Theoretical and Empirical Limits: Reexamining Betz’s Upper Limit towards a Practical Power Coefficients in Wind Turbines*

The aspiration of all wind turbine designers is to attain Betz’s upper limit, which represents the highest efficiency in wind energy extraction. Majority of working turbines operate slightly below this limit with an exception of a few operating in wind tunnels. This study proposes for a comprehensive reevaluation of Betz’s derivation, aiming to establish the gap between a theoretical power limit and a practical limit for realization. There are two common expressions for power coefficient giving the same optimal value of 59%, but they generate different power-coefficient curves when plotted against velocity ratios. This paper presents a new method being referred as “Direct Multiplication Fractional Change” (DMFC) for deriving power-coefficient curves in wind energy, and compares its generated curve with established models. Discrepancies in power-coefficient expressions are identified and harmonized. Three approaches, namely EVAM, LVM, and DMFCM, were used for the numerical derivation of cp in the study, with their evaluation summarized in a table. The study collaborates its findings with a formulated velocity-distance curve, commonly presented as a hypothetical velocity profile in some publications. The results from DMFCM indicate two distinct maxima for the power coefficient. On the front side of the disc, a maximum of 0.5 is achievable in practice, although it is not the highest theoretically. On the rear side, a theoretical maximum of 0.59 is observed, but this value is not attainable in practice. These maxima are separated by their positions along the line of flow relative to the disc. However, this approximation is limited to a streamlined flow model of the rotor disc.

LIMITING EXPRESSION FOR GENERALIZED INVERSE A_(T,S)^(2) AND ITS CORRESPONDING PROJECTORS

This paper presents the limiting expression for the gen calized inverse A T.S(2) and itscorresgonding projectors Since comonon imnortors inverses,such as and AT.S(2) etc are all generalized in e e AT.S(2) In fact,we give a unified limiting formula of computine such imporiant generalined inverses and its corresponding proiectors,Based on this we estalish and imbedling method fire compoting the generalized in verse AT.S(2) The results extend earlier work by various authors.

Likely Limit Sets of a Class of p-order Feigenbaum's Maps

A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.

Initial Rifting Age of the Nearly N–S Rifts in Southern Tibetan Plateau:New Evidence from the Age limit of the Early Sediments

Objective The nearly parallel N-S-trending rifts in southern Tibet represent the E-W extension of the Tibet Plateau. Most data which constrained the age of the extensional deformation come from isotopic dating of the dikes probably related to the activity of the nearly N-S faulting and micas from hydrothermal activity and the low- temperature thermochronology of plateau uplift. Previous research shows that there are at least three different ideas about the age of the rifts： （1） older than 16-12 Ma, （2） 14- 10 Ma, and （3） 8-4 Ma （Fig. la）. For the old sedimentary strata represented the beginning of the rifting, the dating of the sediments helps to better define the initial rifting age.

KELEA (Kinetic Energy Limiting Electrostatic Attraction) Offers an Alternative Explanation to Existing Concepts Regarding Wave-Particle Duality, Cold Fusion and Superconductivity

Existing explanations for several major phenomena in physics may need to be reconsidered in light of the description of a natural force termed KELEA (kinetic energy limiting electrostatic attraction). Three examples are selected for discussion in this paper: i) The proposed wave-particle duality of electrons;ii) cold fusion;and iii) superconductivity. The current interpretations of these enigmatic concepts are incomplete and not fully validated by scientific methods. The observations underlying these processes are seemingly consistent with KELEA acting as a repelling force between opposite electrical charges. Relatively simple experiments can be designed to either confirm or exclude KELEA in these and in various other currently perplexing physical phenomena.

Dynamic Evolution with Limited Learning Information on a Small-World Network

This paper investigates the dynamic evolution with limited learning information on a small-world network.In the system, the information among the interaction players is not very lucid, and the players are not allowed to inspectthe profit collected by its neighbors, thus the focal player cannot choose randomly a neighbor or the wealthiest one andcompare its payoff to copy its strategy.It is assumed that the information acquainted by the player declines in theform of the exponential with the geographical distance between the players, and a parameter V is introduced to denotethe inspect-ability about the players.It is found that under the hospitable conditions, cooperation increases with therandomness and is inhibited by the large connectivity for the prisoner's dilemma; however, cooperation is maximal atthe moderate rewiring probability and is chaos with the connectivity for the snowdrift game.For the two games, theacuminous sight is in favor of the cooperation under the hospitable conditions; whereas, the myopic eyes are advantageousto cooperation and cooperation increases with the randomness under the hostile condition.

Existence of a Limit Cycle in an Intraguild Food Web Model with Holling Type II and Logistic Growth for the Common Prey

In this paper, we prove the existence of a limit cycle for a given system of differential equations corresponding to an asymmetrical intraguild food web model with functional responses Holling type II for the middle and top predators and logistic grow for the (common) prey. The existence of such limit cycle is guaranteed, via the first Lyapunov coefficient and the Andronov-Hopf bifurcation theorem, under certain conditions for the parameters involved in the system.

Development of a Notion of Limit as Proximity From Discourse Analysis in Secondary-School Function Classes

Mathematical teaching and learning of an introductory calculus conception of limit in secondary school before students learn the formal definition of limit in higher education are discussed.In this study,applications of the theory of instruction based on“Formalizing Introductory Notions(FIN)”(Nagle,2013),in which a theory incorporating new pedagogical approaches was introduced to describe static notions of limit,without ignoring dynamic notions of limit,are presented to help foster an informal limit conception better aligned with the formal definition.A qualitative discourse analysis based on students’utterances,including students’drawing pictures on graphs,was done.In the results of the investigation,it was found that the students’utterances drawings on a graph of the secants(segments)used static notions of limit supported by dynamic notions of limit according to the operating activities.There were learning activities in which students developed a notion of limit as the proximity of the predicted tangent line of a function.Consequently,students’discussions changed focus to the validation of limit candidates with static notions of limit.To overcome the contradiction of their explanations of the operating activities with dynamic notions of limit,the students changed to an explanation with static notions of limit.In light of the findings,this study suggests adapting the pedagogical approach used by the Nagle(2013).

The relationship between intermittent limit cycles and postural instability associated with Parkinson’s disease

Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.

Existence of Two Limit Cycles in Zeeman’s Class 30 for 3D Lotka-Volterra Competitive System

Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.

KINGWAY'S DREAM AND GLORY--Interviewing Shenzhen Brewery Company Limited's Manager General, Yuan Youjian and his colleagues

Why could Kingway, brand of Shenzhen Brewery CompanyLimited (SBC). in so short time realize its dream and acquire glories? What is its secret in success? What do itsdecision-makers look like? With all these questions, reporter interviewed mangaer general Yuan Youjian.

Third-Order Corrections and Mass-Shedding Limit of Rotating Neutron Stars Computed By a Complex-Plane Strategy

We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations, required within the framework of Hartle’s perturbation method, in the complex plane. We give emphasis on computing corrections up to third order in the angular velocity, and the mass-shedding limit. We also compute the angular momentum, moment of inertia, rotational kinetic energy, and gravitational potential energy of the models considered.

THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

The Sky’s the Limit

MARCH in Malawi was a significant time for women, In a month that traditionally celebrates the International Women＇s Day （IWD）, glass ceilings were being shattered. Malawi Airlines made history with an all-female operated and supported flight. The company celebrated IWD in style and boldness as an all-women crew took to the skies in a Bombardier Q400 flown from Blantyre in Mafawi to Dar es Salaam in Tanzania, with a stopover at Kamuzu International Airport （KIA） in Malawi.

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

饱和器后煤气中H_(2)S含量升高的原因及解决措施

分析了焦炉煤气中H_(2)S含量在脱硫工段达标,但在饱和器及终冷塔后再次升高的原因以及采取的措施。将一种新型高效除尘捕雾装置成功运用到脱硫工序,不仅使煤气中H2S含量稳定达标,对硫铵工序长期连续稳定运行也具有至关重要的作用。

高效液相色谱法测定板蓝根颗粒中(R,S)-告依春的含量

目的建立高效液相色谱（HPLC）法测定板蓝根颗粒中（R，s）-告依春的含量并讨论含量限度。方法色谱柱为SHIMADZUVP—ODS柱（150mmx4．6mm，5m），流动相为甲醇-0．02％磷酸溶液（7：93），流速1．0mL·min-1，检测波长为245nm，自动进样器进样，进样量10μL-1分别依照转移率、测定结果统计数据讨论含量限度。结果（R，S）-告依春在0-0587～150．3495μg·mL-1质量浓度范围内线性关系良好（r=0．9997，n=7），低、中、高加入量平均回收率分别为98．72％，98．40％，98．60％，RSD分别为1．84％，0．50％，1．82％。依照转移率、测定结果统计数据确定含量限度存在问题。结论该法操作方便、结果准确，精密度好，专属性强，可用于板蓝根颗粒的质量控制；（R，S）-告依春的含量限度应依据药动学和药效学数据确定。

HPLC法测定双根口服液中(R,S)-告依春的含量

目的建立HPLC法测定双根口服液中（R，S）-告依春的含量。方法色谱柱为SHIMADZUVP—ODS色谱柱（150mm×4．6mm，5μm），流动相为甲醇-0．025％磷酸溶液（7：93），流速为1．0ml·min^-1，检测波长为245rim，柱温为30℃；自动进样器进样，进样量10μl。结果（R，S）-告依春在1．8794～60．1398μg·ml^-1浓度范围内线性关系良好（r=0．9999，n=6），平均回收率为98．92％，RSD为1．02％（n=9），并依据试验数据，讨论了（R，S）-告依春的含量限度。结论本法操作方便、结果准确，精密度好，专属性强，可用于双根口服液的质量控制。

车轮轮辐钢S500LF的疲劳性能

采用PX-100高频疲劳试验机,采用升降法在振动频率为100~120 Hz、拉-压对称应力的条件下测定车轮轮辐钢S500LF的疲劳极限,并用数理统计方法分析确认疲劳极限为291 MPa.此值作为母体50%存活率下的疲劳极限估计量时,以95%的置信度,相对误差不超过±5%.在测定的疲劳极限基础上,采用多试样法测得不同应力水平下的疲劳寿命,据此绘制出应力-寿命关系曲线,通过回归得到应力-寿命曲线方程.对试样断口进行了理论分析,结果表明试验钢韧性良好.