2 only one attribute closing price is usually considered in forecasting not multiple attributes such as closing price open price high price and low price therefore this paper proposes a multiple attribute fuzzy time series fts method which incorporates a clustering method and adaptive expectation model to overcome the shortcomings above in verification using actual trading data of the taiwan stock index taiex as experimental datasets we evaluate the accuracy of the proposed method and compare the performance with the chen 1996 7 yu 2005 6 and cheng cheng wang 2008 20 methods the proposed method is superior to the listing methods based on average error percentage maer

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

fuzzy relation analysis in fuzzy time series model fuzzy relation is a crucial connector in presenting fuzzy time series model however how to obtain a fuzzy relation matrix to represent a time invariant relation is still a question based on the concept of fuzziness in information theory the concept of entropy is applied to measure the degrees of fuzziness when a time invariant relation matrix is derived finally an example is illustrated to show that the proposed method could obtain more accurate and robust results in forecasting

a comparison of fuzzy forecasting and markov modeling abstract fuzzy time series models were introduced by song and chissom fuzzy sets and systems 54 1993 269 277 54 1993 1 9 62 1994 1 8 to model and forecast processes whose values are described by linguistic variables song and chissom used as an application the forecasting of educational enrollments this paper reviews the two methods set forth by song and chissom a first order time invariant fuzzy time series model and a first order time variant model these models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions the results of these methods for the enrollment data are compared with three traditional time series models a first order autoregressive ar 1 model and two second order auto regressive ar 2 models all of which are time invariant

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

boson realisation of virasoro and kac moody algebras and their indecomposable representations in this letter we give the boson realisation of virasoro and kac moody algebras without central terms and construct their indecomposable representations from some representations of the heisenberg weyl algebra the boson realisation of the kac moody algebra a 2 associated to the lie algebra su 2 is discussed in detail

a unified description of the representations of the graded lie algebra gsl 2 indecomposable representations of the graded lie algebra gsl 2 are analyzed in detail it is further shown that the study of the irreducible representations finite and infinite dimensional is intimately related to the study of these indecomposable representations

boson fermion realisation of indecomposable representations for lie superalgebras lndecomposable representations of lie superalgebras are studied on quotient spaces of the universal enveloping algebra of the heisenberg weyl superalgebra b b f j e by boson fermion realisation these representations are constructed from certain types of indecomposable representations of the heisenberg weyl superalgebra and induce usual irreducible representations on invariant subspaces of a quotient space as a physically significant example the explicit form of the boson fermion realisation of indecomposable representations of the classical lie superalgebra su 211 are obtained and discussed in this paper

adaptive learning defuzzification techniques and applications abstract in this paper adaptive learning defuzzification techniques are studied under the consideration of system performance indices by treating defuzzification processes as continuous mappings from space 0 1 n to the real line the concept of the optimal defuzzification mapping can be developed since all the continuous defuzzification mappings considered in this paper form a banach space approximation to the optimal mapping with some known functions can be expressed as the parametric optimization problem to find the optimal parameters adaptive learning of the optimal defuzzification mapping is investigated learning laws for the parameters in the defuzzification mapping are derived in one case numerical results indicate that the adaptive learning defuzzification method can give superior defuzzification results to some popular defuzzification methods

matrix elements for indecomposable representations of complex su 2 indecomposable representations of the simple complex lie algebra a1 are investigated in this article from a general point of view first a master representation is obtained which is defined on the space of the universal enveloping algebra of a1 then from this master representation other indecomposable representations are derived which are induced on quotient spaces or subduced on invariant subspaces finally it is shown that the familiar finite dimensional and infinite dimensional irreducible representations of su 2 and su 1 1 are closely related to certain of the indecomposable representations indecomposable representations of a1 su 2 su 1 1 have found increased applications in physical problems including the unusual finite multiplicity indecomposable representations emphasis is placed in this article on an analysis of the more unfamiliar indecomposable representations the matrix elements are obtained in explicit form for all representations which are discussed in this article th

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

predicting daily ozone concentration maxima using fuzzy time series based on a two stage linguistic partition method abstract air pollution is a result of global warming greenhouse effects and acid rain especially in highly industrialization areas air pollution has become a major environmental issue poor air quality has both acute and chronic effects on human health the detrimental effects of ambient ozone on human health and the earth s ecosystem continue to be a national concern in taiwan the pollutant standard index psi has been adopted to assess the degree of air pollution in taiwan the standardized daily air quality report provides a simple number on a scale of 0 to 500 related to the health effects of air quality levels the report focuses on health and the current psi subindices to reflect measured ozone o 3 concentrations therefore this study uses the o 3 attribute to evaluate air quality in an effort to forecast daily maximum ozone concentrations many researchers have developed daily ozone forecasting models however this continuing worldwide environmental problem suggests the need for more accurate models this paper proposes two new fuzzy time series based on a two stage linguistic partition method to predict air quality with daily maximum o 3 concentration stage 1 use the fuzzy time series based on the cumulative probability distribution approach cpda to partition the universe of discourse into seven intervals stage 2 use two linguistic partition methods the cpda and the uniform discretion method udm to repartition each interval into three subintervals to verify the forecasting performance of the proposed methods in detail the practical collected data is used as and evaluating dataset five other methodologies ar ma arma chen s and yu s are used as comparison models the proposed methods both show a greatly improved performance in daily maximal ozone concentration prediction accuracy compared with the other models

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner

numerical solution of the mean field theory of the annni model in an external field a comparison of two methods it is shown how the solution of the mean field equations for the annni model can be reduced to the iteration of an area preserving two dimensional mapping if an external magnetic field is applied this method is analysed in detail and compared with the exact numerical solution of the mean field equations for simple periodic magnetisations

picture fuzzy regression functions approach for financial time series based on ridge regression and genetic algorithm abstract recent years fuzzy inference systems are efficient tools for solving forecasting problems fuzzy inference systems are based on fuzzy sets and use membership values besides original data so a data augmentation mechanism is employed in the fuzzy inference picture fuzzy sets provide additional information to original data via positive degree membership negative degree membership neutral degree membership and refusal degree membership apart from fuzzy sets the data augmentation with this additional information will be provided to build a better inference system than fuzzy inference systems in this study picture fuzzy inference system is proposed for forecasting purpose by using ridge regression and genetic algorithm ridge regression method is used to obtain picture fuzzy functions and genetic algorithm is used to emerge different information coming from systems which are designed for positive degree membership negative degree membership and neutral degree membership in the proposed method picture fuzzification is provided by picture fuzzy clustering the proposed inference system is tested by various stock exchange data sets the forecasting of the proposed method is compared with well known forecasting methods the obtained results are evaluated according to different error measures such as root of mean square error and mean of absolute percentage error

qualitative features and the generalized hough transform abstract in this paper we show how the use of qualitative features can enhance the performance of recognition and localization techniques in particular the generalized hough transform qualitative features i e scene features with qualitative attributes assigned to them are shown to be effective in pruning the search space of possible scene interpretations and also reducing the number of spurious interpretations explored by the recognition and localization technique the redundancy of the computed transform and the probability of spurious peaks of significant magnitude due to random accumulation of evidence are two criteria by which the performance of the generalized hough transform is judged the straightforward generalized hough transform shows a high probability of spurious peaks of significant magnitude even for small values of redundancy and small magnitude of the search space of scene interpretations the use of qualitative features enables us to come up with a weighted generalized hough transform where each match of a scene feature with a model feature is assigned a weight based on the qualitative attributes assigned to the scene feature these weights could be looked upon as membership function values for the fuzzy sets defined by these qualitative attributes analytic expressions for the probability of accumulation of random events within a bucket are derived for the weighted generalized hough transform and compared with the corresponding expression for the straightforward generalized hough transform the weighted generalized hough transform is shown to perform better than the straightforward generalized hough transform an experiment for the recognition of polyhedral objects from range images is described using dihedral junctions as features for matching and pose computation the experimental results bring out the advantages of the weighted generalized hough transform over the straightforward generalized hough transform

handling forecasting problems using fuzzy time series abstract in 6 9 song et al proposed fuzzy time series models to deal with forecasting problems in 10 sullivan and woodall reviewed the first order time invariant fuzzy time series model and the first order time variant model proposed by song and chissom 6 8 where the models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions in this paper we propose a new method to forecast university enrollments where the historical enrollments of the university of alabama shown in 7 8 are used to illustrate the forecasting process the average forecasting errors and the time complexity of these methods are compared the proposed method is more efficient than the ones presented in 7 8 10 due to the fact that the proposed method simplifies the arithmetic operation process furthermore the average forecasting error of the proposed method is smaller than the ones presented in 2 7 8

inhomogeneous boson realization of indecomposable representations of lie algebras by making use of the differential realization of lie algebras in the space of inhomogeneous polynomials of a certain number of variables the corresponding inhomogeneous boson realization of lie algebras is given a new kind of indecomposable representations of lie algebras are studied on the universal enveloping algebra of heisenberg weyl algebra its subspaces and its quotient spaces the finite dimensional representations are naturally obtained on the subspaces of fock space as an example the indecomposable and irreducible representations of the lie algebra su 2 are discussed in detail

a robust method of forecasting based on fuzzy time series present study proposes an improved and versatile method of forecasting based on the concept fuzzy time series forecasting the developed model has been presented in a form of simple computational algorithms it utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in a better way and making it a robust method the developed model has been implemented on the historical student enrollments data of university of alabama adapted by song and chissom and the obtained forecasted values have been compared with the existing methods to show its superiority the robustness of the model has also been tested in comparison the suitability of the developed model has also been examined in the crop production forecasting by implementing it on historical time series data of rice production of pantnagar farm india

indecomposable modules of the poincare algebra in an energy cyclic angular momentum basis the universal enveloping algebra u u u h of the poincare algebra iso 3 1 is considered infinite dimensional induced modules u are studied explicit formulas are obtained for u in the poincare birkhoff witt basis then a change of basis is performed to an energy cyclic angular momentum basis for any c2 u turns out to be indecomposable it can be represented as an infinite family of interacting verma modules of the lorentz algebra so 3 1 finite dimensional modules can be obtained as quotient modules of u if 2 z2

the q analog of the boson algebra its representation on the fock space and applications to the quantum group in this paper a realization of the q deformed boson operators on the fock space from a generally algebraic point of view is given the representations of the quantum group cn q are thereby constructed in terms of this realization some infinite and finite dimensional representations of the q analog of the heisenberg weyl algebra are obtained on certain quotient spaces finally the q deformed differential realization of quantum group given by alvarez gaume gomez and sierra preprint cern th 5369 89 is derived from the boson realization

fuzzy time series and its models based upon the works by zadeh 1973 1975 in this paper a special dynamic process with linguistic values as its observations is defined and studied this dynamic process is called fuzzy time series to describe fuzzy time series fuzzy relational equations are employed as the models there are two classes of fuzzy time series time variant and time invariant the definition of fuzzy time series is given some properties of fuzzy time series are explored and procedures to develop fuzzy time series models are discussed finally a procedure for using fuzzy time series for foracasting is suggested

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

monocular extraction of 2 1d sketch using constrained convex optimization this paper presents an approach to estimating the 2 1d sketch from monocular low level visual cues we use a low level segmenter to partition the image into regions and then estimate their 2 1d sketch subject to figure ground and similarity constraints between neighboring regions the 2 1d sketch assigns a depth ordering to image regions which are expected to correspond to objects and surfaces in the scene this is cast as a constrained convex optimization problem and solved within the optimization transfer framework the optimization objective takes into account the curvature and convexity of parts of region boundaries appearance and spatial layout properties of regions our new optimization transfer algorithm admits a closed form expression of the duality gap and thus allows explicit computation of the achieved accuracy the algorithm is efficient with quadratic complexity in the number of constraints between image regions quantitative and qualitative results on challenging real world images of berkeley segmentation geometric context and stanford make3d datasets demonstrate our high accuracy efficiency and robustness

fuzzy forecasting based on two factors second order fuzzy trend logical relationship groups similarity measures and pso techniques in this paper we propose a new fuzzy forecasting method based on two factors second order fuzzy trend logical relationship groups tsftlrgs particle swarm optimization pso techniques and similarity measures between the subscripts of fuzzy sets fss for forecasting the taiwan stock exchange capitalization weighted stock index taiex and the new taiwan dollar us dollar ntd usd exchange rates first we propose a pso based optimal intervals partition algorithm to get the optimal partition of the intervals in the universe of discourse uod of the main factor taiex and to get the optimal partition of the intervals in the uod of the secondary factor sf where sf dow jones nasdaq m1b based on the proposed pso based optimal intervals partition algorithm the constructed tsftlrgs and similarity measures between the subscripts of fss we propose a new method for forecasting the taiex and the ntd usd exchange rates the main contribution of this paper is that we propose a new fuzzy forecasting method based on tsftlrgs pso techniques and similarity measures between the subscripts of fss for forecasting the taiex and the ntd usd exchange rates to get higher forecasting accuracy rates than the ones of the existing fuzzy forecasting methods

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

a probabilistic and statistical view of fuzzy methods fuzzy set theory has primarily been associated with control theory and with the representation of uncertainty in applications in artificial intelligence more recently fuzzy methods have been proposed as alternatives to traditional statistical methods in statistical quality control linear regression and forecasting among other areas we review some basic concepts of fuzzy methods point out some philosophical and practical problems and offer simpler alternatives based on traditional probability and statistical theory applications in control theory and statistical quality control serve as our primary examples

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

indecomposable representations of the poincare algebra the authors consider indecomposable representations of the poincare algebra iso 3 1 on the space omega omega omega h of its universal enveloping algebra a master representation is obtained on omega which induces representations on k the invariant subalgebra of translations and on omega and omega these representations are discussed in particular in view of finite dimensional indecomposable representations of iso 3 1 the approach taken is analogous to the approach chosen by the authors in their analysis of indecomposable representations of the lorentz algebra so 3 1 1983 thus under restriction of iso 3 1 to so 3 1 the earlier results are recovered the interpretation of the finite dimensional indecomposable representations of iso 3 1 then follows easily as a coupling of a finite number of irreducible so 3 1 representations to an indecomposable iso 3 1 representation with the dimension of the irreducible representations strictly increasing or strictly decreasing the bases for the finite dimensional indecomposable iso 3 1 representations are explicitly determined and thus also their matrix elements via the inducing representations a formula for their dimensionalities is obtained the methods employed are purely algebraic and follow the line of work of jacobson and dixmier 1962 1978

heuristic models of fuzzy time series for forecasting abstract song and chissom first proposed the definitions of fuzzy time series and time invariant and variant models of fuzzy time series chen then proposed arithmetic operations to replace the complex computations in song and chissom s models this study proposes heuristic models by integrating problem specific heuristic knowledge with chen s model to improve forecasting this is because chen s model was easy to calculate was straightforward to integrate heuristic knowledge and forecast better than the others both university enrollment and futures index are chosen as the forecasting targets the empirical analyses show that the heuristic models reflect the fluctuations in fuzzy time series better and provide better overall forecasting results than the previous models

indecomposable representations of the lorentz algebra in an angular momentum basis indecomposable i e reducible but not completely reducible representations of the complex algebra so 3 1 of the lorentz group are analysed a master representation of so 3 1 is obtained on the space of its universal enveloping algebra omega the basis chosen for so 3 1 is the angular momentum basis and for omega a natural basis with respect to the angular momentum basis of so 3 1 the master representation induces representations on a space omega which is obtained from omega as quotient space modulo certain ideals these representations have the property that rho h3 is diagonal a change of basis is made from the natural basis to the angular momentum basis and the representations on omega are analysed in this new basis the indecomposable as well as the irreducible representations which are obtained have the property that their so 3 content consists of infinite dimensional indecomposable and irreducible so 3 representations certain of the indecomposable so 3 1 representations have additional invariant subspaces which lead to quotient spaces which are of finite dimension these quotient spaces then carry the familiar finite dimensional representations of the lorentz algebra it is shown that the standard theory of representations of the lorentz algebra is contained in this analysis as a special case of representations which are induced on certain quotient spaces of the space omega

estimation of illuminant direction albedo and shape from shading a robust approach to the recovery of shape from shading information is presented assuming uniform albedo and lambertian surface for the imaging model two methods for estimating the azimuth of the illuminant are presented one is based on local estimates on smooth patches and the other method uses shading information along image contours the elevation of the illuminant and surface albedo are estimated from image statistics taking into consideration the effect of self shadowing with the estimated reflectance map parameters the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image the algorithm is data driven stable updates the surface slope and height maps simultaneously and significantly reduces the residual errors in irradiance and integrability terms a hierarchical implementation of the algorithm is presented typical results on synthetic and images are given to illustrate the usefulness of the approach