1. Hensel’s lemma 2. Metric definition of p-adic integers Zp and p-adic rationals Qp 3. Elementary/clumsy definitions of adeles A and ideles J 4. Uniqueness of objects characterized by mapping properties 5. Existence of limits 6. Zp and Ẑ as limits 7. Qp and A as colimits 8. Abelian solenoids (R×Qp)/Z[1/p] and A/Q 9. Non-abelian solenoids and SL2(Q)\SL2(A) Although we will also give the more ty...

We introduce a very weak language Lp on Qp, which is just rich enough to have the same definable subsets of the line Qp than one has using the ring language. We prove that the only definable functions in the language Lp are trivial functions. We further give a definitional expansion Lp of Lp in which Qp has quantifier elimination and we obtain a weak cell decomposition. Our language Lp can serv...

Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these challenges. To demonstrate the reliability improvements of ...

Theorem 1. Let L be a locally compact, nondiscrete topological field. a) Then L is a finite extension of one of the following fields: (i) K = R. (ii) K = Qp. (iii) K = Fp((t)). b) In case (i) L = R or L = C. c) In case (ii) the ramification index e(L/Qp) and residual degree f(L/Qp) are uniquely determined by the abstract field L, and for any given e, f ∈ Z, the number of finite extensions L/Qp ...

The aim of this study is to provide a conceptual model that links several key variables including supplier relationship management (SRM) and customer (CRM) organisational factors (OF) knowledge (KM) enhance quality performance (QP) Hong Kong watch trade. Literature review was conducted extensively, the approach employed conceptualized into proposed framework. A framework suggested in paper QP w...

Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the...

We study first-order properties of the quotient rings 9(V)/1 by a prime ideal 9, where 9( V) is the ring of p-adic valued continuous definable functions on some affine p-adic variety V. We show that they are integrally closed Henselian local rings, with a p-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy Vx, y(x Iy2 V y IX2). ...

The growing demand for advanced mobile multimedia let the wireless mobile internet access be developed rapidly. The current mobile network is capable of providing flexible quality of service mechanisms including exact estimation of network bandwidth. In this paper, we propose a new GOP level rate control algorithm which can accurately estimate an initial QP according to the estimated network ba...

Recently, Busemeyer et al. (2011) presented a model for how the conjunction fallacy (Tversky & Kahneman, 1983) emerges, based on the principles of quantum probability (QP) theory. Pothos et al. (2013) extended this model to account for the main similarity findings of Tversky (1977), which have served as a golden standard for testing novel theories of similarity. However, Tversky’s (1977) empiri...

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...