convexity of quasi entropy type functions lieb s and ando s convexity theorems revisited given a positive function f on 0 and a non zero real parameter we consider a function if a b x tr x f larb 1 rb x in three matrices a b 0 and x this generalizes the notion of monotone metrics on positive definite matrices and in the literature 1 has been typical we investigate how operator monotony of f is sufficient and or necessary for joint convexity concavity of if a b x similar discussions are given for quasi entropies and quantum skew informations

on complex lamellar motion of a prim gas an intrinsic formulation of prim s canonical equations of gas dynamics is employed to establish a generalization of crocco s theorem to complex lamellar motion this new result is then employed to establish the existence of a heisenberg spin type equation in such motion the optimal coordinate systems in the generalized lagrangian method which are known to exist only in complex lamellar motion are then shown by intrinsic geometric methods to correspond to a marching direction along geodesics on generalized bernoulli surfaces

fisher information in quantum statistics braunstein and caves braunstein s l and caves c m 1994 phys rev lett 72 3439 43 proposed to use helstrom s quantum information number to define meaningfully a metric on the set of all possible states of a given quantum system they showed that the quantum information is nothing other than the maximal fisher information in a measurement of the quantum system maximized over all possible measurements combining this fact with classical statistical results they argued that the quantum information determines the asymptotically optimal rate at which neighbouring states on some smooth curve can be distinguished based on arbitrary measurements on n identical copies of the given quantum system we show that the measurement which maximizes the fisher information typically depends on the true unknown state of the quantum system we close the resulting loophole in the argument by showing that one can still achieve the same optimal rate of distinguishability by a two stage adaptive measurement procedure when we consider states lying not on a smooth curve but on a manifold of higher dimension the situation becomes much more complex we show that the notion of distinguishability of close by states depends strongly on the measurement resources one allows oneself and on a further specification of the task at hand the quantum information matrix no longer seems to play a central role

geometry of canonical correlation on the state space of a quantum system a riemannian metric is defined on the state space of a finite quantum system by the canonical correlation or kubo mori bogoliubov scalar product this metric is infinitesimally induced by the nonsymmetric relative entropy functional or the von neumann entropy of density matrices hence its geometry expresses maximal uncertainty it is proven that the metric is monotone under stochastic mappings however an example shows that it is not the only such riemannian metric this fact is remarkable because in the probabilistic case the markovian monotonicity property characterizes the fisher information metric the essential difference appears in the curvatures of a classical state space and a quantum one a conjecture is made that the scalar curvature is monotone with respect to the more mixed statistical partial order of density matrices furthermore an information inequality resembling the cramer rao inequality of classical statistics is established the inequality provides a lower bound for the c

on a new defect of shock capturing methods this paper proposes an explanation and a cure or avoidance to the new defect found of eulerian shock capturing methods in a note on the conservative schemes for the euler equations by tang and liu h tang tiegang liu a note on the conservative schemes for the euler equations j comput phys 218 2006 451 459 the latter gives a numerical investigation using several popular high resolution conservative schemes applied to riemann problems of inviscid compressible perfect gas flows in eulerian and lagrangian coordinates with an initial high density ratio as well as a high pressure ratio the results show that these methods work very inefficiently when applied to such problems and may give inaccurate numerical results especially in shock location or speed even with a very fine grid we have found that in problems of this type a strong rarefaction wave srw is present adjacent to a contact line godunov averaging over the wave then produces large errors which when the wave is strong also persist for a long time the cumulative error is thus very large which violates the strength of the contact line adjacent to it which in turn affects the speed and hence the location of the shock on the other side of the contact we confirm this numerically using a method based on the unified coordinates with the shock adaptive godunov scheme plus contact strength preserving the method when applied to the examples 2 1 and 2 2 of tang and liu h tang tiegang liu a note on the conservative schemes for the euler equations j comput phys 218 2006 451 459 produces high quality results even for comparatively coarse grids

monotone riemannian metrics on density matrices with non monotone scalar curvature the theory of monotone riemannian metrics on the state space of a quantum system was established by denes petz in 1996 in a recent paper he argued that the scalar curvature of a statistically relevant monotone metric can be interpreted as an average statistical uncertainty the present paper contributes to this subject it is reasonable to expect that states which are more mixed are less distinguishable than those which are less mixed the manifestation of this behavior could be that for such a metric the scalar curvature has a maximum at the maximally mixed state we show that not every monotone metric fulfils this expectation some of them behave in a very different way a mathematical condition is given for monotone riemannian metrics to have a local minimum at the maximally mixed state and examples are given for such metrics

a new lagrangian method for time dependent inviscid flow computation this paper presents a new lagrangian approach for the two dimensional 2 d time dependent euler equations it may be considered as a sequel to the authors previous lagrangian approaches for steady supersonic flow computations c y loh and w h hui j comput phys 89 1990 pp 207 240 w h hui and c y loh j comput phys 103 1992 pp 450 464 w h hui and c y loh j comput phys 103 1992 pp 465 471 c y loh and m s liou j comput phys 104 1993 pp 150 161 c y loh and m s liou siam j sci comput 15 1994 pp 1038 1058 c y loh and m s liou j comput phys 113 1994 pp 224 248 the theoretical background and the intrinsic flow coordinates as well as the lagrangian conservation form are introduced based on the concept of material functions or path functions a tvd scheme of the godunov type is chosen to describe the numerical procedure several examples are then given to justify the claimed advantages of the new methodology namely a any contact discontinuities are crisply solved and b grids are automatically and accurately generated following pathlines

quantum and fisher information from the husimi and related distributions the two principal immediate influences which we seek to interrelate here upon the undertaking of this study are papers of yczkowski and slomczynski j phys a 34 6689 2001 and of petz and sudar j math phys 37 2262 1996 in the former work a metric the monge one specifically over generalized husimi distributions was employed to define a distance between two arbitrary density matrices in the petz sudar work completing a program of chentsov the quantum analog of the classically unique fisher information monotone metric of a probability simplex was extended to define an uncountable infinitude of riemannian also monotone metrics on the set of positive definite density matrices we pose here the questions of what is the specific unique fisher information metric for the classically defined husimi distributions and how does it relate to the infinitude of quantum metrics over the density matrices of petz and sudar we find a highly proximate small relative entropy relationship bet

correlation immunity of nonlinear combining functions for cryptographic applications corresp pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers these running key generators eau sometimes be broken by ciphertext only correlation attacks on individual subsequences a new class of combining functions is presented which provides better security against such attacks the security is quantified by the smallest number m 1 of subsequences that must be simultaneously considered in a correlation attack a necessary condition for such m th order correlation immunity is proved a recursive construction is given that permits the construction of an m th order immune combining function for n subsequences for any m and n with 1 leq m finally the trade off between the length of the linear equivalent of the nonlinear generator and the order m of its immunity against correlation attacks is considered

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

constructing low weight d th order correlation immune boolean functions through the fourier hadamard transform the correlation immunity of boolean functions is a property related to cryptography to error correcting codes to orthogonal arrays in combinatorics and in a slightly looser way to sequences correlation immune boolean functions in short ci functions have the property of keeping the same output distribution when some input variables are fixed they have been widely used as combiners in stream ciphers to allow resistance to the siegenthaler correlation attack very recently a new use of ci functions has appeared in the framework of side channel attacks sca to reduce the cost overhead of counter measures to sca ci functions need to have low hamming weights this actually poses new challenges since the known constructions which are based on properties of the walsh hadamard transform do not allow to build unbalanced ci functions in this paper we propose constructions of low weight d th order ci functions based on the fourier hadamard transform while the known constructions of resilient functions are based on the walsh hadamard transform these two transforms are closely related but the resulting constructions are very different we first prove a simple but powerful result which makes that one only need to consider the case where d is odd in further research then we investigate how constructing low hamming weight ci functions through the fourier hadamard transform which behaves well with respect to the multiplication of boolean functions we use the characterization of ci functions by the fourier hadamard transform and introduce a related general construction of ci functions by multiplication by using the kronecker product of vectors we obtain more constructions of low weight d ci boolean functions furthermore we present a method to construct low weight d ci boolean functions by making additional restrictions on the supports built from the kronecker product

covariance subspace and intrinsic crame spl acute r rao bounds crame spl acute r rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists the frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail the set of subspaces called the grassmann manifold and the set of covariance positive definite hermitian matrices have no fixed coordinate system associated with them and do not possess a vector space structure both of which are required for deriving classical crame spl acute r rao bounds intrinsic versions of the crame spl acute r rao bound on manifolds utilizing an arbitrary affine connection with arbitrary geodesics are derived for both biased and unbiased estimators in the example of covariance matrix estimation closed form expressions for both the intrinsic and flat bounds are derived and compared with the root mean square error rmse of the sample covariance matrix scm estimator for varying sample support k the accuracy bound on unbiased covariance matrix estimators is shown to be about 10 log 10 n k sup 1 2 db where n is the matrix order remarkably it is shown that from an intrinsic perspective the scm is a biased and inefficient estimator and that the bias term reveals the dependency of estimation accuracy on sample support observed in theory and practice the rmse of the standard method of estimating subspaces using the singular value decomposition svd is compared with the intrinsic subspace crame spl acute r rao bound derived in closed form by varying both the signal to noise ratio snr of the unknown p dimensional subspace and the sample support in the simplest case the crame spl acute r rao bound on subspace estimation accuracy is shown to be about p n p sup 1 2 1 2 snr sup 1 2 rad for p dimensional subspaces it is seen that the svd based method yields accuracies very close to the crame spl acute r rao bound establishing that the principal invariant subspace of a random sample provides an excellent estimator of an unknown subspace the analysis approach developed is directly applicable to many other estimation problems on manifolds encountered in signal processing and elsewhere such as estimating rotation matrices in computer vision and estimating subspace basis vectors in blind source separation

node pair finite volume finite element schemes for the euler equation in cylindrical and spherical coordinates a numerical scheme is presented for the solution of the compressible euler equations in both cylindrical and spherical coordinates the unstructured grid solver is based on a mixed finite volume finite element approach equivalence conditions linking the node centered finite volume and the linear lagrangian finite element scheme over unstructured grids are reported and used to devise a common framework for solving the discrete euler equations in both the cylindrical and the spherical reference systems numerical simulations are presented for the explosion and implosion problems with spherical symmetry which are solved in both the axial radial cylindrical coordinates and the radial azimuthal spherical coordinates numerical results are found to be in good agreement with one dimensional simulations over a fine mesh

out of time order fluctuation dissipation theorem we prove a generalized fluctuation dissipation theorem for a certain class of out of time ordered correlators otocs with a modified statistical average which we call bipartite otocs for general quantum systems in thermal equilibrium the difference between the bipartite and physical otocs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the wigner yanase skew information within this difference the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear response function that involves a time reversed process we show that the theorem can be generalized to higher order n partite otocs as well as in the form of generalized covariance

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

wigner yanase information on quantum state space the geometric approach in the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity or contraction under coarse graining has been proposed by chentsov the metrics with this property have been classified by petz all the elements of this family of geometries can be seen as quantum analogs of fisher information although there exists a number of general theorems shedding light on this subject many natural questions also stemming from applications are still open in this paper we discuss a particular member of the family the wigner yanase information using a well known approach that mimics the classical pull back approach to fisher information we are able to give explicit formulas for the geodesic distance the geodesic path the sectional and scalar curvatures associated to wigner yanase information moreover we show that this is the only monotone metric for which such an approach is possible

on quantum statistical inference interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially in step with dramatic new developments in experimental techniques for studying small quantum systems furthermore developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory the present paper reviews this field and proposes and interrelates some new concepts for an extension of classical statistical inference to the quantum context

monotone riemannian metrics and relative entropy on noncommutative probability spaces we use the relative modular operator to define a generalized relative entropy for any convex operator function g on 0 satisfying g 1 0 we show that these convex operator functions can be partitioned into convex subsets each of which defines a unique symmetrized relative entropy a unique family parametrized by density matrices of continuous monotone riemannian metrics a unique geodesic distance on the space of density matrices and a unique monotone operator function satisfying certain symmetry and normalization conditions we describe these objects explicitly in several important special cases including g w log w which yields the familiar logarithmic relative entropy the relative entropies riemannian metrics and geodesic distances obtained by our procedure all contract under completely positive trace preserving maps we then define and study the maximal contraction associated with these quantities

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

a unified coordinate system for solving the three dimensional euler equations it is well known that the use of eulerian coordinates for shock capturing methods results in badly smeared slip lines and that lagrangian coordinates while capable of producing sharp slip line resolution may result in severe grid deformation causing inaccuracy and even breakdown of computation a unified coordinate system is introduced in which the flow variables are considered to be functions of time and of some permanent identification of pseudo particles which move with velocity hq q being the velocity of fluid particles it includes the eulerian coordinates as a special case when h 0 and the lagrangian when h 1 for two dimensional inviscid flow the free function h is chosen so as to preserve the grid angles this results in a coordinate system which avoids excessive numerical diffusion across slip lines in the eulerian coordinates and avoids severe grid deformation in the lagrangian coordinates yet it retains sharp resolution of slip lines especially for steady flow furthermore the two dimensional unsteady euler equations of gasdynamics in the unified coordinates are found to be hyperbolic for all values of h except when h 1 i e lagrangian in the latter case the euler equations are only weakly hyperbolic lacking one eigenvector although all eigenvalues are real the consequences of this deficiency of the lagrangian coordinates are pointed out in connection with numerical computation

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

on the curvature of the quantum state space with pull back metrics abstract the aim of the paper is to extend the notion of geometry in the classical and in the noncommutative case by introducing a more general class of pull back metrics and to give concrete formulas for the scalar curvature of these riemannian manifolds we introduce a more general class of pull back metrics of the noncommutative state spaces we pull back the euclidean riemannian metric of the space of self adjoint matrices with functions which have an analytic extension to a neighborhood of the interval 0 1 and whose derivative are nowhere zero we compute the scalar curvature in this setting and as a corollary we have the scalar curvature of the classical probability space when it is endowed with such a general pull back metric in the noncommutative setting we consider real and complex state spaces too we give a simplification of gibilisco isola conjecture for the first nontrivial classical probability space and we present the result of a numerical computation which indicate that the conjecture may be true for the space of real and complex qubits and for 3 3 density matrices too

stability of newton tvd runge kutta scheme for one dimensional euler equations with adaptive mesh abstract in this paper we propose a moving mesh method with a newton total variation diminishing tvd runge kutta scheme for the euler equations our scheme improves time discretization in the moving mesh algorithms by analyzing the semi discrete euler equations with the discrete moving mesh equations as constraints the stability of the newton tvd runge kutta scheme is proved thus we can conclude that the proposed algorithm can generate a weak solution to the euler equations finally numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme

quantum covariance quantum fisher information and the uncertainty relations in this paper the relation between quantum covariances and quantum fisher informations is studied this study is applied to generalize a recently proved uncertainty relation based on quantum fisher information the proof given here considerably simplifies the previously proposed proofs and leads to more general inequalities

a note on the unified coordinate system for computing shock waves in 1999 j comput phys 153 596 hui and his co workers proposed a unified coordinate system for computing compressible flows with discontinuous solutions in their coordinate system there is a free parameter h such that the traditional eulerian approach and lagrangian approach correspond to the particular cases h 0 and h 1 respectively hence this approach unifies the two classical methods for describing fluid flows in this note we consider a one dimensional problem and we show that there is a parameter range within 0

hp multilevel monte carlo methods for uncertainty quantification of compressible navier stokes equations we propose a novel hp multilevel monte carlo method for the quantification of uncertainties in the compressible navier stokes equations using the discontinuous galerkin method as deterministic

riemannian metrics on positive definite matrices related to means abstract the riemannian metric on the manifold of positive definite matrices is defined by a kernel function in the form k d h k i j i j 1 tr p i hp j k when i i p i is the spectral decomposition of the foot point d and the hermitian matrices h k are tangent vectors for such kernel metrics the tangent space has an orthogonal decomposition the pull back of a kernel metric under a mapping d g d is a kernel metric as well several riemannian geometries of the literature are particular cases for example the statistical metric for multivariate gaussian distributions and the quantum fisher information in the paper the case x y m x y is mostly studied when m x y is a mean of the positive numbers x and y there are results about the geodesic curves and geodesic distances the geometric mean the logarithmic mean and the root mean are important cases

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

local asymptotic normality in quantum statistics the theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to le cam roughly speaking local asymptotic normality means that the family varphi theta 0 u sqrt n n consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of gaussian state u of an algebra of canonical commutation relations the convergence holds for all local parameters u in mathbb r m such that theta theta 0 u sqrt n parametrizes a neighborhood of a fixed point theta 0 in theta subset mathbb r m

covariance and fisher information in quantum mechanics variance and fisher information are ingredients of the cramer rao inequality we regard fisher information as a riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and fisher information in this approach we show that there is a kind of dual one to one correspondence between the candidates of the two concepts we emphasize that fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold

a subcell resolution method for viscous systems of conservation laws a subcell resolution scheme for viscous systems of conservation laws is presented the scalar model is extended to systems via weakly nonlinear geometrical optics approximations for parabolic perturbations of hyperbolic conservation laws and the roe field by field decomposition

weak superadditivity of skew information we revisit the superadditivity conjecture for skew information which has recently been disproved by hansen 2007 j stat phys 126 643 we establish two weak forms of superadditivity which are conjectured to be optimal our results show that in a certain sense the superadditivity is true with 50 off

modelling the transition between fixed and mobile bed conditions in two phase free surface flows in a two phase free surface flow the transition from a mobile bed condition to a fixed bed one and vice versa occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly this leads to the possibility of conceiving a new type of riemann problem rp which we have called composite riemann problem crp where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity in this paper we present a strategy for solving a crp by reducing it to a standard rp of a single composite system of equations this can be obtained by combining the two original systems by means of a suitable weighting function namely the erodibility variable and the introduction of an appropriate differential equation for this quantity in this way the crp problem can be analyzed theoretically with standard methods and the features of the solutions can be clearly identified in particular a stationary contact wave is able to correctly describe the sharp transition between mobile and fixed bed conditions a finite volume scheme based on the multiple averages generalized roe approach rosatti and begnudelli 2013 22 was used to numerically solve the fixed mobile crp several test cases demonstrate the effectiveness exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model

numerical methods for tracking interfaces an overview is given of special numerical methods for tracking discontinuous fronts and interfaces these methods include surface tracking methods based on connected marker points along the interface volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces and moving mesh methods where the underlying mesh is aligned and moved with the interface the pros and cons of the current methods are discussed and a new method is proposed that overcomes some of the difficulties encountered in approximating equations with multiple interacting interfaces

a new lagrangian method for steady supersonic flow computation i godunov scheme abstract this paper studies the problem of steady two dimensional supersonic flow of an inviscid compressible fluid using the new lagrangian formulation of hui and van roessel in which the stream function and the lagrangian time are used as independent variables a shock capturing method is developed by applying the first order godunov scheme to the conservation form equations of this formulation the method is fast and robust furthermore extensive comparisons with exact solutions and with the second order godunov scheme of glaz and wardlaw based on the eulerian formulation show that the first order lagrangian method generally attains the same level of accuracy as the second order eulerian method and is even better in resolving slip line discontinuities

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

a new attack on the filter generator the filter generator is an important building block in many stream ciphers the generator consists of a linear feedback shift register of length n that generates an m sequence of period 2n 1 filtered through a boolean function of degree d that combines bits from the shift register and creates an output bit zt at any time t the previous best attacks aimed at reconstructing the initial state from an observed keystream have essentially reduced the problem to solving a nonlinear system of d sigmai 1 d n i equations in n unknowns using techniques based on linear algebra this attack needs about d bits of keystream and the system can be solved in complexity o domega where omega can be taken to be strassen s reduction exponent omega log2 7 ap2 807 this paper describes a new algorithm that recovers the initial state of most filter generators after observing o d keystream bits with complexity o d n 2 apo d after a pre computation with complexity o d log2d 3

hyperbolicity and optimal coordinates for the three dimensional supersonic euler equations the two dimensional 2 d steady euler equations for supersonic flow in cartesian coordinates x y is hyperbolic except on the singular line u a where a is the speed of sound and u is the x component of velocity however the cauchy problem for x x circ with initial data prescribed at x x circ is well posed only when u a for the 2 d case the optimal coordinates have been found w h hui and d l chu comput fluid dynamics 4 1996 pp 403 426 to be the orthogonal system consisting of streamlines and their orthogonal lines this gives the most robust and accurate computation for supersonic flow it is commonly thought e g c y loh and m s liou j comput phys 113 1994 pp 224 248 that the system of three dimensional 3 d steady euler equations for supersonic flow is hyperbolic the present paper shows that it is hyperbolic only when the velocity in the marching direction is supersonic in which case it also simultaneously guarantees the well posedness of the cau

some aspects of high speed blunt body flow computations with roe scheme this paper discusses some aspects of three dimensional supersonic and hypersonic inviscid blunt body flow computations the method used is based on the solution of the euler equations employing an explicit upwind total variation diminishing formulation of the roe riemann solver within the cell centered finite volume approach a comparative study of various total variation diminishing limiters and entropy fixes is carried out to identify the most appropriate combination the effect of using cell spacing in the total variation diminishing extrapolations is highlighted furthermore a mach number dependence and grid sensitivity study is carried out on various total variation diminishing limiters scaled with mesh spacing local time stepping and code parallelization has been employed to accelerate convergence in terms of effective wall clock times

a higher order godunov method for the hyperbolic equations modelling shock dynamics a numerical method of solution is developed for steady state hyperbolic equations in conservation form an upwind direction is identified and a smooth mapping is introduced to align the equations with that direction a flux f u in the upwind direction is regarded as the state variable and advanced numerically on a grid according to a second order extension of godunov method the solution u is determined from the computed flux and a constraint on the mapping is that the jacobian det f u is of one sign the method is applied to the equations modelling shock wave propagation according to whitham theory of geometrical shock dynamics in this context the solution vector u gives the components of the gradient of a function whose level curves determine the shock positions at successive times shock propagation in both uniform and non uniform gases is considered and several example calculations are presented a further application of the numerical method is inviscid supersonic flow as governed by the steady euler equations the steady supersonic flow in a converging diverging duct is computed to illustrate the numerical method for this latter application

geometries of quantum states the quantum analog of the fisher information metric of a probability simplex is searched and several riemannian metrics on the set of positive definite density matrices are studied some of them appeared in the literature in connection with cramer rao type inequalities or the generalization of the berry phase to mixed states they are shown to be stochastically monotone here all stochastically monotone riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them a class of metrics can be extended to pure states and a constant multiple of the fubini study metric appears in the extension

how to distinguish quantum covariances using uncertainty relations abstract to each operator monotone function it is possible to associate a quantum version of the classical covariance we show that i only for regular quantum covariances one can prove non trivial uncertainty relations ii the usual quantum covariance gives the best inequalities in this setting

second order efficiency of minimum contrast estimators in a curved exponential family this paper presents a sufficient condition for second order efficiency of an estimator the condition is easily checked in the case of minimum contrast estimators the a minimum contrast estimator is defined and proved to be second order efficient for every a 0 a 1 the fisher scoring method is also considered in the light of second order efficiency it is shown that a contrast function is associated with the second order tensor and the affine connection this fact leads us to prove the above assertions in the differential geometric framework due to amari

a unified coordinates approach to computational fluid dynamics a unified coordinate system is introduced for computational fluid dynamics in which the grid moves with velocity hq q being fluid velocity it includes the eulerian coordinates as a special case when h 0 and the lagrangian when h 1 by suitably choosing the free function h h 1 for 1d flow h chosen to preserve grid angles for 2d flow and to preserve grid skewness for 3d flow the unified coordinate system is shown in a large number of examples involving the euler equations to be superior to both eulerian and lagrangian ones in resolving flow discontinuities shocks and especially slip lines this approach is also successfully extended to shallow water waves and viscous flow

on skew information in this paper we show that skew information introduced by wigner and yanase which is a natural informational extension of variance for pure states can be interpreted as a measure of quantum uncertainty by virtue of skew information we establish a new uncertainty relation in the spirit of schrodinger which incorporates both incompatibility encoded in the commutator and correlations encoded in a new correlation measure related to skew information between observables and moreover is stronger than the conventional ones

completely positive mappings and mean matrices abstract some functions f r r induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices moreover such a function f can define a linear mapping j d f 1 m n m n on matrices which is basic in the constructions of monotone metrics the present subject is to check the complete positivity of j d f 1 in the case of a few concrete functions f this problem has been motivated by applications in quantum information

on the monotonicity of scalar curvature in classical and quantum information geometry we study the monotonicity under mixing of the scalar curvature for the geometries on the simplex of probability vectors from the results obtained and from numerical data we are led to some conjectures about quantum geometries and wigner yanase dyson information finally we show that this last conjecture implies the truth of the petz conjecture about the monotonicity of the scalar curvature of the bogoliubov kubo mori monotone metric