Facet of regular 0–1 polytopes

The role of 0–1 programming problems having monotone or regular feasible sets was pointed out in [6]. The solution sets of covering and of knapsack problems are examples of monotone and of regular sets respectively. Some connections are established between prime implicants of a monotone or a regular Boolean function on the one hand, and facets of the convex hullH of the zeros of on the other. In particular (Corollary 2) a necessary and sufficient condition is given for a constraint of a covering problem to be a facet of the corresponding integer polyhedron. For any prime implicantP of, a nonempty familyF(P) of facets ofH is constructed. Proposition 17 gives easy-to-determine sharp upper bounds for the coefficients of these facets when is regular. A special class of prime implicants is described for regular functions and it is shown that for anyP in this class,F(P) consists of one facet ofH, and this facet has 0–1 coefficients. Every nontrivial facet ofH with 0–1 coefficients is obtained from this class.     

Images and Preimages of D_0 Spaces

ＩｍａｇｅｓａｎｄＰｒｅｉｍａｇｅｓｏｆＤ_０Ｓｐａｃｅｓ￥ＤａｉＭｕｍｉｎ；ＣｈｅｎＨａｉｙａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ．ａｎｄＩｎｆｏｒｍａｔｉｏｎＳｃｉｅｎｃｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＧｕａｎｇｘｉ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐｅｐ?..     

Invariants of an augmentation of Γ0(n)

Let G _n ^× be the 2-group of primary factors of a positive integer n and fix a direct product decomposition of this group. We define an augmentation of Γ₀(n) based on G _n ^×, paralleling augmentations used by Fricke, Cohn and Knopp, and others. Using the decomposition of G _n ^×, we then define a family of functions based on η-functions and use these functions to construct invariants of the augmented group. Along with proving results analogous to those of Cohn and Knopp, we make a complete determination of the multiplier systems for these new functions.     

Convergence of subdiagonal Padé approximations of C 0-semigroups

Let ${(r_{n})_{n \in \mathbb{N}}}$ be the sequence of subdiagonal Padé approximations of the exponential function. We prove that for ?A the generator of a uniformly bounded C ₀-semigroup T on a Banach space X, the sequence ${(r_{n}(-t A))_{n \in \mathbb{N}}}$ converges strongly to T(t) on D(A ^α ) for ${\alpha>\frac{1}{2}}$ . Local uniform convergence in t and explicit convergence rates in n are established. For specific classes of semigroups, such as bounded analytic or exponentially γ -stable ones, stronger estimates are proved. Finally, applications to the inversion of the vector-valued Laplace transform are given.     

Certain Solutions of Equation f（z,0,…,0,uk,0,…,0）=0

ＣｅｒｔａｉｎＳｏｌｕｔｉｏｎｓｏｆＥｑｕａｔｉｏｎｆ（ｚ，０，…，０，ｕ_ｋ，０，…，０）＝０ＬｉｕＧｕａｎｇｍｉｎ（刘光民）（ＫａｉｆｅｎｇＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ）ＬｉｕＧｕａｎｇｍｉｎ（ＫａｉｆｅｎｇＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ）?..     

optimal consump0tion of an investment †

We consider a continuous-time stochastic model for the consumption of an invested resource. The optimal consumption policy is derived. A system of prices which stimulate the optimal consumption is identified. The optimal policy and payoff are found explicitly in the case where the interest process has independent increments.     

Orthogonal sums of 0-σ-simple semigroups

Supported by Grant 0401 A of RFNS through Math. Inst. SANU.     

K0-group Transmissibilities of the Tracial Limit of C^＊-algebras

We introduce the tracial limit A = (t4) limn→n∞ (An,pn) and show that if K0(An) has ordered relation, K0(A) has ordered relation naturally. In the case that A is simple and K0(An) is weakly unperforated for every n, K0(A) is weakly unperforated too. Furthermore, the Riesz interpolation property of K0(An) can be transmitted to K0(A).     

On the complexity of the surrogate dual of 0–1 programming

It is shown that the surrogate dual of a 0–1 programming problem can be solved by 0(m ³) knapsack calls, ifm denotes the number of constraints.

---

Zusammenfassung Es wird gezeigt, daß das surrogate duale Problem zu einer linearen Optimierungsaufgabe mit binären Variablen durch 0(m ³) Rucksackprobleme gelöst werden kann. Dabei bezeichnetm die Anzahl der Nebenbedingungen.

     

Copies of $$c_0(\Gamma )$$ c 0 ( Γ ) in the space of bounded linear operators

Archiv der Mathematik - The space $${{\mathcal {L}}}(X, Y)$$ stands for the Banach space of all bounded linear operators from X to Y endowed with the operator norm. It is shown that $$c_{0}(\Gamma...     

Trace forms of abelian extensions of number fields of type (1, 0)

This article is concerned with describing certain bilinear forms associated with finite abelian extensions N|K of an algebraic number field K. These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring W(K). When the base field K has exactly one dyadic prime and no real embeddings, it is shown that the Witt class of every abelian trace form over K is a product of Witt classes of five specified types.     

Bregman Proximal Relaxation of Large-Scale 0–1 Problems

We apply a recent extension of the Bregman proximal method for convex programming to LP relaxations of 0–1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.     

On complemented copies of c 0 and ℓ ∞

We furnish examples of pairs of Banach spaces X, Y so that none of c ₀ and l _∞ live inside X ^? and Y, but they embed complementably into the space DP(X,Y) of the Dunford–Pettis operators from X into Y.     

Total Contents of Vol.17Ser.BNo.1 March 2 0 0 2

Further Discussion on Statistical Properties of A ctivity Flow Tim e in PERT Wang Xinghua( 1 )……………………Positive H om oclinic Orbits fora Class of Asym ptotically Periodic Second Order Differential EquationsWang Weimin　Wu Shaoping( 7)………………………………………………………………………………………Reflective Function and Periodic Solution of Differential System s Zhou Zhengxin ( 1 3 )…………………………………Positive Solutions to an m- Point Boundary Value Problem Ma R…     

Duals of Hardy Spaces of B-valued Martingales for 0<r≤1

The dual of B-valued martingale Hardy space Hs(p)r(B) with small index 0 r ≤ 1,which is associated with the conditional p-variation of B-valued martingale,is characterized.In order to obtain the results,a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved.Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.     

Polynomial behavior of special values of partial zeta functions of real quadratic fields at s = 0

We compute the special values of partial zeta functions at s = 0 for family of real quadratic fields K _n and ray class ideals ${\mathfrak{b}_n}$ such that ${\mathfrak{b}_n^{-1} = [1, \delta(n)]}$ where the continued fraction expansion of δ(n) ? 1 is purely periodic and terms are polynomials in n of degree bounded by d. With additional assumptions, we prove that the special values of the partial zeta functions at s = 0 are given by a quasi-polynomial of degree less than or equal to d as a function of n. We apply this to conclude that the special values of the Hecke’s L-functions at s = 0 for the family ${(K_n, \mathfrak{b}_n, \chi_n:= \chi \circ N_{K_n/\mathbb{Q}})}$ for any Dirichlet character χ behave like quasi-polynomial as well. We compute explicitly the coefficients of the quasi-polynomials. Two examples satisfying the condition are presented, and for these two families, the special values of the partial zeta functions at s = 0 are given.