一个一阶一次联立微分方程的序数解和肥料三要素自然比率

本文推导出一个一阶一次联立微分方程的序数解,当方程的所有变量均为序数时,其两个独立通解为从第一变量开始依次积分的并列,而与一般的该型方程的两个独立通解为第一变量的积分传递相区别,其一般解为肥料三要素自然比率。

Green-Naghdi Theory,Part A:Green-Naghdi(GN) Equations for Shallow Water Waves

In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.

Improvement of the Mirror Extending in Empirical Mode Decomposition Method and the Technology for Eliminating Frequency Mixing

The mirror extending approach proposed by Zhao and Huang in EMD method is improved in this paper. Mirror extending manner of data is kept unchanged, but the approach for determining envelopes is changed. When the end of data is obviously not extremum, the envelope is determined by the first inner extremum and the image value in the mirror, ignoring the value on the end. This improvement eliminates the frequency compression near the end and decreases the error. Meanwhile, tridiagonal equations are used and the calculation speed is much increased. The temporal process curve is more important in reflecting the real physical process and comparable with other phenomena. Frequency mixing in IMFs makes it impossible. A high frequency reconstruction (HFR) approach is proposed to eliminate common frequency mixing and reconstruct an IMF with all high frequency portions. By this approach, the IMFs without frequency mixing are obtained to express significative processes. The high frequency information restored in high frequency IMF can be extracted by general spectrum method. After obtaining IMFs by EMD method, some of the theoretical and technological issues still exist when using the IMFs. The consistency of IMFs with real physical process is discussed in detail. By virtue of the approach proposed in this paper, the EMD method can be widely used in various fields.

A New Trial Equation Method and Its Applications

As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.

A NEW PUBLIC-KEY ENCRYPTION SCHEME BASED ON LUCAS SEQUENCE

Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in ZN, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in ZN. At last, the efficiency of the proposed schemes is briefly analyzed.

On Smarandache Multiplicative Sequence and Its Generation

The main purpose of this paper is to introduce the general Smarandache mul- tiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequences.

Some Results on Position Restriction Scheduling Problems

In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

Experiments on exactly computing non-linear energy transfer rate in MASNUM-WAM

The Webb-Resio-Tracy(WRT) method for exact computation of the non-linear energy transfer rate was implemented in MASNUM-WAM, which is a third-generation wave model solving the discrete spectral balance equation. In this paper, we describe the transformation of the spectral space in the original WRT method. Four numerical procedures were developed in which the acceleration techniques in the original WRT method, such as geometric scaling, pre-calculating, and grid-searching, are all reorganized. A series of numerical experiments including two simulations based on real data were performed. The availability of such implementation in both serial and parallel versions of the wave model was proved, and a comparison of computation times showed that some of the developed procedures provided good effi cacy. With exact computation of non-linear energy transfer, MASNUM-WAM now can be used to perform numerical experiments for research purposes, which augurs well for further developments of the model.

Solving the Sequence Problems by Constructing Matrices and Determinants

Higher mathematics is more extensive, profound and abstract than elementary mathematics; it is the development and sublimation of elementary mathematics. They have a deep connection, determinant and matrix theories originated in Elementary Mathematics, in tum, they also can be used as tools to solve related problems, and they have important roles in guiding the study of elementary mathematics. This paper will introduce the methods of solving some recursive sequence problems by constructing determinants and matrices.

Analysis on Characteristics of Focal Mechanisms for the M_S7.3 Yutian Earthquake Sequence of February 12,2014

The paper inverts the focal mechanism solutions of the Yutian M_S7. 3 main shock,foreshocks and M_S≥3. 5 aftershocks by using the CAP method,based on the broadband waveforms recorded by the Xinjiang and Tibet Digital Seismic Networks. The results show that the M_S7. 3 strong earthquake is of strike-slip type with a normal faulting component,and combined with the analysis of focal structure and the aftershock distribution,the nodal plane I with strike 241°,dip 90° and rake- 22° is considered to be the seismogenic fault plane of the main shock. The direction of P-axis for the main shock is 194°,close to the near NS direction of the principal stress P-axis of historical strong earthquakes in this region. The focal mechanism solution of the M_S5. 4 foreshock has a good consistency with that of the main shock. Among the 18 aftershocks,10 are of strike-slip type,6 are of normal faulting type and 2 are of thrust type. 70% of the aftershocks in the sequence have a focal mechanism with P-axis in the near-NS direction. The focal depths of this M_S7. 3 earthquake sequences are distributed in the range of 5km- 28 km,with the majority in the depth range of 15km- 20 km,slightly deeper than the depth of 10 km of the main shock as calculated.

Influence of Pipe-Diameter on Water Hammer Phenomenon

The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.

Quasi-binomial coefficients stemming from Nakayama algebras

It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences.To determine the cardinal number of all nonisomorphic indecomposable basic Nakayama algebras,we describe the cardinal number of the set of all t-length admissible sequences using a new type of integers called quasi-binomial coefficients.Furthermore,we find some intrinsic relations among binomial coefficients and quasi-binomial coefficients.

On the size of the intersection of two Lucas sequences of distinct type Ⅱ

Let a and b be positive integers, with a not perfect square and b > 1. Recently, He, Togband Walsh proved that the Diophantine equation x2-a((bk-1)/(b-1))2=1 has at most three solutions in positive integers. Moreover, they showed that if max{a,b} > 4.76·1051, then there are at most two positive integer solutions (x,k). In this paper, we sharpen their result by proving that this equation always has at most two solutions.

The Refined Solutions on Multiobjective Programming Problems with Fuzzy Parameters in the Constraints

This paper investigates the multiobjective programming problems with fuzzy parameters in the constraints. First, by the decomposing theorem, we introduce a fuzzy set to characterize the constraints, then give the definition of α-quasi-efficient solution and a-efficient solution, and discuss their properties. Finally, a numerical example is presented to illustrate the differences between the refined solutions and the α-Pareto solution.

Local and global methods in representations of Hecke algebras

This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.

A sharp estimate of positive integral points in6-dimensional polyhedra and a sharp estimate of smooth numbers

Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.