一般整数规划中有效不等式的同步升维

有效不等式在整数规划的定界研究中具有重要的意义.研究了一般整数规划问题的有效不等式的升维方法,引入超加性函数给出同步升维的条件,并给出有效不等式的同步升维的具体方法,算例表明本文提出的方法是有效的.     

Decidable (= separable) objects and morphisms in lextensive categories

After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively.     

The graphical relaxation: A new framework for the symmetric traveling salesman polytope

A present trend in the study of theSymmetric Traveling Salesman Polytope (STSP(n)) is to use, as a relaxation of the polytope, thegraphical relaxation (GTSP(n)) rather than the traditionalmonotone relaxation which seems to have attained its limits. In this paper, we show the very close relationship between STSP(n) and GTSP(n). In particular, we prove that every non-trivial facet of STSP(n) is the intersection ofn + 1 facets of GTSP(n),n of which are defined by the degree inequalities. This fact permits us to define a standard form for the facet-defining inequalities for STSP(n), that we calltight triangular, and to devise a proof technique that can be used to show that many known facet-defining inequalities for GTSP(n) define also facets of STSP(n). In addition, we give conditions that permit to obtain facet-defining inequalities by composition of facet-defining inequalities for STSP(n) and general lifting theorems to derive facet-defining inequalities for STSP(n +k) from inequalities defining facets of STSP(n).Partially financed by P.R.C. Mathématique et Informatique.     

The essentially tame local Langlands correspondence, I

Let be a non-Archimedean local field (of characteristic or ) with finite residue field of characteristic . An irreducible smooth representation of the Weil group of is called essentially tame if its restriction to wild inertia is a sum of characters. The set of isomorphism classes of irreducible, essentially tame representations of dimension is denoted . The Langlands correspondence induces a bijection of with a certain set of irreducible supercuspidal representations of . We consider the set of isomorphism classes of certain pairs , called ``admissible', consisting of a tamely ramified field extension of degree and a quasicharacter of . There is an obvious bijection of with . Using the classification of supercuspidal representations and tame lifting, we construct directly a canonical bijection of with , generalizing and simplifying a construction of Howe (1977). Together, these maps give a canonical bijection of with . We show that one obtains the Langlands correspondence by composing the map with a permutation of of the form , where is a tamely ramified character of depending on . This answers a question of Moy (1986). We calculate the character in the case where is totally ramified of odd degree.

     

Rings whose cyclic modules are lifting and ⊕-supplemented

It is proved that a semiperfect module is lifting if and only if it has a projective cover preserving direct summands. Three corollaries are obtained: (1) every cyclic module over a ring R is lifting if and only if every cyclic R-module has a projective cover preserving direct summands; (2) a ring R is artinian serial with Jacobson radical square-zero if and only if every (2-generated) R-module has a projective cover preserving direct summands; (3) a ring R is a right (semi-)perfect ring if and only if (cyclic) lifting R-module has a projective cover preserving direct summands, if and only if every (cyclic) R-module having a projective cover preserving direct summands is lifting. It is also proved that every cyclic module over a ring R is ⊕-supplemented if and only if every cyclic R-module is a direct sum of local modules. Consequently, a ring R is artinian serial if and only if every left and right R-module is a direct sum of local modules.     

The weak theory of monads

We construct a ‘weak’ version EMw(K) of Lack and Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between monads in EMw(K) and composite pre-monads in K is discussed. If K admits Eilenberg-Moore constructions for monads, we define two symmetrical notions of ‘weak liftings’ for monads in K. If moreover idempotent 2-cells in K split, we describe both kinds of weak lifting via an appropriate pseudo-functor EMw(K)→K. Weak entwining structures and partial entwining structures are shown to realize weak liftings of a comonad for a monad in these respective senses. Weak bialgebras are characterized as algebras and coalgebras, such that the corresponding monads weakly lift for the corresponding comonads and also the comonads weakly lift for the monads.     

A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics

We prove that there are only finitely many families of codimension two nonsingular subvarieties of quadrics which are not of general type, for and . We prove a similar statement also for the case of higher codimension.

     

Wavelet bi‐frames with uniform symmetry

Wavelet bi‐frames with uniform symmetry are discussed in this paper. Every refinable function in the bi‐frame system is symmetric, which is very useful in the image processing and curve and surface multiresolution processing. By the aid of the lifting scheme, bi‐frame multiresolution algorithms can be divided into several iterative steps, and each step can be shown by a symmetric template. The template‐based procedure is established for constructing bi‐frames with uniform symmetry and N > 2 generators. In particular, we take the bi‐frame with three generators as an example to provide a clearer picture of the template‐based procedure for constructing bi‐frames. Three types of bi‐frames with three generators are studied, and some examples with certain smoothness are constructed. These examples include some bi‐frames with interpolating property. Copyright © 2016 John Wiley & Sons, Ltd.     

Legendre spectral method for solving mixed boundary value problems on rectangle

In this paper, we develop a spectral method for mixed inhomogeneous Dirichlet/Neumann/Robin boundary value problems defined on rectangle. Some results on two‐dimensional Legendre approximation in Jacobi‐weighted Sobolev space are established. As examples of applications, spectral schemes are provided for two model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms are proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy and confirm the theoretical analysis well. Copyright © 2016 John Wiley & Sons, Ltd.     

The 0-1 Knapsack problem with a single continuous variable

Specifically we investigate the polyhedral structure of the knapsack problem with a single continuous variable, called the mixed 0-1 knapsack problem. First different classes of facet-defining inequalities are derived based on restriction and lifting. The order of lifting, particularly of the continuous variable, plays an important role. Secondly we show that the flow cover inequalities derived for the single node flow set, consisting of arc flows into and out of a single node with binary variable lower and upper bounds on each arc, can be obtained from valid inequalities for the mixed 0-1 knapsack problem. Thus the separation heuristic we derive for mixed knapsack sets can also be used to derive cuts for more general mixed 0-1 constraints. Initial computational results on a variety of problems are presented. Received May 22, 1997 / Revised version received December 22, 1997 Published online November 24, 1998