对称幂平方L-函数Fourier系数的高次均值估计

设f(z)为全模群SL(2,Z)上权为偶数k的Hecke特征形式,L(s,sym^(2)f)为其对应的对称幂平方L-函数,λsym^(2)f(n)为对称幂平方L-函数L(s,sym^(2)f)的Fourier展开式中第n个正规化Fourier系数.本文借助Newton和Thorne近期关于函数Symjf的重要工作以及自守L-函数的亚凸界和均值估计结果,研究了λsym^(2)f(n)在四个整数平方和序列上的三次均值估计和四次均值估计,得到了均值估计的渐近公式,改进了之前的结果.

Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers

In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.

Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

上颌不同骨质条件下All-on-Four和翼上颌种植的生物力学分析

背景:种植固定修复已成为患者满意度更高的修复方式,All-on-Four和翼上颌种植在一定条件下均可达到种植要求,目前缺少不同骨质条件下该两种方案生物力学层面的对比分析。目的:采用三维有限元方法比较All-on-Four和翼上颌种植方案在不同骨质下应力分布的差异,探讨适宜的种植方案。方法:选取一名上颌骨骨量严重不足无牙颌患者的锥形束CT数据,建立3种不同皮质骨厚度(1.0,1.5,2.0 mm)及2种不同松质骨密度(高密度、低密度)的实体化模型,每种模型分别设计All-on-Four和翼上颌种植2种方案,共计12组模型。对双侧后牙区各施加200 N垂直静力,计算出种植体、皮质骨的von Mises应力值和钛支架变形量。结果与结论:①两种种植方案下种植体及皮质骨应力最集中处均在最远端位点,钛支架变形最大处均在支架远端;②相同松质骨密度下,无论是All-on-Four还是翼上颌种植,种植体、皮质骨von Mises应力值及钛支架变形量均在皮质骨厚度1 mm时最大,随着皮质骨厚度的增加,种植体、皮质骨von Mises应力值及钛支架变形量减小;③相同种植方案下,低密度松质骨组种植体、皮质骨von Mises应力值及钛支架变形量均大于高密度松质骨组;④相同骨质条件下,翼上颌种植组种植体、皮质骨von Mises应力值及钛支架变形量均小于All-on-Four组(P<0.05);⑤结果表明,皮质骨厚度和松质骨密度增加有利于减小种植体、皮质骨的应力集中和钛支架变形,从生物力学角度,翼上颌种植方案较All-on-Four更有利于种植固定修复的远期预后。

Characteristics and C-E Translation Methods of the Four-Character Frame in the Subtitles of the Documentary Daming Palace

This paper studies the four-character frame in the subtitle of the documentary Daming Palace, aiming to provide a reference for the translation of the documentary four-character case as well as better spread Chinese culture. By analyzing, researching and summarizing the subtitle of Daming Palace and reading a lot of literature, the author has found that in Daming Palace the four-character frame is characterized by the use of the absolute four-character frames and the recurrence of some four-character frames, and that C-E translation methods of the four-character frame are mainly literal translation, free translation, provincial translation and concise translation.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

A Proof of Four-Color Theorem

Four-color theorem has only been proved by computer since it was proposed, many people have proposed their mathematical proof of four-color theorem, but their proof is disputed then, what lead to a situation that the mathematical proof of four-color theorem has been lacking to this day. In this article, we have summarized some laws based on previous researches, and proposed a mathematical proof of four-color theorem by using these laws trough a recursive method.

Four-Electron Systems in the Impurity Hubbard Model. Second Triplet State. Spectra of the System in the ν-Dimensional Lattice Zν

We consider an energy operator of four-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. The spectrum of the systems in the second triplet state in a ν-dimensional lattice is investigated. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model for the second triplet state of the system. The investigations show that the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

Research on the Translation of Chinese Twenty-Four Solar Terms: A Skopos Theory Perspective

In the current era of rapid development, excellent culture needs to be inherited and spread to the world. Therefore, it is essential to consider the translation of the 24 solar terms. China persists in the principle of the Belt and Road Initiative, adheres to the guidance of Chinese traditional excellent culture goes global, and enhances the influence of Chinese culture on the words, the culture of the words communicating and developing constantly. This paper analyzes and compares translations of different versions, explores the necessity of translation strategies for translation, then summaries the translation strategy, ultimately figures out the development space, ted texts and promote the exchange of Chinese and foreign cultures.

上颌无牙颌All-on-Four远中种植体不同倾斜角度和长度的三维有限元应力分析

目的:应用三维有限元法研究上颌无牙颌All-on-Four远中种植体在不同角度和不同长度模型中的应力分布。方法 :选择1例上颌无牙颌女性患者,采集数据,三维重建,构建上颌无牙颌"All-on-Four"种植修复的三维有限元模型。按照远中种植体角度和长度不同分为4组:A组30°11.5 mm,B组30°13.0 mm,C组45°11.5 mm,D组45°13.0 mm。100 N垂直静载荷分别加载于第一、二前磨牙及第一磨牙上模拟咀嚼受力,应用ABAQUS软件测算种植体在上颌无牙颌模型上的等效应力值。结果:垂直载荷下,应力集中在种植体颈部周围骨皮质区;远中种植体长度增加,各区域应力缓慢下降;远中种植体倾斜角度增加,应力分布分散,种植体颈部和根尖区应力明显减小。结论:远中种植体长度增加对应力分布和大小的改变并不显著,远中种植体倾斜45°比倾斜30°更有利于应力分散。

地勘单位“Four Full”安全文化建设体系研究

为提升地勘单位安全文化建设水平,针对地勘单位的特点,总结归纳出安全文化建设中存在的管理不实、基础不牢、支撑不足、参与不够四个方面的突出问题,以制度规范、理念素养培养、措施投入、参与覆盖为主要内容,基于全天候推广、全过程管理、全方位建设、全员参与四个核心,提出了"Four Full"安全文化建设体系以及"TOVPCO安全文化理念系统"和"四步双向循环法"等特色安全文化建设方法,对地勘单位的安全文化建设具有重要的参考价值。

All-on-Four技术在口腔种植领域中的应用进展

种植修复是恢复无牙颌患者咀嚼功能和美观的有效治疗方法,但因可用骨量的不足、上颌窦和下牙槽神经血管束等解剖问题而面临巨大挑战。对该类患者行种植体植入术时,常需要进行相关的骨增量手术。All-on-Four技术是指在无牙颌前牙区植入两颗轴向种植体,在远中端植入两颗角度种植体,并即刻负重,且在4~6个月后完成最终修复的新种植修复技术。该技术避免了人工骨粉植入术及上颌窦提升术等骨增量过程,患者心理反应及术后反应较轻,同时节省了患者的时间和金钱成本。这种联合应用倾斜种植体和直种植体来共同完成无牙颌患者的固定修复治疗被认为是一种可行的治疗方式。本文将就All-on-Four概念、常规技术、评价研究以及近年来提出的一些新的观点进行阐述。

无牙颌患者“All-on-Four”种植即刻负重技术的发展与变迁

无牙颌患者的最佳修复方式一直是颇有争议的话题,随着口腔种植技术的不断发展,目前无牙颌患者种植修复重建面临的挑战是如何在保证修复质量的前提下降低手术难度以及患者的费用。"All-on-Four"种植即刻负重技术是目前临床研究的热点,其避免了复杂植骨手术,最大程度利用剩余牙槽骨量实现即刻负重,患者接受程度高,临床效果理想。然而"All-on-Four"技术也面临着诸多挑战,手术适应证、手术程序、修复方案以及修复并发症等仍有待商榷。本文将就"All-on-Four"种植即刻负重技术在临床应用中的发展变迁及其优缺点等方面展开讨论,为临床医生在临床实际合理应用提供参考。

Research on Vehicle Control Technology Using Four-Wheel Independent Steering System

The enhancement of vehicle handling stability and maneuverability through active and independent rear wheels control is presented. Firstly, the configuration of four-wheel independent steering prototype vehide is introduced briefly. Then the concrete overall design of the electronic controllers of four wheel independent steering system （4WIS） is formulated in details. Under the control strategy of zero sideslip angle at mass center, the mathematical model of 4WIS is established to deduce the equations of separated rear wheel steering angles. According to these equations, simulation analysis for 4WIS vehicle performances is finished to show that 4WIS vehicle can improve the maneuverability greatly at low speed and increase the handling stability at high speed. Finally, the road test of 4WIS vehide has performed to verify the correctness of simulation and show that compared with the conventional four wheel steering （4WS） vehicle, the 4WIS vehicle not only improves the kinematical harmony but also decreases steering resistance and lighten abrasion of tires.

All-on-Four临床应用及研究进展

为寻求简便有效的无牙颌修复方法,Maló等人于2003年提出All-on-Four种植即刻修复概念,通过植入4颗种植体支持整个无牙颌修复重建,并于术后行即刻修复。All-on-Four种植即刻修复具有避免额外植骨手术、避开重要解剖结构及缩短缺牙时间等优势,近年在临床上得到广泛应用。随着外科引导技术及生物力学研究的发展,All-on-Four种植即刻修复获得了理想临床效果,已成为无牙颌患者种植固定修复的一种可行且可靠方案。笔者就All-on-Four概念发展、生物力学研究、外科和修复要点以及临床应用效果作一阐述。

On a Hypothetical Vector Field Associated with the Classic Electromagnetic Wave in a Space of Four Dimensions

In two previous papers [1] and [2], a structure for vector products in n dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.

Translation Compensation Methods under Skopostheorie:A Comparative Study on Four-character Chengyu Translation Compensation in Hong Lou Meng

This article attempts to apply skopos theory and make a comparative study of the translation compensation methods of two English versions of Hong Lou Meng in terms of four-character chengyu from the linguistic perspective.

The Solution to the Dark Energy Mystery in the Universe of Four Distance Dimensions

This study is a continuation of the solution to the dark matter mystery in the earlier study. In that study, the theoretical four-dimensional mass generates similar galaxy rotations as were measured. This proves that the theory of four-dimensional mass is correct, especially as all the calculations are basic mechanics and easy to understand. Most of the mass and energy in the Universe is unknown. The common knowledge is that the ordinary mass is only about 5%, the dark matter that rotates the galaxies comprises 26%, and dark energy that expands the Universe at an accelerating speed is 69%. This study solves the mystery of dark energy by using the structure of the four-dimensional Universe. The theory of the Universe expanding at an accelerating speed has been based on the redshift measurements, in which the redshift of light from distant galaxies increases at an accelerating rate. Therefore, it has been inferred that the whole Universe expands at an accelerating speed. In this study, the model of the Universe is the surface volume of the four-dimensional spherical Universe. This type of structure of the Universe creates the same kind of an accelerating redshift increase which has been measured. In order to prove this theory, the model of the surface volume of the four-dimensional Universe was constructed, the equation of the redshift caused by this Universe was solved, and the theoretical equation was shown to be the same as the measured redshift in the Universe. The measured redshift in the Universe was obtained from the derivative of the model of the expanding Universe. A similar model of the Universe has been published by NASA. The four-dimensional model of the Universe in this study yielded the Universe that was found to have decelerating expansion at this point of time, and a Big Bang that was not very big.

4-Staining of “Staining Dilemma Configuration” in Four-Color Conjecture

This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture.