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Mathematical Proofs (mathematical + proof)
Selected AbstractsSimplified seismic analysis of asymmetric building systemsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2007Jui-Liang Lin Abstract The paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two-degree-of-freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single-degree-of-freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two-storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved. Copyright © 2006 John Wiley & Sons, Ltd. [source] Segregated targeting for multiple resource networks using decomposition algorithmAICHE JOURNAL, Issue 5 2010Santanu Bandyopadhyay Abstract A generalized decomposition technique is presented for determining optimal resource usage in segregated targeting problems with single quality index (e.g., concentration, temperature, etc.) through pinch analysis. The latter problems are concerned with determining minimal resource requirements of process networks characterized by the existence of multiple zones, each consisting of a set of demands and using a unique external resource. However, all the zones share a common set of internal sources. The decomposition algorithm allows the problem to be decomposed into a sequence of subproblems, each of which can in turn be solved using any established graphical or algebraic targeting methodology to determine the minimum requirement of respective resource. This article presents a rigorous mathematical proof of the decomposition algorithm, and then demonstrates its potential applications with case studies on carbon-constrained energy sector planning, interplant water integration, and emergy-based multisector fuel allocation. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilatticeACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2002N. K. Mukhopadhyay The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets. [source] Monetary Policy, Credit and Aggregate Supply: The Evidence from ItalyECONOMIC NOTES, Issue 3 2002Riccardo Fiorentini This paper concerns theory and evidence of the monetary transmission mechanisms. Current research has deeply investigated factors, such as dependence of firms on bank credit, that amplify the impact of monetary policy impulses on aggregate demand exerting strong but temporary effects on output and employment. We present an intertemporal macroeconomic equilibrium model of a competitive economy where current production is financed by bank credit, and then we use it to identify supply,side effects of the credit transmission mechanism in data drawn from the Italian economy. We find evidence that the ,credit variables' identified by the model , the overnight rate as a proxy of monetary policy and a measure of credit risk , have permanent effects on employment and output by altering credit supply conditions to firms. To save on space, mathematical proofs, statistical tests and data sources have been gathered in two separate appendices that can be examined on request. (J.E.L.: E2, E5). [source] Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parametersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2004Zhiping Qiu Abstract The uncertainty present in many practical engineering analysis and design problems can be modelled using probabilistic or non-probabilistic interval analysis methods. One motivation for using non-probabilistic interval analysis models rather than probabilistic models for uncertain variables is the general dearth of information in characterizing the uncertainties. Non-probabilistic interval analysis methods are less information-intensive than probabilistic models, since no density information is required. Instead of conventional optimization studies, where the minimum possible response is sought, here an uncertainty model is developed as an anti-optimization problem of finding the least favourable response and the most favourable response under the constraints within the set-theoretical description. Non-probabilistic interval analysis methods have been used for dealing with uncertain phenomena in a wide range of engineering applications. This paper is concerned with the problem of comparison between the non-probabilistic interval analysis method and the probabilistic approach in the static response problem of structures with uncertain-but-bounded parameters from mathematical proofs and numerical calculations. The results show that under the condition of the interval vector of the uncertain parameters determined from the probabilistic and statistical information, the width of the static displacement obtained by the non-probabilistic interval analysis method is larger than that by the probabilistic approach for structures with uncertain-but-bounded structural parameters. This is just the result that we expect, since according to the definition of probabilistic theory and interval mathematics, the region determined by the non-probabilistic interval analysis method should contain one predicted by the probabilistic approach. Copyright © 2004 John Wiley & Sons, Ltd. [source] Facilitating knowledge management through market mechanismKNOWLEDGE AND PROCESS MANAGEMENT: THE JOURNAL OF CORPORATE TRANSFORMATION, Issue 2 2005Kevin C. Desouza While knowledge markets are in existence and have been shown to be valuable, researchers have yet to systematically investigate them. In this paper, we take the first steps towards an investigation into the mechanisms of knowledge markets. Specifically, we employ a mathematical orientation to demonstrate the pivotal role played by pricing schemes in knowledge management agendas. Our work contributes to the field of knowledge management by providing mathematical proofs rather than anecdotal evidence regarding the significance of pricing knowledge in organizations. Copyright © 2005 John Wiley & Sons, Ltd. [source] A competitive coexistence principle?OIKOS, Issue 10 2009Cathy Neill Competitive exclusion , n species cannot coexist on fewer than n limiting resources in a constant and isolated environment , has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level , i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic , or individual , level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual , or microscopic , level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics , that is, chance , a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from , and only from , their intrinsic kinetic and stoichiometric parameters. [source] | ||||||||||||||||