a nonlocal variable coefficient modified kdv equation derived from a two layer fluid system and its exact solutions abstract a nonlocal form of a two layer fluid system is proposed by a simple symmetry reduction then by applying multiple scale method to it a general nonlocal two place variable coefficient modified kdv vcmkdv equation with shifted space and delayed time reversal is derived various exact solutions of the vcmkdv equation including elliptic periodic waves solitary waves and interaction solutions between solitons and periodic waves are obtained and analyzed graphically as an illustration an approximate solution of the original nonlocal two layer fluid system is also given

lump solitons in a higher order nonlinear equation in 2 1 dimensions we propose and examine an integrable system of nonlinear equations that generalizes the nonlinear schrodinger equation to 2 1 dimensions this integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit the lax pair for the system is derived after applying the singular manifold method we also present an iterative procedure to construct the solutions from a seed solution solutions with one two and three lump solitons are thoroughly discussed

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

lagrangian decomposition for integer nonlinear programming with linear constraints we present a lagrangean decomposition to study integer nonlinear programming problems solving the dual lagrangean relaxation we have to obtain at each iteration the solution of a nonlinear programming with continuous variables and an integer linear programming decreasing iteratively the primal dual gap we propose two algorithms to treat the integer nonlinear programming

an algebraic approach to integer portfolio problems abstract integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model we propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix to reach an optimal portfolio it is an essential ingredient the computation of different test sets via grobner basis of linear subproblems that are used in a dual search strategy

on the hypersurface orbital varieties of sl n c abstract we study the structure of hypersurface orbital varieties of sl n c those that are hypersurfaces in the nilradical of some parabolic subalgebra and how information about this structure is encoded in the standard young tableau associated to it by the robinson schensted algorithm we present a conjecture for the exact form of the unique non linear defining equations of hypersurface orbital varieties and proofs of the conjecture in certain cases

on the variety of a highest weight module 1 2 let u g be the enveloping algebra of g detailed information on the primitive spectrum prim u g of u g was summarized by conjecture 7 4 of 181 here a main question was to relate prim u g with the springer correspondence parts i ii of this conjecture were established in i ii and a partial solution to iii was given in 21 sufficient e g to treat g of type a meanwhile borho and brylinski 5 have established iii for induced ideals while barbasch and vogan 1 2 have established a version of iii in which gr i i e prim u g is replaced by a certain wavefront set known to be contained in y gr 1 this last work involves some case by case analysis and gives little indication as to why the springer correspondence should arise in the study of prim u g

a distributed computation algorithm for solving portfolio problems with integer variables a portfolio problem with integer variables can facilitate the use of complex models including models containing discrete asset values transaction costs and logical constraints this study proposes a distributed algorithm for solving a portfolio program to obtain a global optimum for a portfolio problem with n integer variables the objective function first is converted into an ellipse function containing n separated quadratic terms next the problem is decomposed into m equal size separable programming problems solvable by a distributed computation system composed of m personal computers linked via the internet the numerical examples illustrate that the proposed method can obtain the global optimum effectively for large scale portfolio problems involving integral variables

riemann hilbert approach and n soliton formula for coupled derivative schrodinger equation the coupled derivative schrodinger equation is studied in the framework of the riemann hilbert problem and a compact n soliton solution formula is found taking advantage of this result some properties for single soliton solution and asymptotic analysis of n soliton solution are explored as a by product a coupled fokas lenells equation together its n soliton solution is presented

darboux transformation and nonautonomous solitons for a modified kadomtsev petviashvili equation with variable coefficients abstract we study a modified kadomtsev petviashvili mkp equation with variable coefficients which has important applications in fluid dynamics ferromagnetics and plasma the lax pair hirota bilinear form and darboux transformation dt are obtained through the two singular manifold method the n soliton solution with grammian type in a compact determinant representation is derived from the n fold dt a complete classification of the mkp type solitons is given namely the bright and dark solitons as well as resonant bright and dark solitons dynamics of the nonautonomous solitons with parabolic periodic and kink shapes under different kinds of variable coefficient oscillations are shown interactions between the nonautonomous two bright solitons and two resonant bright solitons are discussed through the asymptotic analysis method

an algebraic geometry algorithm for scheduling in presence of setups and correlated demands we study here a problem of schedulingn job types onm parallel machines when setups are required and the demands for the products are correlated random variables we model this problem as a chance constrained integer program

quasi periodic solutions of the modified kadomtsev petviashvili equation the 2 1 dimensional modified kadomtsev petviashvili equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of lax pairs abel jacobi coordinates are introduced to straighten the flows from which quasi periodic solutions of the modified kadomtsev petviashvili equation are obtained in terms of riemann theta functions

abundant lump type solutions of the jimbo miwa equation in 3 1 dimensions abstract based on the hirota bilinear form of the 3 1 dimensional jimbo miwa equation ten classes of its lump type solutions are generated via maple symbolic computations whose analyticity can be easily achieved by taking special choices of the involved parameters those solutions supplement the existing lump type solutions presented previously in the literature

darboux transformation and rogue wave solutions for the variable coefficients coupled hirota equations abstract we construct the lax pair and darboux transformation for the variable coefficients coupled hirota equations based on modulation instability and by taking the limit approach we derive two types of nth order rogue wave solutions with different dynamic structures in compact determinant representations the explicit first order rogue wave solution is presented prolific vector rogue wave patterns such as the dark bright composite three sister quadruple and sextuple rogue waves with multiple compression points are demonstrated in particular in contrast to the standard peregrine combs unusual vector rogue wave combs such as the dark bright and composite rogue wave combs are revealed by choosing sufficiently large periodic modulation amplitudes further some wave characteristics such as the difference between light intensity and continuous wave background and pulse energy evolution of the dark rogue wave solution that features multiple compression points are discussed in detail

orbital varieties in slnand the smith conjecture abstract let o be a nilpotent orbit in the lie algebra s l n c that is a class of nilpotent elements for conjugation bysln c let v be an orbital variety contained in o andpbe the largest parabolic subgroup ofsln c stabilizing v the smith conjecture asserts that v contains a denseporbit this is shown to fail in general and further those nilpotent orbits for which such a dense orbit exists are determined

rogue waves for a 2 1 dimensional gross pitaevskii equation with time varying trapping potential in the bose einstein condensate abstract the bose einstein condensates becs are seen during the studies in atomic optics cavity opto mechanics cavity quantum electrodynamics black hole astrophysics laser optics and atomtronics under investigation in this paper is a 2 1 dimensional gross pitaevskii equation with time varying trapping potential which describes the dynamics of a 2 1 dimensional bec based on the kadomtsev petviashvili hierarchy reduction we construct the bilinear forms and the n th order rogue wave solutions in terms of the gramian with the help of the analytic and graphic analysis we exhibit the first and second order rogue waves under the influence of the strength of the interatomic interaction t and of t r z where t is the scaled time r and z are the confinement frequencies in the radial and axial directions when t 0 the first order rogue wave exhibits as an eye shaped distribution when t is a periodic function the rogue wave periodically raises when t is an exponential function the rogue wave appears on the exponentially increasing background when t decreases background and amplitude of the rogue wave both increase the second order rogue waves reach the maxima only once or three times when t is a constant with t being the exponential function the backgrounds of the second order rogue waves exponentially increase with t increasing

exact wave solutions for a 3 1 dimensional generalized b type kadomtsev petviashvili equation abstract in this work we investigate a 3 1 dimensional generalized b type kadomtsev petviashvili equation based on the simplified hirota bilinear method we first construct its soliton solutions meanwhile we correct the formula of n soliton solution for this equation on the basis of these solitons we further calculate its lump solutions periodic waves meanwhile rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method some figures are given to display the behavior of these solutions