Solvability of Some Nonlocal Fractional Boundary Value Problems at Resonance in Rn

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable x∈Rn and the effect of the coefficient matrices matrices B and C of boundary value conditions on the solvability of the problem are systematically discussed. By using Mawhin coincidence degree theory, some sufficient conditions for the solvability of the problem are obtained.

Пространственно-типологическая структура и организация населения птиц Тоболо-Иртышской лесостепи и степи Западной Сибири и Северного Казахстана во второй половине лета.

According to the results of bird counts carried out in 138 habitats over 12 years, a hierarchical classification and a structural graph of the similarity of ornithocomplexes in the plain southwestern part of Western Siberia and Northern Kazakhstan have been compiled in the period from 1982 till 2002. The hierarchical classification contains six types of bird populations. The similarity graph is built at the level of types and is represented by three rows (trends). One row consists of bird complexes of residential and recreational areas; the second, of wetlands; and the third, of forest, forest-field, and steppe habitats. The classification taxa characteristics contain information on the three most numerous bird species (leaders in abundance), their share in the community, population density, and the background species wealth. Based on the assessment of the similarity coincidence degree for the of bird communities and environmental factors, a hierarchy of the impact of the main anthropogenic and natural factors, determining the bird population formation, has been established.

Effect of structural parameters and service conditions on the tilt angle of double row angular contact ball bearing

In this paper, for double row angular contact ball bearing, a five-degrees-of-freedom bearing analysis model based on quasi-statics is proposed. This model is used to study the influence of structural parameters and service conditions on the tilt angle and limit tilt angle of the bearing. The results show that the radial clearance will increase the ultimate tilt angle. The coincidence degree between the roller and the inner raceway will reduce the ultimate tilt angle, but the coincidence degree between the roller and the outer raceway has the opposite effect. The increase in the external load of the bearing will increase the tilt angle. The moment load has the greatest effect on the tilt angle. The rotation speed of the bearing has no effect on the tilt angle. The coincidence degree between the roller and the raceway will reduce the tilt angle; furthermore, the influence of the coincidence degree between roller and different ring on the tilt angle is also different when different rings are fixed. The tilt angle will decrease with the increase of the initial contact angle, and this effect is more and more obvious. The fixation of different ring has no effect on this influence.

Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

Research on Music Emotion Recognition Model of Deep Learning Based on Musical Stage Effect

The change of life style of the times has also prompted the reform of many art forms (including musicals). Nowadays, the audience can not only enjoy the wonderful performances of offline musicals but also feel the charm of musicals online. However, how to bring the emotional integrity of musicals to the audience is a technical problem. In this paper, the deep learning music emotion recognition model based on musical stage effect is studied. Firstly, there is little difference between the emotional results identified by the CRNN model test and the actual feelings of people, and the coincidence degree of emotional responses is as high as 95.68%. Secondly, the final recognition rate of the model is 98.33%, and the final average accuracy rate is as high as 93.22%. Finally, compared with other methods on CASIA emotion set, the CRNN-AttGRU has only 71.77% and 71.60% of WAR and UAR, and only this model has the highest recognition degree. This model also needs to update iteration and use other learning methods to learn at different levels so as to make this model widely used and bring more perfect enjoyment to the audience.

Evaluation of ERA-5 Precipitable Water Vapor Data in Plateau Areas: A Case Study of the Northern Qinghai-Tibet Plateau

In order to verify the accuracy of precipitable water vapor (PWV) in remote sensing and reanalysis datasets under different climatic conditions and ensure the reliability of analysis results, the performances of ERA-5 reanalysis PWV data and the Atmospheric Infrared Sounder (AIRS) remotely-sensed PWV data were tested in the northern Qinghai-Tibet Plateau by using weather balloon radiosonde data from meteorological stations from 2002 to 2016. The coincidence degree of total cloud cover was also verified, and then the PWV data precision with different levels of cloud cover was analyzed. The results show that: (1) Both ERA-5 and AIRS data underestimate PWV in the studied high plateau region, and higher altitude leads to greater deviation. (2) Compared with AIRS data, ERA-5 data have better consistency with radiosonde data in PWV and total cloud cover. (3) For the long-term trend of PWV, the ERA-5 data are the opposite to the radiosonde data with a clear sky, but both datasets showed a significant increasing trend in cloudy skies. It can be concluded that in high altitude areas, the ERA-5 data can be used for general analysis, but are not well qualified to reflect the changing trend of PWV under climate change.

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Traditional CCRMs (Constrained Center-and-Range Methods) in solving the problem of interval regression could hardly make tradeoffs between the overall fitting accuracy and the coincidence degree between the observed and predicted intervals and could also hardly reduce the number of disjoint elements between the observed and predicted intervals, as well as raise the average ratio of all predicted intervals contained within their observed intervals. This paper constructed a nonlinear regression model based on center-and-range method, in which the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval was incorporated into the traditional CCRM model’s objective. This novel nonlinear programming model was proven to be a convex one that satisfied K-T condition. Monte Carlo simulation shows that the model is degenerated to the compared CCRM+ model as the objective only contains the minimization of the overall fitting accuracy for both center and range sample series. In this situation, it could obtain a better solution than the use of the compared CCRM model. In addition, when the proposed model only takes into account the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval, the model shows a better performance than the CCRM+ model in terms of the average ratio of all predicted intervals contained within their observed intervals, as well as the average number of forecasts with 0% accuracy.

Existence and uniqueness of periodic solutions for some nonlinear fractional pantograph differential equations with $$\psi $$-Caputo derivative

The aim of this paper is to study the existence and uniqueness of periodic solutions for a certain type of nonlinear fractional pantograph differential equation with a $$\psi $$ ψ -Caputo derivative. The proofs are based on the coincidence degree theory of Mawhin. To show the efficiency of the results, some illustrative examples are included.

n-th Order Functional Problems with Resonance of Dimension One

We consider the nonlinear n-th order boundary value problem Lu=u(n)=f(t,u(t),u′(t),…,u(n−1)(t))=Nu given arbitrary bounded linear functional conditions Bi(u)=0, i=1,…,n and develop a method that allows us to study all such resonance problems of order one, as well as implementing a more general constructive method for deriving existence criteria in the framework of the coincidence degree method of Mawhin. We demonstrate applicability of the formalism by giving an example for n=4.