Empennage sizing with the tail volume complemented with a method for dorsal fin layout

Purpose: Provide good values for the tail volume coefficient and the lever arm as a percentage of the fuselage length. Provide a statistical method for dorsal fin layout. – Methodology: Based on an understanding of flight physics, the statistical correlation of real aircraft parameters is investigated. This is based on the firm conviction that high fidelity parameters for future aircraft need a checked against parameters of existing successful aircraft. – Findings: Typical tail volume coefficients are between 0.5 and 1.0 for the horizontal tail and between 0.03 and 0.08 for the vertical tail depending on aircraft category. Empennage statistics have clear trends. The often weak correlation shows that aircraft design allows for sufficient designer's choice. Only a minority of aircraft feature a dorsal fin. Designers see it as an added surface rather than as part of the vertical tail. It is used to limit the hypothetical risk of vertical tail stall due to high sideslip angles. – Research Limitations: Results obtained from statistics are close to reality, but not a proof to fulfill requirements. – Practical Implications: Methods from the paper can be used for quick initial sizing of a vertical tail with or without dorsal fin or sizing of a horizontal tail. These results can also be used as good starting values for optimization tools in aircraft design. – Originality: Estimation of the tail lever arm is necessary for sizing with the tail volume coefficient, but had not been investigated to any detail. A method for the layout of dorsal fins was missing.

Determination of maintenance Jarlsberg® cheese dose to keep the obtained serum osteocalcin level; a response surface pathway designed de-escalation dose study with individual starting values

<p class="abstract"><strong>Background:</strong> Daily maximum effective dose (MED) of Jarlsberg® increased the serum osteocalcin (tOC) level, vitamin K2 and affected the lipid pattern positively. The aim of the study was to estimate and verify a daily maintenance dose.</p><p class="abstract"><strong>Methods:</strong> 12 healthy female volunteers (HV) were included in a de-escalation study after a six week run-in period on the daily MED of 57 g Jarlsberg® cheese. A 3-level within-patient response surface pathway (RSP) design with individual starting values was developed. Another 12 HVs were included in a new study with a six week run-in period on MED followed with six weeks on the estimated maintenance dose. All HVs were premenopausal female between 20 and 52 years of age. The main variable in the studies was the tOC level.</p><p class="abstract"><strong>Results:</strong> tOC, cOC and the vitamin K2 variants increases significantly (p&lt;0.01) during the run-in period on daily MED of Jarlsberg® in both studies. The maintenance daily dose was estimated to 45 g (95% CI: 38-52 g/day) and used in the new study. The tOC level was reduced from 19.8 ng/ml (95% CI: 12.0-27.6) obtained in the run-in period to 18.5 ng/ml (95% CI: 11.7-25.3) during the maintenance part. This represents a reduction of 6.6%. The sum of vitamin K2 variants changed from 0.58 ng/ml on MED of Jarlsberg® to 0.59 ng/ml (95% CI: 0.37-0.82) during the maintenance period.</p><p class="abstract"><strong>Conclusions: </strong>Daily MED of Jarlsberg® cheese increases tOC, cOC and the vitamin K2 level. The maintenance Jarlsberg® dose was estimated to 45 g/day and verified as sufficient.</p>

Velocity models for routine earthquake monitoring at volcanoes: from deterministic to Bayesian

&lt;p&gt;Earthquake location is a primary function of volcano observatories worldwide and the resulting catalogs of seismicity are integral to interpretations and forecasts of volcanic activity.&amp;#160; Ensuring earthquake location accuracy is therefore of critical importance.&amp;#160; However, accurate earthquake locations require accurate velocity models, which are not always available.&amp;#160; In addition, difficulties involved in applying traditional velocity modeling methods often mean that earthquake locations are computed at volcanoes using velocity models not specific to the local volcano.&amp;#160; &amp;#160;&lt;/p&gt;&lt;p&gt;Traditional linearized methods that jointly invert for earthquake locations, velocity structure, and station corrections depend critically on having reasonable starting values for the unknown parameters, which are then iteratively updated to minimize the data misfit.&amp;#160; However, these deterministic methods are susceptible to local minima and divergence, issues exacerbated by sparse seismic networks and/or poor data quality common at volcanoes.&amp;#160; In cases where independent prior constraints on local velocity structure are not available, these methods may result in systematic errors in velocity models and hypocenters, especially if the full range of possible starting values is not explored.&amp;#160; Furthermore, such solutions depend on subjective choices for model regularization and parameterization.&lt;/p&gt;&lt;p&gt;In contrast, Bayesian methods promise to avoid all these pitfalls.&amp;#160; Although these methods traditionally have been difficult to implement due to additional computational burdens, the increasing use and availability of High-Performance Computing resources mean widespread application of these methods is no longer prohibitively expensive.&amp;#160; In this presentation, we apply a Bayesian, hierarchical, trans-dimensional Markov chain Monte Carlo method to jointly solve for hypocentral parameters, 1D velocity structure, and station corrections using data from monitoring networks of varying quality at several volcanoes in the U.S. and South America.&amp;#160; We compare the results with those from a more traditional deterministic approach and show that the resulting velocity models produce more accurate earthquake locations.&amp;#160; Finally, we chart a path forward for more widespread adoption of the Bayesian approach, which may improve catalogs of volcanic seismicity at observatories worldwide.&amp;#160;&lt;/p&gt;

VIGOROUS 3D ANGULAR RESECTION MODEL USING LEVENBERG – MARQUARDT METHOD

The resection in 3D space is a common problem in surveying engineering and photogrammetry based on observed distances, angles, and coordinates. This resection problem is nonlinear and comprises redundant observations which is normally solved using the least-squares method in an iterative approach. In this paper, we introduce a vigorous angular based resection method that converges to the global minimum even with very challenging starting values of the unknowns. The method is based on deriving oblique angles from the measured horizontal and vertical angles by solving spherical triangles. The derived oblique angles tightly connected the rays enclosed between the resection point and the reference points. Both techniques of the nonlinear least square adjustment either using the Gauss-Newton or Levenberg – Marquardt are applied in two 3D resection experiments. In both numerical methods, the results converged steadily to the global minimum using the proposed angular resection even with improper starting values. However, applying the Levenberg – Marquardt method proved to reach the global minimum solution in all the challenging situations and outperformed the Gauss-Newton method.

Clarifying the Measurement of Relative Ideology in Policy Diffusion Research

Research on policy diffusion has recently paid more attention to ideological patterns of policy adoption. Grossback, Nicholson-Crotty, and Peterson operationalized a measure of ideological diffusion; however, it has not been consistently calculated in subsequent studies. This is mainly due to difficulties in interpreting how to measure ideological distance based solely on the original article. Specifically, there are three factors that prevent common measurement of the concept: starting values, adoption ties, and weighting of recent adoptions. Recommendations are made for each of these. The purpose is to establish a consistent ideological distance measure. To illustrate, a replication of the original lottery diffusion model in the authors’ paper shows how the results change with different measurement choices. Consistently measuring this concept is important as scholars increasingly recognize that states do not always follow their geographic neighbors but increasingly their ideological “neighbors.”

Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials

The problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh quotient methods can be computed. The new methods are compared to Gauss–Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss–Newton and a new Rayleigh quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.

An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.

Fibonacci periods and multiples

The well-known Fibonacci numbers Fn are defined by the recurrence relationFn = Fn – 1 + Fn – 2. (1)together with the starting values F0 = 0, F1 = 1, or equivalently F1 = F2 = 1.We record the first few:The recurrence relation can also be applied backwards in the form Fn = Fn + 2 – Fn + 1 to define Fn for n < 0. An easy induction verifies that F−n = (−1)n – 1Fn for n > 0.

A modified growth function with interpretable parameters applied to the age–height relationship of individual trees

Growth functions frequently used in forestry have in common that among the model parameters to be estimated, only the asymptote is expressed in the dimensions of the input data. By contrast, parameters determining rate and shape of the curve often exhibit indefinite scales. This might cause problems in specifying adequate starting values and in parameter interpretation. We present a mathematical derivation to obtain a modified growth function based on the four-parameter Richards function. Two of the rate and shape parameters were replaced by new parameters directly related to the growth process: time of maximum growth and maximum growth rate. Both the original model and its modified form were fitted to individual-tree height–age data from the National Forest Inventory in Germany. The modified function has several advantages: (i) easier interpretability of model parameters, (ii) easier specification of starting values, (iii) improved linear behavior allowing for more reliable asymptotic inferences and for better convergence, and (iv) reduced correlation between model parameters. As a further benefit, the presented model allows for deriving biologically interpretable forms of the Gompertz function, the von Bertalanffy function, and the logistic function. Based on the results, we suggest using the modified function provided for further applications in growth modeling.