Abstract. Let δ(P) be the δ-vector of a reflexive polytope P ⊂ R of dimension d and δ(P) the δ-vector of the dual polytope P ⊂ R. In general, δ(P) = δ(P) does not hold. In this paper, we give a higher-dimensional construction of a reflexive polytope whose δ-vector equals the δ-vector of the dual polytope. In particular, we consider the case that the reflexive polytope and the dual polytope are ...

The convergence rate of a Krylov method such as the Generalized Conjugate Resid10 ual (GCR) [6] method, to solve a linear system Au = f , A = (ai j) ∈ Rm×m,u ∈ 11 R m, f ∈ Rm, decreases with increasing condition number κ2(A) = ||A||2||A−1||2 12 of the non singular matrix A. Left preconditioning techniques consist of solving 13 M−1Au=M−1 f such that κ2(M−1A)<<κ2(A). The Additive Schwarz (AS) pre...

The KLOE measurements of φ radiative decays and of the ratio Γ(K S → π + π − (γ))/Γ(K S → π 0 π 0) are discussed. The first measurement aims at understanding the real nature of the scalar mesons a 0 and f 0 , whose possible compositions are q ¯ q, qq ¯ q ¯ q, or K ¯ K molecule. The second measurement is related to the estimate of the phase shift difference δ 0 − δ 2. Previous measurements were ...

Definition 0.1 Let δ be a cardinal. We say that δ is Woodin with 3 iff there is some sequence (a κ : κ < δ) such that a κ ⊂ V κ for every κ < δ and for every A ⊂ V δ the set {κ < δ : A ∩ V κ = a κ ∧ κ is A–strong up to δ} is stationary in δ. Proof. Let us define ((a κ , c κ) : κ < δ) recursively as follows. If ((a κ , c κ) : κ < µ) is defined for some µ < δ, then we let (a µ , c µ) be the least...

Let N be a lattice and P ⊂ N ⊗ Z R a lattice polytope, i.e., the convex hull of finitely many points in N. Ehrhart's theorem asserts that the lattice-point counting function f P (m) := # (mP ∩ N) is a polynomial, and thus 1 + P m≥1 f P (m) t m = δ P (t) (1−t) d+1 for some polynomial δ P (t), the δ-vector of P. Motivated by the Knudsen–Mumford–Waterman Conjecture about the existence of unimodula...

The distributed (∆ + 1)-coloring problem is one of most fundamental and well-studied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current state-of-the-art running time is O(∆ log ∆+log∗ n), due to Kuhn and Wattenhofer, PODC’06. Linial (FOCS’87) has proved a lower bound of 1 2 log∗ n f...

In this appendix we present the proofs omitted in “Dynamic Free Riding with Irreversible Investments” by Marco Battaglini, Salvatore Nunnari and Thomas Palfrey. Marco Battaglini Department of Economics Princeton University Princeton NJ 08544 [email protected] Salvatore Nunnari Department of Political Science Columbia University New York, NY 10027 [email protected] Thomas Palfrey Divisi...

In this research Bi2O3 was doped with mixtures of 8, 10, 12 and 18 mol % of Y2O3 and Yb2O3 to stabilizing the δ-Bi2O3 phase using solid state reaction technique. Experimental samples were fabricated by isostatic pressing and sintering at 850 °C for 24 h. X-ray diffraction analysis detected cubic phase (δ-Bi2O3) as the sole stable crystalline phase in samples including 12 and 18 mol % of Y2O3 an...

INTRODUCTION Androgen receptor (AR) CAG polymorphism has been found to influence sexual function. However, no study has evaluated its potential to condition sexual function recovery after testosterone replacement therapy (TRT) in a large cohort of hypogonadic subjects. AIM To evaluate the role of this polymorphism in sexual function improvement after TRT in late-onset hypogonadism (LOH). ME...