Multitiered Supply Chain Networks: Multicriteria Decision—Making Under Uncertainty

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.     

The clamped-plate equation for the limaçon

Hadamard claimed in 1907 that the clamped-plate equation is positivity preserving for domains which are bounded by a Limaçon de Pascal. We will show that this claim is false in its full generality. However, we will also prove that there are nonconvex limaçons for which the clamped-plate equation has the sign-preserving property. In fact we will give an explicit bound for the parameter of the limaçon where sign change may occur. Mathematics Subject Classification (2000) 35J40, 35Q72, 35B50     

Interior penalty method for the indefinite time-harmonic Maxwell equations

Summary In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L²-norm. In particular, the error in the energy norm is shown to converge with the optimal order (h^min{s,}) with respect to the mesh size h, the polynomial degree , and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L²-error is shown to converge with the optimal order (h⁺¹). The theoretical results are confirmed in a series of numerical experiments.Supported by the EPSRC (Grant GR/R76615).Supported by the Swiss National Science Foundation under project 21-068126.02.Supported in part by the Natural Sciences and Engineering Council of Canada.     

Direct measurement of 1J(13C13C) in coordinated double bonds

¹J(¹³C¹³C) has been determined in naturally abundant samples of η¹,η² -alkenyl-η⁵ -cyclopentadienylnickel complexes; for the coordinated double bonds ¹J(CC) lies between the value for free ethylene and cyclopropane, and therefore gives direct insight into the relevant bonding situation.     

Crystal and molecular structure of 17-β-methyllupanine perchlorate

The formula of the title compound is C₁₆H₂₇ClN₂O₅,MW = 362.9 orthorhombic,P2₁2₁2₁,a = 8.403(1),b= 13.133(1),c= 15.972(2) Å,Z = 4,D _x = 1.37 g cm^–3, (CuK) = 2.2 mm^-1. The lupanine skeleton has atrans-trans configuration. The ringA has a half-chair conformation, theB andD rings adopt a chair form, and theC ring forms a boat. The lupanine cations are linked together by the intermolecular hydrogen bonds forming infinite chains alongb. The N(16) ... O(C2) distance is 2.763(7) Å.     

Proton addition to excited diazaphenanthrenes topology determined molecular properties

Absorption and luminescence spectra, depopulation kinetics of the lowest excited singlet and triplet states and acid-base equilibria were investigated for neutral and protonated diazaphenanthrenes: 2,3-, 1,4- and 5,6-DAF. The spectroscopical results are correlated with CNDO/S calculations. Profound influence of topology upon photophysical and chemical (basicity) properties has been stated and discussed.     

The crystal and molecular structure of diaquadichlorotheophyllinecopper(II)

Summary The crystal structure of CuCl₂(C₇H₈N₄O₂)(H₂O)₂ has been determined from diffractometer data by Patterson and Fourier methods and refined by full-matrix least-squares to R=0.067 for 2123 observed reflections. Unit cell constants are:a=9.930(8),b=9.987(8),c=7.483(6) Å,=123.2(1),=94.5(1),= 83.9(1)°. The space group is P¯1 withZ=2. The structure consists of diaquadichlorotheophyllinecopper(II) complexes linked by hydrogen bonds. The coordination polyhedron of copper is a square pyramid whose base, severely tetrahedrally distorted, is formed by a water molecule [Cu-Ow=2.025(7) Å], two chlorines [Cu-Cl=2.273(4), 2.296(4) Å] and an imidazole nitrogen [Cu-N=1.983(9) Å] from the theophylline ligand. A second water molecule is at the apex of the pyramid [Cu-Ow=2.292(7) Å]. Coordination is completed to a distorted octahedral one by a long Cu ... O=3.164(7) Å contact involving the exocyclic oxygen at C₆ of the theophylline ligand.     

Charakteristik der Methansulfonyloxygruppe als ein desaktivierender o-,p-dirigierender Substituent durch ihr UV-Absorptionsspektrum

Ohne ZusammenfassungMit 1 Abbildung     

Sulla influenza della polarizzazione delle radio-onde nei fenomeni di interazione ionosferica

Riassunto Si studia l'influenza della polarizzazione delle radio-onde su alcuni fenomeni non lineari nella ionosfera tramite una nuova e più completa relazione funzionale fra i vettori densità di corrente e campo elettrico. Tale studio riguarda la comparsa di onde di banda laterale e la loro dipendenza dalle direzioni di polarizzazione delle onde interagenti.

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Summary The influence of radio wave polarization on some nonlinear phenomena in the inosphere is studied through a new and more complete functional relation between current density and electric field vectors. This study is concerned with the occurrence of ?sideband? waves and their dependence on the polarization directions of interacting waves.