Solutions to the generalized Sylvester matrixequations by a singular value decomposition

In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × （n ＋ pr）. The algorithm proposed in this paper for the euqation AX - XF = BY does not require the controllability of matrix pair （A, B） and the restriction that A, F do not have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.

The value of Subtitles in second language general comprehension——Literuare review

As second language learning becomes popular,various strategies to improve the learning process have been suggested.One of them includes the implantation of audiovisual materials(video authentic materials),which then leads to a discussion of subtitle usage and the value of subtitles in second language learning.This essay focuses on searching for literature that suggests the value of subtitles,especially teletext subtitles,in improving second language learning.This was achieved by reviewing relevant research and experiments.The results suggested that even though uncertainty remained on what kind of materials fit what level of learners,in general,subtitles,especially teletext subtitles,were seen as a beneficial tool in developing learners' listening abilities and skills.

Research on the Role of Democratic Parties in Colleges and Universities in Building Morality and Cultivating People: Taking the General Branch of the Democratic League of Huizhou College as an Example

This article takes the general branch of the Huizhou College of the Democratic League of Huizhou College in recent years as an example. Through literature review, field research, case analysis, and other research methods, it summarized how the Democratic League of Huizhou College made good use of various activity carriers in ideological and political education. It combined discipline construction, scientific research platforms, school-government-enterprise, and other cooperation platforms. From educational methods to subject transformation and integration, and from daily teaching to social practice, it promoted the role of college teachers in the alliance to play the role of cultivating people in the era of college education reform. The aim was to put forward that in educating others, they should first educate themselves, teachers had two-way morality in terms of teacher ethics and professionalism, effectively integrated ideological and political courses into professional teaching and practice, and realized waiting for flowers to bloom in the “context”1 teaching environment like the cultivation effect of salt in water.

通智测试——基于动态具身物理社会交互环境的通用人工智能测试

The release of the generative pre-trained transformer(GPT)series has brought artificial general intelligence(AGI)to the forefront of the artificial intelligence(AI)field once again.However,the questions of how to define and evaluate AGI remain unclear.This perspective article proposes that the evaluation of AGI should be rooted in dynamic embodied physical and social interactions(DEPSI).More specifically,we propose five critical characteristics to be considered as AGI benchmarks and suggest the Tong test as an AGI evaluation system.The Tong test describes a value-and ability-oriented testing system that delineates five levels of AGI milestones through a virtual environment with DEPSI,allowing for infinite task generation.We contrast the Tong test with classical AI testing systems in terms of various aspects and propose a systematic evaluation system to promote standardized,quantitative,and objective benchmarks and evaluation of AGI.

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY

In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

REDUCING HAIRFALLING AND PILLING STUDY IN RABBIT HAIR/WOOL WORSTED KNITWEAR——CHOOSING AND EVALUATING OF FINISHING AGENT

In the paper, the effects of reducing hairfalling and pilling were compared in rabbit hair/woolworsted knitwear by adding various finishing agents. Reducing rates of hairfalling and pilling wereof 6.7％—66.7％ and 9.3％—73.5％ respectively, while fabric handle changed from grade 1 to grade5 in 12 treating method groups. To evaluate the severity of hairfalling and pilling and the conditionof fabric handle of knitwear objectively, quantitatively and comprehensively, we advocated usingthe concept of "geueral evaluating value(GEV)". The results indicated that GEVs of acrylategroups were low, but GEVs of silicone resin groups were high, especially the group with finishingagent solution containing 7％ silicone resin No.3 in which reducing rates of pilling and hairfallingwere of 53％ (National standard: grade 4.5) and 62％, respectively, and washing stability was verygood, while knitwear’s fabric handle almost did not change.

ECG is not a reliable predictor of sudden cardiac death in the general population

Objectives: To determine the predictive value of the ECG for sudden death in the general population. Design: In the Copenhagen City Heart Study, a randomly selected population sample in Copenhagen, Denmarkhas been followed prospectively since 1976. From this population sample, we analyzed ECGs of individuals who had suffered sudden cardiac death (SCD) before the age of 50 years and compared them with ECGs of a randomly selected control individuals from the same population sample. Specific ECG signs that could point toward a condition associated with a risk of SCD were noted. Results: From a total of 18,974 individuals in the cohort, 207 had died at an age younger than 50 years. Among these, 24 persons with SCD were identified. The most prevalent ECG abnormality was QRS fragmentation. We found no ECGs with long or short QTc, Brugada sign or WPW. The prevalence of signs of left ventricular hyper-trophy, early repolarization, or fragmentation was not different from the prevalence of these signs in the control group. Conclusion: In the Copenhagen City Heart Study, the ECG failed to predict SCD in persons who died before the age of 50 years.

General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution (Ⅰ)

In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.

On the Mean Value of General k-th Gauss Sums

The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given.

General Regular Variation of the n-th Order and 2nd Order Edgeworth Expansions of the Extreme Value Distribution （Ⅱ）

In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.

New Formulation for Arbitrary Cracks Problem and Its Stress Intensity Factor of Plane Elasticity

Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.

TWO CASES OF APPLICATION OF THE METHOD OF CONSTRUCTION BY CONSTANTS IN LATTICE-VALUED MODEL THEORY

This paper is a continuation of the work begun in [2], which is to generalize the theory of the two-valued models to lattice-valued ones. The basic conceptions and the symbols used in this paper are the same as those in [2], but the content discussed is independent of it. The main content of this paper is two cases of application of the method of constructing models by constants. The first one proves the compactness theorem of

Nonlinear and chaotic analysis of a financial complex system

In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China＇s futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.

The Research of Mutual Economic Relations of the World Countries on the Basis of Input-Output Table

＂Input-output＂ table which was designed for solution of mutual relation （impact） problem is a widely applied tool in the world for conducting economic analysis and forecasting. One of the most important problem of today＇s world is to prevent financial-economic crises in several countries of the world and especially in Eurozone countries where it is still ongoing. Input-output balance tables were prepared by modifying input-output table based on relevant economic indicators of the biggest countries of economy in the world as well as simulations were conducted by designing several balance models （mutual impact of GDP and change in general output of countries, mutual impact of added value and prices, mutual impact of GDP and work places）. Level of coverage of relevant indicators used in analysis on the countries of the world were tested on the basis of statistic methods and assessed. It was identified that, level of confidence of the coverage in designed model on world economy is higher than 95%. These models enable to analyze and forecast possible changes in world economy caused by changes which took place in economic conjecture of other big countries of the world, especially in USA, Japan, Germany, and China. It should be noted that, model＇s system was automatized in EXCEL system with the purpose of simplifying simulations and conducting analysis and increasing efficiency on the usage of models.

Cooperation Between Co-operative Business Organization and Investor Owned Firm to Stimulate Economic Growth of a Country： A Cooperative Advantage Approach

This study elaborates that the economic growth of a country depending on not only the business performance of the investor owned firms （IOFs）, but also the business surplus of the cooperative organizations （Co-ops）. The policy maker should have the level of understanding and competence to blend five different factors related to organizational structure and business model of the Co-ops and the IOFs to the five similarities factors on the managerial approach of them into one marked. The study investigated five similarities factors and included into a conceptual structural model with its six measurement models, economic growth model, general national factor model, market and industry factors model, Co-ops/IOFs opportunities/threat model, Co-ops/IOFs strength /weakness model, and lastly the Co-ops/IOFs firm dynamic/active： sales, profit, and lost model. Reliability of the six similarities measurement models was tested by the Delphi technique with a sample of 33 respondents. The study found that, apart from the six measurement models, it also has two intervening factor variables that will reduce the power and magnitude of the economic growth which will come from mismanagement of policy maker： These factors are the different in intemational culture among countries, and the global warming and natural disaster from the excess consumption and excess production. These selfish, competition and economic greedy of people will lead to economic, social, and natural disaster problems. To reduce the socioeconomic disadvantages and global disaster, board＇s committee, and Co-ops manager as well as chief executive officer （CEO） of the IOFs must have a good understanding on these five similarities factors. Appropriate management of these five similarities factors will lead the firms to reach their high managerial efficiency, customer value, firm value, and finally economic growth.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper, using fixed point theorems of general β-concave operators in ordered Banach space, we obtain the existence and uniqueness of positive solutions to a class of fractional boundary problem. In the end, an example is given to illustrate our main result.

General inverse of Stokes, Vening-Meinesz and Molodensky formulae

The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degen- erated into the classic ones.

Development cost prediction of general aviation aircraft projects with parametric modeling

The study of the development cost of general aviation aircraft is limited by small samples with many cost-driven factors. This paper investigates a parametric modeling method for prediction of the development cost of general aviation aircraft. The proposed technique depends on some principal components, acquired by utilizing P value analysis and gray correlation analysis. According to these principal components, the corresponding linear regression and BP neural network models are established respectively. The feasibility and accuracy of the P value analysis are verified by comparing results of model fitting and prediction. A sensitivity analysis related to model precision and suitability is discussed in detail. Results obtained in this study show that the proposed method not only has a certain degree of versatility, but also provides a preliminary prediction of the development cost of general aviation aircraft.