Nonlinear amplitude versus angle inversion for transversely isotropic media with vertical symmetry axis using new weak anisotropy approximation equations

In VTI media,the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs,even more so for unconventional reservoirs with strong seismic anisotropy.Theoretically,the above problems can be solved by utilizing the exact reflection coefficients equations.However,their complicated expression increases the difficulty in calculating the Jacobian matrix when applying them to the Bayesian deterministic inversion.Therefore,the new reduced approximation equations starting from the exact equations are derived here by linearizing the slowness expressions.The relatively simple form and satisfactory calculation accuracy make the reduced equations easy to apply for inversion while ensuring the accuracy of the inversion results.In addition,the blockiness constraint,which follows the differentiable Laplace distribution,is added to the prior model to improve contrasts between layers.Then,the concept of GLI and an iterative reweighted least-squares algorithm is combined to solve the objective function.Lastly,we obtain the iterative solution expression of the elastic parameters and anisotropy parameters and achieve nonlinear AVA inversion based on the reduced equations.The test results of synthetic data and field data show that the proposed method can accurately obtain the VTI parameters from prestack AVA seismic data.

A NEW APPROACH TO THE EQUATIONS FOR THE STEADY STATE CURRENTS AT MICROELECTRODES:EC'PROCESSES(SECOND ORDER REACTION)

With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are present in similar concentrations.

Exotic Localized Coherent Structures of New（2＋1）－Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.

New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

The symmetries of wave equations on new lattices

This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.

ANOTHER CLASS D＇ALEMBERT PRINCIPLE AND A NEW MAGGI EQUATION FOR ARBITRARY ORDER NONHOLONOMIC MECHANICAL SYSTEMS IN DERIVATIVE SPACE

As a concrete application of the concepts of 'derivative space' and'correspondent kinetic energy' in derivative space, and of foe thought of 'treatingnonholonomic systems by changing them into formal holonomic system' which theauthors have previously proposed in references [1. 2, 3]. this paper derived another newuniversal D'Alembert principle and a new Maggi equation for arbitrary ordernonholonomic mechanical systems. An example using the Maggi equation is given.

NEW SCALAR-TYPE EQUILIBRIUM EQUATIONS OF THE GENERAL SPACE FORCE SYSTEM

Using the principle of analytical geometry, several properties of the space straight lille are proved. Based on these properties, the equilibrium of general space force system is considered and its four new scalar-type equilibrium equations are derived which are equivalent to the vector-type necessary and sufficient conditions far equilibrium.

A New Method for Determining the Equation of State of Aluminized Explosive

The time-dependent Jones Wilkins-Lee equation products for aluminized explosives. To obtain the of state （JWL-EOS） is applied to describe detonation state time-dependent JWL-EOS parameters, cylinder tests and underwater explosion experiments are performed. According to the result of the wall radial velocity in cylinder tests and the shock wave pressures in underwater explosion experiments, the time-dependent JWL-EOS parameters are determined by iterating these variables in AUTODYN hydroeode simulations until the experimental values are reproduced. In addition, to verify the reliability of the derived JWL-EOS parameters, the aluminized explosive experiment is conducted in concrete. The shock wave pressures in the affected concrete bodies are measured by using manganin pressure sensors, and the rod velocity is obtained by using a high-speed camera. Simultaneously, the shock wave pressure and the rod velocity are calculated by using the derived time-dependent JWL equation of state. The calculated results are in good agreement with the experimental data.

New Types of Travelling Wave Solutions From （2＋l）-Dimensional Davey-Stewartson Equation

In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixtb-aegree nonnneal term, we study the （2＋l ）-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.

SEVERAL NEW TYPES OF FINITE-DIFFERENCE SCHEMES FOR SHALLOW-WATER EQUATION WITH INITIAL-BOUNDARY VALUE AND THEIR NUMERICAL EXPERIMENT

This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.

NEW PRINCIPLES OF WORK AND ENERGY AS WELLAS POWER AND ENERGY RATE FORCONTINUUM FIELD THEORIES

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

The Equations of Lorentz Transformation

This work consists of two parts. The first part: The Lorentz transformation has two derivations. One of the derivations can be found in the references at the end of the work in the “Appendix I” of the book marked by number one. The equations for this derivation [1]: The other derivation of the Lorentz transformation is the traditional hyperbolic equations:; ; For these equations we found new equations: , . The second part: In the second part is the equation by which we derive Minkowski’s equation. It will be proved that Minkowski’s equation is the integral part of the Lorentz transformation.

A Variant of Fermat’s Diophantine Equation

A variant of Fermat’s last Diophantine equation is proposed by adjusting the number of terms in accord with the power of terms and a theorem describing the solubility conditions is stated. Numerically obtained primitive solutions are presented for several cases with number of terms equal to or greater than powers. Further, geometric representations of solutions for the second and third power equations are devised by recasting the general equation in a form with rational solutions less than unity. Finally, it is suggested to consider negative and complex integers in seeking solutions to Diophantine forms in general.

New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.

Symmetries,optimal system,exact and soliton solutions of(3+1)-dimensional Gardner-KP equation

In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.

On the Mechanism of the Seasonal Variability of SST in the Tropical Indian Ocean

A general form of an equation that 'explicitly' diagnoses SST change is derived. All other equations in wide use are its special case. Combining with the data from an ocean general circulation model (MOM2) with an integration of 10 years (1987-1996), the relative importances of various processes that determine seasonal variations of SST in the tropical Indian Ocean are compared mainly for January, April, July and October. The main results are as follows. (1) The net surface heat flux is the most important factor affecting SST over the Arabian Sea, the Bay of Bengal and the region south of the equator in January; in April, its influence covers almost the whole region studied; whereas in July and October, this term shows significance only in the regions south of 10°S and north of the equator, respectively. (2) The horizontal advection dominates in the East African-Arabian coast and the region around the equator in January and July; in October, the region is located south of 10°S. (3) The entrainment is significant only in a narrow band centered on 10°S in April and the coastal region around the Arabian Sea and the equator in July. (4) As for SST, it decreases in January and July but increases in April and October in the Arabian Sea and the Bay of Bengal, showing a (asymmetrical) semiannual variability; by contrast, the SST in the region south of the equator has an annual variability, decreasing in April and July and increasing in October and January.

Prying Force Assessment Using Nonlinear Finite Element Model

Steel connection design using pre-tensioned bolts depends significantly on the value of the Prying forces exerted from the end plate. The Egyptian Code ECP （205） suggested a formula that can determine the Prying force value. In this research, the Prying force is numerically computed in a T-Stub connection using nonlinear finite element techniques. The model uses plane stress four node elements with two degrees of freedom per node to simulate the flange of the T-Stub. The bolts are simulated using a truss element with large deformation capability to allow modeling of the pretension force. Surface to surface gap elements are used in order to simulate the contact between the T-Stub and the supporting element. Parametric study on the end plate thickness, bolt size, bolt arrangement and pretension forces is performed in order to calibrate the Code formula. The parametric study covers all the practical ranges of the variables. The study revealed that the Code formula, inaccurately, determines the Prying force in a certain range. Moreover, a new equation for the prying force is developed using regression analysis on the finite element results.

Multi Dromion-Solitoff and Fractal Excitations for (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli System

In this short note, a new projective equation （Ф = σФ ＋ Ф^2） is used to obtain the variable separation solutions with two arbitrary functions of the （2＋1）-dimensional Boiti-Leon-Manna Pempinelli system （BLMP）. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as multi dromion-solitoffs and fractal-solitons are investigated.

A NEW STEP-SIZE SKILL FOR SOLVING A CLASS OF NONLINEAR PROJECTION EQUATIONS

In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.