Overcoming roundoff errors in the first-order amplitude for general state-to-state transitions in hydrogen by projectile impact

A computer program to calculate the amplitude for general state-to-state transitions in hydrogen from the analytical result has the potential for significant numerical round-off errors whenever the sum of the angular momenta of the two states is greater than four and the projectile’s impact parameter is less than the ratio of its energy to velocity. This arises from high-order cancellation of terms in the MacDonald functions in that analytical result, whose polynomial portions have been found to obey a new multiplication theorem. The cost for correcting this instability is the replacement of a finite series of MacDonald functions by an infinite series via the multiplication theorem for the full MacDonald function.

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Erratum: First-order amplitude for general state-to-state transitions in hydrogen by projectile impact [Phys. Rev. A43, 1381 (1991)]

Physical Review A ◽

10.1103/physreva.72.069904 ◽

2005 ◽

Vol 72 (6) ◽

Cited By ~ 1

Author(s):

Jack C. Straton

Keyword(s):

State Transitions ◽

General State ◽

Projectile Impact ◽

First Order

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First-order amplitude for general state-to-state transitions in hydrogen by projectile impact

Physical Review A ◽

10.1103/physreva.43.1381 ◽

1991 ◽

Vol 43 (3) ◽

pp. 1381-1388 ◽

Cited By ~ 7

Author(s):

Jack C. Straton

Keyword(s):

State Transitions ◽

General State ◽

Projectile Impact ◽

First Order

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Funding the New Biologics – CCOHTA Report on the Cost Effectiveness of Infliximab for Crohn’s Disease: Pearls and Pitfalls

Canadian Journal of Gastroenterology ◽

10.1155/2002/859517 ◽

2002 ◽

Vol 16 (12) ◽

pp. 877-879 ◽

Cited By ~ 1

Author(s):

John K Marshall

Keyword(s):

Crohn’S Disease ◽

Crohn's Disease ◽

Economic Analysis ◽

Safety Data ◽

Cost Utility ◽

Sensitivity Analyses ◽

State Transitions ◽

Health State ◽

Life Years ◽

The Cost

The Canadian Coordinating Office for Health Technology Assessment (CCOHTA) published an economic analysis, using a Markov model, of infliximab therapy for Crohn’s disease that is refractory to other treatments. This was the first fully published economic analysis that addresses this treatment option. Health state transitions were based on data from Olmsted County, Minnesota, health state resource profiles were created using expert opinion and a number of assumptions were made when designing the model. The analysis was rigorous, the best available efficacy and safety data were used, state-of-the art sensitivity analyses were undertaken and an ‘acceptability curve‘ was constructed. The model found that infliximab was effective in increasing quality-adjusted life years when offered in a variety of protocols, but it was associated with high incremental cost utility ratios compared with usual care. The results should be interpreted, however, in view of a number of limitations. The time horizon for the analysis was short (one year), because of a lack of longer-term efficacy data, and might have led to an underestimation of the benefits from averting surgery. Because the analysis was performed from the perspective of a Canadian provincial ministry of health, only direct medical costs were considered. Patients with active Crohn’s disease are likely to incur significant indirect costs, which could be mitigated by this medication. The analysis should be updated as new data become available. Moreover, small changes in the cost of the medication could make the treatment cost effective, according to this model. Economic analyses, such as the one undertaken by the CCOHTA, cannot by themselves solve dilemmas in the allocation of limited health care resources, and other considerations must be included when formulating policy. This is especially important for patients with severe Crohn’s disease, who have significant disability and for whom few therapeutic options exist.

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UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION

Econometric Theory ◽

10.1017/s0266466611000016 ◽

2011 ◽

Vol 27 (6) ◽

pp. 1117-1151 ◽

Cited By ~ 16

Author(s):

Chirok Han ◽

Peter C. B. Phillips ◽

Donggyu Sul

Keyword(s):

Normal Distribution ◽

Rate Of Convergence ◽

Unit Root ◽

Asymptotic Theory ◽

Signal Strength ◽

Rates Of Convergence ◽

Moment Conditions ◽

First Order ◽

The Cost ◽

Artificial Shrinkage

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

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Determination of cost accounting objects, calculation and improving the calculation of product cost in agriculture

Buhuchet v sel'skom hozjajstve (Accounting in Agriculture) ◽

10.33920/sel-11-2104-03 ◽

2021 ◽

pp. 30-39

Author(s):

Rolan Arkhipovich Alborov ◽

Ekaterina Leonidovna Mosunova ◽

Elena Vyacheslavovna Zakharova ◽

Gregory Rolanovich Alborov

Keyword(s):

Cost Accounting ◽

Second Order ◽

Agricultural Products ◽

Accounting Systems ◽

First Order ◽

Management Accounting Systems ◽

Order Calculation ◽

Livestock Products ◽

The Cost

The article deals with the problems of calculating the cost of agricultural products in crop and livestock production, associated with the methods of production accounting and management accounting systems for production facilities used in practice by agricultural organizations. Variants of definition (selection) of cost accounting objects, objects of calculation of the first order and objects of calculation of the second order are proposed. Conceptual models for the distribution of costs between the objects of the first-order calculation, the objects of the second-order calculation and the calculation of the cost of the received types of agricultural products have been developed. Using the example of the production of the main herd of dairy cattle, it is shown that the use of old methods of calculating the cost of agricultural products is not consistent, and it is recommended to use more justified methods of calculating the cost of crop and livestock products, recommended in the new editions of the relevant guidelines of the Ministry of Agriculture of the Russian Federation.

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Formal Semantics of Dynamic Constraints and Derivation Rules in ORM

International Journal of Information System Modeling and Design ◽

10.4018/ijismd.2016040102 ◽

2016 ◽

Vol 7 (2) ◽

pp. 31-47

Author(s):

Herman Balsters ◽

Terry Halpin

Keyword(s):

Predicate Logic ◽

Formal Semantics ◽

Role Modeling ◽

Single Step ◽

State Transitions ◽

Dynamic Constraints ◽

First Order ◽

Previous State ◽

Object Role Modeling ◽

Post Condition

This paper provides formal semantics for an extension of the Object-Role Modeling approach to support declaration of dynamic rules. Dynamic rules differ from static rules by involving state transitions, rather than simply individual states. This paper restricts application of dynamic rules to single-step transactions, with a previous state (input to the transaction) and a new state (the result of that transaction). These dynamic rules specify an elementary transaction type by indicating which kinds of objects or facts (being added, deleted or updated) are involved. Dynamic rules may declare pre-conditions relevant to the transaction, and a post-condition stating the properties of the new state. In this paper the authors provide such dynamic rules with a formal semantics based on sorted, first-order predicate logic. The key idea underlying their solution is the formalization of dynamic constraints in terms of static constraints on the database transaction history.

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Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

Zeitschrift für Naturforschung A ◽

10.1515/zna-1971-1123 ◽

1971 ◽

Vol 26 (11) ◽

pp. 1926-1928 ◽

Cited By ~ 7

Author(s):

W. E. Köhler

Keyword(s):

Scattering Amplitude ◽

Quantum Mechanical ◽

Collision Term ◽

Tensor Polarization ◽

Collision Integrals ◽

First Order ◽

Relaxation Coefficient ◽

Angular Momenta ◽

Experimental Values ◽

Good Agreement

The magnetic Senftleben-Beenakker effect of the viscosity is mainly determined by two collision integrals of the linearized quantum mechanical Waldmann-Snider collision term, viz. by the relaxation coefficient of the tensor polarization of the molecular rotational angular momenta and by the coefficient which couples the friction pressure tensor and the tensor polarization. Starting from a simple nonspherical potential for HD, the scattering amplitude is evaluated analytically in first order distorted wave Born approximation and the two collision integrals are calculated for room temperature. A fairly good agreement with experimental values is found.

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Path-Cost Bounds for Parameterized Centralized Variants of A* for Static and Certain Environments

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213016500287 ◽

2016 ◽

Vol 25 (04) ◽

pp. 1650028

Author(s):

Amol D. Mali ◽

Minh Tang

Keyword(s):

State Transitions ◽

Weighting Functions ◽

Search Spaces ◽

Path Cost ◽

Computationally Expensive ◽

The Cost ◽

Search Control ◽

Start Node

A* search and its variants have been used in various fields for solving problems with large search spaces where state transitions occur because of application of operators. The key values in A* search are g(n) and h(n), where g(n) is the cost of the path from root (or start) node to node n, and h(n) is the estimated cost of cheapest path from n to goal. In this paper, we report on a space of variants of A* based on the following ideas: (i) using weighting functions for g(n) and h(n), (ii) evaluating different nodes with different heuristics, (iii) evaluating nodes with computationally cheap heuristics and re-evaluating some nodes with computationally expensive heuristics, and (iv) changing the size of the set of nodes from which the node to be expanded next is selected. We report on the bounds on the costs of solutions found by these variants of A*. We also report on the bounds for meta-variants of A* that invoke these variants sequentially. We show how the results can be used to obtain a more flexible search control without increasing the bound on the cost of the solution found by a variant or a meta-variant.

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