二次根式化简的常用方法

二次根式的化简，是各级各类数学竞赛中的常见题型，其常见的处理方法有约分法、取倒法、公式法、配方法、平方法、方程法，下面举例谈谈各种方法的具体应用，供同学们参考．

CONSTRAINED VITERBI ALGORITHM AND ITS APPLICATION TO ERROR RESILIENT TRANSMISSION OF SPIHT CODED IMAGES

To overcome some drawbacks of Viterbi algorithm （VA）, such as exponential growing complexity of decoding, and its poor performance under bad channel conditions, some available known information must be used as constrained condition and apriori knowledge for decoding. A new constrained VA is proposed by adding con- straint bits directly for conventional codec. Compared with the conventional VA, under the bad channel condi- tion, the proposed scheme can improve the peak signal to noise ratio （PSNR） of the decoding image 2--10 dB by changing the number of constrained bits. Experimental results show that it is an efficient error-controlling way for the transmission of set partitioning in hierarchical trees （SPIHT） coded image.

特殊二次根式的简捷解法

1 约分法抓住题目的数学特点巧妙地将分子或分母作类似分解因式的变形,这样可以约去分子和分母的公因式,从而达到化简的目的。

Method of variation of parameters for solving a constrained Birkhoffian system

For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.

A scalable topology aggregation algorithm for QoS routing in hierarchical networks

Topology aggregation is necessary for scalable QoS routing mechanisms. Thekey issue is how to gain good performance while summarizing the topological information. In thispaper, we propose a new method to describe the logical link, which is simple and effective innetwork with additive and constrained concave parameters. We extend the method to network associatedwith multi-parameters. Furthermore, we propose a modified star aggregation algorithm. Simulationsare used to evaluate the performance. The results show that our algorithm is relatively good.

Existence of multi-bump solutions for coupled Schr dinger systems

The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=（u1,u2）∈H1（R3）×H1（R3）, a nonlinear functional Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,is defined,where I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx and I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z ＋ w, where w ∈ （TzZ）⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.

Constrained least squares algorithm for channel vector estimation in 2-D RAKE receiver

Based on the fact that the variation of tile direction of arrival (DOA) isslower than that of the channel fading, the steering vector of the desired signal is estimatedfirstly using a subspace decomposition method and then a constrained condition is configured.Traffic signals are further employed to estimate the channel vector based on the constrained leastsquares criterion. We use the iterative least squares with projection (ILSP) algorithm initializedby the pilot to get the estimation. The accuracy of channel estimation and symbol detection can beprogressively increased through the iteration procedure of the ILSP algorithm. Simulation resultsdemonstrate that the proposed algorithm improves the system performance effectively compared withthe conventional 2-D RAKE receiver.

The Counting Problem of an Order N-group of Set

In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.

An Extended Algorithm of Flexibility Analysis in Chemical Engineering Processes

An extended algorithm of flexibility analysis with a local adjusting method for flexibility region of chemical processes, which is based on the active constraint strategy, is proposed, which fully exploits the flexibility region of the process system operation. The hyperrectangular flexibility region determined by the extended algorithm is larger than that calculated by the previous algorithms. The limitation of the proposed algorithm due to imperfect convexity and its corresponding verification measure are also discussed. Both numerical and actual chemical process examples are presented to demonstrate the effectiveness of the new algorithm.

An Optimized Constraint Decomposition Method in Concurrent Engineering

In order to facilitate solution, a complex problem is normally decomposed into many small sub-problems during product development process. Teams are formed to resolve each sub-problem. The original problem is resolved from solutions of sub-problems. Ideally, sub-problems are not only mutually independent but also inherent parameters of original problem. Solution of original problem can be directly derived from the collection of solutions from simplified sub-problems. In practice, the degree of interdependency is indeed reduced, sub-problems are neither totally independent nor all inherent parameters of original problem. This paper discusses team coordination under this condition and design solution from each team, which not only satisfies total requirements but also is an optimal one. The suggested optimized constraint decomposition method will insure workable Pareto solution.

Variational Approach of Timoshenko Beams with Internal Elastic Restraints

An exact approach for free transverse vibrations of a Timoshenko beam with ends elastically restrained against rotation and translation and arbitrarily located internal restraints is presented. The calculus of variations is used to obtain the equations of motion, the boundary conditions and the transitions conditions which correspond to the described mechanical system. The derived differential equations are solved individually for each segment of the beam with the corresponding boundary and transitions conditions. The derived mathematical formulation generates as particular cases, and several mathematical models are used to simulate the presence of cracks. Some cases available in the literature and the presence of some errors are discussed. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints with their corresponding modal shapes.

Instantaneous phase inversion based on an unwrapping algorithm

The full-waveform inversion method is a high-precision inversion method based on the minimization of the misfit between the synthetic seismograms and the observed data.However,this method suffers from cycle skipping in the time domain or phase wrapping in the frequency because of the inaccurate initial velocity or the lack of low-frequency information.furthermore,the object scale of inversion is affected by the observation system and wavelet bandwidth,the inversion for large-scale structures is a strongly nonlinear problem that is considerably difficult to solve.In this study,we modify the unwrapping algorithm to obtain accurate unwrapped instantaneous phase,then using this phase conducts the inversion for reducing the strong nonlinearity.The normal instantaneous phases are measured as modulo 2π,leading the loss of true phase information.The path integral algorithm can be used to unwrap the instantaneous phase of the seismograms having time series and onedimensional(1 D)signal characteristics.However,the unwrapped phase is easily affected by the numerical simulation and phase calculations,resulting in the low resolution of inversion parameters.To increase the noise resistance and ensure the inversion accuracy,we present an improved unwrapping method by adding an envelope into the path integral unwrapping algorithm for restricting the phase mutation points,getting accurate instantaneous phase.The objective function constructed by unwrapping instantaneous phase is less affected by the local minimum,thereby making it suitable for full-waveform inversion.Further,the corresponding instantaneous phase inversion formulas are provided.Using the improved algorithm,we can invert the low-wavenumber components of the underneath structure and ensure the accuracy of the inverted velocity.Finally,the numerical tests of the 2 D Marmousi model and 3 D SEG/EAGE salt model prove the accuracy of the proposed algorithm and the ability to restore largescale low-wavenumber structures,respectively.

Finite Order Batalin-Fradkin-Tyutin Method for Chiral Bosons in Non-commutative Space

The recently improved finite order BFT Hamiltonian embedding method is applied to the two dimensional chiral bosons in non-commutative space. It is then systematically converted to a first class constraint model. Performing the momentum integrations, the corresponding fully gauge symmetry Lagrangian as well as its partition function in phase space are obtained.

Adaptive Resource Allocation Algorithm for Internet of Things with Bandwidth Constraint

In order to improve the transmission accuracy and efficiency of sensing and actuating signals in Internet of Things （loT） and ensure the system stability, an adaptive resource allocation algorithm is proposed, which dynami- cally assigns the network bandwidth and priority among components according to their signals＇ frequency domain characteristics. A remote sensed and controlled unmanned ground vehicle （UGV） path tracking test-bed was devel- oped and multiple UGV＇s tracking error signals were measured in the simulation for performance evaluation. Results show that with the same network bandwidth constraints, the proposed algorithm can reduce,, the accumulated and maximum errors of UGV path tracking by over 60% compared with the conventional static algorithm.

A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.

Parameter Estimation with Constraints Based on Variational Method

The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.

Investigation on the binding of （-）-epigallocatechin-3-O-gallate to bovine serum albumin by molecular spectroscopy

The binding of （-）-epigallocatechin-3-O-gallate （EGCG） to bovine serum albumin （BSA） were investigated for the first time with spectral methods, including fluorescence and absorption spectrometry under simulative physiological conditions. A strong fluorescence quenching reaction of EGCG to BSA was observed. It was proved that the fluorescence quenching of BSA by addition of EGCG was a result of the formation of EGCG-BSA complex. The binding constant K and the number of binding sites n were determined at physiological conditions and three different temperatures with fluorescence quenching method. The binding distance R and transfer efficiency E between BSA and EGCG were also obtained according to Forster theory of non-radiation energy transfer. The effects of Al^3＋, Cu^2＋, Mg^2＋ and Fe^2＋ on the binding constant between EGCG and BSA were studied at 298 K. The effect of EGCG on the conformation of BSA was also analyzed by synchronous fluorescence spectroscopy. PACS. 21. 10. Dr; 32. 50. ＋d; 32. 30. Jc; 82.80. Dx

二次根式化简求值的常用技巧

二次根式(常见的有分式型，复合二次根式型，无限循环型或混合型)的化简求值，是中考及各级各类数学竞赛中的常见题目．下面举例谈谈八种常见方法——约分法、裂项法、取倒法、配方法、公式法、平方法、方程法、换元法，供读者参考．

Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’s.Before treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n 1.Also,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.