Local singularity and S–A methods for analyzing ore-producing anomalies in the Jianbiannongchang area of Heilongjiang,China

The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.

LOCAL SALINE APPROXIMATION METHODS FOR SINGULAR PRODUCT INTEGRATION

The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.

USING WAVELET TRANSFORM TO STUDY THELIPSCHITZ LOCAL SINGULAR EXPONENTIN WALL TURBULENCE

In this paper, wavelet,transform is introduced to study the Lipschitz local singular exponent for characterising the local singularity behavior of fluctuating velocity in wall turbulence. I, is found that the local singular exponent is negative when the ejections and sweeps of coherent structures occur in a turbulent boundary layer.

Geochemical Anomalies Identified by Multifractal Modeling: Implications for Mineral Exploration in the Ziyoutun Cu-Au District, Jilin Province, China

The Ziyoutun Cu-Au district is located in the Jizhong–Yanbian Metallogenic Belt and possesses excellent prospects. However, the thick regolith and complex tectonic settings present challenges in terms of detecting and decomposition of weak geochemical anomalies. To address this challenge, we initially conducted a comprehensive analysis of 1:10,000-scale soil geochemical data. This analysis included multivariate statistical techniques, such as correlation analysis, R-mode cluster analysis, Q–Q plots and factor analysis. Subsequently, we decomposed the geochemical anomalies, identifying weak anomalies using spectrum-area modeling and local singularity analysis. The results indicate that the assemblage of Au-Cu-Bi-As-Sb represents the mineralization at Ziyoutun. In comparison to conventional methods, spectrumarea modeling and local singularity analysis outperform in terms of identification of anomalies. Ultimately, we considered four specific target areas(AP01, AP02, AP03 and AP04) for future exploration, based on geochemical anomalies and favorable geological factors. Within AP01 and AP02, the geochemical anomalies suggest potential mineralization at depth, whereas in AP03 and AP04 the surface anomalies require additional geological investigation. Consequently, we recommend conducting drilling, following more extensive surface fieldwork, at the first two targets and verifying surface anomalies in the last two targets. We anticipate these findings will significantly enhance future exploration in Ziyoutun.

Detection of P2P botnet based on network behavior features and Dezert-Smarandache theory

In order to improve the accuracy of detecting the new P2P(peer-to-peer)botnet,a novel P2P botnet detection method based on the network behavior features and Dezert-Smarandache theory is proposed.It focuses on the network behavior features,which are the essential abnormal features of the P2P botnet and do not change with the network topology,the network protocol or the network attack type launched by the P2P botnet.First,the network behavior features are accurately described by the local singularity and the information entropy theory.Then,two detection results are acquired by using the Kalman filter to detect the anomalies of the above two features.Finally,the above two detection results are fused with the Dezert-Smarandache theory to obtain the final detection results.The experimental results demonstrate that the proposed method can effectively detect the new P2P botnet and that it considerably outperforms other methods at a lower degree of false negative rate and false positive rate,and the false negative rate and the false positive rate can reach 0.09 and 0.12,respectively.

LOCAL ANALYSIS OF THE FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE TIME-DEPENDENT SINGULARLY PERTURBED PROBLEM

In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.

GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.

Spatio-temporal analysis of Permian-Cretaceous magmatic activities in the Tengchong block:Implications for tectono-magmatic evolution

Understanding the tectono-magmatic evolution history of the Tengchong block is crucial for elucidating the formation of the Eastern Tethys tectonic domain.However,the correlation and evolution of the Tengchong block with the Sibumasu and Lhasa blocks is controversial during the Permian and Cretaceous.This study explores the information contained within magmatic rocks using big data and spatio-temporal analysis,providing quantitative constraints for the discussion of the tectonomagmatic evolution of the Tengchong block.To more accurately assess true magma activities and reduce errors caused by preservation and sampling processes,we utilized local singularity analysis to obtain the singularity index time-series.Correlation analysis of zircon ages and eHf(t)(correlation coefficient0.5)values indicates that the Tengchong block is more similar to the Sibumasu block.Results from timelagged cross-correlation analysis indicate that the Tengchong block and Sibumasu block exhibit a shorter lag in magmatic activities(3 Myr).Wavelet analysis reveals similar periods of collision-related magmatic activities(57 Myr and 43 Myr).Integrating evidence from paleontology and ophiolite belts,we propose that the Tengchong block co-evolved more closely with the Sibumasu block than with the Lhasa block,suggesting similar tectonic processes during the Early Permian to Early Cretaceous.Approximately 250–236 Ma,in the western Tengchong block,partial melting of the lower crust occurs due to crustal thickening.Around 219–213 Ma and 198–180 Ma,after the Tengchong block collided with the Eurasian continent,the subduction of the Meso-Tethys Ocean commenced.Around 130–111 Ma,the overall tectonic feature was a scissor-like closure of the Meso-Tethys Ocean from north to south.

Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

In this paper,the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential equations.We analyze the optimal global convergence and local superconvergence for smooth solutions under uniform meshes.Due to the initial singularity of the forcing term f,solutions of multi-pantograph delay differential equations are singular.We obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded meshes.The numerical examples are provided to illustrate our theoretical results.