low complexity video coding based on two dimensional singular value decomposition in this paper we propose a low complexity video coding scheme based upon 2 d singular value decomposition 2 d svd which exploits basic temporal correlation in visual signals without resorting to motion estimation me by exploring the energy compaction property of 2 d svd coefficient matrices high coding efficiency is achieved the proposed scheme is for the better compromise of computational complexity and temporal redundancy reduction i e compared with the existing video coding methods in addition the problems caused by frame decoding dependence in hybrid video coding such as unavailability of random access are avoided the comparison of the proposed 2 d svd coding scheme with the existing relevant non me based low complexity codecs shows its advantages and potential in applications

associativity of quantum multiplication we proved the associativity of the multiplication of quantum cohomology for a monotone compact symplectic manifold v for which c 1 a 1 for any effective class the same proof also works for any positive compact symplectic manifold with c 1 a 1

constructing and predicting solitary pattern solutions for nonlinear time fractional dispersive partial differential equations building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics physics and engineering in this work a new analytical technique for constructing and predicting solitary pattern solutions of time fractional dispersive partial differential equations is proposed based on the generalized taylor series formula and residual error function the new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software for method evaluation and validation the proposed technique was applied to three different models and compared with some of the well known methods the resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct as well as the prediction of solitary pattern solutions for time fractional dispersive partial differential equations

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

numerical algorithm for solving two point second order periodic boundary value problems for mixed integro differential equations in this study the numerical solution of fredholm volterra integro differential equations for two point second order periodic boundary value problems is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the periodic boundary conditions of the problem are satisfied the exact solution u x is represented in the form of series in the space w 2 3 in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 3 some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear equations

infinitely many monotone lagrangian tori in mathbb r 6 r 6 we construct infinitely many families of monotone lagrangian tori in mathbb r 6 no two of which are related by hamiltonian isotopies or symplectomorphisms these families are distinguished by the arbitrarily large numbers of families of maslov index 2 pseudo holomorphic discs that they bound

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

fourier transform vector quantization for speech coding design algorithms and simulation results are presented for vector quantizers for fourier transformed data transforming the data prior to quantization has two potential advantages first each sample in the transform domain depends on many samples in the original domain thus even scalar quantization in the transform domain is a form of vector quantization or block source coding in the original waveform domain and the basic coding theorems of information theory show that such block codes can provide better performance than scalar codes even for memoryless sources second vector quantization of fourier transformed speech waveforms provides distinctly better subjective quality than ordinary vector quantization of the waveform using codes of comparable complexity while the system is of course more complicated due to the need to take fourier transforms its envisioned application is as a coder for the output of fft chips currently available or under development the proposed implementation of a fourier transform vector quantizer ftvq uses a product code structure providing different codes for different coefficient vectors corresponding to different frequency bands this is a form of subband coding and yields a simple means of optimizing bit allocations among the subcodes two coding structures with corresponding distortion measures are considered those that quantize vectors of pairs of real and imaginary coefficients and those that quantize separate vectors of magnitude and phase coefficients both structures yield good performance for the given complexity in comparison to waveform vector quantizers for speech coding a magnitude phase ftvq yields better subjective quality than a real imaginary ftvq when the rate allocation is properly chosen

rotated orthogonal transform rot for motion compensation residual coding discrete cosine transform dct is the orthogonal transform that is most commonly used in image and video compression the motion compensation residual mc residual is also compressed with the dct in most video codecs however the mc residual has different characteristics from a nature image in this paper we develop a new orthogonal transform rotated orthogonal transform rot that can perform better on the mc residual than the dct for coding purposes we derive the proposed rot based on orthogonal constrained l1 norm minimization problem for its sparse property using the dct matrix as the starting point a better orthogonal transform matrix is derived in addition by exploring inter frame dependency and local motion activity transmission of substantial side information is avoided the experiment results confirm that with small computation overhead the rot is adaptive to change of local spatial characteristic of mc residual frame and provides higher compression efficiency for the mc residual than dct especially for high and complex motion videos

homotopy equivalence of nearby lagrangians and the serre spectral sequence we construct using relatively basic techniques a spectral sequence for exact lagrangians in cotangent bundles similar to the one constructed by fukaya seidel and smith that spectral sequence was used to prove that exact relative spin lagrangians in simply connected cotangent bundles with vanishing maslov class are homology equivalent to the base a similar result was also obtained by nadler the ideas in that paper were extended by abouzaid who proved that vanishing maslov class alone implies homotopy equivalence in this paper we present a short proof of the fact that any exact lagrangian with vanishing maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism when the fundamental group of the base is pro finite this implies homotopy equivalence

approximate analytical solution of the nonlinear fractional kdv burgers equation in this paper explicit and approximate solutions of the nonlinear fractional kdv burgers equation with time space fractional derivatives are presented and discussed the solutions of our equation are calculated in the form of rabidly convergent series with easily computable components the utilized method is a numerical technique based on the generalized taylor series formula which constructs an analytical solution in the form of a convergent series five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution the results reveal that the method is very effective and simple in determination of solution of the fractional kdv burgers equation

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields

regularity and estimates for j holomorphic discs attached to a maximal totally real submanifold we prove that pseudo holomorphic discs attached to a maximal totally real submanifold inherit their regularity to the boundary from the regularity of the submanifold and of the almost complex structure the proof is based on the computation of an explicit lower bound for the kobayashi metric in almost complex manifolds which also yields explicit estimates of holderian norms of such discs

a cotangent fibre generates the fukaya category abstract we prove that the algebra of chains on the based loop space recovers the derived wrapped fukaya category of the cotangent bundle of a closed smooth oriented manifold the main new idea is the proof that a cotangent fibre generates the fukaya category using a version of the map from symplectic cohomology to the homology of the free loop space introduced by cieliebak and latschev

new exact solutions of nonlinear fractional acoustic wave equations in ultrasound in this paper new exact solutions of fractional nonlinear acoustic wave equations have been devised the travelling periodic wave solutions of fractional burgers hopf equation and khokhlov zabolotskaya kuznetsov kzk equation have obtained by first integral method nonlinear ultrasound modelling is found to have an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible taking nonlinear effects into account the ultrasound beam analysis makes more accurate in these applications the burgers hopf equation is one of the extensively studied models in mathematical physics in addition the kzk parabolic nonlinear wave equation is one of the most widely employed nonlinear models for propagation of 3d diffraction sound beams in dissipative media in the present analysis these nonlinear equations have solved by first integral method as a result new exact analytical solutions have been obtained first time ever for these fractional order acoustic wave equations the obtained results are presented graphically to demonstrate the efficiency of this proposed method

solving a system of linear volterra integral equations using the new reproducing kernel method in this paper we present a new numerical technique to obtain the approximation solution for linear volterra integral equations of the second kind based on reproducing kernel theory the approximation solution is expressed by n term summation of reproducing kernel functions the merit of the new method includes 1 it is easy to implement this method 2 high accuracy the numerical examples compared with other methods show that the new method is more efficient

a fractional epidemiological model for computer viruses pertaining to a new fractional derivative abstract in the computer security and for any defensive strategy computer viruses are very significant aspect to understand their expansion and extension is very important component in order to deal with this issue we consider a fractional epidemiological model in this article we analyze moderate epidemiological model to describe computer viruses with an arbitrary order derivative having non singular kernel we obtain the solution of the problem by using an iterative method by using the fixed point theorem the existence of the solution is discussed the uniqueness of the solution is verified we perform some numerical simulations and show graphically to observe the impact of the arbitrary order derivative

combined techniques of singular value decomposition and vector quantization for image coding the combination of singular value decomposition svd and vector quantization vq is proposed as a compression technique to achieve low bit rate and high quality image coding given a codebook consisting of singular vectors two algorithms which find the best fit candidates without involving the complicated svd computation are described simulation results show that the proposed methods are better than the discrete cosine transform dct in terms of energy compaction data rate image quality and decoding complexity

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

scene adaptive coder an efficient single pass adaptive bandwidth compression technique using the discrete cosine transform is described the coding process involves a simple thresholding and normalization operation on the transform coefficients adaptivity is achieved by using a rate buffer for channel rate equalization the buffer status and input rate are monitored to generate a feedback normalization factor excellent results are demonstrated for coding of color images at 0 4 bits pixel corresponding to real time color television transmission over a 1 5 mbit s channel

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

solvability of dirac type equations abstract this paper develops a weighted l 2 method for the half dirac equation for dirac bundles over closed riemann surfaces we give a sufficient condition for the solvability of the half dirac equation in terms of a curvature integral applying this to the dolbeault dirac operator we establish an automatic transversality criteria for holomorphic curves in kahler manifolds on compact riemannian manifolds we give a new perspective on some well known results about the first eigenvalue of the dirac operator and improve the estimates when the dirac bundle has a z 2 grading on riemannian manifolds with cylindrical ends we obtain solvability in the l 2 spaces with suitable exponential weights while allowing mild negativity of the curvature

tight not semi fillable contact circle bundles extending our earlier results we prove that certain tight contact structures on circle bundles over surfaces are not symplectically semi fillable thus confirming a conjecture of ko honda

numerical algorithm for parabolic problems with non classical conditions the parabolic problems with non classical conditions are discussed in a reproducing kernel space in this paper a reproducing kernel space is constructed in which the non classical conditions of the parabolic problems are satisfied based on the reproducing kernel space a new technique for solving the non classical parabolic problems is presented some examples are displayed to demonstrate the validity and applicability of the proposed method

fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel abstract various physical systems exhibit non markovian hereditary and memory effects characteristics in their very inherent structures in this research study the fractional non classical differential operator of caputo s type is used to analyze such a physical system representing chemical kinetic reactions in a batch reactor the governing system of fractional order equations under caputo s type derivative is formulated and later solved via laplace integral transform and its inversion analytically obtained general solutions of the governing equations are expressed in the form of special mittag leffler function and power series expansion with double summation during fractionalization the dimensional analysis has been taken care of and the results are graphically illustrated the obtained simulation results for varying values of fractional order represented various behavior with the fractional caputo s type governing equations for the concentration of three species in other words varying memory effects are observed during simulations of the model based upon different values of and the rate constants the classical model is retrieved for the limiting case when 1

a novel expansion iterative method for solving linear partial differential equations of fractional order in this manuscript we implement a relatively new analytic iterative technique for solving time space fractional linear partial differential equations subject to given constraints conditions based on the generalized taylor series formula the solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations this method can be used as an alternative to obtain analytic solutions of different types of fractional linear partial differential equations applied in mathematics physics and engineering some numerical test applications were analyzed to illustrate the procedure and to confirm the performance of the proposed method in order to show its potentiality generality and accuracy for solving such equations with different constraints conditions numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm

on the topological properties of symplectic maps in this paper we show that symplectic maps have surprising topological properties in particular we construct an interesting metric for the symplectic diffeomorphism groups which is related but not obviously to the topological properties of symplectic maps and phase space geometry we also prove a certain number of generalised symplectic fixed point theorems and give an application to a hamiltonian system

a numerical method for singularly perturbed turning point problems with an interior layer the objective of this paper is to present a numerical method for solving singularly perturbed turning point problems exhibiting an interior layer the method is based on the asymptotic expansion technique and the reproducing kernel method rkm the original problem is reduced to interior layer and regular domain problems the regular domain problems are solved by using the asymptotic expansion method the interior layer problem is treated by the method of stretching variable and the rkm four numerical examples are provided to illustrate the effectiveness of the present method the results of numerical examples show that the present method can provide very accurate approximate solutions

mean curvature flow of monotone lagrangian submanifolds we use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone lagrangian submanifolds in mathbb c n

a c 2 smooth counterexample to the hamiltonian seifert conjecture in r 4 we construct a proper c 2 smooth function on r 4 such that its hamiltonian flow has no periodic orbits on at least one regular level set this result can be viewed as a c 2 smooth counterexample to the hamiltonian seifert conjecture in dimension four

delay asymptotic solutions for the time fractional delay type wave equation abstract a new version of the wave equation endowed with time fractional derivative and multiple time delays is considered a new form of the generalized maclaurin fractional series is suggested to extract analytical solution of the model graphical investigations on the relation between the fractional derivative and the time delay are established finally we reported some remarks regarding the new model

propagation in hamiltonian dynamics and relative symplectic homology the main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating hamiltonian is sufficiently large over the zero section the proof is based on floer homology and on the notion of a relative symplectic capacity applications include results about propagation properties of sequential hamiltonian systems periodic orbits on hypersurfaces hamiltonian circle actions and smooth lagrangian skeletons in stein manifolds

the maslov class of the lagrange surfaces and gromov s pseudo holomorphic curves for an immersed lagrange submanifold w c t x one can define a nonnegative integer topologic invariant m w such that the image of h1 w z under the maslov class is equal to m w z in this paper the value of m w is calculated for the case of a two dimensional oriented manifold x with the universal cover homeomorphic to r2 and an embedded lagrange torus w it is proved that if x t2 and w is homologic to the zero section then m w 0 in all the other cases m w 2 the last result is true also for a wide class of oriented properly embedded lagrange surfaces in t r the proof is based on the gromov s theory of pseudo holomorphic curves some applications to the hamiltonian mechanics are mentioned

irreversibility from staircases in symplectic embeddings abstract we present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of hamiltonian systems of many degrees of freedom we use recent flexibility and rigidity results of symplectic embeddings quantified via the stabilized fibonacci and pell staircases to encode the underlying breadth of the possible initial conditions which alongside the multitude of degrees of freedom of the underlying system give rise to time irreversibility

a method for compact image representation using sparse matrix and tensor projections onto exemplar orthonormal bases we present a new method for compact representation of large image datasets our method is based on treating small patches from a 2 d image as matrices as opposed to the conventional vectorial representation and encoding these patches as sparse projections onto a set of exemplar orthonormal bases which are learned a priori from a training set the end result is a low error highly compact image patch representation that has significant theoretical merits and compares favorably with existing techniques including jpeg on experiments involving the compression of orl and yale face databases as well as a database of miscellaneous natural images in the context of learning multiple orthonormal bases we show the easy tunability of our method to efficiently represent patches of different complexities furthermore we show that our method is extensible in a theoretically sound manner to higher order matrices tensors we demonstrate applications of this theory to compression of well known color image datasets such as the gatech and cmu pie face databases and show performance competitive with jpeg lastly we also analyze the effect of image noise on the performance of our compression schemes

a high order numerical method and its convergence for time fractional fourth order partial differential equations abstract this paper is concerned with design and analysis of a high order numerical approach based on a uniform mesh to approximate the solution of time fractional fourth order partial differential equations in this approach we first approximate the time fractional derivative appearing in the governing equation by means of caputo s definition and then construct a sextic b spline collocation method for solving the resulting equation it is proved that the present method is unconditionally stable convergence analysis of the method is discussed we prove that the method is 2 th order convergence with respect to time variable and fourth order convergence with respect to space variable three test problems are considered to demonstrate the applicability and efficiency of the new method it is shown that the rate of convergence predicted theoretically is the same as that obtained experimentally numerical results have been compared with those reported previously in literature it is shown that our method yields more accurate results when compared to the existing methods

fitted reproducing kernel hilbert space method for the solutions of some certain classes of time fractional partial differential equations subject to initial and neumann boundary conditions latterly many problems arising in different fields of science and engineering can be reduced by applying some appropriate discretization to a series of time fractional partial differential equations unlike the normal case derivative the differential order in such equations is with a fractional order which will lead to new challenges for numerical simulation the purpose of this analysis is to introduce the reproducing kernel hilbert space method for treating classes of time fractional partial differential equations subject to neumann boundary conditions with parameters derivative arising in fluid mechanics chemical reactions elasticity anomalous diffusion and population growth models the method provides appropriate representation of the solutions in convergent series formula with accurately computable components numerical experiments with different order derivatives degree are performed to support the theoretical analyses which are acquired by interrupting the n term of the exact solutions finally the obtained outcomes showed that the proposed method is competitive in terms of the quality of the solutions found and is very valid for solving such time fractional neumann problems

transform and hybrid transform dpcm coding of images using pyramid vector quantization the transform and hybrid transform dpcm methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients an asymptotic mean squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients coding simulations for two images at average rates of 0 5 1 bit pixel demonstrate a 1 3 db improvement in signal to noise ratio for the vector quantization approach in the hybrid coding with more modest improvements in signal to noise ratio in the transform coding however this improvement is quite noticeable in image quality particularly in reducing blockiness in the low bit rate encoded images

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

addendum to floer cohomology of lagrangian intersections and pseudo holomorphic discs i this is an addendum to the author s earlier paper floer cohomology of lagrangian intersection and pseudo holomorphic discs i comm pure appl math 46 1993 pp 949 993 the main result of this addendum extends the definition of the floer cohomology of lagrangian intersection to the case where the minimal maslov number is equal to 2 1996 john wiley sons inc

a computational method for solving periodic boundary value problems for integro differential equations of fredholm volterra type abstract in this paper the numerical solution of periodic fredholm volterra integro differential equations of first order is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the periodic condition of the problem is satisfied the exact solution u x is represented in the form of series in the space w 2 2 in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 2 some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear equations

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

a method for computing the partial singular value decomposition a method for computing the partial singular value decomposition of a matrix is described the method is appropriate to problems where the matrix is known to be of low rank and only the principal singular vectors are of interest the technique is simple easy to implement in integer arithmetic and places modest memory requirements the convergence properties of the algorithm are investigated analytically and by simulation

computational algorithm for solving fredholm time fractional partial integrodifferential equations of dirichlet functions type with error estimates abstract numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science which means increased attention to fractional calculus this paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a class of partial integrodifferential equations of fractional order in hilbert space within appropriate kernel functions the algorithm relies on the reproducing kernel hilbert space method that provides the solutions in rapidly convergent series representations for the reproducing kernel based upon the fourier coefficients of orthogonalization process the caputo fractional derivatives are introduced to address these issues moreover the error estimate of the generated solutions is established as well as the convergence of the iterative method is investigated under some theoretical assumptions the superiority and applicability of the present technique is illustrated by handling linear and nonlinear numerical examples the outcomes obtained are compared with exact solutions and existing methods to confirm the effectiveness of the reproducing kernel method

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

lagrangian non squeezing and a geometric inequality we prove that if the unit codisc bundle of a closed riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest non trivial closed geodesic is at most half the area of the unit disc

periodic fourth order cubic nls local well posedness and non squeezing property abstract in this paper we consider the cubic fourth order nonlinear schrodinger equation 4nls under the periodic boundary condition we prove two results one is the local well posedness in h s t with 1 3 s 0 for the cauchy problem of the wick ordered 4nls the other one is the non squeezing property for the flow map of 4nls in the symplectic phase space l 2 t to prove the former we used the ideas introduced in 36 and 27 and to prove the latter we used the ideas in 8

syz mirror symmetry for hypertoric varieties we construct a lagrangian torus fibration on a smooth hypertoric variety and a corresponding syz mirror variety using t duality and generating functions of open gromov witten invariants the variety is singular in general we construct a resolution of the variety using the wall and chamber structure on the base of the syz fibration

hamiltonian collapsing of irrational lagrangian submanifolds with small first betti number among the main symplectic invariants of a closed lagrange submanifoldl of the cotangent of n is the tubular radiusr l defined as the smallest tube d r n 1 of n t n in whichl can be pushed by an hamiltonian diffeotopy of n we show here using pseudo holomorphic techniques that such a submanifold cannot collapse if the first betti number ofl is smaller than 3 and if the maslov class ofl does not vanish in other words r l is then strictly positive and one can actually give an explicit lower bound in terms of the liouville and maslov classes ofl

solving fredholm integro differential equations using reproducing kernel hilbert space method in this study the numerical solution of fredholm integro differential equation is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the initial condition of the problem is satisfied the exact solution ux is represented in the form of series in the space w 2 2 a b in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 2 a b some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear fredholm integro differential equations

unknottedness of real lagrangian tori in s 2 times s 2 we prove the hamiltonian unknottedness of real lagrangian tori in the monotone s 2 times s 2 namely any real lagrangian torus in s 2 times s 2 is hamiltonian isotopic to the clifford torus the proof is based on a neck stretching argument gromov s foliation theorem and the cieliebak schwingenheuer criterion

approximate solution of fractional integro differential equations by taylor expansion method in this paper taylor expansion approach is presented for solving approximately a class of linear fractional integro differential equations including those of fredholm and of volterra types by means of the mth order taylor expansion of the unknown function at an arbitrary point the linear fractional integro differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions this method gives a simple and closed form solution for a linear fractional integro differential equation in addition illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method