R(D) Definition Domain Deriving of Limited Distortion Source Coding With Different Sources

For limited distortion source coding, it is generally considered that the minimum value of the coding average distortion is 0, and the maximum value is the minimum distortion value of making R(D) = 0. This is the definition domain of the information rate distortion function. In this paper, the upper and lower bounds of the information rate distortion function R(D) are derived and computed for the typical sources. The results show that the lower bound of the coding average distortion D is related to the symbol distortion function, which can further improve the theory of limited distortion source coding.

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.

Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

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.

A Tentative Analysis Of Samuel Johnson's Definition To Metaphysical School In English Literature

The metaphysical poetry,as a rather influential literary school,plays a momentous andpredominant part in eariy seventeenth century English literature.The marked quality ofmetaphysical poetry,as practiced by Donne and his successors,is their philosophical subtlety orintellectual rigor,while the quintessence of which consists in its peculiar blend of thought andpassion of realistic violence and meditative refinements.Doctor Johnson accused the

Second Note on the Definition of S₁-Convexity

In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.

First Note on the Definition of s<i>1</i>-Convexity

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

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。

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.

低变质煤H_(2)S异常和超限形成机理研究

为了研究彬长矿区雅店煤矿的H_(2)S异常和超限的形成机理,通过对矿井主采4号煤层地温条件、不饱和烃、硫酸盐分布、地下水pH值、硫酸盐还原菌(SRB)生存条件及采矿扰动等分析,认为研究区具有20~40℃适宜的地温条件和pH值为7.70~7.78的洛河组弱碱性水良好条件,为硫酸盐还原菌(SRB)苏醒和繁殖提供了生存条件,在硫酸盐还原菌(SRB)的还原作用下,使得煤层中的硫酸盐矿物被还原成为H_(2)S代谢排出(生),进入煤层孔裂隙等储存空间(储),受煤系地层顶底良好的封存作用使得H_(2)S得以保存,受采矿活动的影响,H_(2)S沿裂隙和地下涌水逸散至巷道回风流中(运—逸),造成H_(2)S局部异常和超限,构成了“生—储—保—运(移)—逸”H_(2)S形成机理和条件。

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.

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).

S波段YIG调谐限幅滤波器设计

依据YIG调谐限幅滤波器的工作原理,设计了一款S波段限幅滤波器。对滤波器进行了连续波限幅特性和抗烧毁功率测试,在S波段下,滤波器的限幅电平大于5 dBm,常温下最大为8 dBm;连续波输入情况下,滤波器的限幅输出功率小于10 dBm,为6.5 dBm;滤波器的抗烧毁功率大于50 W连续波,当脉冲输入峰值功率从2 W到200 W范围内变化时,滤波器的输出脉冲峰值功率被限制在18.5 dBm内,起到了很好的限幅滤波作用。试验证明设计的S波段YIG限幅滤波器不仅宽频段可调,具有良好的滤波特性,对高功率输入信号限幅输出,用于接收系统前端可有效保护后续电路的安全。

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.

钢悬链线立管S形铺设极限水深

针对南海某气田铺管船正常铺设钢悬链线立管(Steel Catenary Riser,SCR)的作业,基于OrcaFlex数值模拟对立管进行总体动态分析,确定立管可安全作业的阈值环境条件。研究波浪方向、海流速度、立管外径、壁厚等对立管正常铺设作业窗口的影响,进一步分析不同外径、壁厚立管在不同水深下的适用性,确定立管极限安装水深。研究表明,立管作业窗口对浪向较敏感,在随浪条件下进行铺管作业更安全。随着立管外径、壁厚、表面流速增大,波高-周期作业窗口减小,极限铺设水深减小。

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.