a system of matrix equations and a linear matrix equation over arbitrary regular rings with identity abstract in this paper we consider the classical system of matrix equations a 1 xb 1 c 1 a 2 xb 2 c 2 over r an arbitrary regular ring with identity necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived as an application the linear matrix equation axb cyd e over r is considered

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion householder transformations we present a practical and efficient means to compute the singular value decomposition svd of a real or complex quaternion matrix a based on bidiagonalization of a to a real or complex bidiagonal matrix b using quaternionic householder transformations computation of the svd of b using an existing subroutine library such as lapack provides the singular values of a the singular vectors of a are obtained trivially from the product of the householder transformations and the real or complex singular vectors of b we show in the paper that left and right quaternionic householder transformations are different because of the non commutative multiplication of quaternions and we present formulae for computing the householder vector and matrix in each case

parametrically controlling solitary wave dynamics in the modified korteweg de vries equation we demonstrate the control of solitary wave dynamics of the modified korteweg de vries mkdv equation through the temporal variations of the distributed coefficients this is explicated through exact cnoidal wave and localized soliton solutions of the mkdv equation with variable coefficients the solitons can be accelerated and their propagation can be manipulated by suitable variations of the above parameters in sharp contrast with the nonlinear schrodinger equation the soliton amplitude and widths are time independent

an extended macro traffic flow model accounting for the driver s bounded rationality and numerical tests abstract in this paper we propose a macro traffic flow model to explore the effects of the driver s bounded rationality on the evolutions of traffic waves which include shock and rarefaction waves and small perturbation and on the fuel consumption and emissions that include co hc and no x during the evolution process the numerical results illustrate that considering the driver s bounded rationality can prominently smooth the wavefront of the traffic waves and improve the stability of traffic flow which shows that the driver s bounded rationality has positive impacts on traffic flow but considering the driver s bounded rationality reduces the fuel consumption and emissions only at the upstream of the rarefaction wave while enhances the fuel consumption and emissions under other situations which shows that the driver s bounded rationality has positive impacts on the fuel consumption and emissions only at the upstream of the rarefaction wave while negative effects on the fuel consumption and emissions under other situations in addition the numerical results show that the driver s bounded rationality has little prominent impact on the total fuel consumption and emissions during the whole evolution of small perturbation

bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations in this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra necessary and sufficient conditions are obtained for the matrix equation ax c and the following systemsa 1x c 1 a 1x c 1 xb 3 c 3 a 2x c 2 to have bisymmetric solutions and the systema 1x c 1 a 3xb 3 c 3 to have centrosymmetric solutions the expressions of such solutions of the matrix and the systems mentioned above are also given moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over are also mentioned

the stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow abstract a modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice the stability condition of the modified model is obtained through the linear stability analysis the results show that considering the density difference leads to the stabilization of the system the burgers equation and mkdv equation are derived to describe the density waves in the stable and unstable regions respectively numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic

remarks on the schur complement abstract first a generalization of the schur determinantal formula is given using properties of quasidirect sums of matrices a new characterization of the schur complement is proved

a pair of simultaneous linear matrix equations a1xb1 c1 a2xb2 c2 and a matrix programming problem necessary and sufficient conditions are obtained for a pair of matrix equations a1xb1 c1 a2xb2 c2 on a general field f to have a common solution along with the expression for a general common solution when certain conditions hold common solutions of minimum rank are described a matrix programming problem is solved en route

nonlinear analysis for an improved car following model account for the optimal velocity changes with memory abstract in this paper an extended car following model is developed basing on the full velocity difference model fvdm to investigate the effect of the optimal velocity changes with memory on traffic flow the stability conditions of the improved model are obtained through linear stability analysis then the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived by using nonlinear analysis the kink antikink soliton can describe the traffic jams near the critical point moreover the evolution of traffic jam and corresponding the change of energy consumption are discussed numerical simulations show that the extended model is found not only to enhance the stability of traffic flow but also to depress the energy consumption the numerical results are in good agreement with the theoretical analysis

a system of matrix equations with five variables in this paper we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations a 1 x c 1 y b 1 d 1 a 2 w c 2 z b 2 d 2 a 3 v c 3 v b 3 c 4 a 4 v b 4 c 5 a 5 x y b 5 c 6 w z d 6 e 6 v f 6 g 6 and constitute an expression of the general solution to the system when it is solvable the outcomes of this paper encompass some recognized results in the collected works in addition we establish an algorithm and a numerical example to illustrate the theory constructed in the paper

the general solution to a system of real quaternion matrix equations in this paper we consider the system of matrix equations a 1x c 1 a 2x c 2 a 3xb 3 c 3 and a 4xb 4 c 4 over the real quaternion algebra a necessary and sufficient condition for the existence and the expression of the general solution to the system are given as particular cases the corresponding results on other systems over are also obtained

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

what are schur complements anyway abstract given a matrix m a b c d the schur complements of a in m are the matrices of the form s d cab where a is a generalized inverse of a we survey several recent characterizations of schur complements and discuss where they arose and how they are related

more on maximal and minimal ranks of schur complements with applications the maximal and minimal ranks of the schur complement d cgb are determined with respect to generalized inverse g of a matrix a where g is taken respectively as least squares g inverse a 1 3 minimum norm g inverse a 1 4 as well as a 1 2 3 a 1 2 4 and a 1 3 4 various consequences are also presented

jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing abstract a new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically from linear and non linear stability analysis the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink antikink soliton solution of mkdv equation is derived the stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non interruption effect of passing it is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non interruption effect of passing numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed

metastable states in a microscopic model of traffic flow it is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow which the simple cellular automaton model of traffic flow and its continuous generalization fail to reproduce it is shown that the model can be generalized to give a one parametric family of models a part of which reproduces the metastable states and the hysteresis the models that have that property and those that do not that are separated by a transition that can be clearly identified

a novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two lane highway abstract the optimal estimation of flux difference effect is introduced to construct a new lattice hydrodynamic model for two lane highway through linear stability analysis it is found that the new consideration plays an important influence upon the stability of two lane traffic flow moreover the mkdv equation near the critical point is derived from nonlinear analysis which describes the propagation behavior of traffic jam in two lane traffic system simulation results show that the stability of two lane traffic system can be increased and the emergence of traffic jams are effectively relieved by the optimal estimation of flux difference effect which is in good agreement with theoretical analysis

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two lane highway abstract influence of the honk on traffic flux is taken to construct a new lattice model for two lane freeway the linear stability analysis is applied to obtain the stability condition involving the honk effect on traffic flux in two lane system nonlinear analysis is implemented to get the mkdv equation for the phase transition of two lane lattice traffic flow numerical simulation is worked out to authenticate that the impact of honk on traffic flux strengthens the stability of traffic flow and suppresses the traffic congestion effectively under lane changing in two lane lattice traffic flow which is accordance with the analytic results

the car following model considering traffic jerk abstract based on optimal velocity car following model a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway traffic jerk means the sudden braking and acceleration of vehicles which has a significant impact on traffic movement the nature of the model is researched by using linear and nonlinear analysis method a thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived to describe the traffic flow near the critical point and the traffic jam in addition the connection between the tdgl and the mkdv equations are also given

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

energy consumption investigation for a new car following model considering driver s memory and average speed of the vehicles in this paper a modified car following model is proposed by taking into account the influence of the average speed effect of the vehicles and driver s memory on traffic flow basing on the two velocity difference model tvdm the stability conditions are obtained through the linear stability analysis the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived in the unstable area by means of nonlinear analysis respectively the tdgland mkdv equations are constructed to describe the traffic behavior near the critical point the evolution of traffic congestion and the corresponding energy consumption are discussed numerical simulations are in good agreement with the theoretical results it is found that the extended model can not only to depress the energy consumption but also to enhance the stability of traffic flow

a system of real quaternion matrix equations with applications abstract let h be the real quaternion algebra and h n m denote the set of all n m matrices over h let p h n n and q h m m be involutions i e p 2 i q 2 i a matrix a h n m is said to be p q symmetric if a paq this paper studies the system of linear real quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 a 2 x 2 c 3 x 2 b 2 c 4 a 3 x 1 b 3 a 4 x 2 b 4 c c we present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied as applications we discuss the necessary and sufficient conditions for the system a a x c a xb b c b a c xb c c c to have a p q symmetric solution we also show an expression of the p q symmetric solution to the system when the solvability conditions are met moreover we provide an algorithm and a numerical example to illustrate our results the findings of this paper extend some known results in the literature

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

a new lattice model accounting for multiple optimal current differences anticipation effect in two lane system abstract this paper extends a two lane lattice hydrodynamic traffic flow model to take into account the driver s anticipation effect in sensing the multiple optimal current differences based on the proposed model we derive analytically the effect of driver s anticipation of multiple optimal current differences on the instability of traffic dynamics the phase diagrams have been plotted and discussed that the stability region enhances with anticipation effect in sensing multiple optimal current differences through simulation it is found that the oscillation of density wave around critical density decreases with an increase in lattice number and anticipation time for transient and steady state the simulation results are in good agreement with the theoretical analysis which show that considering the driver s anticipation of multiple optimal current differences in two lane lattice model stabilizes the traffic flow and suppresses the traffic jam efficiently

extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application abstract in this paper we establish the maximal and minimal ranks of the solution to the consistent system of quaternion matrix equations a 1 x c 1 a 2 x c 2 a 3 xb 3 c 3 and a 4 xb 4 c 4 which was investigated recently by wang q w wang the general solution to a system of real quaternion matrix equations comput math appl 49 2005 665 675 moreover corresponding results on some special cases are presented as an application a necessary and sufficient condition for the invariance of the rank of the general solution to the system mentioned above is presented some previous known results can be regarded as the special cases of this paper

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications abstract in this paper we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression c 4 a 4 xb 4 where x is a variant quaternion matrix subject to quaternion matrix equations a 1 x c 1 xb 2 c 2 a 3 xb 3 c 3 as applications we give a new necessary and sufficient condition for the existence of solutions to the system of matrix equations a 1 x c 1 xb 2 c 2 a 3 xb 3 c 3 a 4 xb 4 c 4 which was investigated by wang q w wang a system of four matrix equations over von neumann regular rings and its applications acta math sin 21 2 2005 323 334 by rank equalities in addition extremal ranks of the generalized schur complement d ca b with respect to an inner inverse a of a which is a common solution to quaternion matrix equations a 1 x c 1 xb 2 c 2 are also considered some previous known results can be viewed as special cases of the results of this paper

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

fast multimodel finite difference controlled source electromagnetic simulations based on a schur complement approach we have developed an efficient numerical scheme for fast multimodel 3d electromagnetic simulations by applying a schur complement approach to a frequency domain finite difference method the scheme is based on direct solvers and developed with constrained inversion algorithms in view such algorithms normally need many forward modeling jobs with different resistivities for the target zone and or background formation we geometricallydivide the computational domain intotwo subdomains an anomalous subdomain the resistivities of which were permitted to change and a background subdomain having fixed resistivities the system matrix ispartiallyfactorizedby precomputing a schur complement to eliminate unknowns associated with the background subdomain the schur complement system is then solved to compute fields inside the anomalous subdomain finally the background subdomain fields are computed using inexpensive local substitutions for each successive simulation only the relatively small schur complement system has to be solved which results in significant computational savings we applied this approach to two moderately sized 3d problems in marine controlled source electromagnetic modeling 1 a deepwater model in which the resistivities of the seawater and the air layer were kept fixed and 2 a model in which focused inversion was performed in a scenario in which the resistivities of the background formation the air layer and the seawater were known we found a significant reduction of the modeling time in inversion that depended on the relative sizes of the constrained and unconstrained volumes the smaller the unconstrained volume the larger the savings specifically for a focused inversion of the troll oil field in the north sea the gain amounted up to 80 of the total modeling time

extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications abstract assume that the linear quaternion matrix expression f x 1 x 2 a a 3 x 1 b 3 a 4 x 2 b 4 where x 1 x 2 are variant quaternion matrices in this paper we derive the maximal and minimal ranks of f x 1 x 2 subject to consistent systems of quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 and a 2 x 2 c 3 x 2 b 2 c 4 moreover corresponding results on some special cases are presented as applications we give necessary and sufficient conditions for the existence of solutions to some systems of quaternion matrix equations some previous known results can be regarded as the special cases of this paper

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

ranks and the least norm of the general solution to a system of quaternion matrix equations we in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations a1x1 c1 a2x2 c2 a3x1b1 a4x2b2 c3 which was investigated recently q w wang h x chang c y lin p skew symmetric common solutions to a pair of quaternion matrix equations appl math comput 195 2008 721 732 then derive the maximal and minimal ranks and the least norm of the general solution to the system mentioned above some previous known results can be viewed as special cases of the results of this paper

p skew symmetric common solutions to a pair of quaternion matrix equations abstract an n n quaternion matrix a is termed p symmetric or p skewsymmetric if a pap or a pap where p is an n n nontrivial quaternion involution in this paper we first establish necessary and sufficient conditions for the existence and the expression of the general solution to the system of quaternion matrix equations a 1 x 1 c 1 a 2 x 2 c 2 a 3 x 1 b 1 a 4 x 2 b 2 c b then use the results on the system mentioned above to give necessary and sufficient conditions for the existence and the representations of p symmetric and p skewsymmetric solutions to the system of quaternion matrix equations a a x c a and a b xb b c b furthermore we establish representations of p symmetric and p skewsymmetric quaternion matrices a numerical example is presented to illustrate the results of this paper

jamming transition of high dimensional traffic dynamics phase transition and critical phenomenon are investigated in high dimensional traffic flow numerically and analytically the two dimensional lattice traffic model is extended to the three and d dimensional traffic flows it is shown that the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point in the two three and four dimensional traffic simulations the phase separation line and the critical point of the d dimensional traffic are consistent with those of the one dimensional traffic the time dependent ginzburg landau tdgl equation for the d dimensional traffic is derived by the use of the nonlinear analysis the phase separation line the spinodal line and the critical point are calculated from the tdgl equation it is found that the phase transition and critical phenomenon are independent of the space dimension

influence of the traffic interruption probability on traffic stability in lattice model for two lane freeway abstract in this paper a new lattice model is proposed with the traffic interruption probability term in two lane traffic system the linear stability condition and the mkdv equation are derived from linear stability analysis and nonlinear analysis by introducing the traffic interruption probability of optimal current for two lane traffic freeway respectively numerical simulation shows that the traffic interruption probability corresponding to high reaction coefficient can efficiently improve the stability of two lane traffic flow as traffic interruption occurs with lane changing

right eigenvalues for quaternionic matrices a topological approach abstract we apply the lefschetz fixed point theorem to show that every square matrix over the quaternions has right eigenvalues we classify them and discuss some of their properties such as an analogue of jordan canonical form and diagonalization of elements of the compact symplectic group sp n

rank equalities related to the generalized inverse at s 2 with applications abstract a variety of rank formulas of some matrix expressions and certain partitioned matrices with respect to the generalized inverse a t s 2 are established some necessary and sufficient conditions are given by using the rank formulas presented in this paper for two three and four ordered matrices to be independent in the generalized inverse a t s 2 as special cases necessary and sufficient conditions are derived for two three and four ordered matrices to be independent in the weighted moore penrose inverse and the drazin inverse some known results can be regarded as the special cases of the results in this paper

right eigenvalue equation in quaternionic quantum mechanics we study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n dimensional quaternionic vector spaces for quaternionic linear operators the eigenvalue spectrum consists of n complex values for these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations our discussion is also extended to complex linear operators whose spectrum is characterized by 2n complex eigenvalues we show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products finally we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution

hypercomplex correlation techniques for vector images correlation techniques have been applied to almost every area of signal processing over the past century yet their use has in general been limited to scalar signals while there have been implementations in multichannel applications these can be characterized as a combination of single channel processes true vector correlation techniques with global and interchannel measures have only recently been demonstrated and are still in their infancy by comparison this paper describes our work on vector correlation based on the use of hypercomplex fourier transforms and presents for the first time a unified theory behind the information contained in the peak of a vector correlation response by using example applications for color images we also demonstrate some of the practical implications together with our latest results

jamming transition in traffic flow on triangular lattice abstract phase transitions and critical phenomena are investigated in the two dimensional traffic flow on the triangular lattice numerically and analytically the two dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a site it is shown that the jamming transition between the freely moving and jammed phases depends on the configuration of car moving directions it is found that the three distinct jamming transitions occur the conventional jamming transition to the kink jams the jamming transition to the chaotic jams and the jamming transition to the oscillating jams the conventional jamming transition to the kink jams is analyzed by the use of the linear stability theory and the nonlinear method the coexisting curve between the freely moving and jammed phases is calculated from the solution of the modified korteweg de vries kdv equation

a new lattice model of traffic flow with the consideration of the traffic interruption probability abstract in this paper we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways the stability condition of the new model is obtained by the linear stability analysis and the modified korteweg de vries kdv equation is derived through nonlinear analysis thus the space will be divided into three regions stable metastable and unstable the simulation results also show that the traffic interruption probability could stabilize traffic flow

explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations abstract within the framework of the theory of the column and row determinants we obtain explicit representation formulas analogs of cramer s rule for the minimum norm least squares solutions of quaternion matrix equations ax b xa b and axb d

quaternions and matrices of quaternions abstract we give a brief survey on quaternions and matrices of quaternions present new proofs for certain known results and discuss the quaternionic analogues of complex matrices the methods of converting a quaternion matrix to a pair of complex matrices and homotopy theory are emphasized

the effect of headway variation tendency on traffic flow modeling and stabilization abstract advanced communications technology enables us to obtain the headway variation tendency hvt of the next moment in a car following scenario to maximize the benefits of the new technology we developed a new traffic flow model that takes into consideration the effect of hvt first linear analysis method is used to derive the linear stability condition that determines whether the hvt can improve traffic system stability then using the reductive perturbation method a modified kdv mkdv equation is obtained and the kink antikink solutions are derived the phase diagram of driver sensitivity against equilibrium headway is also plotted by using the neutral stability line derived from linear analysis and the coexisting line derived from nonlinear analysis this diagram demonstrates that hvt does have the ability to improve the stability of traffic stream finally the effect of hvt is validated through numerical simulations where it is evident that the information of hvt can smooth the traffic stream and prevent the formation of traffic congestion

the common solution to six quaternion matrix equations with applications abstract we in this paper establish necessary and sufficient conditions for the existence of and an explicit expression for a common solution to six classical linear quaternion matrix equations a 1 x c 1 xb 1 c 2 a 2 x c 3 xb 2 c 4 a 3 xb 3 c 5 and a 4 xb 4 c 6 as applications symmetric persymmetric and centrosymmetric solutions to certain systems of quaternion matrix equations are presented furthermore we give an example to illustrate the result of this paper some known results can be regarded as the special cases of this paper

solutions to optimization problems on ranks and inertias of a matrix function with applications abstract consider the hermitian matrix function f x a 3 b 3 x b 3 x subject to a consistent system of matrix equations 0 1 a 1 x c 1 a 2 xb 2 c 2 where means conjugate transpose in this paper we first establish explicit expansion formulas to calculate the global maximal and minimal ranks and inertias of the hermitian matrix function f x then we use the derived formulas to give necessary and sufficient conditions for system 0 1 to have re nonnegative definite re nonpositive definite re positive definite and re negative definite solutions moreover as another application of the derived formulas we establish necessary and sufficient conditions for the solvability to the system of matrix equations 0 2 a 1 x c 1 a 2 xb 2 c 2 b 3 x b 3 x a 3 and provide an expression of the general solution to 0 2 when it is solvable the findings of this paper widely extend the known results in the literature

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

time dependent ginzburg landau equation in a car following model considering the driver s physical delay abstract in this paper an extended car following model considering the delay of the driver s response in sensing headway is proposed to describe the traffic jam it is shown that the stability region decreases when the driver s physical delay in sensing headway increases the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point by applying the reductive perturbation method we get the time dependent ginzburg landau tdgl equation from the car following model to describe the transition and critical phenomenon in traffic flow we show the connection between the tdgl equation and the mkdv equation describing the traffic jam

an extended continuum model considering optimal velocity change with memory and numerical tests in this paper an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory the new model s stability condition and kdv burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis respectively numerical simulation is carried out to study the extended continuum model which explores how optimal velocity changes with memory affected velocity density and energy consumption numerical results show that when considering the effects of optimal velocity changes with memory the traffic jams can be suppressed efficiently both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently furthermore numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information which increases the stability of traffic flow on road and so it improve the traffic flow stability and minimize cars energy consumptions

on solutions of the quaternion matrix equation ax b and their applications in color image restoration by using the complex representation of quaternion matrices and the moore penrose generalized inverse we derive the expressions of the least squares solution with the least norm the least squares pure imaginary solution with the least norm and the least squares real solution with the least norm for the quaternion matrix equation ax b respectively finally we discuss their applications in color image restoration

the matrix equations ax c xb d for the pair of matrix equations ax c xb d this paper gives common solutions of minimum possible rank and also other feasible specified ranks

upper and lower bounds for ranks of matrix expressions using generalized inverses abstract the maximal and minimal ranks of the matrix expression a 1 b 1 x 1 c 1 b 2 x 2 c 2 with respect to x 1 and x 2 are presented as applications the maximal and minimal ranks of a 1 b 1 xc 1 subject to a consistent matrix equation b 2 xc 2 a 2 are also determined in addition the maximal and minimal ranks of the schur complement d ca b with respect to the generalized inverse a of a and their various consequences are also considered

a lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference abstract in this paper a lattice hydrodynamic model is derived considering not only the effect of flow rate difference but also the delayed feedback control signal which including more comprehensive information the control method is used to analyze the stability of the model furthermore the critical condition for the linear steady traffic flow is deduced and the numerical simulation is carried out to investigate the advantage of the proposed model with and without the effect of flow rate difference and the control signal the results are consistent with the theoretical analysis correspondingly

littlewood s algorithm and quaternion matrices abstract a strengthened form of schur s triangularization theorem is given for quaternion matrices with real spectrum for complex matrices it was given by littlewood it is used to classify projectors a 2 a and self annihilating operators a 2 0 on a quaternion unitary space and examples of unitarily wild systems of operators on such a space are presented littlewood s algorithm for reducing a complex matrix to a canonical form under unitary similarity is extended to quaternion matrices whose eigenvalues have geometric multiplicity 1

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

delay effect on phase transitions in traffic dynamics a dynamical model of traffic is proposed to take into account the effect of acceleration delay in the limit of no delay the model reproduces the optimal velocity model of traffic when the delay is small it is shown that the phase transition among the freely moving phase the coexisting phase and the uniform congested phase occurs below the critical point above the critical point no phase transition occurs the value a c of the critical point increases with increasing delay time 1 b where a is the friction coefficient or sensitivity parameter when the delay time is longer than frac 1 2 the critical point disappears and the phase transition always occurs the linear stability theory and nonlinear analysis are applied the critical point predicted by the linear stability theory agrees with the simulation result the modified korteweg de vries kdv equation is obtained from the nonlinear analysis near the critical point the phase separation line obtained from the modified kdv equation is consistent with the simulation result

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

exact solutions to mkdv equation with variable coefficients abstract in this paper a special mkdv with variable coefficients is considered a transformation of variables is first applied in order to obtain a mkdv equation with constant coefficients some its one two and three soliton as well as breather type soliton solutions are derived by using hirorta s bilinear approach