THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON FUNCTIONS

This paper mainly discusses the influence of the Weyl fractional integrals on continuous functions and proves that the Weyl fractional integrals can retain good properties of many functions. For example, a bounded variation function is still a bounded variation function after the Weyl fractional integral. Continuous functions that satisfy the Holder condition after the Weyl fractional integral still satisfy the Holder condition, furthermore, there is a linear relationship between the order of the Holder conditions of the two functions. At the end of this paper, the classical Weierstrass function is used as an example to prove the above conclusion.

Novel Technique for Enhancing the Strength of Friction Stir Spot Welds through Dynamic Welding Parameters

Presently, friction stir spot welding (FSSW) has become a common alternative for spot welding technologies. Over the years, researchers have implemented various methods for enhancing weld strength. However, the literature shows that the previously reported approaches have used static (constant) welding parameters set at the beginning of the welding stroke (i.e., the FSSW parameters were kept constant during the welding stroke). In contrast, in this study, an innovative technique is proposed for enhancing the weld strength for Al 1050 material by adjusting the FSSW process parameters during the welding stroke. Two FSSW parameters, namely, feed rate and spindle speed (dynamic parameters), are used in this study with a stepwise variation function and are changed during the welding stroke. The results of this study show that the weld tensile strength is enhanced by 12–21% when using the proposed novel dynamic welding parameter technique. This is a significant increase in the weld strength compared to when static welding parameters are employed during the welding stroke.

A comparison of metrics for quantifying cranial suture complexity

Cranial sutures play critical roles in facilitating postnatal skull development and function. The diversity of function is reflected in the highly variable suture morphology and complexity. Suture complexity has seldom been studied, resulting in little consensus on the most appropriate approach for comparative, quantitative analyses. Here, we provide the first comprehensive comparison of current approaches for quantifying suture morphology, using a wide range of two-dimensional suture outlines across extinct and extant mammals ( n = 79). Five complexity metrics (sinuosity index (SI), suture complexity index (SCI), fractal dimension (FD) box counting, FD madogram and a windowed short-time Fourier transform with power spectrum density (PSD) calculation) were compared with each other and with the shape variation in the dataset. Analyses of suture shape demonstrate that the primary axis of variation captured attributes other than complexity, supporting the use of a complexity metric over raw shape data for sutural complexity analyses. Each approach captured different aspects of complexity. PSD successfully discriminates different sutural features, such as looping patterns and interdigitation amplitude and number, while SCI best-captured variation in interdigitation number alone. Therefore, future studies should consider the relevant attributes for their question when selecting a metric for comparative analysis of suture variation, function and evolution.

Entanglement Control of Two-Level Atoms in Dissipative Cavities

An open quantum bipartite system consisting of two independent two-level atoms interacting nonlinearly with a two-mode electromagnetic cavity field is investigated by proposing a suitable non-Hermitian generalization of the Hamiltonian. The mathematical procedure of obtaining the corresponding wave function of the system is clearly given. Pancharatnam phase is studied to give a precise information about the required initial system state, which is related to artificial phase jumps, to control the degree of entanglement (DEM) and get the highest concurrence. We discuss the effect of time-variation coupling, and dissipation of both atoms and cavity. The effect of the time-variation function appears as frequency modulation (FM) effect in the radio waves. Concurrence rapidly reaches the disentangled state (death of entanglement) by increasing the effect of field decay. On the contrary, the atomic decay has no effect.

Transcriptome-Wide Identification, Evolutionary Analysis, and GA Stress Response of the GRAS Gene Family in Panax ginseng C. A. Meyer

GRAS transcription factors are a kind of plant-specific transcription factor that have been found in a variety of plants. According to previous studies, GRAS proteins are widely involved in the physiological processes of plant signal transduction, stress, growth and development. The Jilin ginseng (Panax ginseng C.A. Meyer) is a heterogeneous tetraploid perennial herb of the Araliaceae family, ginseng genus. Important information regarding the GRAS transcription factors has not been reported in ginseng. In this study, 59 Panax ginseng GRAS (PgGRAS) genes were obtained from the Jilin ginseng transcriptome data and divided into 13 sub-families according to the classification of Arabidopsis thaliana. Through systematic evolution, structural variation, function and gene expression analysis, we further reveal GRAS’s potential function in plant growth processes and its stress response. The expression of PgGRAS genes responding to gibberellin acids (GAs) suggests that these genes could be activated after application concentration of GA. The qPCR analysis result shows that four PgGRAS genes belonging to the DELLA sub-family potentially have important roles in the GA stress response of ginseng hairy roots. This study provides not only a preliminary exploration of the potential functions of the GRAS genes in ginseng, but also valuable data for further exploration of the candidate PgGRAS genes of GA signaling in Jilin ginseng, especially their roles in ginseng hairy root development and GA stress response.

Relationship between well pattern density and variation function of stochastic modelling and database establishment

For 3D geological modelling of oil and gas reservoirs, well pattern density is directly related to the number of samples involved in the calculation, which determines the variation function of stochastic modelling and has great impacts on the results of reservoir modelling. This paper focuses on the relationship between well pattern density and the variogram of stochastic modelling, selects the large Sulige gas field with many well pattern types as the research object, and establishes a variogram database of stochastic models for different well pattern densities. First, the well pattern in the study area is divided into three different types (well patterns A, B, and C) according to well and row space. Several different small blocks (model samples) are selected from each type of well pattern to establish the model, and their reasonable variogram values (major range, minor range and vertical range) are obtained. Then, the variogram values of all model samples with similar well pattern densities are analysed and counted, and the variogram database corresponding to each type of well pattern is established. Finally, the statistical results are applied to the modelling process of other blocks with similar well pattern density to test their accuracy. The results show that the reservoir model established by using the variation function provided in this paper agrees well with the actual geological conditions and that the random model has a high degree of convergence. This database has high adaptability, and the model established is reliable.