frequency domain analysis of exponentially damped linear systems abstract in this paper frequency domain analysis of linear exponentially damped systems subjected to arbitrary initial conditions is studied the standard discrete fourier transform dft procedure combined with fast fourier transform fft algorithms is applied to compute dynamic responses after transforming the original motion equations subjected to non zero initial conditions into new ones with completely null initial conditions by using the pseudo force approach a multi degree of freedom mdof system and a continuum system with exponential damping are considered as the illustrative problems the accuracy of the proposed method is evaluated by comparing the results with those obtained from simulink based on the state space method

linear damping models for structural vibration abstract linear damping models for structural vibration are examined first the familiar dissipation matrix model then the general linear model in both cases an approximation of small damping is used to obtain simple expressions for damped natural frequencies complex mode shapes and transfer functions results for transfer functions can be expressed in the form of very direct extensions of the familiar expression for the undamped case this allows a detailed discussion of the implications of the various damping models for the interpretation of measured transfer functions especially in the context of experimental modal analysis in the case of a dissipation matrix model it would be possible in principle to determine all the model parameters from measurements in the case of the general model however there is a fundamental ambiguity which prevents full determination of the model from measurements on a single structure

a fast algorithm for simulating vesicle flows in three dimensions vesicles are locally inextensible fluid membranes that can sustain bending in this paper we extend the study of veerapaneni et al s k veerapaneni d gueyffier g biros d zorin a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows journal of computational physics 228 19 2009 7233 7249 to general non axisymmetric vesicle flows in three dimensions although the main components of the algorithm are similar in spirit to the axisymmetric case spectral approximation in space semi implicit time stepping scheme important new elements need to be introduced for a full 3d method in particular spatial quantities are discretized using spherical harmonics and quadrature rules for singular surface integrals need to be adapted to this case an algorithm for surface reparameterization is needed to ensure stability of the time stepping scheme and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs to characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi implicit time stepping scheme we perform a spectral analysis of the evolution operator on the unit sphere by introducing these algorithmic components we obtain a time stepping scheme that circumvents the stability constraint on the time step and achieves spectral accuracy in space we present results to analyze the cost and convergence rates of the overall scheme to illustrate the applicability of the new method we consider a few vesicle flow interaction problems a single vesicle in relaxation sedimentation shear flows and many vesicle flows

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

the linear algebra of the generalized pascal matrix abstract this paper discusses three kinds of generalized pascal matrix and generalizes the results of r brawer and m pirovino

explicit factorization of the vandermonde matrix the lu factorization of the vandermonde matrix is obtained using complete symmetric functions and the lower and upper triangular matrices are in turn factorized into 1 banded matrices thus expressing the vandermonde matrix as a product of 1 banded matrices

on a general model for damping when a structure exhibits a damped dynamic behavior that does not conform to the classical and well known viscous or hysteretic models a more general approach must be sought several questions may then be raised like i in which theoretical background should one base the investigation or ii can one apply common modal analysis tools to solve the problem recent works have shown that some types of materials and therefore structures demand a more rigorous behavior description and that it seems possible to address the problem by means of the theory of fractional derivatives leading to a model in terms of general damping parameters such an approach reveals itself somewhat complicated to implement in practice and some simplifications are necessary the authors discuss the use of a generalized damping concept for modeling the dynamic behavior of linear systems and show how this concept allows for a clearer interpretation and explanation of the behavior displayed by the common viscous and hysteretic models

matrices related to the bell polynomials abstract in this paper we study the matrices related to the partial exponential bell polynomials and those related to the bell polynomials with respect to as a result the factorizations of these matrices are obtained which give unified approaches to the factorizations of many lower triangular matrices moreover some combinatorial identities are also derived from the corresponding matrix representations

on several q special matrices including the q bernoulli and q euler matrices abstract in the spirit of our earlier articles 12 14 11 and our work 13 we define two dual q bernoulli polynomials with corresponding vector and matrix forms following aceto trigiante 1 the q l matrix the indefinite q integral of the q pascal matrix is the link between the q cauchy and the q bernoulli matrix the q analogue of the bernoulli complementary argument theorem can be expressed in matrix form through the diagonal a n matrix for the q euler polynomials corresponding results are obtained the umbral calculus for generating functions of q appell polynomials is shown to be equivalent to a transform method which maps polynomials to matrices a true q analogue of arponen 6 this is manifested by the vein 21 matrix which occurs as the transform of the q difference operator the aceto trigiante shifted q bernoulli matrix has a simple connection to the q bernoulli arponen matrix through the q pascal matrix we reintroduce certain q stirling numbers z q from 12 which will be needed for the polynomial matrix definitions

catalan matrix and related combinatorial identities we introduce the notion of the catalan matrix c n x whose non zero elements are expressions which contain the catalan numbers arranged into a lower triangular toeplitz matrix inverse of the catalan matrix is derived correlations between the matrix c n x and the generalized pascal matrix are considered some combinatorial identities involving catalan numbers binomial coefficients and the generalized hypergeometric function are derived using these correlations moreover an additional explicit representation of the catalan number as well as an explicit representation of the sum of the first m catalan numbers are given

notes on particular symmetric polynomials with applications this paper presents some applications using several properties of three important symmetric polynomials elementary symmetric polynomials complete symmetric polynomials and the power sum symmetric polynomials the applications includes a simple proof of el mikkawy conjecture in m e a el mikkawy appl math comput 146 2003 759 769 and a very easy proof of the newton girard formula in addition a generalization of stirling numbers is obtained

identification of linear non viscous damping with different kernel functions in the time domain abstract the non viscous damping model considers the complete velocity history via a convolution over the kernel functions in this paper a procedure is proposed for identifying a damping model involving different kernel functions in the time domain the method uses responses calculated by the generic time domain integration with the known mass matrix and the stiffness matrix the relaxation parameter in the kernel function is identified through a summation of the error function and the damping coefficient matrix is identified via the linear least squares method two examples show that reasonable estimates could be obtained by the proposed method

matrices determined by a linear recurrence relation among entries abstract a matrix a a ij is called a 7 matrix if its entries satisfy the recurrence relation a i 1 j 1 a i 1 j a ij where are fixed numbers a 7 matrix is completely determined by its first row and first column in this paper we determine the structure of 7 matrices and investigate the sequences represented by columns of infinite 7 matrices

coupling of finite element and boundary integral methods for a capsule in a stokes flow we introduce a new numerical method to model the fluid structure interaction between a microcapsule and an external flow an explicit finite element method is used to model the large deformation of the capsule wall which is treated as a bidimensional hyperelastic membrane it is coupled with a boundary integral method to solve for the internal and external stokes flows our results are compared with previous studies in two classical test cases a capsule in a simple shear flow and in a planar hyperbolic flow the method is found to be numerically stable even when the membrane undergoes in plane compression which had been shown to be a destabilizing factor for other methods the results are in very good agreement with the literature when the viscous forces are increased with respect to the membrane elastic forces three regimes are found for both flow cases our method allows a precise characterization of the critical parameters governing the transitions copyright 2010 john wiley sons ltd

generalized leibniz functional matrices and factorizations of some well known matrices in this paper we introduce the generalized leibniz functional matrices and study some algebraic properties of such matrices to demonstrate applications of these properties we derive several novel factorization forms of some well known matrices such as the complete symmetric polynomial matrix and the elementary symmetric polynomial matrix in addition by applying factorizations of the generalized leibniz functional matrices we redevelop the known results of factorizations of stirling matrices of the first and second kind and the generalized pascal matrix

polynomials power series and interpolation in this paper we study the relationship between formal power series sequences of polynomials and polynomial interpolation we do this by extending and applying the techniques of the umbra1 calculus since our approach is a completely fresh one no previous knowledge of the umbra1 calculus is required our main goals are threefold let us begin from the point of view of interpolation let p be the algebra of polynomials in a single variable and let p be the dual vector space of all linear functionals on p if l e p and p x e p we denote the application of l on p x by

viscous regularization and r adaptive remeshing for finite element analysis of lipid membrane mechanics as two dimensional fluid shells lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses this property gives membranes the ability to adopt dramatic shape changes in this paper a finite element model is developed to study static equilibrium mechanics of membranes in particular a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers the augmented lagrangian method is used to enforce global constraints on area and volume during membrane deformations as a validation of the method equilibrium shapes for a shape phase diagram of lipid bilayer vesicle are calculated these numerical techniques are also shown to be useful for simulations of three dimensional large deformation problems the formation of tethers long tube like extensions and ginzburg landau phase separation of a two lipid component vesicle to deal with the large mesh distortions of the two phase model modification of viscous regularization is explored to achieve r adaptive mesh optimization

stirling matrix via pascal matrix abstract the pascal type matrices obtained from the stirling numbers of the first kind s n k and of the second kind s n k are studied respectively it is shown that these matrices can be factorized by the pascal matrices also the ldu factorization of a vandermonde matrix of the form v n x x 1 x n 1 for any real number x is obtained furthermore some well known combinatorial identities are obtained from the matrix representation of the stirling numbers and these matrices are generalized in one or two variables

boundary integral method for the flow of vesicles with viscosity contrast in three dimensions we propose numerical algorithms for the simulation of the dynamics of three dimensional vesicles suspended in viscous stokesian fluid our method is an extension of our previous work s k veerapaneni et al 2011 37 to flows with viscosity contrast this generalization requires a change in the boundary integral formulation of the solution in which a double layer stokes integral is introduced and leads to changes in the fluid dynamics due to the viscosity contrast of the vesicles which can no longer be efficiently resolved with existing algorithms in this paper we describe the algorithms needed to handle flows with viscosity contrast accurately and efficiently we show that a globally semi implicit method does not have any time step stability constraint for flows with single and multiple vesicles with moderate viscosity contrast and the computational cost per simulation unit time is comparable to or less than that of an explicit scheme automatic oversampling adaptation enables us to achieve high accuracy with very low spectral resolution we conduct numerical experiments to investigate the stability accuracy and the computational cost of the algorithms overall our method achieves several orders of magnitude speed up compared to the standard explicit schemes

symmetric bernoulli matrix and its cholesky decomposition abstract this study associates the symmetric bernoulli matrix with various combinatorial matrices such as pascal vandermonde and stirling matrices of the first and second kind including catalan numbers by way of dual matrices of the matrix a recurrence relation related to the entries of the cholesky factor of a symmetric positive definite matrix is presented which sheds new light on examining positive definiteness and cholesky s method of a symmetric matrix this relation is applied to give a necessary and sufficient condition for the positive definiteness of a symmetric matrix which leads to a slightly modified form of the outer product formulation for cholesky s method of a symmetric matrix

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

adaptive time stepping for vesicle suspensions we present an adaptive high order accurate time stepping numerical scheme for the flow of vesicles suspended in stokesian fluids our scheme can be summarized as an approximate implicit spectral deferred correction sdc method applying a fully implicit sdc scheme to vesicle flows is prohibitively expensive for this reason we introduce several approximations our scheme is based on a semi implicit linearized low order time stepping method our discretization is spectrally accurate in space we expect that the accuracy can be arbitrary order but our examples suffer from order reduction which limits the observed accuracy to third order we also use invariant properties of vesicle flows constant area and boundary length in two dimensions to reduce the computational cost of error estimation for adaptive time stepping we present results in two dimensions for single vesicle flows constricted geometry flows converging flows and flows in a couette apparatus we experimentally demonstrate that the proposed scheme enables automatic selection of the time step size and high order accuracy

3d numerical simulations of vesicle and inextensible capsule dynamics vesicles are locally inextensible fluid membranes capsules are endowed with in plane shear elasticity mimicking the cytoskeleton of red blood cells rbcs but are extensible while rbcs are inextensible we use boundary integral bi methods based on the green function techniques to model and solve numerically their dynamics we regularize the single layer integral by subtraction of exact identities for the terms involving the normal and the tangential components of the force the stability and precision of bi calculation is enhanced by taking advantage of additional quadrature nodes located in vertices of an auxiliary mesh constructed by a standard refinement procedure from the main mesh we extend the partition of unity technique to boundary integral calculation on triangular meshes the proposed algorithm offers the same treatment of near singular integration regardless whether the source and the target points belong to the same surface or not bending forces are calculated by using expressions derived from differential geometry membrane incompressibility is handled by using two penalization parameters per suspended entity one for deviation of the global area from prescribed value and another for the sum of squares of local strains defined on each vertex extensible or inextensible capsules a model of rbc are studied by storing the position in the reference configuration for each vertex the elastic force is then calculated by direct variation of the elastic energy various nonequilibrium physical examples on vesicles and capsules will be presented and the convergence and precision tests highlighted overall a good convergence is observed with numerical error inversely proportional to the number of vertices used for surface discretization the highest order of convergence allowed by piece wise linear interpolation of the surface

some identities on catalan numbers and hypergeometric functions via catalan matrix power abstract in this paper we use the catalan matrix power as a tool for deriving identities involving catalan numbers and hypergeometric functions for that purpose we extend earlier investigated relations between the catalan matrix and the pascal matrix by inserting the catalan matrix power and particulary the squared catalan matrix in those relations we also pay attention to some relations between catalan matrix powers of different degrees which allows us to derive the simplification formula for hypergeometric function 3 f 2 as well as the simplification formula for the product of the catalan number and the hypergeometric function 3 f 2 some identities involving catalan numbers proved by the non matrix approach are also given

isogeometric fem bem simulations of drop capsule and vesicle dynamics in stokes flow we develop an algorithm for the three dimensional simulation of the dynamics of soft objects drops capsules vesicles under creeping flow conditions loop elements are used to describe the shape of the soft objects this surface representation is used both for membrane solver based on finite element method fem and for the fluid solver based on the boundary element method bem this isogeometric analysis of the low reynolds fluidstructure interaction problem is then coupled to high order explicit time stepping or second order implicit time stepping algorithm for vesicles simulation a preconditioner is designed for the resolution of the surface velocity incompressibility constraint which is treated by the use of a local lagrange multiplier a mesh quality preserving algorithm is introduced to improve the control mesh quality over long simulation times we test the proposed algorithm on capsule and vesicle dynamics in various flows and study its convergence properties showing a second order convergence o n2 with mesh number of elements

functions and jordan canonical forms of riordan matrices abstract this paper collects results about riordan arrays in the framework of matrix functions actually the following methodology applies to any square matrix m m with exactly one eigenvalue of algebraic multiplicity m n generalized lagrange bases are used to construct hermite polynomials that interpolate a family of functions moreover we show a parallel application of such functions via jordan canonical forms and case studies are given

a lagrange matrices approach to confluent cauchy matrices we present a new approach to study inversion and factorization properties of confluent cauchy matrices we consider a class of generalized vandermonde matrices called lagrange matrices that are connected in a simple way with the cauchy matrices we apply the methods introduced in adv appl math 10 1989 348 to obtain inversion and factorization theorems for lagrange matrices and their confluent forms and then derive corresponding results for cauchy matrices a lagrange matrix v is associated with a pair of vectors x0 x1 xn and y0 y1 yn v is the matrix representation of the substitution operator that sends the vector p x0 p x1 p xn t to the vector p y0 p y1 p yn t for any polynomial p of degree at most n

inverses of generalized vandermonde matrices on demontre plusieurs equations matricielles comprenant des matrices de vandermonde generalisees qui donnent une information algebrique explicite sur les matrices inverses

nonsingular isogeometric boundary element method for stokes flows in 3d abstract isogeometric analysis iga is emerging as a technology bridging computer aided geometric design cagd most commonly based on non uniform rational b splines nurbs surfaces and engineering analysis in finite element and boundary element isogeometric methods fe iga and iga bem the nurbs basis functions that describe the geometry define also the approximation spaces in the fe iga approach the surfaces generated by the cagd tools need to be extended to volumetric descriptions a major open problem in 3d this additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations leading to boundary element isogeometric analysis iga bem the main advantages of such an approach are given by the dimensionality reduction of the problem from volumetric based to surface based by the fact that the interface with cagd tools is direct and by the possibility to treat exterior problems where the computational domain is infinite by contrast these methods produce system matrices which are full and require the integration of singular kernels in this paper we address the second point and propose a nonsingular formulation of iga bem for 3d stokes flows whose convergence is carefully tested numerically standard gaussian quadrature rules suffice to integrate the boundary integral equations and carefully chosen known exact solutions of the interior stokes problem are used to correct the resulting matrices extending the work by klaseboer et al 2012 27 to iga bem

matrix factorization of the n n shift bell matrix abstract let b n b n k n k 0 be the bell matrix define the n n shift bell matrix p n k by p n k i j b k i 1 k j 1 for i j 1 2 n and k 0 1 2 in this paper matrix factorizations of the n n shift bell matrix and the n n generalized riordan matrix are studied as a result many lower triangular matrices related to bell polynomials can be factorized by the corresponding matrices and some identities are derived from the matrix representations in addition some harmonic number identities are obtained from the riordan array method

a spectral boundary integral method for flowing blood cells a spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated the blood cells are modeled as finite deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma but the solver itself is independent of the particular constitutive model employed for the cell membranes the surface integrals developed for solving the viscous flow and thereby the motion of the massless membrane are evaluated using an o nlogn particle mesh ewald pme approach the cell shapes which can become highly distorted under physiologic conditions are discretized with spherical harmonics the resolution of these global basis functions is of course excellent but more importantly they facilitate an approximate de aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step complex geometry no slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine the implementation is verified against solutions for axisymmetric flows reported in the literature and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations it is also used to simulate flow of blood cells at 30 volume fraction in tubes between 4 9 and email protected in diameter for these it is shown to reproduce the well known non monotonic dependence of the effective viscosity on the tube diameter

the linear algebra of the pascal matrix abstract pascal s triangle can be represented as a square matrix in two basically different ways as a lower triangular matrix pn or as a full symmetric matrix qn it has been found that the pn pnt is the cholesky factorization of qn pn can be factorized by special summation matrices it can be shown that the inverses of these matrices are the operators which perform the gaussian elimination steps for calculating cholesky s factorization by applying linear algebra we produce combinatorial identities and an existence theorem for diophantine equation systems finally an explicit formula for the sum of the kth powers is given

symmetric functions and the vandermonde matrix this work deduces the lower and the upper triangular factors of the inverse of the vandermonde matrix using symmetric functions and combinatorial identities the l and u matrices are in turn factored as bidiagonal matrices the elements of the upper triangular matrices in both the vandermonde matrix and its inverse are obtained recursively the particular value x i 1 q qi 1 in the indeterminates of the vandermonde matrix is investigated and it leads to q binomial and q stirling matrices it is also shown that q stirling matrices may be obtained from the pascal matrix

generalized leibniz functional matrices and divided difference form of the lagrange burmann formula abstract in this paper we derive two versions of divided difference form of the lagrange burmann expansion formula the first version expresses all coefficients by a form of a determinant by means of the factorizations of the generalized leibniz functional matrices with respect to a sequence we obtain the second version with coefficients represented by a finite sum some new matrix inversions are also investigated

displacement structure approach to polynomial vandermonde and related matrices abstract we introduce a new class of what we call polynomial vandermonde like matrices this class generalizes the polynomial vandermonde matrices studied earlier by various authors who derived explicit inversion formulas and fast algorithms for inversion and for solving the associated linear systems a displacement structure approach allows us to carry over all these results to the wider class of polynomial vandermonde like matrices

a galerkin method for distributed systems with non local damping in this paper a non local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of euler bernoulli beams and kirchoff plates unlike ordinary local damping models the damping force in a non local model is obtained as a weighted average of the velocity field over the spatial domain determined by a kernel function based on distance measures the resulting equation of motion for the beam or plate structures is an integro partial differential equation rather than the partial differential equation obtained for a local damping model approximate solutions for the complex eigenvalues and modes with non local damping are obtained using the galerkin method numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions for non local and non viscous damping models and different kernel functions

3d vesicle dynamics simulations with a linearly triangulated surface simulations of biomembranes have gained an increasing interest in the past years specificities of these membranes propose new challenges for the numerics in particular vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint a method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described this method is coupled with a boundary element method solver for inner and outer fluids to compute vesicle dynamics under external flows the surface incompressibility constraint is satisfied by the construction of a projection operator

the linear algebra of the generalized pascal functional matrix abstract in this paper we generalize pascal s matrix by defining the polynomials factorial binomial then using this generalization we introduce a two variable pascal s matrix and state its related theorems and prove them finally we introduce pascal s functional matrix associated with a sequence a a n n 0 and obtain several important combinatorial identities

remarks on two symmetric polynomials and some matrices by means of complete symmetric polynomials this paper gives a new proof for the vandermonde determinant formula another alternative proof for this formula is obtained via the collocation matrices it also gives a generalized relationship between the vandermonde the pascal and the stirling matrices a new approach to obtain the explicit inverse of the vandermonde matrix is investigated closed form expressions for some vandermonde related determinants are obtained

an extension of the generalized pascal matrix and its algebraic properties abstract the extended generalized pascal matrix can be represented in two different ways as a lower triangular matrix n x y or as a symmetric n x y these matrices generalize p n x q n x and r n x which are defined by zhang and by call and velleman a product formula for n x y has been found which generalizes the result of call and velleman it is shown that not only can n x y be factorized by special summation but also n x y as q n xy s t y 1 x or n x y p n t y x finally the inverse of n x y and the values of det n x y det n 1 x y det n x y and det n 1 x y are given

extended symmetric pascal matrices via hypergeometric functions in this paper we give a matrix representation of the hypergeometric functions of the type 2f 1 a b c x as a result we obtain a connection between the hypergeometric functions the legendre polynomials and the delannoy numbers moreover it is shown that each entry of p n x y p n x y t can be represented by the hypergeometric functions where p n x y i j x i jy i j 2i 1j 1 is the extended generalized pascal matrix which is defined by zhang and liu linear algebra appl 271 1998 169

on the quantification of damping model uncertainty abstract the characterization of uncertainty in the damping forces in a vibrating structure is of significant interest in structural dynamics the most common approach is to use a viscous damping matrix with uncertain coefficients the viscous damping is not the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model there are many functional forms which can be used as damping models in this paper two approaches are proposed to quantify such model form uncertainty associated with the use of the viscous damping model not only the model parameters the first approach is based on an ensemble of equivalent damping functions and the second approach is based on the random matrix theory the results obtained from the two methods are compared using numerical examples it was observed that the random matrix theory can be used to quantify damping model uncertainty in some cases

generalized pascal functional matrix and its applications in this paper we introduce the generalized pascal functional matrix and show that the existing variations of pascal matrices are special cases of this generalization we study some algebraic properties of such generalized pascal functional matrices in addition we demonstrate a direct application of these properties by deriving several novel combinatorial identities and a nontraditional approach for lu decompositions of some well known matrices such as symmetric pascal matrices

matrix approach to polynomials 2 abstract we continue our study of the structure initiated in t arponen a matrix approach to polynomials linear algebra appl 359 2003 181 196 our main emphasis is exploring further structure into the formalism introduced in t arponen a matrix approach to polynomials linear algebra appl 359 2003 181 196 this formalism reveals beautiful interplay between certain elementary operators and provides tools for example for checking handling and generalizing combinatorial identities as we show in examples in addition to that we discover a group structure among vandermonde matrices a fascinating diophantine equation and new proofs and generalizations of recently found related results

extended bernoulli and stirling matrices and related combinatorial identities abstract in this paper we establish plenty of number theoretic and combinatoric identities involving generalized bernoulli polynomials and stirling numbers of both kinds which generalize various known identities these formulas are deduced from pascal type matrix representations of bernoulli and stirling numbers for this we define and factorize a modified pascal matrix corresponding to bernoulli and stirling cases

fast inversion of chebyshev vandermonde matrices this paper contains two fast algorithms for inversion of chebyshev vandermonde matrices of the first and second kind they are based on special representations of the bezoutians of chebyshev polynomials of both kinds the paper also contains the results of numerical experiments which show that the algorithms proposed here are not only much faster but also more stable than other algorithms available it is also efficient to use the above two algorithms for solving chebyshev vandermode systems of equations with preprocessing

the factorization of block matrices with generalized geometric progression rows abstract generalized geometric progression gp block matrices are introduced and it is shown that such matrices can be factored as the product of one lower triangular matrix and several upper triangular reduced pascal matrices p k x which were introduced by cheon and kim the determinant formula for any gp block matrix follows readily from this factorization this lu factorization and determinant formula are a generalization of results presented by yang and leida as direct applications of the new results we rederive factorizations of the extended generalized symmetric pascal matrix introduced by zhang and liu and the vandermonde matrix in addition determinants of three types of generalized vandermonde matrices are immediate consequences of our main theorem

symmetric polynomials pascal matrices and stirling matrices we consider lower triangular matrices consisting of symmetric polynomials and we show how to factorize and invert them since binomial coefficients and stirling numbers can be represented in terms of symmetric polynomials these results contain factorizations and inverses of pascal and stirling matrices as special cases this work generalizes that of several other authors on pascal and stirling matrices

factorial stirling matrix and related combinatorial sequences abstract in this paper some relationships between the stirling matrix the vandermonde matrix the benoulli numbers and the eulerian numbers are studied from a matrix representation of k s n k which will be called the factorial stirling matrix where s n k are the stirling numbers of the second kind as a consequence a number of interesting and useful identities are obtained

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

the cyclic groups via the pascal matrices and the generalized pascal matrices abstract in this paper given a positive integer m we consider the multiplicative order of upper and lower triangular matrices and symmetric matrices derived from pascal s triangle when read modulo m we also consider the corresponding problems when the binomial coefficients i j are replaced by x i j i j and x i j i j where x is an integer satisfying certain divisibility hypotheses we also offer some open conjectures on these orders

dual operators and lagrange inversion in several variables the original lagrange inversion formula which gives explicitly the inverse under composition of a formal series was obtained by lagrange in 1770 through formal computations involving logarithms of inlmite products see lagrange 121 there exists an extensive literature on various versions of the inversion formula obtained by algebraic analytic and combinatorial methods comtet 3 gives a survey and an ample bibliography during the last ten years there have appeared several papers on generalizations and new proofs of the inversion formula in 1974 abhyankar obtained an inversion formula using algebraic methods see bass connell and wright 11 several authors have related lagrange inversion with rota s finite operator calculus 151 for example joni 8 garsia and joni 4 hofhauer 7 and roman and rota 14 joyal and labelle used a combinatorial theory of formal series to obtain inversion formulas see 9 l i and viskov 161 used ideas from lie algebra theory to prove formulas similar to abhyankar s in the present paper we use operator methods to obtain inversion formulas in several variables that generalize the formulas of abhyankar joni and viskov we get our results studying an algebra with involution of linear operators on the algebra of formal laurent series in several indeterminates we also show that by means of an anti isomorphism of operator algebras which we call the operator bore1 transform the study of finite operator calculus can be reduced to the study of certain groups of operators on the algebra of formal laurent series our approach may be considered as an algebraic analogue of the complex variable methods used by good 5 to obtain the lagrange inversion formula as a consequence of the change of variables theorem for the