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.

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.

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.

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.

Estimation of Acentric Factor of Organic Compounds with Corresponding States Group Contribution Method

A new estimation method was proposed by combining the corresponding state principle with the group contribution method through introducing the concept of assumed-critical properties. Combining it with the Reidel equation, a new acentric factor correlation equation (CSGC-Reidel) was developed. Contribution values of 70 groups were obtained by correlating acentric factor data of 228 organic compounds of 14 type substances including saturated hydrocarbons, unsaturated hydrocarbons, cyclanes, aromatics, oxygen compounds, nitrogen compounds,halohydrocarbons, etc. The average error of acentric factor is 3.52% between the literature data and the predicated with the new estimation method.

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...

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.

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).

A Perfect Shape Factor Corresponding States Principle for Pure Non-Polar and Polar Fluids

In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of 'a' and 'o' fluids are corresponded perfectly by introducing a new pressure shape factor 8. Using methane as the 'o' fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of is a function of temperature and volume while 6 and 5 are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-polar fluids.

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.

Cultural difference in English and Chinese corresponding lexis

The associated meaning of language might be different under different cultural circumstances. This paper mainly concerns about the influence of culture on English and Chinese corresponding lexis and its pedagogical significance, analyzing the issue from three aspects： the analysis and contrast of corresponding lexis, the relationship between corresponding lexis and culture and its implication in teaching practice.

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.

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.

An Analysis and Corresponding Strategies of Memory Difficulties Caused by Psychological Factors in Consecutive Interpreting

This paper is composed of three parts.The first part presents Gile’s effort model and memory mechanism in consecutive interpreting.In the second part and the third part,the author analyzes the psychological factors that cause memory difficulties and proposes corresponding strategies on the basis of the analysis.At last,the author draws a conclusion based on the discussion of the whole paper that sufficient preparation,appropriate pressure and perceived memory can avoid memory difficulties caused by psychological factors.

Research on the Novel Empty Core Needle Transdermal Drug Delivery Mode and the Corresponding Advantages

In this paper, we conduct research on novel empty core needle transdermal drug delivery mode and the corresponding advantages.Compared with the traditional mode of drug delivery, transdermal drug delivery system advantages obvious drug absorbed from the digestivetract, intestinal factors such as interference, “the first effect” can avoid liver can maintain the stability of the human body blood drugconcentration to increase effectiveness. This paper analyzes the issues from the two aspects. （1） Transdermal Therapeutie System Analysis; （2）Microneedles in Transdermal Drug Delivery. By considering the experimental analysis, we conduct the numerical simulation on the mentionedissues. The experiment result verifi es and refl ects the general properties of the designed methodology that will enhance the overall researchperformance of the related topics.

Research on the O2O Mode and Corresponding Influences on the Online and Offline Internet Marketing

In this paper, we conduct research on the O2O mode and corresponding influence on the online and offline Internet marketing. Precision marketing is on the basis of fully understanding of consumer information, according to its characteristics and primary preferences targeted to carry out the one-to-one marketing. Mobile Internet users are mostly fixed which can be the new network technology in-depth insight into consumer interest and demand, and to establish for each specific customer database. Based on the analysis of customer data, then according to the characteristics of the different customers and the preference information such as the precision marketing, at the same time which can also according to customer＇ s feedback information targeted adjustment of products and the marketing, in order to better meet the needs of customers. Our research combines the O2O concepts and the technique to propose the novel marketing paradigm which is of great importance.