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The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity. This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.

A mechanism is a mathematical structure that models institutions through which economic activity is guided and coordinated. There are many such institutions; markets are the most familiar ones. Lawmakers, administrators and officers of private companies create institutions in order to achieve desired goals. They seek to do so in ways that economize on the resources needed to operate the institutions, and that provide incentives that induce the required behaviors. This book presents systematic procedures for designing mechanisms that achieve specified performance, and economize on the resources required to operate the mechanism. The systematic design procedures are algorithms for designing informationally efficient mechanisms. Most of the book deals with these procedures of design. When there are finitely many environments to be dealt with, and there is a Nash-implementing mechanism, our algorithms can be used to make that mechanism into an informationally efficient one. Informationally efficient dominant strategy implementation is also studied.

Although additive manufacturing (AM), or three dimensional (3D) printing, provides significant advantages over existing manufacturing techniques, metallic parts produced by AM are susceptible to distortion, lack of fusion defects and compositional changes. Here we show that the printability, or the ability of an alloy to avoid these defects, can be examined by developing and testing appropriate theories. A theoretical scaling analysis is used to test vulnerability of various alloys to thermal distortion. A theoretical kinetic model is used to examine predisposition of different alloys to AM induced compositional changes. A well-tested numerical heat transfer and fluid flow model is used to compare susceptibilities of various alloys to lack of fusion defects. These results are tested and validated with independent experimental data. The findings presented in this paper are aimed at achieving distortion free, compositionally sound and well bonded metallic parts.

In the present paper the sixth-order nonlinear mathematical model with nonsmooth solutions is studied. We consider a case, when the problem is guaranteed to have one solution and investigate the question on the presence of one more. Using the pointwise approach of Yu. V. Pokorny, which has shown its effectiveness in analyzing models of the second and fourth orders, sufficient conditions of the existence of the second solution for the sixth-order model with derivatives with respect to measure are obtained.

In the process of natural gas transportation, the existence of free water is a disturbing problem. This paper studies the calculation model of the natural gas water content of the China-Russia eastern gas pipeline and the amount and distribution of fluid accumulation in the China-Russia eastern gas pipeline commissioning stage. By comparing the calculation, Li correlation with the Keenan-Keyes model is a suitable model for calculating the natural gas water content of the China-Russia eastern gas pipeline. According to the model and software calculation, under the winter conditions in the first year of production of the China-Russia eastern gas pipeline, the total water accumulation in the pipeline increases with the increase of water content. The water produced in the pipeline can reach 255 × 103 m3 in the case of saturated water content in the first year of production. The water accumulation in the pipeline is mainly distributed in the ascending part of the low-lying pipe section. Where the height difference of the pipeline is greater, the water accumulation is more serious. In the pipeline section with a mileage of 53km - 134km, the water accumulation was the most serious, and the liquid holdup was as high as 0.66.

The correct grasp of objects is a key aspect for the right fulfillment of a given task. Obtaining a good grasp requires algorithms to automatically determine proper contact points on the object as well as proper hand configurations, especially when dexterous manipulation is desired, and the quantification of a good grasp requires the definition of suitable grasp quality measures. This article reviews the quality measures proposed in the literature to evaluate grasp quality. The quality measures are classified into two groups according to the main aspect they evaluate: location of contact points on the object and hand configuration. The approaches that combine different measures from the two previous groups to obtain a global quality measure are also reviewed, as well as some measures related to human hand studies and grasp performance. Several examples are presented to illustrate and compare the performance of the reviewed measures.

In this paper, a detailed review on the dynamics of axially moving systems is presented. Over the past 60 years, vibration control of axially moving systems has attracted considerable attention owing to the board applications including continuous material processing, roll-to-roll systems, flexible electronics, etc. Depending on the system’s flexibility and geometric parameters, axially moving systems can be categorized into four models: String, beam, belt, and plate models. We first derive a total of 33 partial differential equation (PDE) models for axially moving systems appearing in various fields. The methods to approximate the PDEs to ordinary differential equations (ODEs) are discussed; then, approximated ODE models are summarized. Also, the techniques (analytical, numerical) to solve both the PDE and ODE models are presented. The dynamic analyses including the divergence and flutter instabilities, bifurcation, and chaos are outlined. Lastly, future research directions to enhance the technologies in this field are also proposed. Considering that a continuous manufacturing process of composite and layered materials is more demanding recently, this paper will provide a guideline to select a proper mathematical model and to analyze the dynamics of the process in advance.

This paper considers the parameter identification problems of controlled autoregressive systems using observation information. According to the hierarchical identification principle, we decompose the controlled autoregressive system into two subsystems by introducing two fictitious output variables. Then a two-stage gradient-based iterative algorithm is proposed by means of the iterative technique. In order to improve the performance of the tracking the time-varying parameters, we derive a two-stage multi-innovation gradient-based iterative algorithm based on the multi-innovation identification theory. Finally, an example is provided to illustrate the effectiveness of the proposed algorithms.

During gun firing on ground target, because the ammunition consumption is large, it is necessary to select shells in the light of effectiveness-cost. In order to solve the problem of selecting shells, this paper puts forward analysis method of firing effectiveness-cost firstly. Then by using the calculation model of probability ranking decision, we can select appropriate shells by comparing average value of effectiveness-cost expectation extremum. This provides reference for user of gun to make decision during firing on ground target.

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.