Polynomial Expressions for the Thermal Efficiency of the Parabolic Trough Solar Collector

The parabolic trough solar collector (PTC) is the most mature solar concentrating technology, and this technology is applied in numerous thermal applications. Usually, the thermal efficiency of the PTC is expressed with the aid of polynomial expressions. However, there is not a universal expression that is applied in all cases with high accuracy. Many studies use expressions with the first-degree polynomial, second-degree, or fourth-degree polynomial expressions. In this direction, this work is a study that investigates different expressions about the thermal efficiency of a PTC with a systematic approach. The LS-2 PTC module is examined with a developed numerical model in the Engineering Equation Solver for different operating temperatures and solar beam irradiation levels. This model is validated using experimental literature data. The found data are approximated with various polynomial expressions with up to six unknown parameters in every case. In every case, the mean absolute percentage error and the R2 are calculated. According to the final results, the use of the third power term leads to the best fitting results, as well as the use of the temperature difference term (ΔΤ), something that is new according to the existing literature. More specifically, the final suggested formula has the following format: “ηcol = a0 + a3∙ΔT3/Gb + b∙ΔΤ”. The results of this work can be used by the scientists for the optimum fitting of the PTC efficiency curves and for applying the best formulas in performance determination studies.

Computationally approximated solution for the equation for Henssge’s time of death estimation

Background Time of death estimation in humans for the benefit of forensic medicine has been successfully approached by Henssge, who modelled body cooling based on measurements of Marshall and Hoare. Thereby, body and ambient temperatures are measured at the death scene to estimate a time of death based on a number of assumptions, such as initial body temperature and stable ambient temperature. While so far, practical use of the method resorted to paper print outs or copies of a nomogram using a ruler, increasingly, users are interested in computer or mobile device applications. We developed a computational solution that has been available online as a web accessible PHP program since 2005. From that, we have received numerous requests not so much to detail our code but to explain how to efficiently approximate the solution to the Henssge equation. Methods To solve Henssge’s double exponential equation that models physical cooling of a body, it is sufficient to determine a difference term of the equation that will be close to zero for the correct time of death using a discrete set of all sensible possible solutions given that the modelled time frame has practical upper limits. Best post-mortem interval approximation yields minimal difference between equation terms Results The solution is approximated by solving the equation term difference for a discrete set of all possible time of death intervals that are sensibly found, and by then determining the particular time of death where equation term difference is minimal. Conclusions The advantage of a computational model over the nomogram is that the user is also able to model hypothermia and hyperthermia. While mathematically impossible to solve in a straightforward way, solutions to the Henssge equation can be approximated computationally.

Polynomial-time tests for difference terms in idempotent varieties

We consider the following practical question: given a finite algebra [Formula: see text] in a finite language, can we efficiently decide whether the variety generated by [Formula: see text] has a difference term? We answer this question (positively) in the idempotent case and then describe algorithms for constructing difference term operations.

Multiband Radar Signal Coherent Processing Algorithm for Motion Target

In real application, most aerial targets are movable. In this paper, an effective multiple subbands coherent processing method is proposed for moving target. Firstly, an echoed signal model of motion target based on geometrical theory of diffraction is established and the influence of velocity on range profile of the target is analyzed. Secondly, a method based on minimum entropy principle is used to compensate velocity. Then, incoherent factors including a quadratic phase term, a linear phase factor, a fixed factor, and an amplitude difference term are analyzed. Subsequently, efficient methods are applied to estimate other incoherent factors, except that the quadratic term is small enough to be ignored. Finally, the feasibility and performance of the proposed method are investigated through numerical simulation.

From a random to the correct structure: the VLD algorithm

A recent probabilistic reformulation of the difference electron-density Fourier synthesis [Burla, Caliandro, Giacovazzo & Polidori (2010).Acta Cryst.A66, 347–361] suggested that the most suitable Fourier coefficients are the sum of the classical difference term (mF−DFp) with a flipping term, depending on the model and on its quality. The flipping term is dominant when the model is poor and is negligible when the model is a good representation of the target structure. In the case of a random model the Fourier coefficient does not vanish and therefore could allow the recovery of the target structure from a random model. This paper describes a new phasing algorithm which does not require use of the concept of structure invariants or semi-invariants: it is based only on the properties of the new difference electron density and of the observed Fourier synthesis. The algorithm is cyclic and very easy to implement. It has been applied to a large set of small-molecule structures to verify the suitability of the approach.

A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive

We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the TC-commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety V is congruence meet semi-distributive iff V is neutral, iff M3 is not a sublattice of Con A, for A ∈ V, iff there is a positive integer n such that .