A General Theta Function Identity and Modular Equations

In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.

Sharp estimates for Hübner’s upper bound function with applications

New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.

MONOTONICITY AND INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTION

The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.

Some inequalities for the generalized linear distortion function

In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.

APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.

Conceptual Modular Design of Auto Body Frame Based on Hybrid Optimization Method

This article presents a systematic research methodology of modular design for conceptual auto body frame by hybrid optimization method.A modified graph-based decomposition optimization algorithm is utilized to generate an optimal BIW assembly topo model composed of“potential modules”.The consistency constraint function in collaborative optimization is extended to maximize the commonality of modules and minimize the performance loss of all car types in the same product family simultaneously.A novel screening method is employed to select both“basic structures”and“reinforcement”modules based on the dimension optimization of the manufacturing elements and the optimal assembly mode;this allows for a more exhaustive modular platform design in contrast with existing methods.The proposed methodology is applied to a case study for the modular design of three conceptual auto body types in the same platform to validate its feasibility and effectiveness.

模糊化的Modular模糊神经网络降水预报模型研究

以广西西南部前汛期5、6月25个气象站平均逐日降水量作为预报对象,采用自然正交分解方法和模糊化方法对输入因子预处理后,结合Modular模糊神经网络建立了一种新的降水预报模型,并进行了逐日业务预报应用试验。结果表明,该降水预报模型比常规Modular模糊神经网络方法及逐步回归方法有更高的预报精度,具有较好的业务应用前景。

基于MF-LSTM的城市电动汽车集中充电负荷可调潜力评估

在新型电力系统背景下,电网需求侧可调控资源对于系统稳定的重要性日益提升。电动汽车作为重要的可调度负荷资源,对其可调度潜力进行准确评估,能有效提升电网安全稳定运行能力。现有研究较少考虑电动汽车用户行为偏好对电网负荷调控的影响,因此,提出一种考虑用户充电偏好的电动汽车集中式电站可调潜力评估方法。考虑电动汽车充电时的外部条件与自身行为偏好因素,建立基于隶属度函数的用户充电行为模型,并结合长短期记忆神经网络算法对充电站的可调潜力进行评估。最后,通过实际充电站算例,分析了电动汽车用户与负荷可调度潜力之间的耦合关系,验证了所提方法对负荷可调控容量评估的有效性,为电动汽车可调负荷参与削峰填谷等需求响应服务提供了理论支撑。

Optimization of Membership Function for Fuzzy Control Based on Genetic Algorithm and Its Applications

In this paper, a simple and practicable algorithm for optimization of membership function (MF) is proposed. As it is known that MF is very important in the fuzzy control. Unfortunately, to find, especially to optimize MF is always rather complex even difficult. So, to study and develop an effectual aglorithm for MF optimization is a good topic. Allow for the inner advantages of genetic algorithm (GA), it is adopted in the algorithm .The principle and executive procdeure are first presented. Then it is applied in the fuzzy control system of a typical plant. Results of real time run show that the control strategy is encouraging, and the developed algorithm is practicable.

On Certain Theta Function Identities Analogous to Ramanujan’s <i>P-Q</i>Eta Function Identities

The purpose of this paper is to provide direct proofs of certain theta function identities analogous to Ramanujan’s P-Q eta functions identities.

Mid-Term Review of ADEPT Metal-On-Metal Hip Prosthesis. Functional, Radiological and Metal Ion Analysis

Background: There is much interest regarding metal-on-metal implants in medical and general media. Much of this has been regarding failure of specific implant systems and metal ion toxicity. We present our early mid-term experience of the ADEPT metal-on-metal system which has both modular and non-modular hip options. Methods: Functional assessment, blood metal ion quantification, and radiographic analysis were performed for the modular and non-modular ADEPT variants. Fifty implants were implanted with a mean follow up time of 28 months. Unpaired t-tests were used to compare modular and resurfacing groups, standardised hip scores were used to compare function to conventional total hip arthroplasty. Results: Metal ion levels were significantly higher in modular prostheses compared to resurfacing implants, but not at “harmful” levels (as determined by a previous metal-on-metal implant recall). Functional outcomes were excellent and revision rates were lower than expected. Conclusions: At our institution we have good outcomes with the ADEPT hip prosthesis. Though patient selection and implant position are crucial, poor performance of metal-on-metal hip replacements is implant specific.

Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system(FIS)is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs.The system starts with identifying input from data,applying the fuzziness to input using membership functions(MF),generating fuzzy rules for the fuzzy sets and obtaining the output.There are several types of input MFs which can be introduced in FIS,commonly chosen based on the type of real data,sensitivity of certain rule implied and computational limits.This paper focuses on the construction of interval type 2(IT2)trapezoidal shape MF from fuzzy C Means(FCM)that is used for fuzzification process of mamdani FIS.In the process,upper MF(UMF)and lower MF(LMF)of the MF need to be identified to get the range of the footprint of uncertainty(FOU).This paper proposes Genetic tuning process,which is a part of genetic algorithm(GA),to adjust parameters in order to improve the behavior of existing system,especially to enhance the accuracy of the system model.This novel process is a hybrid approach which produces Genetic Fuzzy System(GFS)that helps to enhance fuzzy classification problems and performance.The approach provides a new method for the construction and tuning process of the IT2 MF,based on the FCM outcomes.The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method.It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches.The work implies a wider range of IT2 MF types,constructed based on FCM outcomes,and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction,analytics and rule-based solutions.

Linux-based Platform for Open Architecture Controller and Its Modular Developing Method

Linux-based Platform for Open Architecture Controller ( POAC ), a new open architecture controller and its modular developing method are discussed. POAC divides the application software of controller into the developing system and the application system. In the developing system, PAOC abstracts a series of function modules with unified data interface and function interface. In the application system, POAC defines the model of the architecture module, realizing the interoperability and interchangeability between the architecture modules. The modular developing method entities the users to make up an application system with some architecture modules, which consist of a set of function modules. The modular developing method decreases the developing time from the standard of controller architecture to the product.

Probability density analysis of SINR in massive MIMO systems with matched filter beamformer

This paper derives an approximate formula for probability density function(PDF) of received signal-to-interference-and-noise ratio(SINR) at user terminal when matched filter(MF) is adopted at a base station(BS).This distribution of SINR can be used to make an analysis of average sum-rate,outage probability,and symbol error rate of massive MIMO downlink with MF at BS.From simulation,it is found that the derived approximate analytical expression for PDF of SINR is consistent with the simulated exact PDF from the definition of SINR in medium-scale and large-scale MIMO systems.

On the Convexity of Generalized Grotzsch Ring Function

In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized modular equations,and obtain some inequalities for this function.

巧用Function Block功能简化FANUC梯形图程序

研究了FANUC Function Block的功能原理,分析了FB功能块的运行机制逻辑,阐述了FB功能块在简化编程方面的作用。结合实际案例介绍FB功能块的设计方法与过程,提高数控机床PMC编程的效率。

基于M^3-DGMF的债券评级算法研究

KNN、SVM等算法已经较为普遍地使用在信用评级中,但债券评级数据有着数量庞大、样本向量不一致、多分量等特征,经典算法在解决这种问题时往往局限性较大。采取双高斯合成函数的最小最大模块化神经网络的监督聚类算法对债券评级数据进行学习、泛化,实验结果表明该算法具有较大优势。

功能性食品课程模块化教学改革探索

模块化教学不仅有利于学生适应不断发展的岗位任职需要,掌握相关技能;还有利于教师提高教学效率,提升专业素养和研究能力。基于此,探索了功能性食品课程教学中的模块化教学。首先依据岗位需求进行内容选取,其次建设模块化课程,通过模块化教学,培养学生的实践能力和独立学习能力。

集中绕组模块组合式定子结构对低速大功率永磁电机性能影响

针对集中绕组模块组合式定子结构对低速大功率直驱永磁同步电机性能的影响进行研究。首先介绍了模块化定子的分块规则和分块数。基于绕组函数法推导了单个定子单元模块在不同拆分方式下的绕组函数和电感表达式。基于有限元仿真先分析了仅绕组分块对电机性能影响;然后分析了冲片和绕组都分块对电机性能影响。通过对比空载和负载性能,总结出各种定子模块化拆分方案的优缺点,为大功率低速直驱永磁同步电机的模块化设计与制造建立了基础。