Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering

Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.

基于Ackermann's formula的类反斜线回滞系统滑模控制

回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然是个研究的领域,针对类反斜线回滞系统进行研究。把类反斜线回滞模型分解为确定的线性部分和已知上界的不确定非线性部分,利用Ackermann's formula给出了类反斜线回滞系统的滑模控制律。仿真表明此滑模控制律是有效的,同时此滑模控制保证了整个系统的稳定性。

Schur Convexity and the Dual Simpson’s Formula

In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.

A generalized Liouville's formula

A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.

Solution of Cauchy's Problem for Wave Equations in Higher Space Dimensions by Means of D'Alembert's Formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.

The Rocky Planets’ Magnetic Field: A New Parameter for the Drake’s Formula

The Drake formula is a statistical method of forecasting the possible number N of technically evolved extraterrestrial and galactic civilizations able to communicate with the human species. It is based on seven different factors that can be grouped into factors of type A, fA (“Astrophysicist”) and type B, fB (“Astrobiological”). The quantitative analysis of these factors at the time of the presentation of the formula was subjective and highly variable for both factors fA and fB. Current scientifical and technological development has made it possible to refine the quantitative estimates of the fA group whose definition is now less uncertain. In group fA the parameter ne is understood as the number of planets capable of sustaining life. By means of ne Drake defines this possibility exclusively from the geometric point of view. In particular, the planet’s orbit must be included in the circumstellar space in which the planetary temperature allows the presence of liquid water. This is not enough because, for liquid (and gaseous) water to be present on the planet’s surface, it is also essential that the planet has a magnetic field of adequate intensity to shield the flow of charged particles coming from its star (solar wind). The solar wind is able to break up and disperse the liquid and gaseous water molecules and any organic molecules in times much shorter than theoretically necessary for the formation of life and above all, except for singularities, than necessary for evolution to arrive at intelligent life. Here the planetary magnetic field parameter nm is introduced into the Drake formula and its statistical probability of existence is discussed.

ON THE DIVIDED DIFFERENCE FORM OF FAA DI BRUNO＇S FORMULA

The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm） and divided differences of g at several partial group of nodes t0,t1,…,tn, where m = 1,2,…,n. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno＇s formula of higher derivatives of function h.

On the Urbach's formula for evaluation of electron trapping parameter:The case of persistent luminescent materials

Urbach’s formula for evaluation of electron trapping parameter that happens to be the earliest has emerged as a popular method amongst researchers of persistent luminescence. In this study, we analysed the thermoluminescence curves of glow-in-the-dark phosphors. Those included some curves recorded by us and others that solely used the Urbach’s formula. Using the parameter obtained by rigorous analysis by fitting the whole TL curves, we presented a comprehensive picture of the potentialities and limitations of the simple Urbach’s relation E=T_m/500, where E is the trap-depth and T_m the peak temperature in absolute scale, first proposed by Urbach in 1930. Some simple thumb rules on the use of the formula were presented for beginners as well as non-specialists so that entry of physically unrealistic data into the literature was prevented.

The Two Relativistic Rydberg Formulas of Suto and Haug: Further Comments

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.

The Theoretical Significance and Reality of Imaginary Number

It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, imaginary numbers have been applied in many theoretical theories. One of the biggest functions of imaginary numbers is to represent changes in phase, which is indispensable in signal analysis theory. The imaginary numbers in quantum mechanics pose a greater mystery: do the imaginary numbers really exist? This question still needs further scientific development to be answered.

ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.

Fractional sum and fractional difference on non-uniform lattices and analogue of Euler and Cauchy Beta formulas

As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.

基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方改善CSE诱导小鼠肺泡巨噬细胞炎症反应的作用机制

目的:基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方(SQTS)改善香烟烟雾提取物(Cigarette smoking extract,CSE)诱导小鼠肺泡巨噬细胞(MH-S)炎症反应的作用机制。方法:以MH-S细胞为研究对象,通过CCK-8法分析SQTS对MH-S细胞的安全性及药效浓度;随后MH-S分为空白组、模型组(8%CSE)和SQTS低、中、高剂量组(40、80、160 mg/L)。ELISA检测细胞上清TNF-α、IL-1β和IL-6含量;DCFH-DA荧光探针法检测细胞中ROS水平;Westernblot检测TLR4/NF-κB/NLRP3通路蛋白的表达,使用TLR4抑制剂TAK-242验证SQTS在TLR4/NF-κB/NLRP3通路上的作用。结果:与空白组比较,CSE组细胞活力降低,炎症因子TNF-α、IL-1β和IL-6的含量增加(P<0.05),ROS荧光表达水平显著升高(P<0.01),TLR4/NF-κB/NLRP3通路蛋白表达明显增加(P<0.05);与模型组比较,参芪调肾方各剂量组细胞活力升高,以上各指标表达水平均有所降低(P<0.05),且TAK-242各组细胞TLR4/NF-κB/NLRP3通路蛋白减少(P<0.05)。结论:参芪调肾方可减轻CSE诱导的MH-S细胞的炎症反应,其机制可能与抑制TLR4/NF-κB/NLRP3通路有关。

AN INTERPOLATION FORMULA OF THE DERIVATIVES OF HIGHER ORDER

In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.

A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD

A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.

Why Bell’s EPRBA Experiment Is Meaningless

We demonstrate that a Bell type of experiment asks the impossible of a Kolmogorovian correlation. An Einstein locality explanation in Bell’s format is therefore excluded beforehand by way of the experimental and statistical method followed.

Bell’s Theorem and Einstein’s Worry about Quantum Mechanics

With the use of a local dependency on instrument setting parameters of the probability density of local hidden variables, it is demonstrated that a Kolmogorov formulation reproduces the quantum correlation. This is the novelty of the work. In a Bell experiment, one cannot distinguish between Bell’s formula and the here presented local Kolmogorov formula. With the presented formula, no CHSH can be obtained. Therefore, the famous CHSH inequality has no excluding power concerning local extra Einstein parameter models. This result concurs with other previous research concerning difficulties with Bell’s formula.

Shift, the Law of the Invention of Zero

After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.