Corresponding Prime Number Distribution Equation

The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.

Statics of FGM circular plate with magneto-electro-elastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

Dual Branch PnP Based Network for Monocular 6D Pose Estimation

Monocular 6D pose estimation is a functional task in the field of com-puter vision and robotics.In recent years,2D-3D correspondence-based methods have achieved improved performance in multiview and depth data-based scenes.However,for monocular 6D pose estimation,these methods are affected by the prediction results of the 2D-3D correspondences and the robustness of the per-spective-n-point(PnP)algorithm.There is still a difference in the distance from the expected estimation effect.To obtain a more effective feature representation result,edge enhancement is proposed to increase the shape information of the object by analyzing the influence of inaccurate 2D-3D matching on 6D pose regression and comparing the effectiveness of the intermediate representation.Furthermore,although the transformation matrix is composed of rotation and translation matrices from 3D model points to 2D pixel points,the two variables are essentially different and the same network cannot be used for both variables in the regression process.Therefore,to improve the effectiveness of the PnP algo-rithm,this paper designs a dual-branch PnP network to predict rotation and trans-lation information.Finally,the proposed method is verified on the public LM,LM-O and YCB-Video datasets.The ADD(S)values of the proposed method are 94.2 and 62.84 on the LM and LM-O datasets,respectively.The AUC of ADD(-S)value on YCB-Video is 81.1.These experimental results show that the performance of the proposed method is superior to that of similar methods.

Selective sampling with Gromov–Hausdorff metric:Efficient dense-shape correspondence via Confidence-based sample consensus

Background Functional mapping, despite its proven efficiency, suffers from a “chicken or egg” scenario, in that, poor spatial features lead to inadequate spectral alignment and vice versa during training, often resulting in slow convergence, high computational costs, and learning failures, particularly when small datasets are used. Methods A novel method is presented for dense-shape correspondence, whereby the spatial information transformed by neural networks is combined with the projections onto spectral maps to overcome the “chicken or egg” challenge by selectively sampling only points with high confidence in their alignment. These points then contribute to the alignment and spectral loss terms, boosting training, and accelerating convergence by a factor of five. To ensure full unsupervised learning, the Gromov–Hausdorff distance metric was used to select the points with the maximal alignment score displaying most confidence. Results The effectiveness of the proposed approach was demonstrated on several benchmark datasets, whereby results were reported as superior to those of spectral and spatial-based methods. Conclusions The proposed method provides a promising new approach to dense-shape correspondence, addressing the key challenges in the field and offering significant advantages over the current methods, including faster convergence, improved accuracy, and reduced computational costs.

Evaluation of Soil Fertility Quality and Environmental Driving Factors in Different Soil Types of Artificial Forests

The aim was to clarify the environmental driving factors of soil fertility indicators in artificial forests of Guangxi and comprehensively evaluate the soil fertility level.By collecting data on the current status of soil in artificial forests,the spatial distribution of major soil fertility indicators was analyzed,and the distribution map of the fertility index of artificial forests in the entire region and the comprehensive fertility index of artificial forests of different soil types were obtained.Canonical correspondence analysis method was used to analyze soil fertility indicators and environmental factors,and the environmental driving factors of soil fertility indicators for artificial forests of the main soil types in Guangxi were obtained.The results showed that over 90%of the soil fertility index of artificial forests in the entire region was between 0.20 and 0.50.The order of soil fertility index of different soil types of artificial forests from high to low was yellow brown soil>yellow red soil>yellow soil>red soil>limestone soil>latosolic red soil>laterite.In artificial forests of latosolic red soil,the correlation between soil alkaline nitrogen and organic matter,annual average temperature was high,while the correlation between soil available phosphorus and organic matter,pH was high,and the correlation between soil available potassium and environmental factors such as slope,altitude,rainfall,accumulated temperature,and slope aspect was high.In artificial forests of red soil,the correlation between soil alkaline nitrogen and slope,altitude was high,while the correlation between soil available phosphorus and accumulated temperature,rainfall was high,and the correlation between soil available potassium and pH was high.In artificial forests of limestone soil,there was a high correlation between soil alkaline nitrogen and slope,organic matter,a high correlation between soil available phosphorus and accumulated temperature,rainfall,and a high correlation between soil available potassium and pH.

The Deconvolution Method for Obtaining Correspondence in Data-Independent Acquisition Mass Spectrometry Data

Although data-independent acquisition (DIA) shows powerful potential in achieving comprehensive peptide information acquisition, the difficulty in determining the precursor m/z and distinguishing fragment ions has posed challenges in DIA data analysis. To address this challenge, a common approach is to recover the correspondence between precursor ions and fragment ions, followed by peptide identification using traditional data-dependent acquisition (DDA) database searching. In this study, we propose a cosine similarity-based deconvolution method that rapidly establishes the correspondence between chromatographic profiles of precursor ions and fragment ions through matrix calculations. Experimental results demonstrate that our method, referred to as CosDIA, yields a peptide identification count close to that of DIA-umpire. However, compared to DIA-umpire, we can establish the correspondence between original MS/MS spectra and pseudo-MS/MS spectra. Furthermore, compared to the CorrDIA method, our approach achieves higher efficiency in terms of time, reducing the time cost of the analysis process. These results highlight the potential advantages of the CosDIA method in DIA data analysis, providing a powerful tool and method for large-scale proteomics research.

Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question

Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.

Comprehensive precursor anomaly research based on earthquake corresponding relevancy spectrum

With the aim to the quantification of anomaly identification and extraction for observed or analyzed records, we present two statistical methods of earthquake corresponding relevancy spectrum （ECRS） and sliding mean relevancy （SMR）. With ECRS method, we can obtain the abnormal confidence attribute of data in different value ranges. Based on the relevancy spectrum in different studied time-intervals, we convert the original time sequence into relevancy time sequence, and can obtain the SMR time series by using the multi-point cumulative sliding mean method. Then we can identify the seismic precursor anomaly. We test this method by taking the time sequence of r/-value in the northern Tianshan region as original data. The result shows that when the studied time-interval is 18 months, the precursor anomaly can be identified bet- ter from sliding mean relevancy. The anomaly corresponding rate is 83 percent, the earthquake corresponding rate is 86 per- cent, and the anomaly is characteristic of the middle term. To try the research on multi-parameter comprehensive application, we take the Kalpin tectonic block in Xinjiang as our studied region, and analyze the spatial and temporal abnormal characters of multi-parameter sliding extreme-value relevancy （MSER） before mid-strong earthquakes in the Kalpin block. The result indicates that ECRS and SMR sequence in different time-intervals can not only be used to identify the precursor anomaly of single-item data, but also offer the data of quantitative single-item anomaly for comprehensive earthquake analysis and prediction.

Behavior Consistency Computation for Workflow Nets With Unknown Correspondence

Consistency degree calculation is established on the basis of known correspondence, but in real life, the correspondence is generally unknown, so how to calculate consistency of two models under unknown correspondence has become a problem. For this condition, we should analyze unknown correspondence due to the influence of different correspondences.In this paper we obtain the relations of transitions based on event relations using branching processes, and build a behavioral matrix of relations. Based on the permutation of behavioral matrix, we express different correspondences, and define a new formula to compute the maximal consistency degree of two workflow nets. Additionally, this paper utilizes an example to show these definitions, computation as well as the advantages.

NEW SHAPE FACTOR FOR CORRESPONDING STATES PRINCIPLE

1 INTRODUCTIONThe CSP(Corresponding States Principle)has been considered to be a useful methodfor the prediction of fluid properties from a minimum amount of information.One ofits form,the shape factor methods is developed through relating the pVT of any interestedpure fluid"a"to that of another"0"by

ESTIMATION OF THEMAL PRESSURE COEFFICIENTS FOR LIQUIDS BASED ON THE LAW OF CORRESPONDING STATE

1 INTRODUCTIONThe p-V-T relation of liquids can be represented not only by equations of state,but alsoby the following three partial differentials: α=(V/T)_p/V (1) β=-(V/p)_T/V (2) γ=(p/T)_V (3)Where p,V and T denote the pressure,volume and temperature of liquids;α,βand γ are thethermal expansion,isothermal compressibility and thermal pressure coefficient,respectively. Since the densities of liquids at various temperature and constant pressure can easily bemeasured by experiments,values of α can be obtained easily.If the values of.γ can beestimated,then values of β can be acquired from the following equation:

THE CORRESPONDING ANALYSIS OF HEAVY-METAL POLLUTION OF SOIL IN ZHUZHOU CITY

ＴＨＥ ＣＯＲＲＥＳＰＯＮＤＩＮＧ ＡＮＡＬＹＳＩＳ ＯＦ ＨＥＡＶＹ－ＭＥＴＡＬ ＰＯＬＬＵＴＩＯＮ ＯＦ ＳＯＩＬ ＩＮ ＺＨＵＺＨＯＵ ＣＩＴＹ ＳｈａｎｇＪｉｎｃｈｅｎｇ（尚金城）；ＬｏｎｇＡｉｍｉｎ（龙爱民）ＬｉＢｉｎ（李斌）；ＪｉａｎｇＪ...

A NEW ROUTE FROM HETEROAROMATIC BORON COMPOUNDS TO CORRESPONDING KETONES VIA DICHLOROCARBENE INSERTION UNDER PHASE TRANSFER CONDITIONS

The reactions of tri-2-benzofuranylborane or aminoethyl di-2-thienylborinate and 2-thienylphenylborinate with dichlorocarbene generated in situ from chloroform under phase transfer conditions were explored as a new route for the preparation of heteroaromatic ketones. It was found that a good yield of the ketones can be obtained by solid-liquid system.

DETERMINATION OF STABILITY CONSTANTS OF THE COORDINATION COMPOUNDS OF Au(Ⅲ)-2-MERCAPTOPYRIDINE-1-OXIDE AND METHYL DERIVATIVES——METHOD OF DUAL-WAVELENGTH CORRESPONDING SOLUTIONS

In this paper,we report the deductive formula used for the method of dual-wavelength corresponding solutions under condition of having ligand interference and the stability constants of three new coordination compounds [AuL_2]^+determined with this method.The stability of the three compounds,the necessity of controlling pH in experimental systems and the advantage of this method are discussed in detail.

CHARACTERIZATION OF HLDER SPACES CORRESPONDING TO DITZIAN-TOTIK MODULUS OF SMOOTHNESS

For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.

Synthesis of(±)-Deoxyschisandrin and the Corresponding Trans-lsomer

Deoxyschisandrin 1 and the corresponding trans - isomer 2 were readily prepared by intramolecular oxidative coupling of 1.4 -diaryl-2.3-dimethylbutanes 7 and 6 with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) in trifluoroacetic acid(TFA).

Route Optimization for Network Mobility Based Aeronautical Network Using Correspondent Router

The future aeronautical network will be based on IPv6 and the services over the aeronautical network will be classified into 3 domains: Air Traffic Services (ATS), Airline Operational Services (AOS) and Passenger Information and Entertainment Services (PIES), among which the ATS and AOS domains are important for aircraft safety and airline business operation. Some schemes have been proposed to provide IP mobility support for aeronautical network, and Network Mobility (NEMO) scheme is the most promising one. However, using NEMO technology will lead to sub-optimal routing, so route optimization technology is highly desired for NEMO. A route optimization scheme is proposed for the ATS and AOS domains, which introduces the Correspondent Routers to realize the optimal routing and employs an improved procedure to reduce the handoff delay. The route optimization for the PIES domain is also discussed to provide better performance for some special scenarios.

Subset Multiple Correspondence Analysis as a Tool for Visualizing Affiliation Networks

In this paper we investigate the potential of Subset Multiple Correspondence Analysis (s-MCA), a variant of MCA, to visually explore two-mode networks. We discuss how s-MCA can be useful to focus the analysis on interesting subsets of events in an affiliation network while preserving the properties of the analysis of the complete network. This unique characteristic of the method is also particularly relevant to address the problem of missing data, where it can be used to partial out their influence and reveal the more substantive relational patterns. Similar to ordinary MCA, s- MCA can also alleviate the problem of overcrowded visualizations and can effectively identify associations between observed relational patterns and exogenous variables. All of these properties are illustrated on a student course-taking affiliation network.