an application for a modified kdv equation by the decomposition method and finite element method a numerical solution to a modified korteweg de vries mkdv equation is obtained using a lumped galerkin method with quadratic b spline finite element method fem and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm classical problems concerning the development motion and interaction of solitons are used to validate the methods the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

symplectic lie algebras with degenerate center abstract every symplectic lie algebra with degenerate including non abelian nilpotent symplectic lie algebras has the structure of a quadratic extension we give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets finally we give a scheme to classify the isomorphism classes of symplectic lie algebras with degenerate center we also give a classification scheme for nilpotent symplectic lie algebras and compute a complete list of all 6 dimensional nilpotent symplectic lie algebras which removes inaccuracies in an older list

a numerical application of the decomposition method for the combined kdv mkdv equation we consider solitary wave solutions of the combined korteweg de vries modified korteweg de vries kdv mkdv equation we prove the convergence of adomian decomposition method adm applied to the combined kdv mkdv equation then we obtain the exact solitary wave solutions and numerical solutions of the combined kdv mkdv equation for the initial conditions the numerical solutions are compared with the known analytical solutions their remarkable accuracy are finally demonstrated for the combined kdv mkdv equation

a unified treatment of multiple testing with prior knowledge using the p filter there is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision some common forms of prior knowledge include a beliefs about which hypotheses are null modeled by nonuniform prior weights b differing importances of hypotheses modeled by differing penalties for false discoveries c multiple arbitrary partitions of the hypotheses into possibly overlapping groups and d knowledge of independence positive or arbitrary dependence between hypotheses or groups suggesting the use of more aggressive or conservative procedures we present a unified algorithmic framework called p filter for global null testing and false discovery rate fdr control that allows the scientist to incorporate all four types of prior knowledge a d simultaneously recovering a variety of known algorithms as special cases

hom nijienhuis operators and t extensions of hom lie superalgebras abstract in this paper we study hom nijienhuis operators and t extensions of hom lie superalgebras we show that a linear map between hom lie superalgebras is a morphism if and only if its graph is a hom subalgebra and show that the infinitesimal deformation generated by a hom nijienhuis operator is trivial moreover we introduce the definition of t extensions of hom lie superalgebras and show that t extensions preserve many properties such as nilpotency solvability and decomposition in some sense in particular we discuss the equivalence of t extensions using cohomology

double products and hypersymplectic structures on ℝ4n in this paper we give a procedure to construct hypersymplectic structures on 4n beginning with affine symplectic data on 2n these structures are shown to be invariant by a 3 step nilpotent double lie group and the resulting metrics are complete and not necessarily flat explicit examples of this construction are exhibited

flat affine or projective geometries on lie groups abstract this paper deals essentially with affine or projective transformations of lie groups endowed with a flat left invariant affine or projective structure these groups are called flat affine or flat projective lie groups we give necessary and sufficient conditions for the existence of flat left invariant projective structures on lie groups we also determine lie groups admitting flat bi invariant affine or projective structures these groups could play an essential role in the study of homogeneous spaces m g h having a flat affine or flat projective structures invariant under the natural action of g on m a medina asked several years ago if the group of affine transformations of a flat affine lie group is a flat projective lie group in this work we provide a partial positive answer to this question

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

symplectic product and complex structures on 3 lie algebras abstract in this paper first we introduce the notion of a phase space of a 3 lie algebra and show that a 3 lie algebra has a phase space if and only if it is sub adjacent to a 3 pre lie algebra then we introduce the notion of a product structure on a 3 lie algebra using the nijenhuis condition as the integrability condition a 3 lie algebra enjoys a product structure if and only if it is the direct sum as vector spaces of two subalgebras we find that there are four types special integrability conditions and each of them gives rise to a special decomposition of the original 3 lie algebra they are also related to o operators rota baxter operators and matched pairs of 3 lie algebras parallelly we introduce the notion of a complex structure on a 3 lie algebra and there are also four types special integrability conditions finally we add compatibility conditions between a complex structure and a product structure between a symplectic structure and a paracomplex structure between a symplectic structure and a complex structure to introduce the notions of a complex product structure a para kahler structure and a pseudo kahler structure on a 3 lie algebra we use 3 pre lie algebras to construct these structures furthermore a levi civita product is introduced associated to a pseudo riemannian 3 lie algebra and deeply studied

solitary wave solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this letter based on the idea of adomian s decomposition method and with help of mathematica we obtain the exact solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this paper by considering the decomposition scheme we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions their remarkable accuracy is finally demonstrated in the study of some values p 1 of the compound kdv type and compound kdv burgers type equations

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

double extension symplectique d un groupe de lie symplectique resume lie groups carrying a left invariant symplectic form symplectic groups are described in terms of semi direct product of lie groups or symplectic reduction and principal fiber bundles with affine fiber we give a generalization of medina and revoy s symplectic double extension which realizes a symplectic group as the reduction of another symplectic group we show that every group obtained by this process carries an invariant lagrangian foliation such that the affine structure defined by the simplectic form over each leaf is complete

symplectic structures on quadratic lie algebras abstract we study quadratic lie algebras over a field k of null characteristic which admit at the same time a symplectic structure we see that if k is algebraically closed every such lie algebra may be constructed as the t extension of a nilpotent lie algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic lie algebra by the one dimensional lie algebra finally we prove that every symplectic quadratic lie algebra is a special symplectic manin algebra and we give an inductive description in terms of symplectic quadratic double extensions

on series expansions giving closed form solutions of korteweg de vries like equations korteweg devries kdv like equations with higher degree nonlinearity are solved by a direct algebraic technique due to hereman et al j phys a 19 1986 pp 607 628 for two kdv like equations one with fifth degree nonlinearity the other a combined kdv and mkdv equation for particular choices of the coefficients of the nonlinear terms the kink and antikink solutions found by dey are recovered furthermore soliton solutions of the combined kdv and mkdv equation are found for all values of the coefficients closed form solutions for the calogero degasperis fokas modified mkdv equation are also developed applications of the solutions of these equations in quantum field theory plasma physics and solid state physics are mentioned the hereman et al method is illustrated and slightly extended and this direct series method is briefly compared to hirota s method

an explicit and numerical solutions of some fifth order kdv equation by decomposition method in this paper by considering the adomian decomposition method explicit and numerical solutions are calculated for a various fifth order korteweg de vries equations with initial condition the method does not need linearization or weak nonlinearity assumptions perturbation theory the decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self canceling noise terms where sum of components vanishes in the limit

signal classification for the integrative analysis of multiple sequences of large scale multiple tests the integrative analysis of multiple data sets is becoming increasingly important in many fields of research when the same features are studied in several independent experiments it can often be useful to analyse jointly the multiple sequences of multiple tests that result it is frequently necessary to classify each feature into one of several categories depending on the null and non null configuration of its corresponding test statistics the paper studies this signal classification problem motivated by a range of applications in large scale genomics two new types of misclassification rate are introduced and two oracle procedures are developed to control each type while also achieving the largest expected number of correct classifications corresponding data driven procedures are also proposed proved to be asymptotically valid and optimal under certain conditions and shown in numerical experiments to be nearly as powerful as the oracle procedures in an application to psychiatric genetics the procedures proposed are used to discover genetic variants that may affect both bipolar disorder and schizophrenia as well as variants that may help to distinguish between these conditions

solitary wave solutions for a generalized hirota satsuma coupled kdv equation the solitary wave solutions of a generalized hirota satsuma coupled kdv equation are obtained exactly by using the decomposition method the solutions were calculated in the form of a convergent power series with easily computable components a variety of initial value system is considered the convergence of the method as applied to the coupled kdv equation is illustrated numerically the present algorithm performs extremely well in terms of accuracy and simplicity

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

an application of the decomposition method for the kdvb equation a relatively new decomposition method is presented to find the explicit and numerical solutions of the korteweg de vries equation kdv for short burgers equation and korteweg de vries burgers equation kdvb for short for the initial conditions in this method the solution is constructed in the form of a convergent power series with easily computable components the computed results show that this method can be readily implemented to this type of nonlinear equations and good accuracy can be also achieved furthermore this method does not require any transformations linearization or weak nonlinearity assumptions for finding the explicit solution and any discretization technique for computing the numerical solution

a general interactive framework for false discovery rate control under structural constraints we propose a general framework based on selectively traversed accumulation rules star for interactive multiple testing with generic structural constraints on the rejection set it combines accumulation tests from ordered multiple testing with data carving ideas from post selection inference allowing for highly flexible adaptation to generic structural information our procedure defines an interactive protocol for gradually pruning a candidate rejection set beginning with the set of all hypotheses and shrinking with each step by restricting the information at each step via a technique we call masking our protocol enables interaction while controlling the false discovery rate fdr in finite samples for any data adaptive update rule that the analyst may choose we suggest update rules for a variety of applications with complex structural constraints show that star performs well for problems ranging from convex region detection to fdr control on directed acyclic graphs and show how to extend it to regression problems where knockoff statistics are available in lieu of p values

quadratic symplectic lie superalgebras and lie bi superalgebras abstract we establish some relations between quadratic symplectic lie superalgebras and manin superalgebras next we introduce some concepts of double extensions of quadratic symplectic lie superalgebras and of manin superalgebras in order to give inductive descriptions of quadratic symplectic lie superalgebras

t extension of lie triple systems abstract in this paper we introduce the notion of t extension of a lie triple system then we show that t extension is compatible with nilpotency solvability and it preserves in certain sense the decomposition properties in addition we investigate the equivalence of t extensions using cohomology finally we show that every finite dimensional nilpotent metrised lie triple system over an algebraically closed field is the t extension of an appropriate quotient system

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

imbedding of lie triple systems into lie algebras abstract we show that the category of lie triple systems is equivalent to a full subcategory of the category of z 2 graded lie algebras and give two intrinsic characterizations of this subcategory as a corollary we obtain an analogous result for imbedding of symmetric spaces into lie groups with involutions

a sequential algorithm for false discovery rate control on directed acyclic graphs summary we propose a linear time single pass top down algorithm for multiple testing on directed acyclic graphs where nodes represent hypotheses and edges specify a partial ordering in which the hypotheses must be tested the procedure is guaranteed to reject a sub directed acyclic graph with bounded false discovery rate while satisfying the logical constraint that a rejected node s parents must also be rejected it is designed for sequential testing settings where the directed acyclic graph structure is known a priori but the p values are obtained selectively such as in a sequence of experiments however the algorithm is also applicable in nonsequential settings where all p values can be calculated in advance such as in model selection our algorithm provably controls the false discovery rate under independence positive dependence or arbitrary dependence of the p values and specializes to known algorithms in the special cases of trees and line graphs it simplifies to the classical benjamini hochberg procedure when the directed acyclic graph has no edges we explore the empirical performance of our algorithm through simulations and analysis of a real dataset corresponding to a gene ontology and we demonstrate its favourable performance in terms of computational time and power

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

pseudo kahler lie algebras with abelian complex structures we study lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure we prove that each of those lie algebras is completely determined by a pair u h where u is a complex commutative associative algebra and h is a sesquilinear hermitian form on u which verifies certain compatibility conditions with respect to the associative product on u the riemannian and ricci curvatures of the associated pseudo kahler metric are studied and a characterization of those lie algebras which are einstein but not ricci flat is given it is seen that all pseudo kahler lie algebras can be inductively described by a certain method of double extensions applied to the associated complex associative commutative algebras

oscillatory instability of traveling waves for a kdv burgers equation the stability of traveling wave solutions of a generalization of the kdv burgers equation o u u p o u 03u a o u is studied as the parameters p and a are varied the eigenvalue problem for the linearized evolution of perturbations is analyzed by numerically computing evans function d a an analytic function whose zeros correspond to discrete eigenvalues in particular the number of unstable eigenvalues in the complex plane is evaluated by computing the winding number of d a analytical and numerical evidence suggests that a hopf bifurcation occurs for oscillatory traveling wave profiles in certain parameter ranges dynamic simulations suggest that the bifurcation is subcritical no stable time periodic solution is found

on para kahler and hyper para kahler lie algebras abstract in this study we consider lie algebras that admit para kahler and hyper para kahler structures we provide new characterizations of these lie algebras and develop many methods for building large classes of examples previously bai considered para kahler lie algebras as left symmetric bialgebras we reconsider this viewpoint and make improvements in order to obtain some new results the study of para kahler and hyper para kahler is intimately linked to the study of left symmetric algebras particularly those that admit invariant symplectic forms in this study we provide many new classes of left symmetric algebras and complete descriptions of all the associative algebras that admit an invariant symplectic form we also describe all four dimensional hyper para kahler lie algebras

on the numerical solution of korteweg de vries equation by the iterative splitting method abstract in this paper we apply the method of iterative operator splitting on the korteweg de vries kdv equation the method is based on first splitting the complex problem into simpler sub problems then each sub equation is combined with iterative schemes and solved with suitable integrators von neumann analysis is performed to achieve stability criteria for the proposed method applied to the kdv equation the numerical results obtained by iterative splitting method for various initial conditions are compared with the exact solutions it is seen that they are in a good agreement with each other