Multiple time periods

Floquet theory [60] represents a powerful method to analyze and describe NMR experiments including, in the present context, methods for dipolar recoupling. In particular the bimodal variants are promising in the sense that they may handle perturbations/interactions involving multiple time periodicities, as for example induced by combined sample spinning and rf irradiation in the case of dipolar... 

Can optimize routes across multiple time periods, respect space/time constraints, optimize number and location of terminals and service areas. 

The benchmark case is of greater stand-alone interest when the network exhibits complexities such as stochastic demand that is filtered through the inventory policies implemented at the successive echelons, intricate cost structures, lead times, and multiple time periods of activity. This is the theme of the bulk of multi-echelon inventory theory, dating back to the serial supply chain analysis of Clark and Scarf (1960). This literature also considers system architectures that move product from a manufacturer to end customers along, multiple parallel paths, such as a 1-depot N-warehouse network. 

C3) Finite horizon but with multiple time periods and dynamic demand. 

Before reviewing existing results, we first give a typical model of this problem class that involves two stages (one manufacturer and some customers), multiple products, and multiple time periods. Many problems to be reviewed are either special cases or extensions of this model. A manufacturer produces m products to satisfy n customers demand over T time periods. Customer k"s demand (fc = 1,. .., n) for product j (j = 1, m) in period t(t= I,..., T) is djkt which is known in advance and must be satisfied without backlog. The parameters associated with the production at the manufacturer, inventory at the manufacturer and the customers, and the transportation between the manufacturer and the customers are as follows ... 

We review results on problems with one time period separately from results on problems with multiple time periods. Cohen and Lee (1988, 1989), Zuo et al. (1991), Chen and Wang (1997), and Sabri and Beamon (2000) consider problems with a single time period but multiple products. Each of these papers is reviewed in the following paragraphs. 

The simplest option is not to verify any information, but households have an obvious incentive to convey wrong information to become eligible. Moreover, concepts such as total income are complex. People with multiple or seasonal jobs and those with earnings from selhemployment where household and business accounts are intertwined may honestly not know how much their income is, or at least not as a program official would have calculated it. Household surveys that make serious efforts to build comprehensive income aggregates can include hundreds of questions for multiple time periods, enterprises, jobs, and miscellaneous sources of income (McKay 2000a). 

This chapter presents a mathematical model for designing the best distribution network so that profit is maximized while optimizing the other key criteria discussed in Section 5.1. The model also considers multiple time periods. This allows the company to plan for actions to be taken in future periods. That is, the model results show the time period when a DC should be used, its location, and its capacity. It also allows for expanding the capacity of an already opened DC in die future. Adding this type of dynamic decision makes the model more realistic and useful for companies. 

In multi-period inventory selection problem, one or more suppliers can be chosen in each of the periods or the products can be carried forward to a future period incurring holding cost. Inventory lot size and supplier selection are closely related. Supplier selection problem that include multiple time periods can lead to reduction in purchasing price and also can improve inventory management. 

Watanabe, M., Karplus, M. Dynamics of Molecules with Internal Degrees of Freedom by Multiple Time-Step Methods. J. Chem. Phys. 99 (1995) 8063-8074 Figueirido, F., Levy, R. M., Zhou, R., Berne, B. J. Large Scale Simulation of Macromolecules in Solution Combining the Periodic Fast Multiple Method with Multiple Time Step Integrators. J. Chem. Phys. 106 (1997) 9835-9849 Derreumaux, P., Zhang, G., Schlick, T, Brooks, B.R. A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications. J. Comp. Chem. 15 (1994) 532-555... 

We have derived time-reversible, symplectic, and second-order multiple-time-stepping methods for the finite-dimensional QCMD model. Theoretical results for general symplectic methods imply that the methods conserve energy over exponentially long periods of time up to small fluctuations. Furthermore, in the limit m —> 0, the adiabatic invariants corresponding to the underlying Born-Oppenheimer approximation will be preserved as well. Finally, the phase shift observed for symmetric methods with a single update of the classical momenta p per macro-time-step At should be avoided by... 

Computational issues that are pertinent in MD simulations are time complexity of the force calculations and the accuracy of the particle trajectories including other necessary quantitative measures. These two issues overwhelm computational scientists in several ways. MD simulations are done for long time periods and since numerical integration techniques involve discretization errors and stability restrictions which when not put in check, may corrupt the numerical solutions in such a way that they do not have any meaning and therefore, no useful inferences can be drawn from them. Different strategies such as globally stable numerical integrators and multiple time steps implementations have been used in this respect (see [27, 31]). 

HyperChem includes a number of time periods associated with a trajectory. These include the basic time step in the integration of Newton s equations plus various multiples of this associated with collecting data, the forming of statistical averages, etc. The fundamental time period is Atj s At, the integration time step stt in the Molecular Dynamics dialog box. 

The philosophy of RISC is that the CPU performs a very small number of very simple operations. Whereas a CISC-based computer might have an iastmction that fetches a number from memory and updates a counter, a RISC system implements such an operation with multiple, but simple, iastmctions. By keeping the CPU simple, it can be more readily scaled up to ever greater speeds. The idea is that, although it might execute many more iastmctions than a CISC machine, it can perform its simple iastmctions so much faster that it gets more work done ia a given time period. 

ACUTE TOXICITY Advcfse health effects occumng within a short time period of exposure to a single dose of a chemical or as a result of multiple exposures over a short time period, e.g. 24 hours. 

In the cases where liquid formulations are applied, calibration is normally performed by collecting the output volume over a given time period. Generally a minimum of three such measurements should be taken in order to estimate output consistency. Where output is collected from multiple nozzles or outlets, each nozzle or outlet should be evaluated in order to ensure uniformity of output across all the nozzles or outlets. If the deviation from the manufacturer s recommended value is not within 5% (or the value specified in an appropriate SOP), the nozzle or outlet should be replaced. The use of a patternator allows the droplet distribution pattern of the nozzles or outlets to be measured accurately, and this check should be conducted annually. Having estimated the output of the equipment, the time required to treat a specific area with a known quantity of test item solution can be calculated. 

She also had experimented with LSD and cocaine freebasing numerous times within the past 2 years. Throughout her history of substance abuse she experienced an increasing frequency of periods of dazed consciousness and blackouts multiple times yearly, while under the influence of alcohol. Further, she reported that other family members had chemical dependency problems, though her parents never abused drugs/a1cohol. 

Minimizing the quantity of contrast media administered may be beneficial in preventing nephropathy. Some studies, but not all, have directly associated dose of contrast media and nephrotoxicity. Avoidance of contrast dye with alternative diagnostic procedures should be considered in high-risk patients, but may not always be feasible. In addition, avoidance of multiple contrast studies in a short time period will allow renal function to return to normal between procedures. 

When comparing alternative types of equipment that last different lengths of time and are then replaced, it is important that the period considered be the expected life of the project. If the project is expected to last indefinitely, either a time that is a multiple of both replacement time periods or an infinite amount of time should be considered (perpetuity). 

Input Errors. Errors in model input often constitute one of the most significant causes of discrepancies between observed data and model predictions. As shown in Figure 2, the natural system receives the "true" input (usually as a "driving function") whereas the model receives the "observed" input as detected by some measurement method or device. Whenever a measurement is made possible source of error is introduced. System inputs usually vary continuously both in space and time, whereas measurements are usually point values, or averages of multiple point values, and for a particular time or accumulated over a time period. Although continuous measurement devices are in common use, errors are still possible, and essentially all models require transformation of a continuous record into discrete time and space scales acceptable to the model formulation and structure. 

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