Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.     

On the performance of peeling algorithms

The peeling of a d-dimensional set of points is usually performed with successive calls to a convex hull algorithm; the optimal worst-case convex hull algorithm, known to have an O(n^˙ Log (n)) execution time, may give an O(n^˙n^˙ Log (n)) to peel all the set; an O(n^˙n) convex hull algorithm, m being the number of extremal points, is shown to peel every set with an O(n-n) time, and proved to be optimal; an implementation of this algorithm is given for planar sets and spatial sets, but the latter give only an approximate O(n^˙n) performance.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

The optimal coefficients in Daubechies wavelets

The construction of wavelets begins with a dilation equation (x) = Σc_k(2x-k). The choice of the coefficients c_k controls the accuracy and orthogonality of wavelet expansions. We show how the Daubechies coefficients, which give pth order accuracy with 2p coefficients (the minimum number), follow from orthogonality and accuracy conditions applied to the polynomial Σc_ke^ikξ.     

Construction,sur un anneau de Dedekind,d'une base reguliere de polynomes a valeurs entieres

Let A be a domain of field of fractions K, and A[X]_sub the ring of integral valued polynomials over A, i. e., polynomials P(X), with coefficients in K, such that P(A) is contained in A. In [2] and [3], P.-J. Cahen characterized the Dedekind domains A for which the A-module A[X]_sub admits a regular basis, i. e. a basis Q₀(X), Q₁(X), ..., Q_n(X), ... such that degQ_n(X)=n for any n.For these Dedekind domains, we give, in this paper, a method to construct explicitly such a basis.     

Use of solvent sorption to detect structural changes in rigid PVC compounds

The effects of type of PVC and its thermal history on solvent sorption behaviour were investigated. Samples were immersed in toluene at 25°C, and the equilibrium solvent uptake and sorption half-times were measured for a variety of samples. The shape of the sorption curve was also observed. Equilibrium sorption was found to decrease with increasing amount of crystallinity in the sample. Sorption half-time increased with increased crystallinity, but minimum equilibrium sorption did not correspond with maximum half-time, possibly due to the type of crystallinity present. The shape of the sorption curve (Fickian or Case II sorption) also depended on the ype of PVC used and is thermal history. The solvent sorption technique was shown to be a sensitive method for detecting small structural changes in PVC.     

organocuprate reactions of enone lactones. I. Synthesis of trans-fused rings via conjugate addition.

Control of the stereochemistry of substituents needed to construct a bicyclic system (e.g. a hydrindanone) is achieved by conjugate addition of an organocuprate to a cyclohexenone made conformationally rigid by the attachment of a 1,3-lactone.     

Neutral oxygen atom density in the MESOX air plasma solar furnace facility

The density of neutral oxygen atoms in the MESOX set-up, one device of the PROMES-CNRS solar facilities, was determined by a fiber-optics catalytic probe (FOCP). Plasma was created in a flowing air within a quartz tube with the outer diameter of 5 cm by a 2.45 GHz microwave generator with the output power up to 1000 W. The flow of air was varied between 4 and 20 l/h. The O-atom density was found to increase monotonously with the increasing discharge power, and it decreased with the increasing flow rate. The degree of dissociation of oxygen molecules in the plasma column depended largely on the flow rate. At the air flow of 4 l/h it was about 80% but it decreased to about 20% at the flow of 20 l/h.