The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions

We extend the Tikhonov regularization method widely used in optimization and monotone variational inequality studies to equilibrium problems. It is shown that the convergence results obtained from the monotone variational inequality remain valid for the monotone equilibrium problem. For pseudomonotone equilibrium problems, the Tikhonov regularized subproblems have a unique solution only in the limit, but any Tikhonov trajectory tends to the solution of the original problem, which is the unique solution of the strongly monotone equilibrium problem defined on the basis of the regularization bifunction.     

Impact of some parameters on investments in oligopolistic electricity markets

It is seldom the case that one has the opportunity to compare investments as projected by a long-term multi-period model to what is eventually realized in practice. Further, although sensitivity analysis is of common use in any optimization setting, the impact of some parameters on strategic investments is not yet fully assessed in the context of the deregulated electricity industry. Starting with a benchmark model of the Finnish industry, we precisely explore the impact on equilibrium investments of varying such parameters as direct- and cross-price elasticities, length of the planning horizon and the depreciation rate of capacity. We run the model with different parameter values and compare the predicted equilibrium with what companies have actually done. The model is a stochastic dynamic game involving three players and played over a ten-year period.Our results show the depreciation rate and the planning horizon have a notable effect on investment levels, whereas price elasticities seem to play a lesser role. Although the model’s results are rather well aligned to total industry investments, it diverges from individual levels. This may be due to the cost parameter used and/or to the open-loop information structure adopted in the computations. In any event, these results should be of methodological and practical interest to scholars and practitioners involved in strategic investment in the electricity industry.     

Binary integer modeling of the traffic flow optimization problem,in the case of an autonomous transportation system

Our research aimed to optimize the transportation processes through the binary integer modeling of cooperative vehicle control by linking the dynamic traffic assignment approach and controlling the autonomous transport system. Our paper’s main contribution is a model transforming the optimal vehicle control problem into binary integer formulation, optimizing transport processes at the system level, and representing safety and dynamics related constraints on the vehicle level. Two small numerical case studies have illustrated the applicability and effectiveness of the model.     

Local limit of nonlocal traffic models: Convergence results and total variation blow-up

Consider a nonlocal conservation law where the flux function depends on the convolution of the solution with a given kernel. In the singular local limit obtained by letting the convolution kernel converge to the Dirac delta one formally recovers a conservation law. However, recent counter-examples show that in general the solutions of the nonlocal equations do not converge to a solution of the conservation law. In this work we focus on nonlocal conservation laws modeling vehicular traffic: in this case, the convolution kernel is anisotropic. We show that, under fairly general assumptions on the (anisotropic) convolution kernel, the nonlocal-to-local limit can be rigorously justified provided the initial datum satisfies a one-sided Lipschitz condition and is bounded away from 0. We also exhibit a counter-example showing that, if the initial datum attains the value 0, then there are severe obstructions to a convergence proof.     

Isobaric Vapor-Liquid Equilibria and Densities for the Binary Systems Oxolane + Ethyl 1,1-Dimethylethyl Ether,Oxolane + 2-Propanol and Propan-2-One + Trichloromethane

Vapor-liquid equilibrium data have been determined at 50 kPa for the binary systems oxolane (THF) + ethyl 1,1-dimethylethyl ether (ETBE) and oxolane + 2-propanol, and at 94 kPa for the system propan-2-one + trichloromethane. Excess volumes have also been determined from density measurements at 298.15 K. The systems oxolane + ethyl 1,1-dimethylethyl ether and oxolane + 2-propanol exhibit slight to moderate positive deviations from ideal behavior and no azeotrope is present. The system propan-2-one + trichloromethane exhibits negative deviations from ideal behavior and presents an azeotrope. The excess volumes of the system oxolane + ethyl 1,1-dimethylethyl ether are negative over the whole mole fraction range while those of the system oxolane + 2-propanol are positive. Excess volumes of the system propan-2-one + trichloromethane, change from negative to positive as the concentration of propan-2-one increases. The activity coefficients and boiling points of the solutions were correlated with the mole fraction by the Wohl, Wilson, UNIQUAC, and NRTL equations, and predicted by the UNIFAC group contribution method. Excess volume data were correlated using the Redlich-Kister expansion. The chemical association theory was applied for explaining the equilibrium behavior of the systems oxolane + 2-propanol and propan-2-one + trichloromethane.     

Complex Formation Reactions of Divinyltin(IV) Complexes with Amino Acids,Peptides, Dicarboxylic acids and Related Compounds

Complex formation equilibria of divinyltin(IV) with amino acids, peptides, and dicarboxylic acids have been investigated. Stoichiometry and stability constants for the complexes formed were determined at 25°C and ionic strength 0.1 M NaNO₃. The results showed the formation of ML, MLH, and ML₂ (organotin : ligand : hydrogen) complexes with amino acids. Peptides form ML complexes and the corresponding deprotonated amide species MLH_?1. In the latter species the binding with divinyltin(IV) occurs through the terminal amino group, carboxylate oxygen, and the amide nitrogen atoms (CO^? ₂, N^? _amide, NH₂). The results showed the formation of ML and ML₂ complexes with dicarboxylic acids. The concentration distribution of the complexes in solution was evaluated. The bonding sites of the divinyltin(IV) complex in solid state with oxalic acid was investigated by means of elemental analyses, FTIR, and mass spectra. Non-isothermal decomposition of the above complex has been studied and the result was statistically analyzed. The main steps were identified for the thermal decomposition reaction and each step proved to be a first order reaction. The kinetic parameters E _a and A were calculated for each step in the reaction. The thermodynamic functions H, G, and S* were calculated for each step of the reaction.     

Synthesis,Properties and X-ray Crystal Structures of Nickel(II) Complexes of a Hexaazamacrotetracyclic Ligand

The complexes [N₂(L²)₂(H₂O)₄]Cl₄(1) and [Ni(L²)](ClO₄)₂ [sdot]2H₂O (2) (L = 1,3,10,12,16,19-hexaazatetracyclo [17,3,1,1 ^12.16,0^4.9]tetracosane) have been synthesized and structurally characterized by X-ray crystallography, spectroscopic and cyclic voltammetry. The crystal structure of 1 has a distorted octahedral geometry with two secondary and two tertiary amines of the macrocycle and two water molecules. In 2, the coordination geometry around the nickel atom is square-planar with four nitrogen atoms of the macrocycle. The equilibrium [Ni(L²)]²⁺ + 2H₂O &rlhar2; [Ni(L²)(H₂O)₂]²⁺ has been studied in aqueous solution over a temperature range, yielding Δ H° = -19.0 ± 0.2 kJ mol^-1 and Δ S° = - 56.0 ± 0.4 JK^-1 mol^-1. Cyclic voltammetry of the complexes give two one-electron waves corresponding to Ni(II)/Ni(III) and Ni(II)/Ni(I) processes. The electronic spectra and redox potentials of the complexes are influenced significantly by the geometry.     

Equilibrium in an ambiguity-averse mean–variance investors market

In a financial market composed of n risky assets and a riskless asset, where short sales are allowed and mean–variance investors can be ambiguity averse, i.e., diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets, we derive a closed form portfolio rule based on a worst case max–min criterion. Then, in a market where all investors are ambiguity-averse mean–variance investors with access to given mean return and variance–covariance estimates, we investigate conditions regarding the existence of an equilibrium price system and give an explicit formula for the equilibrium prices. In addition to the usual equilibrium properties that continue to hold in our case, we show that the diffidence of investors in a homogeneously diffident (with bounded diffidence) mean–variance investors’ market has a deflationary effect on equilibrium prices with respect to a pure mean–variance investors’ market in equilibrium. Deflationary pressure on prices may also occur if one of the investors (in an ambiguity-neutral market) with no initial short position decides to adopt an ambiguity-averse attitude. We also establish a CAPM-like property that reduces to the classical CAPM in case all investors are ambiguity-neutral.     

Equilibrium network design of shared-vehicle systems

An equilibrium network design model is formulated to determine the optimal configuration of a vehicle sharing program (VSP). A VSP involves a fleet of vehicles (bicycles, cars, or electric vehicles) positioned strategically across a network. In a flexible VSP, users are permitted to check out vehicles to perform trips and return the vehicles to stations close to their destinations. VSP operators need to determine an optimal configuration in terms of station locations, vehicle inventories, and station capacities, that maximizes revenue. Since users are likely to use the VSP resources only if their travel utilities improve, a generalized equilibrium based approach is adopted to design the system. The model takes the form of a bi-level, mixed-integer program. Model properties of uniqueness, inefficiency of equilibrium, and transformations that lead to an exact solution approach are presented. Computational tests on several synthetic instances demonstrate the nature of the equilibrium configuration, the trade-offs between operator and user objectives, and insights for deploying such systems.