forced responses of solid axially polarized piezoelectric ceramic finite cylinders with internal losses a method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the gauss electrostatic conditions one infinite set of solutions is chosen such that each field variable is expressed in terms of bessel functions that form a complete set in the radial direction another infinite set of solutions is chosen such that each field variable is expressed in terms of trigonometric functions that form a complete set in the axial direction another solution is used to account for the electric field that can exist even when there is no vibration the weights are determined by using the orthogonal properties of the functions and are used to satisfy specified arbitrary axisymmetric boundary conditions on all the surfaces special cases including simultaneous mechanical and electrical excitation of cylinders are presented all numerical results are in excellent agreement with those obtained using the finite element software atila for example the five lowest frequencies at which the conductance and susceptance of a stress free cylinder of length 10 mm and radius 5 mm reach a local maximum or minimum differ by less than 0 01 from those computed using atila

exact t 0 partition functions for potts antiferromagnets on sections of the simple cubic lattice we present exact solutions for the zero temperature partition function of the q state potts antiferromagnet equivalently the chromatic polynomial p on tube sections of the simple cubic lattice of fixed transverse size l x ifmmode times else texttimes fi l y and arbitrarily great length l z for sizes l x ifmmode times else texttimes fi l y 2 ifmmode times else texttimes fi 3 and 2 ifmmode times else texttimes fi 4 and boundary conditions a mathrm fbc x mathrm fbc y mathrm fbc z and b mathrm pbc x mathrm fbc y mathrm fbc z where fbc pbc denote free periodic boundary conditions in the limit of infinite length l z ensuremath rightarrow ensuremath infty we calculate the resultant ground state degeneracy per site w exponent of the ground state entropy generalizing q from z to c we determine the analytic structure of w and the related singular locus mathcal b which is the continuous accumulation set of zeros of the chromatic polynomial for the l z ensuremath rightarrow ensuremath infty limit of a given family of lattice sections w is analytic for real q down to a value q c we determine the values of q c for the lattice sections considered and address the question of the value of q c for a d dimensional cartesian lattice analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph k m m

vibration analysis of coupled conical cylindrical spherical shells using a fourier spectral element method this paper presents a fourier spectral element method fsem to analyze the free vibration of conical cylindrical spherical shells with arbitrary boundary conditions cylindrical conical and cylindrical spherical shells as special cases are also considered in this method each fundamental shell component i e cylindrical conical and spherical shells is divided into appropriate elements the variational principle in conjunction with first order shear deformation shell theory is employed to model the shell elements since the displacement and rotation components of each element are expressed as a linear superposition of nodeless fourier sine functions and nodal lagrangian polynomials the global equations of the coupled shell structure can be obtained by adopting the assembly procedure the fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution numerical results show that the fsem can be effectively applied to vibration analysis of the coupled shell structures numerous results for coupled shell structures with general boundary conditions are presented furthermore the effects of geometric parameters and boundary conditions on the frequencies are investigated

density of states potts zeros and fisher zeros of the q state potts model for continuous q the q state potts model can be extended to noninteger and even complex q by expressing the partition function in the fortuin kasteleyn f k representation in the f k representation the partition function z q a is a polynomial in q and v a ensuremath 1 a e ensuremath beta j and the coefficients of this polynomial ensuremath phi b c are the number of graphs on the lattice consisting of b bonds and c connected clusters we introduce the random cluster transfer matrix to compute ensuremath phi b c exactly on finite square lattices with several types of boundary conditions given the f k representation of the partition function we begin by studying the critical potts model z mathrm cp z q a c q where a c q 1 sqrt q we find a set of zeros in the complex w sqrt q plane that map to or close to the beraha numbers for real positive q we also identify q c l the value of q for a lattice of width l above which the locus of zeros in the complex p v sqrt q plane lies on the unit circle by finite size scaling we find that 1 q c l ensuremath rightarrow 0 as stackrel ensuremath rightarrow l ensuremath infty we then study zeros of the antiferromagnetic af potts model in the complex q plane and determine q c a the largest value of q for a fixed value of a below which there is af order we find excellent agreement with baxter s conjecture q c mathrm af a 1 ensuremath a a 3 we also investigate the locus of zeros of the ferromagnetic potts model in the complex q plane and confirm that q c mathrm fm a a ensuremath 1 2 we show that the edge singularity in the complex q plane approaches q c as q c l ensuremath sim q c al ensuremath y q and determine the scaling exponent y q for several values of q finally by finite size scaling of the fisher zeros near the antiferromagnetic critical point we determine the thermal exponent y t as a function of q in the range 2l ql 3 using data for lattices of size 3l ll 8 we find that y t is a smooth function of q and is well fitted by y t 1 au bu 2 c du where u ensuremath 2 ensuremath pi mathrm cos ensuremath 1 sqrt q 2 for q 3 we find y t ensuremath simeq 0 6 however if we include lattices up to l 12 we find y t ensuremath simeq 0 50 8 in rough agreement with a recent result of ferreira and sokal j stat phys 96 461 1999

exact partition functions for potts antiferromagnets on cyclic lattice strips abstract we present exact calculations of the zero temperature partition function of the q state potts antiferromagnet on arbitrarily long strips of the square triangular and kagome lattices with width l y 2 or 3 vertices and with periodic longitudinal boundary conditions from these in the limit of infinite length we obtain the exact ground state entropy s 0 k b ln w these results are of interest since this model exhibits nonzero ground state entropy s 0 0 for sufficiently large q and hence is an exception to the third law of thermodynamics we also include results for homeomorphic expansions of the square lattice strip the analytic properties of w q are determined and related to zeros of the chromatic polynomial for long finite strips

ground state entropy of the potts antiferromagnet on strips of the square lattice abstract we present exact solutions for the zero temperature partition function chromatic polynomial p and the ground state degeneracy per site w exponent of the ground state entropy for the q state potts antiferromagnet on strips of the square lattice of width ly vertices and arbitrarily great length lx vertices the specific solutions are for a ly 4 fbcy pbcx cyclic b ly 4 fbcy tpbcx mobius c ly 5 6 pbcy fbcx cylindrical and d l y 5 fbc y fbc x open where fbc pbc and tpbc denote free periodic and twisted periodic boundary conditions respectively in the lx limit of each strip we discuss the analytic structure of w in the complex q plane the respective w functions are evaluated numerically for various values of q several inferences are presented for the chromatic polynomials and analytic structure of w for lattice strips with arbitrarily great ly the absence of a nonpathological lx limit for real nonintegral q in the interval 0 0 for strips of the square triangular lattice is discussed

complex temperature phase diagrams for the q state potts model on self dual families of graphs and the nature of the q limit exact calculations of the potts model partition function z g q v have been presented for arbitrary q and temperature like variable v on self dual strip graphs g of the square lattice with fixed width l y and arbitrarily great length lx with two types of boundary conditions letting lx infinity the resultant free energy and complex temperature phase diagram have been computed including the locus b where the free energy is nonanalytic results are analyzed for widths l y 1 2 3 these results have been used to study the approach to the large q limit of b

chromatic polynomials for j h i strip graphs and their asymptotic limits abstract we calculate the chromatic polynomials p for n vertex strip graphs of the form j l 1 m h i where j and i are various subgraphs on the left and right ends of the strip whose bulk is comprised of m fold repetitions of a subgraph h the strips have free boundary conditions in the longitudinal direction and free or periodic boundary conditions in the transverse direction this extends our earlier calculations for strip graphs of the form l 1 m h i we use a generating function method from these results we compute the asymptotic limiting function w lim n p 1 n for q z this has physical significance as the ground state degeneracy per site exponent of the ground state entropy of the q state potts antiferromagnet on the given strip in the complex q plane w is an analytic function except on a certain continuous locus b in contrast to the l 1 m h i strip graphs where b i is independent of i and ii consists of arcs and possible line segments that do not enclose any regions in the q plane we find that for some j l 1 m h i strip graphs b i does depend on i and j and ii can enclose regions in the q plane our study elucidates the effects of different end subgraphs i and j and of boundary conditions on the infinite length limit of the strip graphs

asymptotic limits and zeros of chromatic polynomials and ground state entropy of potts antiferromagnets we study the asymptotic limiting function w g q lim n to infty p g q 1 n where p g q is the chromatic polynomial for a graph g with n vertices we first discuss a subtlety in the definition of w g q resulting from the fact that at certain special points q s the following limits do not commute lim n to infty lim q to q s p g q 1 n ne lim q to q s lim n to infty p g q 1 n we then present exact calculations of w g q and determine the corresponding analytic structure in the complex q plane for a number of families of graphs g including circuits wheels biwheels bipyramids and cyclic and twisted ladders we study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs all but a finite number of the zeros lie exactly on a unit circle whose position depends on the family using the connection of p g q with the zero temperature potts antiferromagnet we derive a theorem concerning the maximal finite real point of non analyticity in w g q denoted q c and apply this theorem to deduce that q c sq 3 and q c hc 3 sqrt 5 2 for the square and honeycomb lattices finally numerical calculations of w hc q and w sq q are presented and compared with series expansions and bounds

exact potts model partition functions on strips of the honeycomb lattice abstract we present exact calculations of the partition function of the q state potts model on i open ii cyclic and iii mobius strips of the honeycomb brick lattice of width l y 2 and arbitrarily great length in the infinite length limit the thermodynamic properties are discussed the continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values we also give exact calculations of the zero temperature partition function chromatic polynomial and w q the exponent of the ground state entropy for the potts antiferromagnet for honeycomb strips of type iv l y 3 cyclic v l y 3 mobius vi l y 4 cylindrical and vii l y 4 open in the infinite length limit we calculate w q and determine the continuous locus of points where it is nonanalytic we show that our exact calculation of the entropy for the l y 4 strip with cylindrical boundary conditions provides an extremely accurate approximation to a few parts in 10 5 for moderate q values to the entropy for the full 2d honeycomb lattice where the latter is determined by monte carlo measurements since no exact analytic form is known

transfer matrices and partition function zeros for antiferromagnetic potts models iii triangular lattice chromatic polynomial we study the chromatic polynomial pg q for m n triangular lattice strips of widths m 12p 9f with periodic or free transverse boundary conditions respectively and arbitrary lengths n with free longitudinal boundary conditions the chromatic polynomial gives the zero temperature limit of the partition function for the q state potts antiferromagnet we compute the transfer matrix for such strips in the fortuin kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q plane in the limit n we recompute the limiting curve obtained by baxter in the thermodynamic limit m n and find new interesting features with possible physical consequences finally we analyze the isolated limiting points and their relation with the beraha numbers

transfer matrices for the partition function of the potts model on cyclic and mobius lattice strips abstract we present a method for calculating transfer matrices for the q state potts model partition functions z g q v for arbitrary q and temperature variable v on cyclic and mobius strip graphs g of the square sq triangular tri and honeycomb hc lattices of width l y vertices and of arbitrarily great length l x vertices for the cyclic case we express the partition function as z l y l x q v d 0 l y c d tr t z l y d m where denotes lattice type c d are specified polynomials of degree d in q t z l y d is the transfer matrix in the degree d subspace and m l x l x 2 for sq tri hc respectively an analogous formula is given for mobius strips we exhibit a method for calculating t z l y d for arbitrary l y explicit results for arbitrary l y are given for t z l y d with d l y and l y 1 in particular we find very simple formulas the determinant det t z l y d and trace tr t z l y corresponding results are given for the equivalent tutte polynomials for these lattice strips and illustrative examples are included we also present formulas for self dual cyclic strips of the square lattice

general structural results for potts model partition functions on lattice strips abstract we present a set of general results on structural features of the q state potts model partition function z g q v for arbitrary q and temperature boltzmann variable v for various lattice strips of arbitrarily great width ly vertices and length lx vertices including i cyclic and mobius strips of the square and triangular lattices and ii self dual cyclic strips of the square lattice we also present an exact solution for the chromatic polynomial for the cyclic and mobius strips of the square lattice with width ly 5 the greatest width for which an exact solution has been obtained so far for these families in the lx limit we calculate the ground state degeneracy per site w q and determine the boundary b across which w q is singular in the complex q plane

exact potts model partition functions on wider arbitrary length strips of the square lattice abstract we present exact calculations of the partition function of the q state potts model for general q and temperature on strips of the square lattice of width l y 3 vertices and arbitrary length l x with periodic longitudinal boundary conditions of the following types i fbc y pbc x cyclic ii fbc y tpbc x mobius iii pbc y pbc x toroidal and iv pbc y tpbc x klein bottle where fbc and t pbc refer to free and twisted periodic boundary conditions results for the l y 2 torus and klein bottle strips are also included in the infinite length limit the thermodynamic properties are discussed and some general results are given for low temperature behavior on strips of arbitrarily great width we determine the submanifold in the c 2 space of q and temperature where the free energy is singular for these strips our calculations are also used to compute certain quantities of graph theoretic interest

families of graphs with w r g q functions that are nonanalytic at 1 q 0 denoting p g q as the chromatic polynomial for coloring an n vertex graph g with q colors and considering the limiting function w g q lim n to infty p g q 1 n a fundamental question in graph theory is the following is w r g q q 1 w g q analytic or not at the origin of the 1 q plane where the complex generalization of q is assumed this question is also relevant in statistical mechanics because w g q exp s 0 k b where s 0 is the ground state entropy of the q state potts antiferromagnet on the lattice graph g and the analyticity of w r g q at 1 q 0 is necessary for the large q series expansions of w r g q although w r is analytic at 1 q 0 for many g there are some g for which it is not for these w r has no large q series expansion it is important to understand the reason for this nonanalyticity here we give a general condition that determines whether or not a particular w r g q is analytic at 1 q 0 and explains the nonanalyticity where it occurs we also construct infinite families of graphs with w r functions that are non analytic at 1 q 0 and investigate the properties of these functions our results are consistent with the conjecture that a sufficient condition for w r g q to be analytic at 1 q 0 is that g is a regular lattice graph lambda this is known not to be a necessary condition

tutte polynomial of scale free networks the tutte polynomial of a graph or equivalently the q state potts model partition function is a two variable polynomial graph invariant of considerable importance in both statistical physics and combinatorics the computation of this invariant for a graph is np hard in general in this paper we focus on two iteratively growing scale free networks which are ubiquitous in real life systems based on their self similar structures we mainly obtain recursive formulas for the tutte polynomials of two scale free networks lattices one is fractal and large world while the other is non fractal but possess the small world property furthermore we give some exact analytical expressions of the tutte polynomial for several special points at x y plane such as the number of spanning trees the number of acyclic orientations etc

transfer matrices for the partition function of the potts model on lattice strips with toroidal and klein bottle boundary conditions abstract we present a method for calculating transfer matrices for the q state potts model partition functions z g q v for arbitrary q and temperature variable v on strip graphs g of the square sq triangular tri and honeycomb hc lattices of width l y vertices and of arbitrarily great length l x vertices subject to toroidal and klein bottle boundary conditions for the toroidal case we express the partition function as z l y l x q v d 0 l y j b j d z l y d j m where denotes lattice type b j d are specified polynomials of degree d in q z l y d j are eigenvalues of the transfer matrix t z l y d in the degree d subspace and m l x l x 2 for sq tri hc respectively an analogous formula is given for klein bottle strips we exhibit a method for calculating t z l y d for arbitrary l y in particular we find some very simple formulas for the determinant det t z l y d and trace tr t z l y illustrative examples of our general results are given including new calculations of transfer matrices for potts model partition functions on strips of the square triangular and honeycomb lattices with toroidal or klein bottle boundary conditions

improved lower bounds on the ground state entropy of the antiferromagnetic potts model we present generalized methods for calculating lower bounds on the ground state entropy per site s 0 or equivalently the ground state degeneracy per site w e s 0 k b of the antiferromagnetic potts model we use these methods to derive improved lower bounds on w for several lattices

algebraic models of deviant modal operators based on de morgan and kleene lattices an algebraic model of a kind of modal extension of de morgan logic is described under the name mds5 algebra the main properties of this algebra can be summarized as follows 1 it is based on a de morgan lattice rather than a boolean algebra 2 a modal necessity operator that satisfies the axioms n k t and 5 and as a consequence also b and 4 of modal logic is introduced it allows one to introduce a modal possibility by the usual combination of necessity operation and de morgan negation 3 the necessity operator satisfies a distributivity principle over joins the latter property cannot be meaningfully added to the standard boolean algebraic models of s5 modal logic since in this boolean context both modalities collapse in the identity mapping the consistency of this algebraic model is proved showing that usual fuzzy set theory on a universe u can be equipped with a mds5 structure that satisfies all the above points 1 3 without the trivialization of the modalities to the identity mapping further the relationship between this new algebra and heyting wajsberg algebras is investigated finally the question of the role of these deviant modalities as opposed to the usual non distributive ones in the scope of knowledge representation and approximation spaces is discussed

chromatic polynomials for families of strip graphs and their asymptotic limits abstract we calculate the chromatic polynomials p gs m q and from these the asymptotic limiting functions w g s q lim n p g s q 1 n for families of n vertex graphs gs m comprised of m repeated subgraphs h adjoined to an initial graph i these calculations of w gs q for infinitely long strips of varying widths yield important insights into properties of w q for two dimensional lattices in turn these results connect with statistical mechanics since w q is the ground state degeneracy of the q state potts model on the lattice for our calculations we develop and use a generating function method which enables us to determine both the chromatic polynomials of finite strip graphs and the resultant w gs q function in the limit n from this we obtain the exact continuous locus of points b where w gs q is nonanalytic in the complex q plane this locus is shown to consist of arcs which do not separate the q plane into disconnected regions zeros of chromatic polynomials are computed for finite strips and compared with the exact locus of singularities b we find that as the width of the infinitely long strips is increased the arcs comprising b elongate and move toward each other which enables one to understand the origin of closed regions that result for the infinite 2d lattice

flow polynomials and their asymptotic limits for lattice strip graphs we present exact calculations of flow polynomials f g q for lattice strips of various fixed widths l y 4 and arbitrarily great lengths l x with several different boundary conditions square honeycomb and triangular lattice strips are considered we introduce the notion of flows per face fl in the infinite length limit we study the zeros of f g q in the complex q plane and determine exactly the asymptotic accumulation sets of these zeros in the infinite length limit for the various families of strips the function fl is nonanalytic on this locus the loci are found to be noncompact for many strip graphs with periodic or twisted periodic longitudinal boundary conditions and compact for strips with free longitudinal boundary conditions we also find the interesting feature that aside from the trivial case l y 1 the maximal point q cf where crosses the real axis is universal on cyclic and mobius strips of the square lattice for all widths for which we have calculated it and is equal to the asymptotic value q cf 3 for the infinite square lattice

ground state entropy of potts antiferromagnets on homeomorphic families of strip graphs abstract we present exact calculations of the zero temperature partition function and ground state degeneracy per site w for the q state potts antiferromagnet on a variety of homeomorphic families of planar strip graphs g ch k1 k2 k m where k1 k2 and k describe the homeomorphic structure and m denotes the length of the strip several different ways of taking the total number of vertices to infinity by sending i m with k1 k2 and k fixed ii k1 and or k2 with m and k fixed and iii k with m and p k1 k2 fixed are studied and the respective loci of points b where w is nonanalytic in the complex q plane are determined the b s for limit i are comprised of arcs which do not enclose regions in the q plane and for many values of p and k include support for re q b for limits ii and iii is the unit circle q 1 1

eigenfunction analysis of radially polarized piezoelectric cylindrical shells of finite length an eigenfunction approach is presented to determine the response of radially polarized piezoelectric cylindrical shells of finite length to electrical excitation the equations of motion of the piezoelectric cylinder are first derived by using the membrane approximation then they are solved by expressing the displacement distribution as the sum of the static solution and a weighted sum of a complete set of functions the eigenfunctions of the short circuited cylinder the static solution is necessary to exactly satisfy the boundary conditions of the electrically excited cylinder moreover in some cases the series solution does not converge to the correct displacement distribution when some other terms instead of the static solution are used to satisfy the boundary conditions the weights or displacement coefficients are determined by using the orthogonal property of the eigenfunctions finally the input electrical admittance is determined by using the equation of state and the displacement distribution analyses of cylinders with various boundary conditions are presented to illustrate the approach numerical results are used to show that the series solutions converge very rapidly to the closed form solutions

exact series model of langevin transducers with internal losses an exact series method is presented to analyze classical langevin transducers with arbitrary boundary conditions the transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders all three cylinders are of the same diameter the length to diameter ratio is arbitrary complex piezoelectric and elastic coefficients are used to model internal losses solutions to the exact linearized governing equations for each cylinder include four series each term in each series is an exact solution to the governing equations bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions respectively are used in the series asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti symmetric sets of functions all interface and boundary conditions are satisfied in a weighted average sense the computed input electrical admittance displacement and stress in transducers are pres

free vibration analysis of circular cylindrical shells abstract a general analytical method is presented for evaluating the free vibration characteristics of a circular cylindrical shell with classical boundary conditions of any type the solution is obtained through a direct solution procedure in which sanders shell equations are used with the axial modal displacements represented as simple fourier series expressions stokes transformation is exploited to obtain correct series expressions for the derivatives of the fourier series an explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions the accuracy of the method is checked against available data the method is used to find the modal characteristics of the thermal liner model of the u s fast test reactor ftp the numerical results obtained are compared with finite element method solutions

analysis of solid elastic cylinders with internal losses using complete sets of functions abstract a method to determine the response of a solid elastic isotropic cylinder with internal losses and arbitrary length to radius ratio to excitations acting on its surface is presented the method is based on the use of complete sets of functions and the response to arbitrary excitations can be analysed it is illustrated for axisymmetric excitations that are anti symmetric with respect to the plane midway between the ends of the cylinder excitations that are symmetric have been considered earlier d d ebenezer et al forced vibrations of solid elastic cylinders journal of sound and vibration 282 2005 991 1007 all components of displacement and stress are expressed as a sum of two infinite series that contain terms that are complete in the axial and radial direction respectively therefore arbitrary boundary conditions can be satisfied in lossless cylinders for each chosen set there are difficulties at those frequencies at which certain functions become zero some other complete set of functions can be used at these frequencies however this difficulty does not arise for cylinders with losses two different sets are used to compute the resonance frequencies of lossless cylinders the responses of cylinders with internal losses to uniform and concentrated excitations on the flat and curved surfaces are also presented to illustrate the approach they are in good agreement with results obtained using atila a finite element software package

exact potts model partition functions on ladder graphs abstract we present exact calculations of the partition function z of the q state potts model and its generalization to real q for arbitrary temperature on n vertex ladder graphs i e strips of the square lattice with width ly 2 and arbitrary length lx with free cyclic and mobius longitudinal boundary conditions these partition functions are equivalent to tutte whitney polynomials for these graphs the free energy is calculated exactly for the infinite length limit of these ladder graphs and the thermodynamics is discussed by comparison with strip graphs of other widths we analyze how the singularities at the zero temperature critical point of the ferromagnet on infinite length finite width strips depend on the width we point out and study the following noncommutativity at certain special values q s lim n lim q q s z 1 n lim q q s lim n z 1 n it is shown that the potts antiferromagnet on both the infinite length line and ladder graphs with cyclic or mobius boundary conditions exhibits a phase transition at finite temperature if 0 b in the corresponding c 2 space arising as the accumulation set of partition function zeros as n in particular we study the connection with the t 0 limit of the potts antiferromagnet where b reduces to the accumulation set of chromatic zeros certain properties of the complex temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice showing that exact solutions on infinite length strips provide a way of gaining insight into these complex temperature phase diagrams

potts model partition functions for self dual families of strip graphs abstract we consider the q state potts model on families of self dual strip graphs g d of the square lattice of width l y and arbitrarily great length l x with periodic longitudinal boundary conditions the general partition function z and the t 0 antiferromagnetic special case p chromatic polynomial have the respective forms j 1 n f l y c f l y j f l y j l x with f z p for arbitrary l y we determine i the general coefficient c f l y j in terms of chebyshev polynomials ii the number n f l y d of terms with each type of coefficient and iii the total number of terms n f l y we point out interesting connections between the n z l y d and temperley lieb algebras and between the n f l y and enumerations of directed lattice animals exact calculations of p are presented for 2 l y 4 in the limit of infinite length we calculate the ground state degeneracy per site exponent of the ground state entropy w q generalizing q from z to c we determine the continuous locus b in the complex q plane where w q is singular we find the interesting result that for all l y values considered the maximal point at which b crosses the real q axis denoted q c is the same and is equal to the value for the infinite square lattice q c 3 this is the first family of strip graphs of which we are aware that exhibits this type of universality of q c

axisymmetric free vibrations of finite anisotropic cylinders abstract a technique is presented for obtaining estimates for the natural frequencies of axisymmetric free vibration for anisotropic cylinders of finite length the weak forms of the governing differential equations are solved by using the ritz method with terms of power series in the co ordinate directions as the approximating functions the dimensions of the cylinder are arbitrary and a wide range of geometries can be considered the solution technique is applied to the example problems of an isotropic cylinder and a cylinder composed of a material with hexagonal symmetry the method gives natural frequencies and mode shapes that are in excellent agreement with existing solutions the condition of traction free faces of the cylinder is also accurately satisfied

analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on flat surfaces a method to analyze axially polarized piezoelectric ceramic cylinders with arbitrary length to radius ratio and arbitrary boundary conditions on the flat surfaces is presented the method is based on the use of functions that individually exactly satisfy the axisymmetric equations of motion and the gauss electrostatic conditions the axial and radial components of displacement and the potential are expressed as weighted sums of these functions the functions form complete sets in the radial direction and arbitrary boundary conditions can therefore be satisfied on the flat surfaces on the curved surface certain uniform boundary conditions can be exactly satisfied the weights are easily determined by using the orthogonal property of the functions the input electrical admittance is a function of only the average boundary conditions and is very easily determined several special cases and numerical results are presented for electrically and mechanically excited cylinders to illustrate the method the se

lower bounds and series for the ground state entropy of the potts antiferromagnet on archimedean lattices and their duals we prove a general rigorous lower bound for w lambda q exp s 0 lambda q k b the exponent of the ground state entropy of the q state potts antiferromagnet on an arbitrary archimedean lattice lambda we calculate large q series expansions for the exact w r lambda q q 1 w lambda q and compare these with our lower bounds on this function on the various archimedean lattices it is shown that the lower bounds coincide with a number of terms in the large q expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions w r lambda q for large q on the various lattices lambda plots of w r lambda q are given and the general dependence on lattice coordination number is noted lower bounds and series are also presented for the duals of archimedean lattices as part of the study the chromatic number is determined for all archimedean lattices and their duals finally we report calculations of chromatic zeros for several lattices these provide further support for our earlier conjecture that a sufficient condition for w r lambda q to be analytic at 1 q 0 is that lambda is a regular lattice

wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section in this paper the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non extensible membranes the three dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations which relate the frequencies of elastic waves to their wavenumbers numerical results for waveguides with various boundary conditions are presented to illustrate the approach analysis of the dispersion spectra is carried out and cutoff frequencies are obtained and characterized mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed the main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed the results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder

on the dobrakov submeasure on fuzzy sets the well known fact that any nonatomic measure has the darboux property has been generalized in many directions particularly by dobrakov dissertationes math 112 1974 1 and recently by klimkin and svistula mat sb 192 2001 41 in this paper the fuzzy sets are taken instead of sets as elements of domain of considered mappings

submeasures on nuanced mv algebras abstract this paper further investigates the properties of submeasures on n nuanced mv algebras introduced by the author in a previous work we prove that there is a one to one correspondence between the set of submeasures on an n nuanced mv algebra and the set of submeasures on its mv center as a main result we prove an extension theorem for submeasures on n nuanced mv algebras this result generalizes the extension theorems which have been proved by riecan for mv algebras and by georgescu for ukasiewicz moisil algebras the perfect nmva n is defined and studied and the notion of a bounded local submeasure on a perfect nmva n is introduced it is proved that any bounded local submeasure on a perfect nmva n l can be extended to a submeasure on l

transfer matrices for the zero temperature potts antiferromagnet on cyclic and mobius lattice strips abstract we present transfer matrices for the zero temperature partition function of the q state potts antiferromagnet equivalently the chromatic polynomial on cyclic and mobius strips of the square triangular and honeycomb lattices of width l y and arbitrarily great length l x we relate these results to our earlier exact solutions for square lattice strips with l y 3 4 5 triangular lattice strips with l y 2 3 4 and honeycomb lattice strips with l y 2 3 and periodic or twisted periodic boundary conditions we give a general expression for the chromatic polynomial of a mobius strip of a lattice and exact results for a subset of honeycomb lattice transfer matrices both of which are valid for arbitrary strip width l y new results are presented for the l y 5 strip of the triangular lattice and the l y 4 and l y 5 strips of the honeycomb lattice using these results and taking the infinite length limit l x we determine the continuous accumulation locus of the zeros of the above partition function in the complex q plane including the maximal real point of nonanalyticity of the degeneracy per site w as a function of q

chromatic polynomials of large triangular lattices evaluating the q colourings of a lattice is equivalent to solving the q state zero temperature antiferromagnetic potts model this has recently been done exactly for an infinite triangular lattice with q real here the results are extended to the full complex q plane giving the limiting distribution of the zeros of the chromatic polynomial the results are compared with finite lattice calculations and the occurrence of isolated real zeros converging on the beraha numbers is noted

exact potts model partition function on strips of the triangular lattice abstract in this paper we present exact calculations of the partition function z of the q state potts model and its generalization to real q for arbitrary temperature on n vertex strip graphs of width ly 2 and arbitrary length of the triangular lattice with free cyclic and mobius longitudinal boundary conditions these partition functions are equivalent to tutte whitney polynomials for these graphs the free energy is calculated exactly for the infinite length limit of the graphs and the thermodynamics is discussed considering the full generalization to arbitrary complex q and temperature we determine the singular locus b in the corresponding c 2 space arising as the accumulation set of partition function zeros as n in particular we study the connection with the t 0 limit of the potts antiferromagnet where b reduces to the accumulation set of chromatic zeros comparisons are made with our previous exact calculation of potts model partition functions for the corresponding strips of the square lattice our present calculations yield as special cases several quantities of graph theoretic interest

comments on accurate vibration frequencies of circular cylinders from three dimensional analysis j acoust soc am 98 2136 2141 1995 leissa and so presented accurate frequencies for solid cylinders using the rayleigh ritz method for both a completely traction free solid cylinder and a solid cylinder which is fixed at one end they compared their frequencies for the traction free case with my series solution in their tables vi and vii the comparison does not demonstrate the accuracy which can be achieved with the series solution a table demonstrating the convergence of the series solution is presented in this comment discrepancies were found between the rayleigh ritz solutions and the converged series solution for some of the frequencies in table vi further discrepancies were found in some of the other results all discrepancies are tabulated for the traction free case

forced vibrations of solid elastic cylinders abstract a method is presented to determine the vibration response of a solid elastic isotropic cylinder with arbitrary length to radius ratio when subject to arbitrary distribution of axisymmetric excitation on its surfaces in this method the axial and radial components of displacement are expressed as a sum of two infinite series each term in both the series is an exact solution to the governing equations of motion and has a coefficient that is used to satisfy boundary conditions one series contains bessel functions that form a complete set in the radial direction and the other contains trigonometric functions that form a complete set in the axial direction the components of stress are also expressed in terms of complete sets of functions by using the expression for displacement the coefficients in the series are determined by using the orthogonal properties of the functions to satisfy the boundary conditions in a mean square error sense numerical results are presented to illustrate the broadband responses of cylinders to uniform and concentrated loads on the flat and curved surfaces they are in good agreement with results obtained using atila a commercial finite element software

ground state degeneracy of potts antiferromagnets on two dimensional lattices approach using infinite cyclic strip graphs the q state potts antiferromagnet on a lattice lambda exhibits nonzero ground state entropy s0 kb ln w for sufficiently large q and hence is an exception to the third law of thermodynamics an outstanding challenge has been the calculation of w sq q on the square sq lattice we present here an exact calculation of w on an infinite length cyclic strip of the square lattice which embodies the expected analytic properties of w sq q similar results are given for the kagome lattice

t 0 partition functions for potts antiferromagnets on lattice strips with fully periodic boundary conditions abstract we present exact calculations of the zero temperature partition function for the q state potts antiferromagnet equivalently the chromatic polynomial for families of arbitrarily long strip graphs of the square and triangular lattices with width ly 4 and boundary conditions that are doubly periodic or doubly periodic with reversed orientation i e of torus or klein bottle type these boundary conditions have the advantage of removing edge effects in the limit of infinite length we calculate the exponent of the entropy w q and determine the continuous locus b where it is singular we also give results for toroidal strips involving crossing subgraphs these make possible a unified treatment of torus and klein bottle boundary conditions and enable us to prove that for a given strip the locus b is the same for these boundary conditions

elastic waves in piezoceramic cylinders of sector cross section abstract the propagation of elastic waves in piezoceramic cylindrical waveguides of circular cross sections with sector cut is investigated on the basis of the linear theory of electroelasticity dispersion functions are obtained from boundary conditions in an analytical form of functional determinants for each value of the generalized wave number a selected set of numerical results including real imaginary and complex branches of full dispersion spectrums with various symmetry of wave movements is presented to describe the essential characteristics of the waves leading effects of spectrums transformation by change of waveguide s angular measure are enlightened and wave asymptotic behavior is analyzed the variation of the cross section is considered as a mechanism to control the dispersion characteristics of waveguides

finite solid circular cylinders subjected to arbitrary surface load part i analytic solution abstract this paper presents a general framework for obtaining analytic solutions for finite elastic isotropic solid cylinders subjected to arbitrary surface load the method of solution uses the displacement function approach to uncouple the equations of equilibrium the most general solution forms for the two displacement functions for solid cylinders are proposed in terms of infinite series with z and dependencies in terms of trigonometric and hyperbolic functions and with r dependency in terms of bessel and modified bessel functions of the first kind of fractional order all possible combinations of odd and even dependencies of and z are included and the curved boundary loads are expanded into double fourier series expansion while the end boundary loads are expanded into fourier bessel expansion it is showed analytically that only one set of the end boundary conditions needs to be satisfied a system of simultaneous equations for the unknown constants is given independent of the type of the boundary loads this new approach provides the most general theory for the stress analysis of elastic isotropic solid circular cylinders of finite length application of the present solution to the stress analysis for the double punch test is presented in part ii of this study

an exact series solution for calculating the eigenfrequencies of orthotropic plates with completely free boundary abstract an analysis for solving boundary value problems in structural mechanics which was proposed by wang and lin 1996 journal of sound and vibration 196 285 293 1999 journal of applied mechanics 66 380 387 1 2 has been extended to the calculation of the eigenfrequencies of an orthotropic plate under all free boundary conditions the convergence of the series solution is assured and the procedure leads to pointwise exact solutions the calculated eigenfrequencies have been verified by a different approach and indicate that the present method is simple and effective

structural properties of potts model partition functions and chromatic polynomials for lattice strips abstract the q state potts model partition function equivalent to the tutte polynomial for a lattice strip of fixed width l y and arbitrary length l x has the form z g q v j 1 n z g c z g j z g j l x where v is a temperature dependent variable the special case of the zero temperature antiferromagnet v 1 is the chromatic polynomial p g q using coloring and transfer matrix methods we give general formulas for c x g j 1 n x g c x g j for x z p on cyclic and mobius strip graphs of the square and triangular lattice combining these with a general expression for the unique coefficient c z g j of degree d in q c d u 2d q 2 where u n x is the chebyshev polynomial of the second kind we determine the number of z g j s with coefficient c d in z g q v for these cyclic strips of width l y to be n z l y d 2d 1 l y d 1 1 2l y l y d for 0 d l y and zero otherwise for both cyclic and mobius strips of these lattices the total number of distinct eigenvalues z g j is calculated to be n z l y 2l y l y results are also presented for the analogous numbers n p l y d and n p l y for p g q we find that n p l y 0 n p l y 1 1 m l y 1 motzkin number n z l y 0 c l y the catalan number and give an exact expression for n p l y our results for n z l y and n p l y apply for both the cyclic and mobius strips of both the square and triangular lattices we also point out the interesting relations n z l y 2 n da tri l y and n p l y 2 n da sq l y where n da n denotes the number of directed lattice animals on the lattice we find the asymptotic growths n z l y l y 1 2 4 l y and n p l y l y 1 2 3 l y as l y some general geometric identities for potts model partition functions are also presented