an iterative approach for estimation of student performances based on linguistic evaluations in group decision analysis numerous approaches have been suggested in an attempt to solve the problem of aggregation of individual fuzzy opinions to form a group consensus as the basis of a group decision in this study an optimization model which reflects different points of view of many decision makers by weighting fuzzy opinions is proposed for the evaluation of student performances in student centered learning an iterative algorithm is provided for the solution of this model and the consequent theorem is proved experimental results show that the proposed iterative algorithm yields more efficient results than do the classical optimization methods moreover the wabl weighted averaging based on the levels method produces more accurate results than do the other frequently used defuzzification methods such as coa center of area and mom mean of maxima

multi soliton and double wronskian solutions of a 2 1 dimensional modified heisenberg ferromagnetic system a 2 1 dimensional modified heisenberg ferromagnetic system which arises in the motion of magnetization vector of the isotropic ferromagnet and biological pattern formation is investigated via the hirota bilinear method multi soliton solutions of such a system are derived it is proved that the system possesses the n soliton solutions expressed in terms of the double wronskian determinant head on and overtaking elastic interactions are exhibited elastic interaction behavior between the two solitons has been interpreted through the asymptotic analysis namely amplitude and velocity of each soliton remain unchanged except for the phase shift after the interaction inelastic interactions including the soliton fusion and fission between two solitons are shown during the soliton propagation for the product of two fields the soliton with the smaller amplitude can travel faster than with the larger while for the third field the soliton with the larger amplitude can travel faster than with the smaller on the other hand the soliton for the third field may exhibit the solitoff like property with respect to the three solitons head on elastic interaction can be found

identifying nonlinear biomechanical models by multicriteria analysis in this study the methodology developed by srdjevic and cveticanin international journal of industrial ergonomics 34 2004 307 318 for the nonbiased objective parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n degree of freedom dof nonlinear biomechanical models the dynamic performance of the n dof nonlinear model is described in terms of response functions in the frequency domain such as the driving point mechanical impedance and seat to head transmissibility function for randomly generated parameters of the model nonlinear equations of motion are solved using the runge kutta method the appropriate data transformation from the time to frequency domain is performed by a discrete fourier transformation squared deviations of the response functions from the target values are used as the model performance evaluation criteria thus shifting the problem into the multicriteria framework the objective weights of criteria are obtained by applying the shannon entropy concept the suggested methodology is programmed in pascal and tested on a 4 dof nonlinear lumped parameter biomechanical model the identification process over the 2000 generated sets of parameters lasts less than 20 s the model response obtained with the imbedded identified parameters correlates well with the target values therefore justifying the use of the underlying concept and the mathematical instruments and numerical tools applied it should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

self similar solutions for the 1 d schrodinger map on the hyperbolic plane in this paper we will study self similar solutions for x t x x ss the equivalent in the minkowski 3 space mathbb r 2 1 to the localized induction approximation flow trying to adapt some results given by gutierrez rivas and vega we will show the existence of a one parameter family of smooth solutions developing a corner in finite time the main difference with respect to the euclidean case studied by those authors will be the proof of the boundedness of t e 1 and e 2 the equivalents of t b and n in mathbb r 2 1

the gauge equivalence of the davey stewartson equation and 2 1 dimensional continuous heisenberg ferromagnetic model the gauge equivalence between the davey stewartson ds equation and the 2 1 dimensional continuous heisenberg ferromagnetic model is shown explicitly through the gauge transformation solutions of the dsii are obtained from the vortex type solutions of the former equation

the gauge equivalence of the nls and the schrodinger flow of maps in 2 1 dimensions the gauge equivalence of the analogues of the nonlinear schrodinger equation nls and those of the schrodinger flow of maps into h2 the minkowski hf model in 2 1 dimensions are proved respectively combining these with the already known results we obtain a complete understanding of the gauge equivalence of the analogous models of the nonlinear schrodinger equation for 1 or 1 and those of the heisenberg ferromagnet model for euclidean or minkowski in 2 1 dimensions

lower extremity control during turns initiated with and without hip external rotation the pirouette turn is often initiated in neutral and externally rotated hip positions by dancers this provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole body level when using different leg kinematics the purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation skilled dancers n 5 performed pirouette turns with and without hip external rotation joint kinetics during turn initiation were determined for both legs using ground reaction forces grfs and segment kinematics hip muscle activations were monitored using electromyography using probability based statistical methods variables were compared across turn conditions as a group and within dancer despite differences in grfs and impulse generation between turn conditions at least 90 of each grf was aligned with the respective leg plane a majority of the net joint moments at the ankle knee and hip acted about an axis perpendicular to the leg plane however differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh during the initiation of both turns most participants used ankle plantar flexor moments knee extensor moments flexor and abductor moments at the push leg s hip and extensor and abductor moments at the turn leg s hip representation of joint kinetics using multiple reference systems assisted in understanding control priorities

mathematical models for the apparent masses of standing subjects exposed to vertical whole body vibration linear lumped parameter models of the apparent masses of human subjects in standing positions when exposed to vertical whole body vibration have been developed simple models with a single degree of freedom d o f and with two d o f were considered for practical use model parameters were optimised using both the mean apparent mass of 12 male subjects and the apparent masses of individual subjects measured in a previous study the calculated responses of two d o f models with a massless support structure showed best agreement with the measured apparent mass and phase with errors less than 0 1 in the normalised apparent mass i e corresponding to errors less than 10 of the static mass and errors less than 5 in the phase for a normal standing posture the model parameters obtained with the mean measured apparent masses of the 12 subjects were similar to the means of the 12 sets of parameters obtained when fitting to the individual apparent masses it was found that the effects of vibration magnitude and postural changes on the measured apparent mass could be represented by changes to the stiffness and damping in the two d o f models

some integrable hierarchies in 2 1 dimensions and their twistor description the twistor space construction due to mason and sparling for solutions of the nonlinear schrodinger and korteweg devries hierarchies is generalized resulting in families of integrable models in 2 1 dimensions soliton solutions to one such hierarchy associated with the gauge group su 2 are constructed by adapting the methods used to construct instanton and monopole solutions these integrable models have the feature that their solutions depend on a number of arbitrary functions as well as arbitrary constants in contrast to the closely related davey stewartson hierachy

on the relation between compromise programming and ordered weighted averaging operator this paper will demonstrate a strong relationship between the compromise programming cp method and the ordered weighted averaging owa operator we will mathematically prove that the application of the cp method reflects the pessimistic view of the decision maker dm if the distance from the ideal point is minimized it will however present an optimistic dm if the distance from the nadir is maximized the owa operator may cover all of the optimistic neutral and pessimistic views a practical relationship will be developed between the power value of the cp method and the optimism degree of the dm based on fuzzy quantifiers the theoretical results will be illustrated by a real case study of a water resources management problem

lower extremity control and dynamics during backward angular impulse generation in forward translating tasks observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control when comparing two forward translating tasks performed with and without backward angular impulse we have learned that both trunk leg coordination and reaction force time characteristics are significantly different between tasks this led us to hypothesize that differences in trunk leg coordination and reaction force generation would induce between task differences in the control of the lower extremity joints during impulse generation phase of the tasks eight highly skilled performers executed a series of forward jumps with and without backward rotation reverse somersault and reverse timer respectively sagittal plane kinematics reaction forces and electromyograms of lower extremity muscles were acquired during the take off phase of both tasks lower extremity joint kinetics were calculated using inverse dynamics the results demonstrated between task differences in the relative angles between the lower extremity segments and the net joint forces reaction force and the joint angular velocity profiles significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer between task differences in lower extremity joint kinetics were regulated by selectively activating the bi articular muscles crossing the knee and hip these results indicate that between task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem

gauge equivalence between dimensional continuous heisenberg ferromagnetic models and nonlinear schrodinger type equations the gauge equivalence between the 2c 1 dimensional zakharov equation and the 2c 1 dimensional integrable continuous heisenberg ferromagnetic model is established their integrable reductions are also shown explicitly

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

derivative nonlinear schrodinger equations and hermitian symmetric spaces it is shown that to each hermitian symmetric space there corresponds an integrable system of generalised derivative nonlinear schrodinger equations nls the nonlinear terms are related to the curvature tensor of the associated symmetric space the hamiltonian form of the equations is presented the results are an extension of those presented in an earlier paper 1983 on generalised nls equations associated with symmetric and reductive homogeneous spaces

on the simplest 2 1 dimensional integrable spin systems and their equivalent nonlinear schrodinger equations using a moving space curve formalism geometrical as well as gauge equivalence between a 2 1 dimensional spin equation m i equation and the 2 1 dimensional nonlinear schrodinger equation nlse originally discovered by calogero discussed then by zakharov and recently rederived by strachan have been estabilished a compatible set of three linear equations are obtained and integrals of motion are discussed through stereographic projection the m i equation has been bilinearized and different types of solutions such as line and curved solitons breaking solitons induced dromions and domain wall type solutions are presented breaking soliton solutions of 2 1 dimensional nlse have also been reported generalizations of the above spin equation are discussed

darboux transformation and soliton solutions for the 2 1 dimensional nonlinear schrodinger hierarchy with symbolic computation abstract in this paper the n fold darboux transformation is applied to the lax pair associated with the 2 1 dimensional nonlinear schrodinger hierarchy the general explicit formula for n soliton solution is derived in terms of vandermonde like determinant expression on the zero background two different families of soliton solutions multi line soliton and multi parabola soliton solutions are constructed by applying the darboux transformation successively based on the figures for several sample solutions the soliton interactions are discussed by virtue of the physical parameters amplitude velocity and direction of the interacting solitons

a new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization the main goal of this paper is to provide simple parameter identification process for most of hyperelastic constitutive laws in biomechanics of soft tissues the advantage of our approach lies on its rapidity and effectiveness by reducing analytically the number of parameters to identify in the model during the identification procedure with the use of genetic algorithms the search for an adequate initial guess point is avoided and the space solution of the objective function is reduced to meet only parameters that cannot be calculated analytically as an example we focus on models that predict arterial wall behaviour such as laws based on fung s type energy function holzapfel 2006 14 and holzapfel et al 2000 model 15 our approach is applied on uniaxial extension tests and the results are compared with available data in the literature

vendor selection by integrated fuzzy mcdm techniques with independent and interdependent relationships vendor selection is an evaluation process that is based on many criteria that uses inaccurate or uncertain data but while the criteria are often numerous and the relationships between higher level criteria and lower level sub criteria are complex most conventional decision models cannot help us clarify the interrelationships among the sub criteria our proposed integrated fuzzy multiple criteria decision making mcdm method addresses this issue within the context of the vendor selection problem first we use triangular fuzzy numbers to express the subjective preferences of evaluators second we use interpretive structural modeling ism to map out the relationships among the sub criteria third we use the fuzzy analytical hierarchy process ahp method to compute the relative weights for each criterion and we use non additive fuzzy integral to obtain the fuzzy synthetic performance of each common criterion fourth the best vendor is determined according to the overall aggregating score of each vendor using the fuzzy weights with fuzzy synthetic utilities fifth we use an empirical example to show that our proposed method is preferred to the traditional method especially when the sub criteria are interdependent finally our results provide valuable suggestions to vendors on how to improve each sub criterion so that they can bridge the gap between actual and aspired performance values in the future

a discretization of the matrix nonlinear schrodinger equation in this paper we shall show that a class of solutions to the discrete coupled matrix nonlinear schrodinger equation dcmnlse is gauge equivalent to the discrete equation of the schrodinger flow of maps into the grassmannian and the realizing gauge transformation is only the discretization of a classical gauge transformation between the matrix nonlinear schrodinger equation mnlse and the schrodinger flow of maps into the grassmannian in other words from the viewpoint of gauge equivalence a class of solutions of the dcmnlse is a correct discretization of the mnlse

prolongation structure of the 2 1 dimensional integrable heisenberg ferromagnet model we investigate the integrable 2 1 dimensional modified heisenberg ferromagnet hf model using the prolongation structure theory for the integrable 2 1 dimensional modified hf models the corresponding geometrical equivalent counterparts such as the 2 1 dimensional nonlinear schrodinger equation and the coupled 2 1 dimensional integrable equations are also presented through the motion of minkowski space curves endowed with an additional spatial variable

a tool for aggregation with words the need of computing with words has become an important topic in many areas dealing with vague information the aim of this paper is to present different tools which support computing with words especially we are concerned with the weighted aggregation of linguistic term sets whose results are just the words themselves without using the fuzzy numbers that represent the semantics of their linguistic terms we propose a new aggregation operator referred to as the symbolic weighted median that computes the most representative element from an ordered collection of weighted linguistic terms this operator aggregates the linguistic labels such that its result is expressed in terms of the initial linguistic term set though is modified by using dedicated tools called the generalized symbolic modifiers one advantage of this proposal is that the expression domain does not change we increase or decrease the granularity only where it becomes necessary additionally this new operator exhibits several interesting mathematical properties

mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force the purpose of this study was to determine how diverse momentum conditions and anatomical orientation at contact influences mechanical loading and multijoint control of the reaction force during landings male collegiate gymnasts n 6 performed competition style landings n 3 of drop jumps front saltos and back saltos from a platform 0 72 m onto landing mats 0 12 m kinematics 200 fps reaction forces 800 hz and muscle activation patterns surface emg 1600 hz of seven lower extremity muscles were collected simultaneously between task differences in segment orientation relative to the reaction force contributed to significant between task differences in knee and hip net joint moments njm during the impact phase during the stabilization phase ankle knee and hip njms acted to control joint flexion between task differences in muscle activation patterns indicated that gymnasts scaled biarticular muscle activation to accommodate for between task differences in njm after contact activation of muscles on both sides of the joint suggests that impedance like control was used to stabilize the joints and satisfy the mechanical demand imposed on the lower extremity between subject differences in the set of muscles used to control total body center of mass tbcm trajectory and achieve lower extremity njms suggests that control of multijoint movements involving impact needs to incorporate mechanical objectives at both the total body and local level the functional consequences of such a control structure may prove to be an asset to gymnasts particularly when required to perform a variety of landing tasks under a variety of environmental constraints

bicomplex formulation and moyal deformation of 2 1 dimensional fordy kulish systems using bicomplex formalism we construct generalizations of fordy kulish systems of matrix nonlinear schrodinger equations on two dimensional space time in two respects firstly we obtain corresponding equations in three space time dimensions secondly a moyal deformation is applied to the space time coordinates and the ordinary product of functions replaced by the moyal product in a suitable way both generalizations preserve the existence of an infinite set of conservation laws

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations

exterior differential expression of the 1 1 dimensional nonlinear evolution equation with lax integrability abstract a 1 1 dimensional nonlinear evolution equation with lax integrability is investigated in this paper with the aid of differential forms and exterior differentials equivalent definition of the lax integrability is given relation between the lax integrability and complete integrability is discussed geometric interpretation of the lax equation is presented gauge transformation and darboux transformation are restated in terms of the differential forms and exterior differentials if i s is a darboux transformation between two lax equations the system that the matrix s should satisfy is given where is the spectral parameter and i is the identity matrix the completely integrable condition of that system is obtained according to the frobenius theorem and it is shown that s h h 1 satisfies that completely integrable condition with h and as two matrices