some notes on the paper cone metric spaces and fixed point theorems of contractive mappings abstract huang and zhang reviewed cone metric spaces in 2007 huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we shall prove that there are no normal cones with normal constant m 1 and for each k 1 there are cones with normal constant m k also by providing non normal cones and omitting the assumption of normality in some results of huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we obtain generalizations of the results

some theorems on existence and uniqueness of fixed points for decreasing operators in this paper we employ partial order method cone theory and monotone iterative technique to prove several new theorems on the existence and uniqueness of fixed points for decreasing operators without compactness some applications are also given

the equations of motion of curved pipes conveying fluid abstract the non linear differential equations of motion of a fluid conveying pipe the no flow configuration of which is in the shape of a one dimensional line arbitrarily curved and twisted in space are derived by making use of the newtonian approach the extensible dynamics of the beam is based on the timoshenko beam theory some significant differences with the equations available in the open literature are discussed the stressed by flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe fluid systems

tripled coincidence theorems for contractive type mappings in partially ordered metric spaces abstract in this paper we establish tripled coincidence point theorems for a pair of mappings f x x x x and g x x satisfying a nonlinear contractive condition ordered metric spaces presented theorems extend reveral existing results in the literature v lakshmikantham l ciric coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces nonlinear anal 70 2009 4341 4349 and harjani lopez and sadarangani in article j harjani b lopez k sadarangani fixed point theorems for mixed monotone operators and applications to integral equations nonlinear anal 74 2011 1749 1760

convergence theorems best approximation and best proximity for set valued dynamic systems of relatively quasi asymptotic contractions in cone uniform spaces abstract in cone uniform spaces x using the concept of the d family of cone pseudodistances the distance between two not necessarily convex or compact sets a and b in x is defined the concepts of cyclic and noncyclic set valued dynamic systems of d relatively quasi asymptotic contractions t a b 2 a b are introduced and the best approximation and best proximity point theorems for such contractions are proved also conditions are given which guarantee that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and the limit is a best proximity point moreover d families are constructed characterized and compared the results are new for set valued and single valued dynamic systems in cone uniform cone locally convex and cone metric spaces various examples illustrating ideas methods definitions and results are constructed

out of plane vibrations of curved non uniform beams of constant radius the governing differential equations for out of plane vibrations of curved non uniform beams of constant radius are derived two physical parameters are introduced to simplify the analysis the explicit relations between the flexural displacement its first three order derivatives and the torsional displacement are derived with these explicit relations the two coupled governing characteristic differential equations can be decoupled and reduced to a sixth order ordinary differential equation with variable coefficients in the torsional displacement it is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms of spatial variable then exact solutions for the out of plane vibrations of the beam can be obtained the derived explicit relations can also be used to reduce the difficulty in experimental measurements finally the influence of taper ratio center angle and arc length on the first two natural frequencies of the beams is illustrated

the equations of motion of initially stressed timoshenko tubular beams conveying fluid abstract in this paper the equations of motion of an initially stressed timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of hamilton s principle this latter is obtained first for open systems the instantaneous total mass of which does not necessarily remain constant in the course of deformation open denoting that there is momentum transport in and out of the system the equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped yet another derivation for the cantilevered tube is presented with the system considered to be quasi closed where all flow induced effects are incorporated through the virtual work as if they were external forces all three sets of equations are found to be identical these equations are then compared with those obtained more simply by the newtonian force balance approach some differences between them are found to exist the principal of which are associated with the follower or other tensile forces these are discussed at some length and the equations of motion obtained here are compared to those obtained by other researchers for timoshenko beams subjected to follower or tensile forces

the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

worst case analysis of an algorithm for cellular manufacturing abstract two measures for the efficiency of grouping in cellular manufacturing are discussed in this paper we first analyze the effectiveness of the first measure grouping efficiency a worst case bound is then derived for the minimum spanning tree algorithm with respect to this measure we then show a newly proposed measure grouping efficacy is not suitable from an algorithmic point of view a weighted grouping efficacy is then proposed and worst case bounds are derived with respect to this new measure we also propose several policies to improve grouping efficiency and grouping efficacy during the decomposition of larger machine cells computational results will also be presented to demonstrate the effectiveness of these measures and the worst case bounds

greedy random adaptive memory programming search for the capacitated clustering problem in the capacitated clustering problem ccp a given set of n weighted points is to be partitioned into p clusters such that the total weight of the points in each cluster does not exceed a given cluster capacity the objective is to find a set of p centers that minimises the total scatter of points allocated to these centers in this paper we propose a merger of greedy random adaptive search procedure grasp and adaptive memory programming amp into a new gramps framework for the ccp a learning process is kept in charge of tracking information on the best components in an elite set of gramps solutions the information are strategically combined with problem domain data to restart the construction search phase at early stage of constructions priorities are given to problem domain data and progressively shifted towards generated information as the learning increases gramps is implemented with an efficient local search descent based on a restricted interchange neighbourhood extensive experiments are reported on on a standard set of bench marks from the literature and on a new set of large instances the results show that gramps has an efficient learning mechanism and is competitive with the existing methods in the literature

positive solutions of operator equations on ordered banach spaces and applications this paper is concerned with an operator equation on ordered banach spaces the existence and uniqueness of its positive solutions is obtained by using the properties of cones and monotone iterative technique as applications we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for two classes of integral equations

boyd wong type common fixed point results in cone metric spaces abstract some common fixed point results in cone metric spaces of c di bari and p vetro c di bari p vetro pairs and common fixed points in cone metric spaces rend cir mat palermo 57 2008 279 285 as well as p raja and s m vaezpour p raja s m vaezpour some extensions of banach s contraction principle in complete metric spaces fixed point theory appl 2008 doi 10 1155 2008 768294 are extended using generalized contractive type conditions and cones which may be nonnormal cone metric versions of several well known results such as boyd wong s theorem d w boyd j s wong on nonlinear contractions proc amer math soc 20 1969 458 464 are obtained as special cases

common fixed points for maps on cone metric space the purpose of this paper is to generalize and to unify fixed point theorems of das and naik ciric jungck huang and zhang on complete cone metric space

vibration of an axially moving string with geometric non linearity and translating acceleration the vibration of an axially moving string is studied when the string has geometric non linearity and translating acceleration based upon the von karman strain theory the equations of motion are derived considering the longitudinal and transverse deflections the equation for the longitudinal vibration is linear and uncoupled while the equation for the transverse vibration is non linear and coupled between the longitudinal and transverse deflections these equations are discretized by the galerkin method after they are transformed into the variational equations i e the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively with the discretized equations the natural frequencies the time histories of the deflections and the distributions of the deflection and stress are investigated in addition comparisons between the results of linear and non linear theories are provided

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces in the first part of this paper we generalize results on common fixed points in ordered cone metric spaces obtained by i altun and g durmaz i altun g durmaz some fixed point theorems on ordered cone metric spaces rend circ mat palermo 58 2009 319 325 and i altun b damnjanovic and d djoric i altun b damnjanovic d djoric fixed point and common fixed point theorems on ordered cone metric spaces appl math lett 2009 doi 10 1016 j aml 2009 09 016 by weakening the respective contractive condition then the notions of quasicontraction and g quasicontraction are introduced in the setting of ordered cone metric spaces and respective common fixed point theorems are proved in such a way known results on quasicontractions and g quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces examples show that there are cases when new results can be applied while old ones cannot

application of the transfer matrix method to non conservative systems involving fluid flow in curved pipes abstract the application of the transfer matrix method to problems of fluid flow in planar curved pipes is presented also a presentation is given of how to deal with the stability of non conservative problems when using the dynamic method in the method proposed account is taken of the effect of the initial state of stress on the dynamic behaviour of the pipe three well known problems are solved to verify the convergence and applicability of the transfer matrix formulation to non conservative problems involving fluid flow

vibration of high speed rotating rings coupled to space fixed stiffnesses abstract this study investigates the vibration of high speed rotating rings coupled to space fixed discrete stiffnesses the ring radial and tangential deformations are defined using space fixed eulerian coordinates where material particles pass through fixed locations in space engineering strain is used in the strain energy expression the derived nonlinear equations from hamilton s principle are linearized about the steady non trivial configuration that results from constant ring rotation comparisons are made to other models in the literature that use different assumptions the governing equations are cast in terms of matrix differential operators that reveal the system s standard gyroscopic system structure the natural frequencies and vibration modes are calculated over a wide range of rotation speeds for axisymmetric free rings and a non axisymmetric ring with a space fixed discrete stiffness element

new fluid velocity expression in an extensible semi circular pipe conveying fluid a new expression for fluid velocity is presented for a fluid conveying semi circular pipe with an extensible centreline the proposed fluid velocity expression is obtained from the material derivative while the previous velocity expressions are from love s kinematical relations in order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions the equations of in plane motion derived with the new expression are compared to the equations derived with the previous expressions furthermore the equilibrium positions natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed

new existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation abstract in this paper we obtain some new and general existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation which extend the corresponding results in z t zhang new fixed point theorems of mixed monotone operators and applications j math anal appl 204 1996 307 319 theorem 1 corollaries 1 and 2 moreover some applications to nonlinear integral equations on unbounded region are given

the dynamics of a piping system with internal unsteady flow abstract the dynamics of a pipeline conveying one dimensional unsteady flow is considered the dynamics of the fluid pipe system is represented by a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow the vibration equations of the pipeline are derived by use of newton s law of motion while the fluid equations are derived based on the concept of a deformable moving control volume the equations are fully coupled to each other and thus can be applied to various fluid pipe interaction problems which can be generated by the diverse operations of valves and pumps attached to the pipeline the equations are applied to a simply supported inclined straight pipeline to investigate the stabilities and dynamic responses of the pipeline the stability analysis is conducted by use of bolotin s method the dynamic responses are numerically investigated for both stable and unstable conditions it is observed that unstable regions in the stability chart expand as the flow velocity and the mass density of the fluid increase and that natural frequencies of the pipeline increase as the fluid friction acting on the inner surface of pipeline increases

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

dynamic processes and fixed points of set valued nonlinear contractions in cone metric spaces abstract investigations concerning the existence of dynamic processes convergent to fixed points of set valued nonlinear contractions in cone metric spaces are initiated the conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established our theorems generalize recent results obtained by huang and zhang l g huang x zhang cone metric spaces and fixed point theorems of contractive maps j math anal appl 332 2007 1467 1475 for cone metric spaces and by klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 1 2007 132 139 for metric spaces the examples and remarks provided show an essential difference between our results and those mentioned above

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

common fixed points under contractive conditions in cone metric spaces the aim of this paper is to present coincidence point result for two mappings in cone metric space which satisfy new contractive conditions our results generalize fixed point theorems of jungck g jungck commuting maps and fixed points amer math monthly 83 1976 261 263 abbas jungck m abbas g jungck common fixed point results for noncommuting mappings without continuity in cone metric spaces j math anal appl 341 2008 416 420 and fisher b fisher four mappings with a common fixed point arabic summary j univ kuwait sci 8 1981 131 139 in cone metric spaces to symmetric spaces

fixed points of decreasing operators in ordered banach spaces and applications to nonlinear second order elliptic equations in this paper we consider some decreasing operators in ordered banach spaces we study the existence and uniqueness of fixed points and properties of the iterative sequences for these operators lastly the results are applied to nonlinear second order elliptic equations

measures of grouping efficiency in cellular manufacturing systems abstract grouping efficiency is a measure of goodness of machine part groups in cellular manufacturing systems this paper briefly presents a critical review of existing grouping measures introduces a new measure called doubly weighted grouping efficiency measure and evaluates its relative performance of with other existing measures here special emphasis is given evaluation of the goodness of clustering solutions in block diagonalization of machine part incidence matrix in order to provide information on the measures results are collected and compiled from discretely reported sources and are reported both descriptively and quantitatively categorization and generalization of these measures are made to use them for goodness of clustering in order to overcome a number of drawbacks in the previously known measures a new doubly weighted grouping efficiency measure is presented and its performance is demonstrated with respect to several efficiency measures

common fixed point theorems on generalized distance in ordered cone metric spaces in this paper we introduce a concept of the c distance in a cone metric space and by using the concept of the c distance prove some fixed point theorems in ordered cone metric spaces

on the in plane vibrations of rotating rings the general problem of the in plane vibrations of a rotating ring is investigated the potential and kinetic energy functionals including the effects of extensional and shear deformation and of rotatory inertia respectively are derived the governing differential equations for the inextensional case are derived by using hamilton s principal and shown to have additional terms not present in previous works numerical studies which show the importance of these additional terms are presented

a note on cone metric fixed point theory and its equivalence abstract the main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense we show that the banach contraction principles in general metric spaces and in t v s cone metric spaces are equivalent our theorems also extend some results in huang and zhang 2007 l g huang x zhang cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 rezapour and hamlbarani 2008 sh rezapour r hamlbarani some notes on the paper cone metric spaces and fixed point theorems of contractive mappings j math anal appl 345 2008 719 724 and others

the p median problem for cluster analysis a comparative test using the mixture model approach recently mulvey and crowder mulvey j h crowder 1979 cluster analysis an application of lagrangian relaxation management sci 25 329 340 suggested that the p median problem might be useful for cluster analysis problems where the goal is to group objects described by a vector of characteristics in such a way that objects in the same group are somehow more alike than objects in different groups the intent of this paper is to test mulvey and crowder s proposal using the mixture model approach i e by applying a number of algorithms including one for the p median problem to a set of objects randomly sampled from a number of known multivariate populations and comparing the ability of each algorithm to detect the original populations in order to evaluate the results a generalized partition comparison measure and its distribution are developed using this measure results from various algorithms are compared

an alternative approach for the analysis of nonlinear vibrations of pipes conveying fluid based on a novel extended version of the lagrange equations for systems containing non material volumes the nonlinear equations of motion for cantilever pipe systems conveying fluid are deduced an alternative to existing methods utilizing newtonian balance equations or hamilton s principle is thus provided the application of the extended lagrange equations in combination with a ritz method directly results in a set of nonlinear ordinary differential equations of motion as opposed to the methods of derivation previously published which result in partial differential equations the pipe is modeled as a euler elastica where large deflections are considered without order of magnitude assumptions for the equations of motion a dimensional reduction with arbitrary order of approximation is introduced afterwards and compared with existing lower order formulations from the literature the effects of nonlinearities in the equations of motion are studied numerically the numerical solutions of the extended lagrange equations of the cantilever pipe system are compared with a second approach based on discrete masses and modeled in the framework of the multibody software hotint mbs instability phenomena for an increasing number of discrete masses are presented and convergence towards the solution for pipes conveying fluid is shown

positive solutions for nonlinear operator equations and several classes of applications in this paper we study a class of nonlinear operator equations x ax x 0 on ordered banach spaces where a is a monotone generalized concave operator using the properties of cones and monotone iterative technique we establish the existence and uniqueness of solutions for such equations in particular we do not demand the existence of upper lower solutions and compactness and continuity conditions as applications we study first order initial value problems and two point boundary value problems with the nonlinear term is required to be monotone in its second argument in the end applications to nonlinear systems of equations and to nonlinear matrix equations are also considered

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

flexural vibration of a thin rotating ring abstract flexural vibration of a thin rotating ring has been investigated experimentally and from some theoretical points of view the frequencies of forward and backward flexural traveling waves were measured by using strain gages the range of rotational speeds of the ring was such as to include frequencies comparable with that of the fundamental flexural mode of a non rotating ring and the stability of flexural vibration was examined with consideration of the effects of the centrifugal and coriolis forces it was ascertained that for all the flexural modes of the rotating ring no instability phenomenon exists in the sense that the natural frequencies of the rotating ring never become zero over the whole range of rotational speed in the light of the experimental results previous theories for a rotating ring or a circular cylindrical shell and the author s theory for a ring are examined and some differences among them discussed

a fixed point theorem for convex and decreasing operators abstract in this paper we present a new fixed point theorem for noncompact convex and decreasing operators which extends the existing corresponding results as a sample we give an application of the fixed point theorem to the two point boundary value problem for a second order differential equation

parametric vibration of an elastic structure with stationary and rotating rings subjected to traveling loads abstract this work examines the parametric vibration of an elastic dual ring structure an analytical model is developed through hamilton theory where stationary supports and rotating loads between stationary and rotating rings are included analytical results are obtained by using galerkin s and multi scale methods the results imply that there exist four types of excitations and that vibration can occur in a coupled uncoupled principal or combination manner the unstable boundaries are derived as closed form expressions of basic parameters influences of the ratio of the wavenumber to the support number the stiffness ratio of the rotating supports to ring bending and their speed ratios are also identified all analytical results are validated by numerical calculations via floquet theory this study suggests applications in electric motors to suppress parametric vibration or piezoelectric energy harvesters to arouse such vibration to improve the energy efficiency

in plane free vibration of a single crystal silicon ring in this paper the natural frequencies and the associated mode shapes of in plane free vibration of a single crystal silicon ring are analyzed it is found that the si 1 1 1 ring is two dimensionally isotropic in the 1 1 1 plane for elastic constants but three dimensionally anisotropic while the si 1 0 0 ring is fully anisotropic hamilton s principle is used to derive the equations of vibration which is a set of partial differential equations with coefficients being periodic in polar variable expressing the radial and tangential displacements in sinusoidal form with non predetermined amplitudes and through the integration with respect to the circumferential variable the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form the exact expressions for frequencies and mode shapes are obtained it is found that for si 1 0 0 rings the frequencies of a pair of modes which are equal for an isotropic ring split due to the anisotropic effect only for the second in plane vibration mode the phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups when the single crystal silicon is replaced by the polycrystalline silicon which is isotropic in elastic constants the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting

common fixed point results for noncommuting mappings without continuity in cone metric spaces the existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions without appealing to continuity in a cone metric space is established these results generalize several well known comparable results in the literature

free non linear vibration of a rotating thin ring with the in plane and out of plane motions free non linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in plane and out of plane motions the geometric non linearity of displacements is considered by adopting the lagrange strain theory for the circumferential strain instead of the infinitesimal strain theory by using hamilton s principle the coupled non linear partial differential equations are derived which describe the out of plane bending and torsional motions as well as the in plane bending and extensional motions during deriving the equations of motion we discuss how to model the circumferential stress and strain in order to consider the geometric non linearity four models are established three non linear models and one linear model for the four models the linearized equations of motion are obtained in the neighbourhood of the steady state equilibrium position based on the linearized equations of the four cases the natural frequencies are computed at various rotational speeds and then they are compared through the comparison this study recommends which model is appropriate to describe the non linear behaviour more precisely

new non linear modelling for vibration analysis of a straight pipe conveying fluid abstract a new non linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends using the euler bernoulli beam theory and the non linear lagrange strain theory from the extended hamilton s principle the coupled non linear equations of motion for the longitudinal and transverse displacements are derived these equations of motion are discretized by using the galerkin method after the discretized equations are linearized in the neighbourhood of the equilibrium position the natural frequencies are computed from the linearized equations on the other hand the time histories for the displacements are also obtained by applying the generalized time integration method to the non linear discretized equations the validity of the new modelling is provided by comparing results from the proposed non linear equations with those from the equations proposed by paidoussis

on cone metric spaces a survey abstract using an old m krein s result and a result concerning symmetric spaces from s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces banach j math anal 5 1 2011 38 50 we show in a very short way that all fixed point results in cone metric spaces obtained recently in which the assumption that the underlying cone is normal and solid is present can be reduced to the corresponding results in metric spaces on the other hand when we deal with non normal solid cones this is not possible in the recent paper m a khamsi remarks on cone metric spaces and fixed point theorems of contractive mappings fixed point theory appl 2010 7 pages article id 315398 doi 10 1115 2010 315398 the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant also that underlying banach space and the associated cone subset are not necessary in fact khamsi s approach includes a small class of results and is very limited since it requires only normal cones so that all results with non normal cones which are proper extensions of the corresponding results for metric spaces cannot be dealt with by his approach

clustering of objects and attributes for manufacturing and marketing applications abstract the problem of optimally grouping a set of n objects into a set of k clusters is one of the classic unresolved problems in the clustering literature thus prior work in clustering has primarily focused on developing computationally efficient heuristics for grouping objects into clusters however there are a variety of applications where both the object and associated attribute set needs to be simultaneously grouped in this paper we propose such an alternative view of the clustering problem essentially we adopt the perspective that not only do we want to group the set of n objects into clusters but that the attribute set q associated with the object set n is also to be simultaneously grouped into clusters given the combinatorial nature of this problem we develop a two phase sequential algorithm at the first phase we identify the optimal set of k object clusters this is followed by a polynomially bounded procedure at the second phase for optimally assigning the attribute set to each object cluster identified in the first phase we illustrate our approach by applying it to two decision problems in manufacturing and retailing that require a determination of object and attribute clusters

endpoints and fixed points of set valued contractions in cone metric spaces abstract in this paper we introduce the concept of set valued contractions in cone metric spaces and establish new endpoint and fixed point theorems for such contractions the paper includes examples

fixed point theorem for two non self mappings in cone metric spaces in this paper we extend a fixed point theorem of imdad and kumar for a pair of non self maps to non normal cone spaces

positive fixed points for nonlinear operators this paper is concerned with the existence and uniqueness of positive fixed points for nonlinear decreasing operators with sublinear perturbation operators in ordered banach spaces a new fixed point theorem without the assumption of compactness and continuity of operators is established and an iterative sequence yielding the fixed point is also given in addition an application to nonlinear integral equations is shown

generalized contractions in partially ordered metric spaces and applications to ordinary differential equations the purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions we also present some applications to first and second order ordinary differential equations

non linear vibration of a flexible spinning disc with angular acceleration non linear dynamic responses are analyzed for a flexible spinning disc with angular acceleration based on the kirchhoff plate theory and the von karman strain theory non linear equations of motion are derived which are coupled equations between the radial tangential and transverse displacements the equations of motion are discretized by using the galerkin method from the discretized equations the dynamic responses are computed by the generalized time integration method the analysis results show the effects of angular acceleration on the dynamic responses

dynamical behaviors of a fluid conveying curved pipe subjected to motion constraints and harmonic excitation this paper investigates the nonlinear dynamics of a fluid conveying curved pipe subjected to motion constraints and harmonic excitation at first the background theory for curved pipes conveying fluid with motion constraints is presented then emphasis is placed on the possible nonlinear dynamic behaviors of a constrained curved pipe subject to a harmonic excitation for such a forced dynamical system calculations of bifurcation diagrams phase plane portraits time responses power spectrum diagrams and poincare maps of the oscillations clearly establish the existence of the chaotic motions and quasi periodic motions moreover it is found that the route to chaos is through a sequence of period doubling bifurcations finally the difference in the nonlinear dynamics between the self vibration system and forced system is further discussed

a sum operator equation and applications to nonlinear elastic beam equations and lane emden fowler equations article history this paper is concerned with an operator equation ax bx cx x on ordered banach spaces where a is an increasing concave operator b is an increasing sub homogeneous operator and c is a homogeneous operator the existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general concave operators as applications we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth order two point boundary value problems for elastic beam equations and elliptic value problems for lane emden fowler equations

machine part cell formation using biclustering abstract cellular manufacturing is the cornerstone of many modern flexible manufacturing techniques taking advantage of the similarities between parts in order to decrease the complexity of the design and manufacturing life cycle part machine grouping pmg problem is the key step in cellular manufacturing aiming at grouping parts with similar processing requirements or similar design features into part families and by grouping machines into cells associated to these families the pmg problem is np complete and the different proposed techniques for solving it are based on heuristics in this paper a new approach for solving the pmg problem is proposed which is based on biclustering biclustering is a methodology where rows and columns of an input data matrix are clustered simultaneously a bicluster is defined as a submatrix spanned by both a subset of rows and a subset of columns although biclustering has been almost exclusively applied to dna microarray analysis we present that biclustering can be successfully applied to the pmg problem we also present empirical results to demonstrate the efficiency and accuracy of the proposed technique with respect to related ones for various formations of the problem

dynamic stability of a semi circular pipe conveying harmonically oscillating fluid the dynamic stability of a semi circular pipe conveying harmonically oscillating fluid is investigated in this study for analysis harmonically oscillating flow is regarded as a parametrically excited system with time varying coefficients considering the extensibility and nonlinearity of the semi circular pipe the equations of motion and the associated boundary conditions are obtained by using the extended hamilton principle applying floquet theory to the derived equations the stability of the pipe is analyzed for variations of the amplitude and oscillating frequency of the fluid velocity the effects of the mean value for the fluid velocity on the stability are also analyzed it is found that the semi circular pipe may become unstable when the fluctuation frequency approaches some multiples or sum of the out of plane natural frequencies furthermore it is observed that the instability regions increase with the mean value of the velocity the results obtained via the stability analysis are verified by time responses computed by using a direct time integration method

parametric instability of spinning elastic rings excited by fluctuating space fixed stiffnesses abstract this study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space fixed discrete stiffnesses with periodically fluctuating stiffnesses the rotating elastic ring is modeled using thin ring theory with radial and tangential deformations primary and combination instability regions are determined in closed form using the method of multiple scales the ratio of peak to peak fluctuation to average discrete stiffness is used as the perturbation parameter so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses the natural frequencies and vibration modes are determined by discretizing the governing equations using galerkin s method results are demonstrated for compliant gear applications the perturbation results are validated by direct numerical integration of the equations of motion and floquet theory the bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses for rings with multiple discrete stiffnesses the phase differences between them can eliminate large amplitude response under certain conditions

parametric instability of a circular ring subjected to moving springs this work investigates parametric instabilities of in plane bending vibrations of a thin elastic ring subject to forces from discrete rotating springs of arbitrary number spacing and orientation several configurations are examined including systems with symmetric and asymmetric circumferential spring spacing and systems with and without fixed springs the method of multiple scales is applied to analytically identify principal and combination instability boundaries as closed form expressions two different numerical approaches are used to verify the analytical results the effects of different system parameters on the instability boundaries are studied analytically the bending stiffness of the ring the number of springs and their stiffness location orientation and rotation speed for several cases well defined properties for the occurrence or suppression of instabilities are obtained as simple relations in the system parameters

the in plane free vibration of an elastically supported thin ring rotating at high speeds revisited abstract the in plane free vibration of a rotating thin ring is revisited in this paper a new model is proposed which accounts for the elastic foundation and the through thickness variation of the radial stress the emphasis is placed on a proper consideration of the geometrical nonlinearity which is essential for the consistent modelling of the ring stiffening resulting from the radial expansion caused by rotation the in plane stability of a thin ring rotating at relatively high speeds is analysed thoroughly it is shown that the ring can become unstable should the rotational speed exceed a critical value this result is new as in most known to the authors previous studies the stability problem is either not considered or it is stated that the in plane vibration of a rotating ring is stable in the studies which did address the instability the conclusions and the employed models are prone to criticism a parametric study is conducted to illustrate the effects of the ring properties on the in plane stability finally modes which appear as stationary displacement patterns of the ring to an observer in the space fixed reference system are investigated it is shown that the stationary patterns can occur prior to the onset of the instability for certain ring parameters

solving capacitated clustering problems abstract this paper presents two effective algorithms for clustering n entities into p mutually exclusive and exhaustive groups where the size of each group is restricted as its objective the clustering model minimizes the sum of distance between each entity and a designated group median empirical results using both a primal heuristic and a hybrid heuristic subgradient method for problems having n 100 i e 10 100 binary variables show that the algorithms locate close to optimal solutions without resorting to tree enumeration the capacitated clustering model is applied to the problem of sales force territorial design

vibration analysis of a flexible rotating disk with angular misalignment abstract the dynamic characteristics and responses of a flexible rotating disk are analyzed when the disk has angular misalignment that is defined by the angle between the rotation and symmetry axes based on the von karman strain theory and the kirchhoff plate theory three equations of motion are derived for the transverse radial and tangential displacements when the disk has angular misalignment the derived equations are fully coupled partial differential equations through the transverse radial and tangential displacements in particular the equation of transverse motion is non linear while the others are linear after these partial differential equations and the associated boundary conditions are transformed into a weak form the weak form is discretized to a non linear matrix vector equation by using the finite element method the non linear equation is linearized in the neighbourhood of a dynamic equilibrium position and then the natural frequencies and mode shapes are computed in addition the dynamic time responses are obtained by applying the generalized method the effects of angular misalignment on the natural frequencies the mode shapes and the dynamic responses are investigated the analysis shows that the angular misalignment causes the natural frequency split and the out of plane mode with only one nodal diameter and no nodal circle has the largest frequency split it is also found that the angular misalignment yields the amplitude modulations in the transverse radial and tangential dynamic responses