linear fuzzy graphs we introduce the concept of linear fuzzy graph and give its matrix and functional representations this allows a generalization of the notions of semiorder and pseudo order

traces of fuzzy binary relations abstract in this paper the right and left trace of a fuzzy binary relation is defined and investigated basic properties of a fuzzy relation such as reflexivity different kinds of transitivity linearity etc are characterized by means of its traces

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

compressible large eddy simulation of separation control on a wall mounted hump compressible large eddy simulations of turbulent flow over a wall mounted hump with active flow control are performed and compared with previous experiments the flow is characterized by the unsteady separation before the steep trailing edge which naturally reattaches downstream of the hump to form an unsteady turbulent separation bubble the low mach number large eddy simulation demonstrated a good prediction of surface pressure coefficient separation bubble length and velocity profiles compared with experiments the effect of compressibility on the baseline flow is documented and analyzed and is found to increase the separation bubble size due to a reduced growth rate control is applied just before the natural separation point via steady suction and zero net mass flux oscillatory forcing and steady suction is shown to be more effective in decreasing the size of the separation bubble and pressure drag for the control parameters investigated controlled flow at a compressible subsonic mach number is applied and found to be slightly less effective than the same control parameters at low mach numbers

stabilized non dissipative approximations of euler equations in generalized curvilinear coordinates we discuss stabilization strategies for finite difference approximations of the compressible euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables our approach rather relies on a skew symmetric like splitting of the convective derivatives that guarantees preservation of kinetic energy in the semi discrete low mach number limit a locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers the validity of the approach is tested for benchmark flow cases including the propagation of a cylindrical vortex and the head on collision of two vortex dipoles the tests support high accuracy and superior stability over conventional central discretization of the convective derivatives the potential use for dns les of turbulent compressible flows in complex geometries is discussed

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

on the average number of octahedral newforms of prime level we show that on average the number of octahedral newforms of prime level is bounded by a constant

error estimates for the davenport heilbronn theorems we obtain the first known power saving remainder terms for the theorems of davenport and heilbronn on the density of discriminants of cubic fields and the mean number of 3 torsion elements in the class groups of quadratic fields in addition we prove analogous error terms for the density of discriminants of quartic fields and the mean number of 2 torsion elements in the class groups of cubic fields these results prove analytic continuation of the related dirichlet series to the left of the line r s 1

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

on the use of higher order finite difference schemes on curvilinear and deforming meshes this study enables the use of very high order finite difference schemes for the solution of conservation laws on stretched curvilinear and deforming meshes to illustrate these procedures we focus on up to 6th order pade type spatial discretizations coupled with up to 10th order low pass filters these are combined with explicit and implicit time integration methods to examine wave propagation and wall bounded flows described by the navier stokes equations it is shown that without the incorporation of the filter application of the high order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability inclusion of the discriminating low pass high order filter restores the advantages of high order approach even in the presence of large grid discontinuities when three dimensional curvilinear meshes are employed the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated to overcome this problem a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes for dynamically deforming grids an effective numerical treatment is described to evaluate expressions containing the time varying transformation metrics with these techniques metric cancellation is guaranteed regardless of the manner in which grid speeds are defined the efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel

beyond endoscopy and special forms on gl 2 we carry out with technical modifications some cases of a procedure proposed by r langlands in beyond endoscopy this gives a new proof of the classification of dihedral forms on gl 2 avoiding endoscopic methods instead it uses an infinite limiting process in the trace formula we also explain the relationship of langlands idea to the results of 10 that count automorphic forms associated to galois representations we prove results of a similar nature over an arbitrary number field the main tool is a version of the relative trace formula namely a slight variant for pgl 2 of the kuznetsov bruggeman miatello formula msc 11f72 11f70

higher entropy conservation and numerical stability of compressible turbulence simulations we present a numerical formulation for the treatment of nonlinear instabilities in shock free compressible turbulence simulations the formulation is high order and contains no artificial dissipation numerical stability is enhanced through semi discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation the numerical implementation is achieved using a conservative skew symmetric splitting of the nonlinear terms the robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high reynolds number results show the scheme is capable of capturing the statistical equilibrium of low mach number compressible turbulent fluctuations at infinite reynolds number comparisons with the entropy splitting technique j comput phys 162 2000 33 j comput phys 178 2002 307 staggered method j comput phys 191 2 2003 392 and skew symmetric like schemes j comput phys 161 2000 114 confirm the superiority of the current approach we also discuss a flaw in the skew symmetric splitting implemented in the literature very good results are obtained based on the proper splitting

integral points on elliptic curves and 3 torsion in class groups we give new bounds for the number of integral points on elliptic curves the method may be said to interpolate between approaches via diophantine techniques bp hbr and methods based on quasi orthogonality in the mordell weil lattice sil6 gs he we apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the 3 torsion part of the class group of a quadratic field the same ideas can be used to count rational points on curves of higher genus

general transitivity conditions for fuzzy reciprocal preference matrices a reciprocal fuzzy matrix relation is a non negative matrix q qij such that qij qji 1 for all i j 1 2 n we define general transitivity conditions named fg transitivities for fuzzy reciprocal preference relations and show that they generalize some well known transitivities we also study relationships of these conditions with two models of rational preferences the so called utility model and the multidimensional model

on families of semiorders and interval orders imbedded in a valued structure of preference a survey abstract the paper presents all the families of semiorders and interval orders that can be built up on the basis of some valued preference relations some of these families called row and column homogeneous generalize the homogeneous families of semiorders studied by roberts and include the p families studied by fishburn the families are then examined from the view point of interval representation models also called threshold models

a high order low dispersion symmetry preserving finite volume method for compressible flow on curvilinear grids a new high order finite volume method is presented that preserves the skew symmetry of convection for the compressible flow equations the method is intended for large eddy simulations les of compressible turbulent flows in particular in the context of hybrid rans les computations the method is fourth order accurate and has low numerical dissipation and dispersion due to the finite volume approach mass momentum and total energy are locally conserved furthermore the skew symmetry preservation implies that kinetic energy sound velocity and internal energy are all locally conserved by convection as well the method is unique in that all these properties hold on non uniform curvilinear structured grids due to the conservation of kinetic energy there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection this enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid scale model by minimizing the numerical dispersion the numerical errors are reduced by an order of magnitude compared to a standard fourth order finite volume method

an effective chebotarev density theorem for families of number fields with an application to formula see text torsion in class groups we prove a new effective chebotarev density theorem for galois extensions l mathbb q that allows one to count small primes even as small as an arbitrarily small power of the discriminant of l this theorem holds for the galois closures of almost all number fields that lie in an appropriate family of field extensions previously applying chebotarev in such small ranges required assuming the generalized riemann hypothesis the error term in this new chebotarev density theorem also avoids the effect of an exceptional zero of the dedekind zeta function of l without assuming grh we give many different appropriate families including families of arbitrarily large degree to do this we first prove a new effective chebotarev density theorem that requires a zero free region of the dedekind zeta function then we prove that almost all number fields in our families yield such a zero free region the innovation that allows us to achieve this is a delicate new method for controlling zeroes of certain families of non cuspidall functions this builds on and greatly generalizes the applicability of work of kowalski and michel on the average density of zeroes of a family of cuspidall functions a surprising feature of this new method which we expect will have independent interest is that we control the number of zeroes in the family of l functions by bounding the number of certain associated fields with fixed discriminant as an application of the new chebotarev density theorem we prove the first nontrivial upper bounds for ell torsion in class groups for all integers ell ge 1 applicable to infinite families of fields of arbitrarily large degree