behavior of plane waves propagating through a temperature inhomogeneous region abstract description and analysis of acoustic waves in ducts with a region containing temperature inhomogeneous fluid represent a significant problem of scientific and practical interest this interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature homogeneous regions smoothly in our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient a polynomial character of the used temperature profile ensures smooth connection with constant temperature regions the one dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically the derived solutions based on heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method

analytic spread modulo an element and symbolic rees algebras let t n be a d dimensional regular local ring p a prime ideal of t having height equal d 1 and f p within this setting we are interested in computing the analytic spread of p f t we have two reasons for seeking this analytic spread the first is to identify prime ideals in local hypersurface rings whose analytic spreads and heights are the same the second is to aid in a better understanding of the symbolic rees algebra p t of p the ideal pen is the nth symbolic power of p our interest in hypersurface rings essentially originated in hug there we were interested in determining when powers and symbolic powers are equal for a prime ideal in a local hypersurface ring for a prime ideal q adjacent to the maximal ideal i e height m q l the only time such an equality can occur for all large powers is when the analytic spread of q equals the height of q equality does not however necessarily occur under this analytic spread condition cf hu2 example 2 lo in order to force equality for all powers one must make additional assumptions on the associated graded ring of p f t q cf hu2 theorem 2 11 section 2 of the present article contains some general methods for recognizing the analytic spread of p f t and section 3 contains some illustrative examples where the analytic spread of p f t equals the height of p f t the noetherian property of the symbolic rees algebra has created recent interest due to a question of cowsik in connection with his result in c that p t noetherian implies p is a set theoretic complete intersection when t is a regular local ring and dim t p 1 cowsik asked whether p t is noetherian for every prime ideal in a regular local ring an example due to p roberts ro showed the answer is no in general but the question has continued to draw attention hl h2 kr 0 e the

prime divisors asymptotic r sequences and unmixed local rings a current trend in commutative algebra has been to characterize properties of prime divisors in the completion of a local ring in terms of the independence of various elements and sequences in the local ring itself for instance in 2 bruns characterizes the minimal depth of prime divisors of zero in the completion r of a local ring r m as the largest number of elements which are p independent for n sufficiently large more recently the notion of asymptotic sequence has been used to characterize the minimal depth of minimal prime divisors of zero in r this was done by the author in s and l j ratliff jr in 19 elements x xd form an asymptotic sequence if x p u pi pe 2 x x where a z ass r i large n and r is the integral closure of i using this result as a starting point a full blown theory of asymptotic grade has been developed in 19 and 7 in this paper we seek a similar characterization of the minimal depth of all prime divisors of zero in r in particular we introduce the set

an exact solution for one dimensional acoustic fields in ducts with an axial temperature gradient abstract in this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient the one dimensional wave equation for ducts with an axial mean temperature gradient is derived the analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0 1 the derived wave equation is then transformed to the mean temperature space it is shown that by use of suitable transformations the derived wave equation can be reduced to analytically solvable equations e g bessel s differential equation the applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile this solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile furthermore the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems e g flames the results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall

free transverse vibrations of an elastically connected rectangular plate membrane complex system abstract this paper theoretically analyzes undamped free transverse vibrations of an elastically connected rectangular plate membrane system solutions of the problem are formulated by using the navier method natural frequencies of the system in the form of two infinite sequences are determined normal mode shapes of vibration expressing two kinds of vibration synchronous and asynchronous are presented the initial value problem is also solved in a numerical example the effect of membrane tension on the natural frequencies of this mixed system is discussed

on the finite generation of symbolic blow ups symbolic blow up p n s a noetherian ring if s is noetherian and dim n 0 rip l cowsik observed that p must be a set theoretic complete intersection if r is not regular there is no hope in general of s being noetherian in fact if r is any normal two dimensional local ring and p is a height one prime ideal of r which is not torsion in the class group of r then s is never noetherian this idea is behind the rees counterexample 6 to the generalized zariski question as far as the author knows there are no known counter examples to the question of cowsik the most trivial case is the following if r is nagata and

exponential stability analysis of xa long chain of coupled vibrating strings with dissipative linkage consider a long chain of coupled vibrating strings where a stabilizer is installed at each internal node and perhaps also at a boundary point the exponential stability of the stabilizers arrangement for this large dynamic structure will be determined through a careful transformation of the coupled wave equations for this structure into an equivalent hyperbolic system and analysis of the eigendeterminant it will be proven that the energy of the system decays uniformly exponentially if there is a stabilizer installed at a boundary point if the stabilizers are installed only at internal nodes it will be proven that the energy may decay either uniformly exponentially or nonuniformly or may not decay at all depending on the different wave speeds and the stabilizers arrangement all possible outcomes have been classified

independent elements unmixedness theorems and asymptotic prime divisors abstract it is shown that d sequences are a useful tool in order to construct independent elements second the i adic topology i an ideal of a commutative noetherian ring is compared with another well defined topology both are used to express the asymptotic number of independent elements in terms of local invariants as applications there are results on asymptotic prime divisors and unmixedness theorems

the uniform symbolic topology property for diagonally f regular algebras abstract let k be a field of positive characteristic building on the work of the second named author we define a new class of k algebras called diagonally f regular algebras for which the so called uniform symbolic topology property ustp holds effectively we show that this class contains all essentially smooth k algebras we also show that this class contains certain singular algebras such as the affine cone over p k r p k s when k is perfect by reduction to positive characteristic it follows that ustp holds effectively for the affine cone over p c r p c s and more generally for complex varieties of diagonal f regular type

optimal pointwise control for a parallel system of euler bernoulli beams abstract the optimal control of a distributed system consisting of two euler bernoulli beams coupled in parallel with pointwise controllers is considered an index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces the minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations the imposed initial condition as well as the boundary conditions a maximum principle is derived for optimal point controls of one dimensional coupled structures undergoing transverse vibrations the optimal control law is obtained using a maximum principle and the applicability of the results is demonstrated a method of solution for such a type of structure is suggested by using the eigenfunction expansion and the maximum principle the solution involves reducing the original problem to a system of ordinary differential equations the effectiveness of this approach is illustrated numerically by comparing the behavior of the controlled and uncontrolled problem

exact solutions to one dimensional acoustic fields with temperature gradient and mean flow an exact solution for one dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper the analysis is valid for mean mach numbers such that the square of the mean mach number is much less than one the one dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived by appropriate transformations the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile the developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow the results obtained using the analytical solution compare very well with the numerical results the developed solution is also compared with an existing analytical solution

control of planar networks of timoshenko beams the present study is concerned with the questions of controllability and stabilizability of planar networks of vibrating beams consisting of several timoshenko beams connected to each other by rigid joints at all interior nodes of the system some of the exterior nodes are either clamped or free controls may be applied at the remaining exterior nodes and or at interior joints in the form of forces and or bending moments for a given configuration is it at all possible to drive all vibrations to the rest configuration in a given finite time interval by means of controls acting at some or all of the available nonclamped nodes of the network and if so where should such controls be placed alternatively a control objective is to construct energy absorbing boundary feedback controls that will guarantee uniform energy decay it is demonstrated that if such a network does not contain closed loops and if at most one of the exterior nodes is clamped exact controllability and uniform stabilizability of the

locally unmixed modules and ideal topologies let r be a commutative noetherian ring and let n be a non zero finitely generated r module in this paper the main result asserts that n is locally unmixed if and only if for any n proper ideal a of r generated by htn a elements the topology defined by an n n 0 is equivalent to the a adic topology

optimal control of an elastically connected rectangular plate membrane system the optimal control of an elastically connected rectangular plate membrane system by point wise actuators is considered problems of the type are of significant practical interest in most real mechanical structures widely used in aeronautical civil naval and mechanical engineering an index of performance is formulated which consists of a modified energy functional of the two coupled structure at a specified time and penalty functions involving the point control actuators necessary conditions of optimality are derived in the form of independent integral equations which lead to explicit expressions for the point wise actuators the results are applied to a specific problem and numerical results are given that reveal the effectiveness of the proposed control mechanism

symbolic powers of monomial curves the answer is positive for ideal theoretic local complete intersection e g smooth curves s mk and for arbitrary curves if char k is non zero c n problem 1 remains open for most singular curves over say c in fact we look at an algebraic problem related to problem 1 let p be a prime ideal in a commutative noetherian ring a denote by s p the direct sum ora0 p of the symbolic powers of p see section 0 for definitions which is canonically a graded a algebra it is called the symbolic rees algebra of p or of x if x is the variety defined by p in spec a

noetherian symbolic blow ups the following question was raised by cowsik cw if p is a prime ideal in a regular local ring r n is the symbolic rees ring rep 120 pc a noetherian ring where pc is the n symbolic power of p i e p p r n r this question appears in works of rees re and nagata

dimension and singularity theory for local rings of finite embedding dimension abstract in this paper we develop an algebraic theory for local rings of finite embedding dimension several extensions of krull dimension are proposed which are then used to generalize singularity notions from commutative algebra finally variants of the homological theorems are shown to hold in equal characteristic this theory is then applied to noetherian local rings in order to get i over a cohen macaulay local ring uniform bounds on the betti numbers of a cohen macaulay module in terms of dimension and multiplicity and similar bounds for the bass numbers of a finitely generated module ii a characterization for being respectively analytically unramified analytically irreducible unmixed quasi unmixed normal cohen macaulay pseudo rational or weakly f regular in terms of certain uniform arithmetic behavior iii in mixed characteristic the improved new intersection theorem when the residual characteristic or ramification index is large with respect to dimension and some other numerical invariants

controllability and stabilizability of coupled strings with control applied at the coupled points controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied by investigating the properties of certain exponential series it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue a sufficient condition for exact controllability is also obtained in terms of the riesz basis properties of those exponential series

exact solution for one dimensional acoustic fields in ducts with a quadratic mean temperature profile the purpose of this letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile using appropriate transformations the one dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation whose solution can be expressed in terms of hypergeometric functions the analysis neglects the effects of mean flow and is therefore valid only for small mean mach numbers

essential prime divisors and projectively equivalent ideals let z be an ideal in a noetherian ring r we concern ourselves with the essential prime divisors of z an interesting subset of ass r p for all large n we first take z br with b a regular element of r we show that there is a ring t with r c te r such that t is a finite r module and the essential primes of bt are exactly the prime divisors of bt we next consider an arbitrary ideal z and apply our principal arguments to the element u in the kees ring of z we thereby deduce that there is an idcal j projectively equivalent to z such that the set of essential primes of z equals the set u ass r j over ii 1 2 3 notation let z be an ideal in a noetherian ring r we will use w or

prime ideals in ultraproducts of commutative rings abstract we describe classes of prime ideals in ultraproducts of commutative rings we consider in particular prime ideals in ultraproducts of noetherian rings krull domains finite character rings and qr domains

on the symbolic topology of an ideal abstract for an ideal i in a noetherian ring it is proved that the i adic and the i symbolic topologies are equivalent if and only if the only essential prime divisors of i are its minimal associated primes we investigate rings where these two topologies are linearly equivalent for all ideals locally unmixed rings are characterized as those noetherian rings in which these two topologies are equivalent for every ideal of the principal class an example is given to show that two results given by o zariski and p samuel commutative algebra vol ii p 274 van nostrand princeton nj 1960 in this area are not true as stated

pointwise stabilization in the middle of the span for second order systems nonuniform and uniform exponential decay of solutions two vibrating strings are coupled at the connecting point where a damping device is installed this device modeled by one of two sets of intermediate nodal conditions causes the vibration to dissipate energy a good design should satisfy the requirement that all modes be uniformly damped in this paper we show a simultaneous diagonalization procedure which can determine the rate of damping for certain coupled strings by solving a simple matrix eigenvalue problem in particular we show how to choose the impedance coefficient so that all of the vibration energy is absorbed within finite time duration we can also see that for certain systems with symmetry there exist modes which are not damped at all therefore the vibration energy does not decay uniformly we then use the legendre spectral method to compute the eigenvalues of the damped operators numerical results have confirmed the theoretical estimates and eigenvalue distributions patterns possible mechanical designs of those damping devices are

optimal boundary control of one dimensional multi span vibrating systems a class of optimal control problems of one dimensional coupled vibrating systems with control applied at the coupled points is considered a maximum principle is developed for a class of such optimal problems governed by n linear hyperbolic partial differential equations of second order in time and fourth order in space with variable coefficients the maximum principle given involves a hamiltonian which contains an adjoint variable as well as an admissible boundary control function the proof of the maximum principle is given with the help of convexity arguments the uniqueness theory of the solution of the optimal control problem is given using convexity arguments

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

a family of exact transient solutions for acoustic wave propagation in inhomogeneous non uniform area ducts abstract this paper presents a family of exact solutions for quasi one dimensional transient acoustic wave propagation in ducts with mean temperature and area variations in the absence of mean flow these solutions are obtained using a transformation of the spatial and acoustic variables in a manner suggested by the wkb approximation exact travelling wave type solutions are obtained for a class of temperature and area profiles these solutions differ from the classical travelling wave solution however in that the acoustic pressure and velocity are not algebraically related by the local value of the acoustic impedance x c x although these solutions resemble the approximate high frequency wkb form of solution of the wave equation they have the interesting property that they are exact regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity

the influence of a liquid flow on sound fields confined by conical walls abstract sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co ordinate r only a general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the green function method in the second part of this paper flow measurement properties are discussed the designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide instead the so called pseudo guide wave number and pseudo phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively it is shown that changes due to a background flow in pseudo guide wave number pseudo phase speed and zero point crossing times all exhibit an oscillatory behavior as a function of the r co ordinate this is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter the oscillatory behavior in the changes in zero point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is in principle that a one to one correspondence between measured output changes in zero point crossing times and actual flow determined by v 0 at a specific receiver location exists it is shown that this requirement is fulfilled as changes in zero point crossing times depend linearly on the flow coefficient v 0 at a given r co ordinate there are however certain discrete r co ordinate values where this is not the case namely those where changes in zero point crossing times become zero for any value of v 0 in other words if the receiver is positioned near r co ordinates where zero point crossing times are at a maximum or a minimum for a given value of v 0 the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero point crossing times induced by a background flow

quantifying singularities with differential operators abstract the f signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties for example this invariant detects non singularity and strong f regularity however it is very difficult to compute motivated by different aspects of the f signature we define a numerical invariant for rings of characteristic zero or p 0 that exhibits many of the useful properties of the f signature we also compute many examples of this invariant including cases where the f signature is not known we also obtain a number of results on symbolic powers and bernstein sato polynomials

linear equivalence of ideal topologies it is proved that whenever p is a prime ideal in a commutative noetherian ring such that the p adic and thep symbolic topologies are equivalent then the two topologies are equivalent linearly several explicit examples are calculated in particular for all prime ideals corresponding to non torsion points on nonsingular elliptic cubic curves

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

uniform bounds on symbolic powers abstract we study the question of obtaining uniform bounds for the growth of symbolic powers of ideals in noetherian rings first we use a generalized version of artin s strong approximation theorem to obtain uniform bounds for prime ideals in the integral closure of a finite galois field extension of the fraction field of an excellent henselian regular local ring as a corollary we obtain a similar result for a complete noetherian local domains we also obtain linear uniform bounds for the growth of symbolic powers in certain normal subrings of equicharacteristic regular rings under mild conditions