Applying the classical Lie symmetry method, we investigated the problem of determining the largest possible set of Lie point symmetries for an improved Boussinesq equation. The most general Lie point symmetry group of the improved Boussinesq equation was determined and the corresponding group\|invariant solutions, such as travelling wave solutions were obtained.

We studied a coupled system of nonlinear fractional equations with initial value condition and got the existence and uniqueness of it by means of  the Schauder fixed point theorem and Banach fixed point theorem.

A class of p-biharmonic equations with critical nonlinearity to obtain infinitely many solutions by means of a version
of the symmetric mountain pass theorem. Finally, we showed that this sequence of solutions converge to zero.

This paper deals with the existence of solutions for p-Kirchhoff type equations in bounded domains under Dirichlet boundary condition. When the nonlinearity is asymptotically linear at infinity, there exist two nontrivial solutions of the p-Kirchhoff type equation which can be proved with the aid of the mountain pass theorem.

We studied the existence and uniqueness of solutions for a class of the sequential fractional q-differences equation. Firstly, a representation for the solution to this equation was given via q-exponential. Then the existence and uniqueness of solutions were proven by means of Banach fixed point theorem, Krasnoselskii fixed point theorem and LeraySchauder alternative theorem.

We generalized the stability criteria for the equilibrium of the periodic system to those for that of quasiperiodic system, applying the method of main integration. Concretely, we showed the stability for the equilibrium x=x′=0 of the quasiperiodic second order differential equation x″+h(t)x′+a(t)x²ⁿ⁺¹+e(t,x)=0, n≥1, where h(t),a(t),e(t,x) are quasi-periodic coefficients, whose frequency vectors meet the requirements proposed by Diophantine. And moreover, |e(t,x)|=O(x²ⁿ⁺²) near x=x′=0. The results we obtained also imply that, under some conditions, the equilibrium of the quasiperiodic oscillator with damping changing sign can still be stable.

In view of the higher computational complexity of the osculatory rational interpolation method of higher derivative mostly based on the idea of generalized vandermonde matrix, by means of basis function of polynomial interpolation and error nature of polynomial interpolation, we proposed an osculatory rational interpolation algorithm that not only satisfies different interpolation order but also makes the toppest of interpolation order equal 2, and it also meets the vectorvalued osculatory rational interpolation. It solves the problem of the existence of osculatory rational interpolation function and complexity of algorithm. In the end, we illustrated the effectiveness of the algorithm with a numerical example.

The control problems of a class of nonlinear Sprott simple chaotic systems were solved via an adaptive backstepping method. Firstly, the conditions of stability of the equilibria point and the existence of Hopf bifurcation were obtained. Secondly, chaotic phenomenon of the system was verified by means of presenting Lyapunov exponent and chaotic attractor, and complex dynamic behaviors were found via analyzing bifurcation diagram. Finally, an adaptive backstepping controller was  designed  to control chaotic system to a given equilibrium point. Numerical simulation has shown the effectiveness of the controller designed.

We presented a generalized Uzawa iterative method for solving the generalized saddlepoint problems based on the positive definite and skewHermitian splitting (PSS) iterative method, that is, the modified local PSS iterative method, and analyzed the convergence of the method. Numerical results are illustrated to show that the effectiveness of the new algorithm.

A lattice Boltzmann model for the Poisson equation was proposed. By means of the ChapmanEnskog expansion and the multiscale time expansion, a series of partial differential equations in different time scales was obtained. Moreover, the equilibrium distribution functions and the modified partial differential equation of the Poisson equation with the thirdorder truncation error were obtained. In numerical examples, the Kolmogorov flow and GreenTaylor vortex flow were simulated, and the comparison between numerical results of the lattice Boltzmann models and exact solutions were given. The numerical results are acceptable.

This paper deals with  the verification for minimum 2norm solutions of underdetermined nonlinear systems. The minimum 2norm solution of underdetermined nonlinear system is the minimum point of the 2norm of solution vectors. For the given undetermined nonlinear system,  combining the verification for simple solutions of square systems with the verification for symmetric positive definite matrices presented an algorithm for verifying minimum 2norm solutions of underdetermined nonlinear systems with full rank Jacobian matrices.

A fast algorithm was proposed for the numerical computation of the electromagnetic scattering by multiple rectangular cavities embedded on an infinite ground plane, the algorithm can be used to compute the scattering problems with large cavities and high wave numbers. The numerical experiments confirm the effectiveness of our method.

be a factor von Neumann algebra and δ be a mapping from M into itself (without assumption of additivity or continuity), we can show that if δ satisfies mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A) for all A,B∈M, then δ is an additive derivation  using the method of decomposing matrix.

Using rough set theory, we proposed the congruences induced by fuzzy (prime) ideals of an m-semilattice and studied the properties of the upper (lower) rough fuzzy approximation operators with respect to these congruences. Then we introduced the notions of rough fuzzy (prime) ideals of m-semilattice, and established the relationships between rough fuzzy (prime) ideals and fuzzy (prime) ideals and the relationships between rough fuzzy (prime) ideals and (prime) ideals of m-semilattices.

Based on internal P-set,  the concepts and structures of assistant set, σ-assistant set and function internal P(σ)-set related to function internal P-set were obtained, and then  the relationship between function internal P-set and function internal P(σ)-set was discussed. Moreover, we derived the theorems about dynamic change depending on attributes and threshold value. Because of  the law characteristics of function internal P(σ)-set, its dynamic change was also researched and identification theorems about law change were found.

To combat autocorrelation in errors and multicollinearity among the regressors in linear regression model, we proposed a new estimator by combining the principal components regression (PCR) estimator and the s-K estimator. Then necessary and sufficient conditions for the superiority of the new estimator over the GLS, the PCR, the r-k and the s-K estimators were derived by the mean squared error matrix criterion. Finally, a Monte
Carlo simulation study was carried out to investigate the performance of the proposed estimator.

We made an investigation into the  stochastic optimal control problem of the stochastic delayed system described by forwardbackward stochastic pantograph equations with the aid of classical variational approach, duality method and the anticipated backward stochastic differential equations,  obtaining the maximum principle for this problem.

We used the first integral method to solve a class of nonlinear wave equations and obtained the exact form of traveling wave solutions. Furthermore, the validity and efficiency of this method were shown by numerical calculation of nonlinear wave equation, indicating that it can be applied to other hyperbolic evolution equations.

Based on the moving frames, an integral inequality about maximal timelike submanifold was obtained in the locally symmetric pseudoRiemannian manifold and a pinching theorem about the squared norm of the second fundamental form for the compact maximal timelike submanifold was gived in locally symmetric pseudoRiemannian manifold.

We studied the limit of the largest eigenvalue of the  block adjacency matrix using the moment method and spectral theory in random matrix theory. Under some moments assumptions, we obtained a bound of the super limit of the largest eigenvalue.

The authors dealt with the random attractor for the stochastic Zakharov system perturbed by a small random item. Based on the tail-estimate method,  the asymptotic compactness of random dynamical systems was testified and  the existence of a random compact invariant set was proved, which is a random attractor on unbounded domain in Rⁿ.

Using convex variation method and a duality technique, we studied stochastic optimal control problem for backward stochastic partial differential equations with abstract evolution form driven by Lévy noises, and obtained the maximum principle of this problem.

Based on the chain rule of composite function, the differential viscosity function of nonNewtonian fluid was simplified so that the problem of singularity is avoided, which is encountered in solving the differential viscosity function by the average value method commonly used in fluid mechanics. Then three approximation formula of the differential viscosity were established, the precision of the approximations was analyzed and compared, and the optimal scopes of application of the approximations were given.

In order to solve the shortest path problem with fuzzy constraint, based on the fuzzy linear programming model, tolerance method and penalty function method were adopted to convert the original model to obtain a transformed model with the same optimal solution and optimal value as those of the original model. Then, a modified firefly algorithm was proposed to solve the transformed model. In addition, the computational complexities of the modified algorithm as well as the firefly algorithm were analyzed and compared. Finally, numerical example was given to illustrate the efficiency of the new model and algorithm to solve the shortest path problem with fuzzy constraint.

In view of QoS rounting problem in mobile ad hoc networks, the author proposed a QoS routing algorithm integrated with Qlearning and improved ant colony algorithm. The algorithm combines the advantages of Qlearning with those of ant colony algorithm, and it takes Q value of Qlearning algorithm as the initial pheromone of ant colony algorithm, improves the initial convergence speed of the algorithm, at the same time, takes the node energy and load into account in path selection. Simulation results show that on the premise of guaranteeing QoS demand, the algorithm increases the effectiveness and robustness of routing and reduces energy consumption, and besides, packet delivery ratio, network lifetime and other indicators display better performances.

In view of some shortcomings about currently shape recognition algorithms such as a large amount of calculation, long processing time, fewer species recognition, a fast geometry figure recognition algorithm based on chain code feature was presented. The algorithm combines the chain code histogram and chain code spatial distribution entropy, which considers both the statistical feature and the spatial feature of the chain code, having the advantages of being invariant to the position, rotation and scale of the image content and having nothing to do with the start point of the chain code. The simulation results show that the algorithm is able to identify many types of graphics with high recognition accuracy and shorter time consuming, and the overall performance is excellent.

In view of classical FCM clustering algorithm being too sensitive to the initial cluster centers, a rapid global FCM clustering algorithm was proposed. The algorithm uses dynamic incrementally phased selection of initial cluster centers, avoiding the problem of poor stability of clustering results due to random settings. The experiments show that the clustering result of the improved FCM clustering algorithm is better than that of classical FCM in image segmentation of brain tumors, while the clustering accuracy of multiple data sets also shows that the clustering stability of the rapid global FCM algorithm is enhanced
greatly.

For synchronous safety problems existed in RFID technology, the paper proposes a new security authentication protocol based on a oneway Hash function, a more comprehensive solution to the presence of RFID systems in various security problems. The proposed protocol was formally proven and comparatively analyzed based on GNY logic. The results show that the protocol can effectively solve the eavesdropping, replay attacking and  synchronization losing problems and other safety issues, and is prior to  a series of agreements in the current mainstream in energy, security and performance.

The authors analyzed the intrusion feature selection methods and algorithms based on ReliefF. Combining with the characteristics, in which data points have high similarity in the same class and nonsimilarity in different classes, and optimizing the compute method of intrusion feature weight, we proposed an improved algorithm ReReliefF. It resolved the problems about processing efficiency with the data dimensions in network security. Experiments on the network security test datasets showed the effectiveness of the proposed algorithms, and the improved algorithm has advantages on performance compared to the traditional one.

A new algorithm of quaternion extended Kalman filter was adopted to estimate the attitude of small UAV. After the establishment of the models of quaternion attitude movement and magnetic, angular rate, and gravity sensor measurement, a new designed extended Kalman filter was given with the quaternion and random drifting of gyro being the static vectors and the accelerometer measurements and the heading solved by the magnetometer being the observational vectors. What’s more, an innovation amendment method based on an adaptive approach to construct the measurement noise covariance matrix was designed. Experimental results show that the algorithm not only solves the problems of micro electro mechanical systems inertial sensors used for attitude measurement to show low accuracy and to be easy to diverge and to disturb, but also significantly reduces the effect of random drifting of gyro scope on attitude estimation, and proves to be effective at improving the accuracy of attitude estimation.

Analyzing the impact of normalization method applied in isolated word speech dominant and noise characteristics to discover the continuous speech characteristic curve adjustment problems. The authors raised optimized solutions to further solve the problem of instability and unpredictability of the noise characteristics for voice effects. Robust continuous speech recognition model by normalization method in this paper can achieve a clean environment in the laboratory and real noise environment so as to get the best recognition results.

An algorithm suitable for spatial vector data placement based on graph coloring theory was presented in the parallel system of computing distributed to data nodes. The deployment problem was transferred into graph vertex coloring problem, and the information query efficiency of any spatial area was thus improved. Moreover, the algorithm based on graph vertex coloring problem was proposed and improved by the task of nodes. This algorithm can achieve discrete deployment of massive spatial data granularity and storage load balance of the nodes, improve the degree of parallelism spatial data retrieval and query, and make full use of parallel computing resources.

In view of the extended Web service architecture, we formally modeled the Web service composition with probabilistic timed automata (PTA). The process of Web service composition was understood as a realtime system operation process. We then overcame the limitation of existing research approach of Web service quality which focused the service quality on a single Web service, by quantitatively analyze the quality of Web service composition on the basis of the model we built before. The stochastic and nondeterministic characteristics in the execution of Web service composition were fully taken into account in the whole analysis so as to make the result credible. Finally, an example was given to illustrate the feasibility of the modeling analysis method, proving that
 the corresponding service selection strategy can improve the success probability of Web service composition.

A tagbased file search method was designd for point to point (P2P) system to solve the large consumption of network bandwidth and slow query problem, which determines a way of uploading associated files held by each peer in the bottom layer to subservers in the middle layer and a way of forwarding a query received by the central server in the top layer to an appropriate subserver relevant to the query. A technique of priority sequence of tags was introduced to realize a quick forwarding of queries. The result of performance evaluation indicates that the number of tags which must be examined in forwarding a given query is bounded by a small constant, so as to save network bandwidth and raise the speed of file searching.

We investigated the changes of the WignerYanase information in the processes of the spontaneous emission of a twolevel atom system, and calculated the WignerYanase information for the reduced density matrix of the atom and that for the quantum radiation respectively. Our investigations show that both of them depend on the expectation of 〈S_z〉. And the WignerYanase information for the radiation field reach the maximum when the atom stays in the ground state. Additionally, the results also show that both the atom and the field will not simultaneously become the maximal mixed state.

A complete Bellbasetype unextendible maximally entangled basis in C₂×C₃ was proved. Based on a constructed orthonormal basis in C₃, another complete Bellbasetype unextendible maximally entangled basis was constructed, which is mutually unbiased with the first one. Finally, two classes of Bellbasetype unextendible maximally entangled bases which are mutually unbiased were presented.

Diluted magnetic semiconductors (DMS) which are used as spinelectron devices have been researched popularly because of their excellent electronic and magnetic properties. We used VASP code based on the density functional theory to calculate the stability, electronic and magnetic properties of the unit cell of CrTe,MnTe and compared the stability, electric and magnetic properties of CrTe with those of MnTe with the same structure as that of CrTe. We found that the stable state of CrTe exibits the NiAstype hexagonal structure. The metastable state of it displays three structures called zincblende structure, wurtzite structure and rock salt structure, the three structures are all half metallic properties.

The electronic structure and optical properties of CrSi₂ with vacancy defect were calculated based on the first principles method, and the photoelectric properties of CrSi₂ with Cr or Si vacancy defect were analyzed. The results show that the lattice constants and volume are all decreased with Cr or Si vacancy defect. The band structure becomes intensive and gentle, and moves upward. The band structure of CrSi₂ with Si vacancy defect is p type indirect semiconductor with a band gap of 0.35 eV; while two new energy levels are induced in the forbidden band with Crvacancy defect. Density of states of
 the valence band top and conduction band bottom are mainly composed of Cr 3d. Sivacancy defect has a little effect on the density of states; Crvacancy defect improves the density of states of the Fermi energy. Compared with that of pure CrSi₂, the dielectric peak slightly moves to the lower energy and decreases with vacancy defect, and the absorption index obviously decreases.

The title compound delavirdine (C₂₃H₃₂N₆O₄S) has been synthesized from nicotinamide, 4nitrophenylhydrazine and ethyl pyruvate. It was characterized by means of ¹H NMR and ¹³C NMR. Its crystal and molecular structures were determined by Xray diffractometry. It belongs to the orthorhombic system, with space group P2₁2₁2₁ with a=1.096 9(4)nm, b=1.152 5(4)nm, c=1.951 0(7)nm, α=90°, β=90°, γ=90°, V=2.468 5(15) nm³, Mr=488.61, Z=4, Dc=1.315 g/cm³, λ=0.071 073 nm, μ=0.172 mm^-1, F(000)=1 040, the final R=0.040 7 and wR=0.090 5. A total of 14 875 reflections were collected, of which 4 851 were independent (Rint=0.040 7) and 4 099 were observed with I>2σ(I).

The nifedipine liposome was prepared from an appropriate amount of lecithine, cholesterol and nifedipine by the ether injection method. On the basis of single factor experiment, we used statistical methods to investigate the effects of phospholipid amount, lipid drug ratio, cholesterol phospholipid ratio on the encapsulation efficiency of liposome. The results show that the encapsulation rate of the liposome prepared based on multivariate quadratic regression model was 8654%, and the encapsulation rate of the liposome prepared based on artificial neural network model was 9725%. Compared with the quadratic regression model, artificial neural network model combined with genetic algorithm is more suitable for optimizing the preparation technique of nifedipine liposome. After optimizing, the best preparation formulation is 612.4 mg of phospholipid with a lipid drug ratio of 60.02 and a cholesterol phospholipid ratio of 6.401.

Based on the GIS technology and remote sensing images of 2005 and 2010, the special characteristics of landuse change were revealed for the section of the Liao River. The authors analyzed the fundamental drivingforce factors of landuse change and set up a multiple linear regression equation using the principle component analysis based on the software of SPSS and the socialeconomy statistical data. As a result, the demographic factor, socioeconomic factor, levels of industrialization and urbanization and agricultural development factor were the main factors affecting the landuse change for the Jilin section of the Liaohe River, which provided the basis and the reference for economic development of survey region.