Constructing cotorsion pairs over generalized path algebras

We introduce two adjoint pairs （eλ^i（）i） and （（）i,ep^i） and give a new method to construct cotorsion pairs. As applications, we characterize all projective and injective representations of a generalized path algebra and exhibit projective and injective objects of the category Mp which is a generalization of monomorphisms category.

RELIABILITY-BASED ANALYSIS AND SYNTHESIS OF MECHANICAL ERROR FOR PATH GENERATING LINKAGES

A reliability-based analysis approach to mechanical error in path generating linkages is pre- sented . The reliability index is taken as a measure for the deviation of the actual path of a coupler point from the desired one. A reliability-based synthesis procedure of the mechanical error for path generating linkages to allocate optimal tolerances and clearances is developed. A four-bar path generating mechanism is considered for numerical illustration.

Traffic assignment problem under tradable credit scheme in a bi-modal stochastic transportation network: A cumulative prospect theory approach

The traffic equilibrium assignment problem under tradable credit scheme(TCS) in a bi-modal stochastic transportation network is investigated in this paper. To describe traveler’s risk-taking behaviors under uncertainty, the cumulative prospect theory(CPT) is adopted. Travelers are assumed to choose the paths with the minimum perceived generalized path costs, consisting of time prospect value(PV) and monetary cost. At equilibrium with a given TCS, the endogenous reference points and credit price remain constant, and are consistent with the equilibrium flow pattern and the corresponding travel time distributions of road sub-network. To describe such an equilibrium state, the CPT-based stochastic user equilibrium(SUE) conditions can be formulated under TCS. An equivalent variational inequality(VI) model embedding a parameterized fixed point(FP) model is then established, with its properties analyzed theoretically. A heuristic solution algorithm is developed to solve the model, which contains two-layer iterations. The outer iteration is a bisection-based contraction method to find the equilibrium credit price, and the inner iteration is essentially the method of successive averages(MSA) to determine the corresponding CPT-based SUE network flow pattern. Numerical experiments are provided to validate the model and algorithm.

Seneralized Path Algebras and Pointed Hopf Algebras

Most of pointed Hopf algebras of dimension p^m with large coradtical are shown to be generalized path algebras. By the theory of generalized path algebras, the representations, homological dimensions and radicals of these Hopf algebras are obtained. The relations between the radicals of path algebras and connectivity of directed graphs are given.

Optimization of equimolar reverse constant-temperature mass-diffusion process for minimum entransy dissipation

The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies the equimolar reverse constant-temperature mass-diffusion process with Fick's law( g∝Δ(c)). The optimal concentration paths for the MED(Minimum Entransy Dissipation) are derived and compared with those for the MEG(Minimum Entropy Generation) and CCR(Constant Concentration Ratio) operations. It is indicated that the strategy of the MED is equivalent to that of the CCD(Constant Concentration Difference) of the same component; whether the MED or the MEG is selected as the optimization objective, the strategy of the CCD is much better than that of the CCR.