On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

Optimal mining sequence for coal faces under a bedding slope:insight from landslide prevention

Repetitive mining beneath bedding slopes is identified as a critical factor in geomorphic disturbances, especially landslides and surface subsidence. Prior research has largely concentrated on surface deformation in plains due to multi-seam coal mining and the instability of natural bedding slopes, yet the cumulative impact of different mining sequences on bedding slopes has been less explored. This study combines drone surveys and geological data to construct a comprehensive three-dimensional model of bedding slopes. Utilizing FLAC3D and PFC2D models, derived from laboratory experiments, it simulates stress, deformation, and failure dynamics of slopes under various mining sequences. Incorporating fractal dimension analysis, the research evaluates the stability of slopes in relation to different mining sequences. The findings reveal that mining in an upslope direction minimizes disruption to overlying strata. Initiating extraction from lower segments increases tensile-shear stress in coal pillar overburdens, resulting in greater creep deformation towards the downslope than when starting from upper segments, potentially leading to localized landslides and widespread creep deformation in mined-out areas. The downslope upward mining sequence exhibits the least fractal dimensions, indicating minimal disturbance to both strata and surface. While all five mining scenarios maintain good slope stability under normal conditions, recalibrated stability assessments based on fractal dimensions suggest that downslope upward mining offers the highest stability under rainfall, contrasting with the lower stability and potential instability risks of upslope downward mining. These insights are pivotal for mining operations and geological hazard mitigation in multi-seam coal exploitation on bedding slopes.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

Isolation of the Flanking Sequences Adjacent to Transgenic T-DNA in Brassica napus Genome by an Improved Inverse PCR Method

[Objective] The research aimed to isolate flanking sequences adjacent to the transgenic T-DNA in Brassica napus by an improved inverse PCR method.[Method] Using single clone of transgenic FS4 in Brassica napus as the research materials,total DNA was extracted from transgenic Brassica napus by using modified CTAB method.After enzyme digestion and purification,self-joining was made.Two circles of nested PCR and the sequence alignment were carried out.[Result] A fragement with the size of 4.0 kb was amplified ...

Characterization of the sequence spectrum of DNA based on the appearance frequency of the nucleotide sequences of the genome——A new method for analysis of genome structure

The nucleotide (base) sequence of the genome might reflect biological information beyond the coding sequences. The appearance frequencies of successive base sequences (key sequences) were calculated for entire genomes. Based on the appearance frequency of the key sequences of the genome, any DNA sequences on the genome could be expressed as a sequence spectrum with the adjoining base sequences, which could be used to study the corresponding biological phenomena. In this paper, we used 64 successive three- base sequences (triplets) as the key sequences, and determined and compared the spectra of specific genes to the chromosome, or specific genes to tRNA genes in Saccharomyces cerevisiae, Schizosaccharomyces pombe and Escherichia coli. Based on these analyses, a gene and its corresponding position on the chromosome showed highly similar spectra with the same fold enlargement (approximately 400-fold) in the S. cerevisiae, S. pombe and E. coli genomes. In addition, the homologous structure of genes that encode proteins was also observed with appropriate tRNA gene(s) in the genome. This analytical method might faithfully reflect the encoded biological information, that is, the conservation of the base sequences was to make sense the conservation of the translated amino acids sequence in the coding region, and might be universally applicable to other genomes, even those that consisted of multiple chromosomes.

Effects of Voltage Sag on the Performance of Induction Motor Based on a New Transient Sequence Component Method

Voltage sag is one of the most common power quality disturbances in industry,which causes huge inrush currents in stator windings of induction motors,and adversely impacts the motor secure operation.This paper firstly introduces a 2D Time-Stepping multi-slice finite element method(2D T-S multi-slice FEM)which is used for calculating the magnetic field distribution in induction motors under different sag events.Then the paper deduces the transient analytical expression of stator inrush current based on the classical theory of AC motors and presents a separation method for the positive,negative and zero sequence values based on instantaneous currents.With this method,the paper studies the influences of voltage sag amplitude,phase-angle jump and initial phase angle on the stator positive-and negative-sequence peak currents of 5.5 kW and 55 kW induction motors.This paper further proposes a motor protection method under voltage sag condition with the stator negative-sequence peak currents as the protection threshold,so that the protection false trip can be avoided effectively.Finally,the calculation and analysis results are validated by the comparison of calculated and measured stator peak value of the 5.5 kW induction motor.

STUDY ON THE SEQUENCE STRUCTURE OF SBR BY ^(13)C-NMR METHOD Ⅱ. PEAK ASSIGNMENT FOR ALIPHATIC CARBONS SPECTRA

The study on ^(13)C-NMR spectra of aliphatic carbon region of emuision-processed and solution-processed (by lithium catalyst) SBR was carried out. The assignments for more than thirty odd peaks observed experimentally were made by using 'corresponding analysis' method, combined with the empirical parameters reported in literature. The peak intensifies were calculated based on BemouUian statistic assumption.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

Analysis method and algorithm design of biological sequence problem based on generalized k-mer vector

K-mer can be used for the description of biological sequences and k-mer distribution is a tool for solving sequences analysis problems in bioinformatics.We can use k-mer vector as a representation method of the k-mer distribution of the biological sequence.Problems,such as similarity calculations or sequence assembly,can be described in the k-mer vector space.It helps us to identify new features of an old sequence-based problem in bioinformatics and develop new algorithms using the concepts and methods from linear space theory.In this study,we defined the k-mer vector space for the generalized biological sequences.The meaning of corresponding vector operations is explained in the biological context.We presented the vector/matrix form of several widely seen sequence-based problems,including read quantification,sequence assembly,and pattern detection problem.Its advantages and disadvantages are discussed.Also,we implement a tool for the sequence assembly problem based on the concepts of k-mer vector methods.It shows the practicability and convenience of this algorithm design strategy.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

Intercombination transitions of the carbon-like isoelectronic sequence

Energy levels, wavelengths, transition rates, oscillator strengths, and lifetimes between the 2s22p23P1,2s22p23P2,and 2s2p35S2 levels of ions in the carbon-like （C-like） isoelectronic sequence （nuclear charges Z=7-92） are calculated in the valence and core-valence limits using the multiconfiguration Dirac–Fock method. The Breit interaction, quantum electrodynamics （QED）, and finite nuclear mass effects are taken into account in subsequent relativistic configuration-interaction calculations. The calculated energies and transition rates are compared with the critically evaluated experimental values and other recent calculated results. Our calculated data are in good agreement with these data.

Comparison of different inversion methods of D-T_(2)two-dimensional nuclear magnetic resonance logging and applicability analysis

D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.

Disassembly Sequence Planning:A Survey

It is well-recognized that obsolete or discarded products can cause serious environmental pollution if they are poorly be handled.They contain reusable resource that can be recycled and used to generate desired economic benefits.Therefore,performing their efficient disassembly is highly important in green manufacturing and sustainable economic development.Their typical examples are electronic appliances and electromechanical/mechanical products.This paper presents a survey on the state of the art of disassembly sequence planning.It can help new researchers or decision makers to search for the right solution for optimal disassembly planning.It reviews the disassembly theory and methods that are applied for the processing,repair,and maintenance of obsolete/discarded products.This paper discusses the recent progress of disassembly sequencing planning in four major aspects:product disassembly modeling methods,mathematical programming methods,artificial intelligence methods,and uncertainty handling.This survey should stimulate readers to be engaged in the research,development and applications of disassembly and remanufacturing methodologies in the Industry 4.0 era.

Evolutionary Computation for Realizing Distillation Separation Sequence Optimization Synthesis

Evolutionary algorithm is applied for distillation separation sequence optimization synthesis problems with combination explosion. The binary tree data structure is used to describe the distillation separation sequence, and it is directly applied as the coding method. Genetic operators, which ensure to prohibit illegal filial generations completely, are designed by using the method of graph theory. The crossover operator based on a single parent or two parents is designed successfully. The example shows that the average ratio of search space from evolutionary algorithm with two-parent genetic operation is lower, whereas the rate of successful minimizations from evolutionary algorithm with single parent genetic operation is higher.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

In this paper, an infinite sequence of conservation laws for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids are constructed based on the Backlund transformation. Hirota bilinear form and symbolic computation are applied to obtain three kinds of solutions. Variable coefficients can affect the conserved density, associated flux, and appearance of the characteristic lines. Effects of the wave number on the soliton structures are also discussed and types of soliton structures, e.g., the double-periodic soliton, parallel soliton and soliton complexes, are presented.

CONVERGENCE OF INEXACT CONIC NEWTON METHODS

A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals.

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

Determination of Focal Depths of the MS5.8 Alxa Left Banner,Inner Mongolia Earthquake Sequence

Using the double-difference earthquake location algorithm,the deterministic method (PTD method) and the CAP seismic moment tensor inversion method,the paper selects the primary waveform data of 78 earthquakes recorded by the "China Earthquake Science Array Probe Project in the Northern Part of North South Seismic Belt ",the "China Earthquake Scientific Exploration Array Data Center"of Institute of Geophysics,China Earthquake Administration,and the Inner Mongolia Digital Seismic Network to calculate the focal depths of the mainshock and the seismic sequence of the M_S5.8 Alxa Left Banner earthquake in Inner Mongolia. The results show that the focal depth of the main shock is 20. 6 km,determined by the double-difference earthquake location method,18. 1 km by the PTD method,and 19. 2 km by the CAP method. The focal depth of the earthquake sequence calculated by the double-difference location method is larger. The deterministic method (PTD method) and double-difference location method are the methods that fit the tectonic characteristics of the seismic source area,and the CAP method is suitable for larger earthquakes.

Simulation on Calculation Accuracy of Three Methods for Live Line Measuring the Parameters of Transmission Lines with Mutual Inductance

Live line measurement methods can reduce the loss of power outages and eliminate interference. There are three live line measurement methods including integral method, differential method and algebraic method. A simulation model of?two coupled parallel transmission lines spanning on the same towers is built in PSCAD and the calculation errors of these three methods are compared with different sampling frequencies by using of Matlab. The effect of harmonic on calculation is also involved. The simulation results indicate that harmonic has the least effect on the algebraic method which provides stable result and small error.

Preliminary Analysis of Smart Grid Risk Index System and Evaluation Methods

Combined the purpose and requirements of security and stability economic operations of the smart grid, a more comprehensive, risk indicator system of smart grid is established from five aspects of the smart grid strategic risk, external risk, financial risk, compliance risk, operational risks. On this basis, it is conducted smart grid risk assessments by integrated of the use of Borda sequence value method of the original risk matrix and AHP (hierarchical analysis method), in order to assess risk facing the smart grid and enterprise development more comprehensively, objectively and systematically and conveniently, and prompt companies continue to reduce risk, improve economic efficiency, continuously improve the targeted improvement measures and continue to improve the level of grid development.