Researches in graphical statics

UANL

Object allocation via deferred-acceptance: strategy-proofness and comparative statics

We study the problem of assigning indivisible and heterogenous objects (e.g., houses, jobs, offices, school or university admissions etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. We consider mechanisms satisfying a set of basic properties (unavailable-type-invariance, individual-rationality, weak non-wastefulness, or truncation-invariance). In the house allocation problem, where at most one copy of each object is available, deferred-acceptance (DA)-mechanisms allocate objects based on exogenously fixed objects' priorities over agents and the agent-proposing deferred-acceptance-algorithm. For house allocation we show that DA-mechanisms are characterized by our basic properties and (i) strategy-proofness and population-monotonicity or (ii) strategy-proofness and resource-monotonicity. Once we allow for multiple identical copies of objects, on the one hand the first characterization breaks down and there are unstable mechanisms satisfying our basic properties and (i) strategy-proofness and population-monotonicity. On the other hand, our basic properties and (ii) strategy-proofness and resource-monotonicity characterize (the most general) class of DA-mechanisms based on objects' fixed choice functions that are acceptant, monotonic, substitutable, and consistent. These choice functions are used by objects to reject agents in the agent-proposing deferred-acceptance-algorithm. Therefore, in the general model resource-monotonicity is the «stronger» comparative statics requirement because it characterizes (together with our basic requirements and strategy-proofness) choice-based DA-mechanisms whereas population-monotonicity (together with our basic properties and strategy-proofness) does not.

Programming Principles: Statics

Slides for COMP1004 Lecture on Statics

Consistent comparative statics for the food industries

Consistent conjectures are derived in an oligopoly model with homogeneous products and identical firms. The exercise uncovers two important findings. Absent entry, the monopolistic conjecture, is the unique consistent conjecture. With endogenous entry, no consistent conjecture exists. These results provide foundations for deriving consistentc omparatives taticsf or the food industries

Statics and dynamics of a binary dipolar Bose-Einstein condensate soliton

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nanoscale insight into the statics and dynamics of polarization behavior in thin film ferroelectric capacitors

In this study, we review recent advances in PFM studies of micrometer scale ferroelectric capacitors, summarize the experimental PFM-based approach to investigation of fast switching processes, illustrate what information can be obtained from PFM experiments on domains kinetics, and delineate the scaling effect on polarization reversal mechanism. Particular attention is given to PFM studies of mechanical stress effect on polarization stability.

Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods

In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases.

Mr. Herbert Spencer on the land question : being a reprint (by permission) of Chapter IX of "Social statics" (1851), together with certain extracts from "Justice" (1891) ...

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