on extensions of the deterministic online model for bipartite matching and max sat abstract the surprising results of karp vazirani and vazirani 39 and respectively buchbinder et al 18 are examples where rather simple randomization provides provably better approximations than the corresponding deterministic counterparts for online bipartite matching and respectively unconstrained non monotone submodular we show that seemingly strong extensions of the deterministic online computation model can at best match the performance of naive randomization more specifically for bipartite matching we show that in the priority model allowing very general ways to order the input stream we cannot improve upon the trivial 1 2 approximation achieved by any greedy maximal matching algorithm and likewise cannot improve upon this approximation by any l o g n log log n number of online algorithms running in parallel the latter result yields an improved log log n log log log n lower bound for the number of advice bits needed to beat the simple deterministic greedy algorithm for max sat we adapt the recent de randomization approach of buchbinder and feldman 16 applied to the buchbinder et al 17 algorithm for max sat to obtain a deterministic 3 4 approximation algorithm using width 2n parallelism in order to improve upon this approximation we show that exponential width parallelism of online algorithms is necessary in a model that is more general than what is needed for the width 2n algorithm we relate our results to previous work concerning the priority branching tree pbt model of alekhnovich et al 2

a polar theory for vibrations of thin elastic shells abstract in relation to a polar continuum this paper presents a 2 d shear deformable theory for the high frequency vibrations of a thin elastic shell to begin with the 3 d fundamental equations of the micropolar elastic continuum are expressed as the euler lagrange equations of a unified variational principle next the kinematic variables of the shell are represented by the power series expansions in its thickness coordinate and then they are used to establish the 2 d theory by means of the variational principle the 2 d theory is derived in invariant variational and differential forms and governs all the types of vibrations of the functionally graded micropolar shell lastly the uniqueness is investigated in solutions of the initial mixed boundary value problems defined by the 2 d theory and some of special cases are indicated in the theory

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

on the structure of the solution set for first order differential equations we study the structure of the solution set for the periodic boundary value problem for first order differential equations we present some existence results and give conditions under which the solution set is compact connected or acyclic if any of the assumptions is slightly modified then it is shown that the solution set may be chaotic

open loop and closed loop attitude dynamics and controls of miniature spacecraft using pseudowheels this paper presents open loop and closed loop attitude control strategies of miniature spacecraft using pseudowheels which are composed of multiple bimorphs and are mounted on the three principal axes of the spacecraft due to the conservation of angular momentum the vibrations of the bimorph excited by applied voltages can rotate the spacecraft by applying a sequence of rotations along the three axes the attitude of the spacecraft can be changed the modeling of the spacecraft pseudowheel system includes the inverse piezoelectric effect and the gravity gradient torques since one cannot guarantee that a solution will be found for every rotation sequence this paper proposes an approach to solve this problem in addition the voltages applied to the bimorphs are reduced to meet the specifications of the voltage amplifiers furthermore a closed loop attitude control strategy is presented to reduce the applied voltages and to compensate the attitude error caused by the gravity gradient torques

remarks on j j nieto s paper nonlinear second order periodic boundary value problems and proved the following assertions suppose that f c 0 2n x r r is decreasing in u for each fixed t e 0 27r and that x p e c2 0 27r are lower and upper solutions for 1 then 1 if c d p on 0 2n then 1 admits a solution and the solution set of 1 in the sector a i is an rg 2 if c 2 i on 0 2rc then a 1 admits a solution b there exist positive constants sr s such that the solution set of 1 in the sector lx s fl s2 is an r the aim of this paper is to improve these assertions

second order periodic boundary value problems on time scales in this paper we study the existence of solutions of periodic boundary value problem for second order nonlinear dynamic equations on time scales for this purpose we use two methods here first sign properties of the green s function are investigated and existence results of bounded solutions of nonlinear boundary value problems are established as a result of schauder fixed point theorem second the monotone method is discussed to assure the existence and uniqueness of solutions of such periodic boundary value problems on time scales

on the fundamental equations of piezoelasticity of quasicrystal media abstract the three dimensional fundamental equations of elasticity of quasicrystals with extension to quasi static electric effect are expresses in both differential and variational invariant forms for a regular region of quasicrystal material the principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material a theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument the sufficient boundary and initial conditions are enumerated for the uniqueness hamilton s principle is stated for the regular region and a three field variational principle is obtained under some constraint conditions the constraint conditions which are generally undesirable in computation are removed by applying an involutory transformation then a unified variational principle is obtained for the regular region with one or more fixed internal surface of discontinuity the variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions the resulting equations which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions pave the way to the study of important dislocation fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials

modal analysis of magneto electro elastic plates using the state vector approach the state vector approach is proposed to analyze the free vibration of magneto electro elastic laminate plates the extended displacements and stresses can be divided into the so called in plane and out of plane variables once the state equation for the out of plane variables is obtained a complex boundary value problem is converted into an equivalent simple initial value problem through the state equation the propagator matrix between the top and bottom interfaces of every layer can be easily derived the global propagator matrix can also be assembled using the continuity conditions it is obvious that the order of global propagator matrix is not related to the number of layers consequently this approach possesses certain virtues including simple formulation less expensive computation etc to test the formulation the developed solution is then applied to a simply supported multilayered plate constructed of piezoelectric and or piezomagnetic materials the natural frequencies and corresponding mode shapes are computed and compared with existing results furthermore the fundamental modes along with a couple of other higher modes which have never been reported in previous literature are presented therefore this completed set of frequencies and mode shapes can be used as benchmarks for future research in this field it is also believed that the approach could be useful in the analysis and design of smart structures constructed from piezoelectric piezomagnetic composites

resolution and linear cnf formulas improved n 3 maxsat algorithms abstract we study techniques for solving the maxsat problem on instances in which the variable degree is bounded by 3 the problem is np hard we show how resolution principle can be applied that converts an instance into an equivalent instance in which the cnf formula becomes a linear cnf formula we then show how more efficient branching strategies can be applied on linear cnf formulas as applications we present two algorithms one of running time o 1 194 k that solves the parameterized version of the problem and the other of running time o 1 237 n that solves the optimization version of the problem both significantly improving previous best upper bounds

solution of nonlinear pull in behavior in electrostatic micro actuators by using he s homotopy perturbation method the work presented here is about the nonlinear pull in behavior of different electrostatic micro actuators he s homotopy perturbation method hpm is applied to solve different types of micro actuators like fixed fixed beam and cantilever beam actuators simulated results are presented for further analysis also the obtained results compare well with the literature

the transient responses of a special non homogeneous magneto electro elastic hollow cylinder for axisymmetric plane strain problem by virtue of the introduction of new dependent variable and the separation of variables technique the transient responses of a special non homogeneous magneto electro elastic hollow cylinder are transformed to two volterra integral equations of the second kind of about two functions with respect to time these integral equations can be solved successfully by means of the interpolation method then the complete solutions of displacements stresses electric potential electric displacements magnetic potential and magnetic inductions are obtained the present method is suitable for a magneto electro elastic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric mechanical and electromagnetic loads numerical results are finally presented

on the fundamental equations of electromagnetoelastic media in variational form with an application to shell laminae equations abstract the fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials and the uniqueness of solutions is examined alternatively the fundamental equations are stated as the euler lagrange equations of a unified variational principle which operates on all the field variables the variational principle is deduced from a general principle of physics by modifying it through an involutory transformation then a system of two dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell also a theorem is given which states the conditions sufficient for the uniqueness in solutions of the shell equations on the basis of a discrete layer modeling the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness the resulting equations in differential and fully variational invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well the invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell plate or laminae the results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material geometry and or effects

static fields in magnetoelectroelastic laminates the through thickness elastic electric and magnetic fields of laminates composed of elastic piezoelectric and magnetostrictive layers are considered under static conditions to determine their fundamental behavior and to investigate the limits of simplified plate theories in which the fields are assumed to possess a specific type of behavior the weak form of the equations of motion equilibrium gauss s law and gauss s law for magnetism are formulated for a rectangular laminate with arbitrary edge boundary conditions under the application of applied surface displacement traction electric potential electric flux or magnetic potential magnetic flux the layers within the laminate are allowed to possess any linear constitutive law consistent with a magnetoelectroelastic solid and the number of layers is arbitrary the ritz method is used in combination with a discrete layer theory and approximate solutions for the displacements electric potential and magnetic potential are sought to the weak form of the governing equations the use of linear combinations of through thickness approximations along with separate approximations for the in plane behavior allows an accurate representation of the break in variable slope across an interface with dissimilar material properties the model is applied to problems with either known exact solutions or a finite element approximation to the governing equations excellent agreement is obtained for all cases

existence and uniqueness results for discrete second order periodic boundary value problems abstract we prove existence and uniqueness results for solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions the results are based on the notion of upper and lower solutions

state vector approach to analysis of multilayered magneto electro elastic plates abstract the state vector equations for three dimensional orthotropic and linearly magneto electro elastic media are derived from the governing equations by eliminating x y xy b x b y d x and d y an efficient method is presented for analysis of multilayered magneto electro elastic plates the methodology is based on the mixed formulation in which basic unknowns are formed by collecting not only displacements electrical potential and magnetic potential but also some of stresses electrical displacements and magnetic induction as special case simply supported and multilayered rectangular plate is analyzed under the surface loading numerical results are presented graphically the procedure of numerical calculation shows that the formulation presented here is simple and direct

free vibration studies of simply supported non homogeneous functionally graded magneto electro elastic finite cylindrical shells in this article free vibration studies on functionally graded materials fgm magneto electro elastic cylindrical shells have been carried out a series solution is assumed in circumferential and axial direction such that the three dimensional character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material one of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency in addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted

free vibration of simply supported functionally graded and layered magneto electro elastic plates by finite element method in this article free vibration studies on functionally graded anisotropic and linear magneto electro elastic plates have been carried out by semi analytical finite element method a series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three dimensional 3 d character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect the present finite element is modeled with displacement components electric potential and magnetic potential as nodal degree of freedom the functionally graded material is assumed to be exponential in the thickness direction the numerical results obtained by the present model are in good agreement with the isotropic 3 d exact benchmark solutions available in literature numerical study includes the influence of the different exponential factor magneto electro elastic properties and effect of mechanical and electrical type of loading on induced magneto electro elastic fields further study has been carried out on higher harmonic study has been extended on functionally graded and layered magneto electro elastic plate

monotone method for second order periodic boundary value problems in recent years there has been an extensive study of the existence of periodic solutions l s 11 14 151 in 8 111 the existence of solutions of first and second order pbvp period boundary value problems has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems lyapunovschmidt method which provide conditions that are easily verifiable and which covers previous known results of other authors as a constructive method for obtaining extremal solutions of initial and boundary value problems the monotone iterative procedure has been employed by several researchers 5 7 11 13 151 the objective of this paper is to employ this useful technique for second order pbvp to obtain the minimal and maximal solutions as limits of monotone iterates our method can be used to study semilinear parabolic initial boundary value problems and other problems at resonance

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

some comments on the higher order theories of piezoelectric piezothermoelastic and thermopiezoelectric rods and shells in this note the derivations of the higher order 1 d or 2 d theories are discussed for the dynamic analysis of electroelastic i e piezoelectric piezothermoelastic and thermopiezoelectric structural elements of uniform cross section or uniform thickness certain oversights are clarified concerning the higher order theories including their variational formulation invariant form and uniqueness of solutions that obscure the availability of earlier contributions in the open literature in this respect a higher order theory with some applications by wu et al most recently appeared in this journal int j solids struct 39 2002 5325 is mentioned as one of the examples

a monotone method for constructing extremal solutions to second order periodic boundary value problems abstract in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u t f t u u t t 0 2 u 0 u 2 u 0 u 2 in the presence of an upper solution and a lower solution with

existence of periodic solutions for first order differential equations in this paper we study the periodic boundary value problem for first order differential equations by combining techniques of the theory of differential inequalities namely the method of upper and lower solutions and the alternative method for nonlinear problems at resonance the results obtained are in terms of the behavior of the nonlinear part at infinity

resolution for max sat max sat is the problem of finding an assignment minimizing the number of unsatisfied clauses in a cnf formula we propose a resolution like calculus for max sat and prove its soundness and completeness we also prove the completeness of some refinements of this calculus from the completeness proof we derive an exact algorithm for max sat and a time upper bound we also define a weighted max sat resolution like rule and show how to adapt the soundness and completeness proofs of the max sat rule to the weighted max sat rule finally we give several particular max sat problems that require an exponential number of steps of our max sat rule to obtain the minimal number of unsatisfied clauses of the combinatorial principle these results are based on the corresponding resolution lower bounds for those particular problems

solving singular nonlinear second order periodic boundary value problems in the reproducing kernel space abstract in this paper we present a new method for solving a singular nonlinear second order periodic boundary value problem its analytical solution is represented in the form of series in the reproducing kernel space in the mean time the n term approximation u n x to the analytical solution u x is obtained and is proved to converge to the analytical solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

fixed point theorems for discontinuous multivalued operators on ordered spaces with applications in this paper some fixed point theorems for discontinuous multivalued operators on ordered spaces are proved these theorems improve the earlier known fixed point theorems of 1 2 the main fixed point theorems are applied to first order discontinuous differential inclusions for proving the existence of extremal solutions under certain monotonicity conditions

a monotone method for constructing extremal solutions to fourth order periodic boundary value problems in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu 4 t f t u t u t email protected 0 email protected u 0 u email protected u 0 u email protected u 0 u email protected u 0 u email protected in the presence of an upper solution b and a lower solution a with b a

a generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems abstract the purpose of this paper is to study a periodic boundary value problem for a nonlinear ordinary differential equation of second order we generalize the monotone iterative method to cover some new situations and present a new approach considering the monotone iterates as orbits of a discrete dynamical system

generalized variational principles for micromorphic magnetoelectroelastodynamics a family of generalized variational principles is established for the initial boundary value problem of micromorphic magnetoelectroelastodynamics by he s semi inverse method this paper aims at providing a more complete theoretical basis for the finite element applications

tracking control of a biaxial piezo actuated positioning stage using generalized duhem model nonlinear hysteresis modeling is studied using a novel pzt actuated flexure based mechanism to compare the performance of variant hysteresis models with respect to the tracking reference we reformulate the bouc wen model the dahl model and the duhem model as a generalized duhem model system parameters for these three hysteresis models are formulated into nonlinear optimization problems with constraints these optimization problems are solved by the particle swarm optimization method since the duhem model includes both electrical and mechanical domains it has a smaller modeling error compared to the other two hysteresis models the simulation results are confirmed by modeling the proposed biaxial piezo actuated positioning stage of these hysteresis models cross coupling effects between the x and y axis actuation are also alleviated by a novel feedforward compensation mechanism based on the duhem model with crossover terms finally a real time experiment is performed to confirm the feasibility of the proposed method the experimental results validate the capability of the proposed controller to achieve precision tracking tasks with submicron precision

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

simplified gurtin type generalized variational principles for fully dynamic magneto electro elasticity with geometrical nonlinearity abstract the fundamental equations governing all the variables of the initial boundary value problem in fully dynamic magneto electro elasticity with geometrical nonlinearity are expressed in covariant differential form the generalized principle of virtual work is given in terms of convolutions for the present problem two simplified gurtin type generalized variational principles directly leading to all the fundamental equations are deduced by using he s semi inverse method instead of laplace transforms by enforcing some fundamental equations as constraint conditions one of various constrained variational principles is given as an example by simply dropping out selected field functions several reduced variational principles are obtained as special forms for piezoelectricity elastodynamics and electromagnetics respectively this paper aims at providing a more complete theoretical foundation for the finite element applications for the discussed problem

periodic boundary value problems for nonlinear higher order ordinary differential equations we study a class of boundary value problems for linear and nonlinear ordinary differential equations of higher order we study the solution set and present a maximum principle as a consequence we show the validity of the monotone method and obtain the extremal solutions between the upper and lower solutions

one more occurrence of variables makes satisfiability jump from trivial to np complete a boolean formula in a conjunctive normal form is called a k s formula if every clause contains exactly k variables and every variable occurs in at most s clauses the k s text sat problem is the satisfiability problem restricted to k s formulas it is proved that for every k geqslant 3 there is an integer f k such that k s text sat is trivial for s leqslant f k because every k s formula is satisfiable and is np complete for s geqslant f k 1 moreover f k grows exponentially with k namely lfloor 2 k ek rfloor leqslant f k leqslant 2 k 1 2 k 4 1 for k geqslant 4

periodic solutions for functional differential equations with infinite lead and delay abstract this paper discusses the existence of periodic solutions for functional differential equations with infinite lead and delay on the basis of fixed point theorems topological degree theories comparison principles and differential inequality methods some general results are proved

positive solution of a singular nonlinear third order periodic boundry value problem abstract the singular nonlinear third order periodic boundary value problem u 3 u f t u 0 t 2 with u i 0 u i 2 i 0 1 2 is studied where 0 and f is singular at u 0 under suitable conditions on f it is proved by employing a priori estimates perturbation technique and schauder fixed point theorem that the problem has at least one positive solution if 0 1 3

coupled thermoelastic shell equations with second sound for high frequency vibrations of temperature dependent materials guided by the three dimensional theory of coupled thermoelasticity with second sound a system of shear deformable shell equations is consistently derived in invariant differential and variational forms for the high frequency vibrations of temperature dependent materials the first part of the paper is concerned with a unified variational principle describing the fundamental equations of thermoelasticity the differential type of variational principle is presented by expressing hamilton s principle for the thermal part of a thermoelastic region and then combining it with its mechanical part in the second part the hierarchic system of non isothermal shell equations is systematically established by use of the variational principle together with mindlin s kinematic hypothesis for shells the system of two dimensional approximate equations which may take account of all the significant mechanical and thermal effects including the temperature dependency of material governs the extensional thickness shear flexural and torsional as well as coupled vibrations of shells of uniform thickness lastly in the third part emphasis is placed on certain cases involving special material geometry and kinematics besides a theorem is devised so as to enumerate the initial and boundary conditions sufficient for the uniqueness in solutions of the system of non isothermal shell equations

an initial boundary value problem for model electromagnetoelasticity system in this paper we consider an initial boundary value problem related to the electrodynamics of vibrating elastic media the aim is to prove an existence and uniqueness result for a model describing the nonlinear interactions of the electromagnetic and elastic waves we assume that the motion of the continuum occurs at velocities that are much smaller than the propagation velocity of the electromagnetic waves through the elastic medium the model under study consists of two coupled differential equations one of them is the hyperbolic equation an analog of the lame system and another one is the parabolic equation an analog of the diffusion maxwell system one stability result is proved too

fuzzy incremental control algorithm of loop heat pipe cooling system for spacecraft applications reliable and high precision thermal control technologies are essential for the safe flight of advanced spacecraft a fuzzy incremental control strategy is proposed for control of an lhp space cooling system comprising a loop heat pipe and a variable emittance radiator with mems louver the generating and performing algorithm of the fuzzy control rules is provided with an analytical form based on the understanding of dynamics and control mechanisms of the space cooling system this paper also presents a novel integrated mathematical model for the dynamic analysis of the lhp space cooling system and a numerical evaluation of the investigated control schemes numerical simulation results on the closed loop control effects suggest that the proposed control strategy takes advantage of no steady error small overshoots and short settling times thus benefiting safe highly accurate and reliable operation of the entire space cooling system the overshoots of the most important operating parameters t o b q r and p under the proposed fuzzy incremental control have been reduced to 16 3 17 6 and 18 6 of the compared pid control s while the respective settling times have been shortened to 33 9 42 3 and 30 5 of the reference values

orientation control on so 3 with piecewise sinusoids this paper addresses rigid body orientation control for the case that angular velocity is restricted to a class of piecewise sinusoidal signals the orientation kinematics are represented by the group of rotation matrices so 3 we present a new closed form solution of the rotation matrix kinematics and we use this solution to prove controllability we then present kinematic level orientation feedback controllers for setpoint tracking and command following

remarks on the lower and upper solutions method for second and third order periodic boundary value problems we study the solvability and the approximation of the solutions by monotone iteration of the second and third order periodic boundary value problems bvps u cu t u u 0 u email protected u 0 u email protected and email protected au bu t u u 0 u email protected u 0 u email protected u 0 u email protected in the presence of lower and upper solutions which may not satisfy the usual ordering condition to this end some maximum and antimaximum principles are stated and proved for certain linear differential operators naturally associated with the previously stated problems

application of the differential transformation method to bifurcation and chaotic analysis of an afm probe tip the afm atomic force microscope has become a popular and useful instrument for measuring intermolecular forces with atomic resolution that can be applied in electronics biological analysis and studying materials semiconductors etc this paper conducts a systematic investigation into the bifurcation and chaotic behavior of the probe tip of an afm using the differential transformation dt method the validity of the analytical method is confirmed by comparing the dt solutions for the displacement and velocity of the probe tip at various values of the vibrational amplitude with those obtained using the runge kutta rk method the behavior of the probe tip is then characterized utilizing bifurcation diagrams phase portraits power spectra poincare maps and maximum lyapunov exponent plots the results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude specifically the tip motion changes first from subharmonic to chaotic motion then from chaotic to multi periodic motion and finally from multi periodic motion to subharmonic motion with windows of chaotic behavior as the non dimensional vibrational amplitude is increased from 1 0 to 5 0

monotone iterative technique for second order delayed periodic problem in banach spaces in this paper we deal with the existence of periodic solutions for second order functional differential equation with delay in e u t f t u t u t t r where e is an ordered banach space f r e e e is a continuous function which is periodic in t and 0 is a constant we first build a new maximum principle for the periodic solutions of the corresponding linear equation with delay with the aid of this maximum principle under the assumption that the nonlinear function is quasi monotonicity we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions

greedy algorithms for the maximum satisfiability problem simple algorithms and inapproximability bounds we give a simple randomized greedy algorithm for the maximum satisfiability problem max sat that obtains a frac 3 4 approximation in expectation in contrast to previously known frac 3 4 approximation algorithms our algorithm does not use flows or linear programming hence we provide a positive answer to a question posed by williamson in 1998 on whether such an algorithm exists moreover we show that johnson s greedy algorithm cannot guarantee a frac 3 4 approximation even if the variables are processed in a random order thereby we partially solve a problem posed by chen friesen and zheng in 1999 in order to explore the limitations of the greedy paradigm we use the model of priority algorithms of borodin nielsen and rackoff since our greedy algorithm works in an online scenario where the variables arrive with their set of undecided clauses we wonder if a better approximation ratio can be obtained by further fine tuning its random decisions for a particular information model

algorithms for n 3 maxsat and parameterization above the all true assignment abstract in this paper we consider the n 3 maxsat problem the problem is a special case of the maximum satisfiability problem with an additional requirement that in the input formula each variable appears at most three times here we improve previous upper bounds for n 3 maxsat in terms of n number of variables and in terms of k number of clauses that we are required to satisfy moreover we prove that satisfying more clauses than the simple all true assignment is an np hard problem