AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

AN ALGORITHM FOR COMPUTING ISODUCTILE RESPONSE SPECTRA

The computation of constant ductility (or isoductile) response spectra for single-degree-of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a “check-reject” approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.     

AN ECONOMIC INTERPRETATION OF KUHN'S DUAL FOR THE STEINER-WEBER PROBLEM A NOTE*

In this paper, we given an economic interpretation of Kuhn's dual of the Steiner-Weber problem. It depends essentially on the notion that different transportation systems arerelevant for the primal and the dual. Moreover, the Euclidean metric underlies the interpretation of the primal, the block one that of the dual.     

AN EFFICIENT APPROACH FOR PUSHOVER ANALYSIS OF UNREINFORCED MASONRY (URM) STRUCTURES

This article presents a new method for the calculation of the moment-rotation (M-θ) curves of URM elements using an analytical phenomenogical closed form solution for flexure, combined with a hybrid analytical-statistical model for shear. These are used to define the constitutive law of nonlinear springs located at the areas of lumped inelasticity of an equivalent frame model. The method constitutes an analytical design/assessment tool, to be used by the practicing engineer, for the pushover analysis of URM buildings. The proposed procedure is implemented as a pre-processor to a commercial nonlinear software codes capable of static pushover analysis using the point hinge approach.     

南极旅游开发与设想

本文提出,随着我国南极长城站和中山站的建立、以及"极地号"和"雪龙号"破冰船的购置,更由于人民生活水平的逐步提高,我国开发南极旅游的时机已经到来。本文认为与低层次的物质享受相比,南极旅游更有助于促进国民素质提高和全国主义、国际主义精神的培养。本文对南极旅游资源作了评价.划分出南极半岛等4个旅游区。本文构思了我国未来南极旅游组织实施的规划和设想,提出可先开辟南极半岛旅游区和环南极旅行两条旅游线路,沿途可开展海外观光、远洋考察和远洋捕捞业,以促进我国旅游业、南大洋考察和远洋捕捞运输业的全面发展。     

NORTH AND SOUTH AT THE END OF THE MYCENAEAN AGE: ASPECTS OF AN OLD PROBLEM

Summary. The end of the Mycenaean age calls for an explanation outside the immediate Aegean area. The evidence is more likely to come from changes in habit than in the importation of objects of bronze or pottery. In order to understand events it is necessary to look beyond Greek frontiers to the Danube and Balkans. Among important changes are those in fighting tactics with a return to the sword in the Aegean and new workshop practice in Europe with more bronze forging against casting. Evidence for actual arrival of people is never likely to be conclusive; various alternatives are considered.