幂级数sum from k=0 to ∞() ((k+1)~n/k!)t^k的计算定理及应用

论述了一类无穷幂级数的和函数问题，并提出新的计算定理，解决了此类问题的计算。

无界函数的反常积分的计算

运用牛顿-莱布尼茨公式和无界函数的反常积分的定义证明无界函数的反常积分的计算定理,运用这个定理计算无界函数的反常积分简单快捷,通过举例说明这个定理的应用,并指出多种大学数学参考书中存在的一个共同错误.

First principles calculation of intermetallic compounds in FeTiCoNiVCrMnCuAl system high entropy alloy

The structural, electronic and elastic properties of common intermetallic compounds in FeTiCoNiVCrMnCuAI system high entropy alloy were investigated by the first principles calculation. The calculation results of formation enthalpy and cohesive energy show that FeTi, Fe2Ti, AlCrFe2, Co2Ti, AlMn2V and Mn2Ti phases may form in the formation process of the alloy. Further studies show that FeTi, FezTi, AlCrFe2, Co2Ti and AlMn2V phases with higher shear modulus and elastic modulus would be excellent strengthening phases in high entropy alloy and would improve the hardness of the alloy. In addition, the partial density of states was investigated for revealing the bonding mode, and the analyses on the strength of p-d hybridization also reveal the underlying mechanism for the elastic properties of these compounds.

A ROBUST OPTICAL FLOW COMPUTATION

This paper presents a new method for robust and accurate optical flow estimation.The sig- nificance of this work is twofold.Firstly,the idea of bi-directional scheme is adopted to reduce the model error of optical flow equation,which allows the second order Taylor's expansion of optical flow equation for accurate solution without much extra computational burden;Secondly,this paper establishs a new optical flow equation based on LSCM (Local Structure Constancy Model) instead of BCM (Brightness Constancy Model),namely the optical flow equation does not act on scalar but on tensor-valued (ma- trix-valued) field,due to the two reason:(1) structure tensor-value contains local spatial structure information,which provides us more useable cues for computation than scalar;(2) local image structure is less sensitive to illumination variation than intensity,which weakens the disturbance of non-uniform illumination in real sequences.Qualitative and quantitative results for synthetic and real-world scenes show that the new method can produce an accurate and robust results.

Quantitative analysis of Boehm' s GC

The term garbage collection describes the automated process of finding previously allocated memorythatis no longer in use in order to make the memory available to satisfy subsequent allocation requests. Wehave reviewed existing papers and implementations of GC, and especially analyzed Boehm' s C codes, which isa real-time mark-sweep GC running under Linux and ANSI C standard. In this paper, we will quantitatively an-alyze the performance of different configurations of Boehm' s collector subjected to different workloads. Reportedmeasurements demonstrate that a refined garbage collector is a viable alternative to traditional explicit memorymanagement techniques, even for low-level languages. It is more a trade-off for certain system than an all-or-nothing proposition.

Set Valued Vitali-Hahn-Saks-Nikodym Theorem

In this paper, we establish the set valued Vitali-Hahn-Saks-Nikodym Theorem.

A new method determining safe thickness of karst cave roof under pile tip

Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.

A Comparative Study of the Performance of Symmetric and Asymmetric Mixed-conducting Membranes

According to the configuration,mixed-conducting membranes are classified as symmetric membranes and asymmetric membranes consisting of a thin dense layer and a porous support.In this study,these two kinds of SrCo0.4Fe0.5Zr0.1O3-δ oxide-based membranes were systematically compared in terms of oxygen permeability and chemical stability,and their differences were elucidated by means of the theoretical calculation.For the oxygen permeability,the asymmetric membrane was greater than the symmetric membrane due to the significant decrease of bulk diffusion resistance in the thin dense layer of the asymmetric membrane.In regard to the chemical stability,the increase of oxygen partial pressure on the asymmetric membrane surface at CH4 side produced the stable time of over 1032h in partial oxidation of methane at 1123K,while the symmetric membrane was only of 528h.This study demonstrated that the asymmetric membrane was a promising geometrical configuration for the practical application.

Image Distortion Metric Based on Total Bounded Variation

Image definition measurement plays an important role in various image processing applications.And a reliable objective image definition metrics is critical for evaluating the definition of the restored image.In this paper,a novel image distortion metric based on minimal Total Bounded Variation(TBV) is presented.It is clarified that when the restored image approximates to the original clear image,the smaller the TBV is,the better the definition of the restored image is.Furthermore,the difference between the restored image and the original clear image is the smallest when the TBV is minimum.In numerical results,the TBV of the original clear image,blur image and restored image are presented and compared,and the results demonstrate the validity of the distortion metric proposed.

Structures and Stability of Metal Amidoboranes (MAB): Density Functional Calculations

Molecule geometry structures, frequencies, and energetic stabilities of ammonia borane （AB, NH3BH3 ） and metal amidoboranes （MAB, MNH2BH3）, formed by substituting H atom in AB with one of main group metal atoms, have been investigated by density-functional theory and optimized at the B3LYP levels with 6-311G＋＋ （3dr, 3pd） basic set. Their structural parameters and infrared spectrum characteristic peaks have been predicted, which should be the criterion of a successfully synthesized material. Several parameters such as binding energies, vibrational frequencies, and the energy gaps between the HOMO and the LUMO have been adopted to characterize and evaluate their structure stabilities. It is also found that the binding energies and HOMO-LUMO energy gaps of the MAB obviously change with the substitution of the atoms. MgAB has the lowest binding energy and is easier to decompose than any other substitutional structures under same conditions, while CaAB has the highest chemical activity.

Modified Projective Synchronization of a New Hyperchaotic System via Nonlinear Control

In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.

Arithmetical Proof and Open Sentences

If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） are blocked. In these standard accounts （Godel＇s own paper and the exposition in Boolos＇ Computability and Logic are treated as exemplars）, it is assumed that certain formulas （notably so called ＂Godel sentences＂） containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term ＂provable＂ （and indeed ＂unprovable＂） favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.

Selection of Trusted Service Providers by Enforcing Bayesian Analysis in iVCE

The initiative of internet-based virtual computing environment （iVCE） aims to provide the end users and applications with a harmonions, trustworthy and transparent integrated computing environment which will facilitate sharing and collaborating of network resources between applications. Trust management is an elementary component for iVCE. The uncertain and dynamic characteristics of iVCE necessitate the requirement for the trust management to be subjective, historical evidence based and context dependent. This paper presents a Bayesian analysis-based trust model, which aims to secure the active agents for selecting appropriate trusted services in iVCE. Simulations are made to analyze the properties of the trust model which show that the subjective prior information influences trust evaluation a lot and the model stimulates positive interactions.

Stable High-Energy Density Super-Atom Clusters of Aluminum Hydride

With the concept of super-atom, first principles calculations propose a new type of super stable cage clusters AlnH3n that are much more energetic stable than the well established clusters, AlnHn＋2. In the new clusters, the aluminum core-frame acts as a super-atom with n vertexes and 2n A1-A1 edges, which allow to adsorb n hydrogen atoms at the top-site and 2n at the bridge-site. Using Al12H36 as the basic unit, stable chain structures, （Al12H36）m, have been constructed following the same connection mechanism as for （A1H3）n linear polymeric structures. Apart from high hydrogen percentage per molecule, calculations have shown that these new clusters possess large heat of formation values and their combustion heat is about 4.8 times of the methane, making them a promising high energy density material.

QUALITATIVE REASONING BY COMPUTING WITH WORDS IN HERRERA-MARTíNEZ’S LINGUISTIC MODEL

Most of modern systems for information retrieval, fusion and management have to deal with more and more qualitative information （by linguistic labels） besides information expressed quantitatively （by numbers）, since human reports are better and easier expressed in natural language than with numbers. In this paper, Herrera-Martfnez＇s 2-Tuple linguistic representation model is extended for reasoning with uncertain and qualitative information in Dezert-Smarandache Theory （DSmT） framework, in order to overcome the limitations of current approaches, i.e., the lack of precision in the final results of linguistic information fusion according to 1-Tuple representation （ q1 ）- The linguistic information which expresses the expert＇s qualitative beliefs is expressed by means of mixed 2 Tuples （equidistant linguistic labels with a numeric biased value）. Together with the 2-Tuple representation model, some basic operators are presented to carry out the fusion operation among qualitative information sources. At last, through simple example how 2-Tuple qualitative DSmT-based （q2 DSmT） fusion rules can be used for qualitative reasoning and fusion under uncertainty, which advantage is also showed by comparing with other methods.

Structural, thermodynamics and elastic properties of Mg_(17)Al_(12), Al_2Y and Al_4Ba phases by first-principles calculations

Structural stabilities, thermodynamics stabilities, elastic properties and electronic structures of Mgl7Al12, Al2Y and AlaBa phases were analyzed by first-principles calculations with Castep and Drool3 program based on the density functional theory. The calculated results of heat of formation indicate that AI2Y phase has the strongest alloying ability. The calculated thermodynamic properties show that the thermal stability of these compounds gradually increases in the order ofMgl7Al12, A12Y and Al4Ba phases. Y or Ba addition to the Mg-Al alloys could improve the heat resistance. The calculated bulk modulus B, shear modulus G, elastic modulus E and Poisson ratio v show that the adding Y or Ba to Mg-Al alloys could promote the brittleness and stiffness, and reduce tenacity and plasticity by forming Al4Ba and Al2Y phases. The calculated cohesive energy and density of state （DOS） show that Al2Y has the strongest structural stability, then AlaBa and finally Mg17Al12. The calculated electronic structures show that Al2Y has the strongest structure stability because of the strong ionic bonds and covalent bonds combined action.

Uncertainty Assessment of Soil Erosion Model Using Particle Filtering

Recent advances in computer with geographic information system(GIS) technologies have allowed modelers to develop physics-based models for modeling soil erosion processes in time and space.However, it has been widely recognized that the effect of uncertainties on model predictions may be more significant when modelers apply such models for their own modeling purposes.Sources of uncertainty involved in modeling include data, model structural, and parameter uncertainty.To deal with the uncertain parameters of a catchment-scale soil erosion model(CSEM) and assess simulation uncertainties in soil erosion, particle filtering modeling(PF) is introduced in the CSEM.The proposed method, CSEM-PF, estimates parameters of non-linear and non-Gaussian systems, such as a physics-based soil erosion model by assimilating observation data such as discharge and sediment discharge sequences at outlets.PF provides timevarying feasible parameter sets as well as uncertainty bounds of outputs while traditional automatic calibration techniques result in a time-invariant global optimal parameter set.CSEM-PF was applied to a small mountainous catchment of the Yongdamdam in Korea for soil erosion modeling and uncertainty assessment for three historical typhoon events.Finally, the most optimal parameter sets and uncertainty bounds of simulation of both discharge and sediment discharge at each time step of the study events are provided.

Direct observation of Pt nanocrystal coalescence induced by electron-excitation-enhanced van der Waals interactions

Nanocrystal coalescence has attracted paramount attention in nanostructure fabrication in the past decades. Tremendous endeavor and progress have been made in understanding its mechanisms, benefiting from the development of transmission electron microscopy. However, many mechanisms still remain unclear, especially for nanocrystals that lack a permanent dipole moment standing on a solid substrate. Here, we report an in situ coalescence of Pt nanocrystals on an amorphous carbon substrate induced by electron-excitation- enhanced van der Waals interactions studied by transmission electron microscopy and first principles calculations. It is found that the electron-beam-induced excitation can significantly enhance the van der Waals interaction between Pt nanocrystals and reduce the binding energy between Pt nanocrystals and the carbon substrate, both of which promote the coalescence. This work extends our understanding of the nanocrystal coalescence observed in a transmission electron microscope and sheds light on a potential pathway toward practical electron- beam-controlled nanofabrication.

On the uniform estimate in the Calabi-Yau theorem,Ⅱ

We show that a pluripotential proof of the uniform estimate in the Calabi-Yau theorem works also in the Hermitian case.

A simple compliance modeling method for flexure hinges

Various types of flexure hinges have been introduced and implemented in a variety of fields due to their superior performances.The Castigliano’s second theorem,the Euler–Bernoulli beam theory based direct integration method and the unit-load method have been employed to analytically describe the elastic behavior of flexure hinges.However,all these methods require prior-knowledge of the beam theory and need to execute laborious integration operations for each term of the compliance matrix,thus highly decreasing the modeling efficiency and blocking practical applications of the modeling methods.In this paper,a novel finite beam based matrix modeling(FBMM)method is proposed to numerically obtain compliance matrices of flexure hinges with various shapes.The main concept of the method is to treat flexure hinges as serial connections of finite micro-beams,and the shearing and torsion effects of the hinges are especially considered to enhance the modeling accuracy.By means of matrix calculations,complete compliance matrices of flexure hinges can be derived effectively in one calculation process.A large number of numerical calculations are conducted for various types of flexure hinges with different shapes,and the results are compared with the ones obtained by conventional modeling methods.It demonstrates that the proposed modeling method is not only efficient but also accurate,and it is a more universal and more robust tool for describing elastic behavior of flexure hinges.