equation

and that this corrected equation is itself only an imperfect approximation to an infinite set of quantum field-theoretical equations.

OK, so let me move on a bit and point out that with parametric equations, we've looked also at things like velocity and acceleration.

Number consecutively any equations that have to be displayed separate from the text (if referred to explicitly in the text).

Einstein is trying to come up with these equations that will describe how space is curved. He's working deep into the night.

These operations can be called discrete 3 operation. Quantity of these operations and of equations constructed by them will be very huge.

The procedure is only equivalent to the orthogonal extension of the matrix and solution of a set of equations.

In this field, uniform beams have previously been used to depict the buffeting motion of the deck in terms of partial derivative equations.

I remember as a, as a mathematics student, thinking, well, you know, where am I ever gonna use simultaneous equations.

This paper presents a very efficient method, referred to as the aggregate function method, for solving nonlinear equations.

By means of the qualitative theory, we obtain sufficient conditions and a necessary condition for this kind of equations.

The subject of partial differential equations, which had its beginnings in the eighteenth century, burgeoned in the nineteenth.

That stance might comfort the authors, but to many readers they will nonetheless seem to pluck equations out of thin air.

We find simultaneous equations hard so the lessons seem to go on forever!

Probably she or he is out there today, working on the equations, getting ready to publish the paper that will win the Nobel Prize.

Turns out, some of these equations were very familiar: the law of conservation of momentum, and Newton's second law of motion.

The Stern book may be careful to avoid academic gobbledygook and complex equations, but it cannot be described as a light read.

In the analysis of very complex systems, the governing equations for the system components form a large set of simultaneous equations.

Finally, the paper will elicit the general equations of motion about six-DOF, considering the relative motion between the two aircraft.

Secondly, the equations of every joint angle in all lower limbs were derived by real-time inverse kinematics analytic method.

Case studies indicate the correctness and practicability of these equations which can be used in reservoir engineering study and prediction.

Now, it's also very useful to look at some of the relations that come out of these fundamental equations.

Jared stands up and begins to write frenzied equations on the board, Bill counters with an equation of his own.

We live in a society that completely tends to valorize symbolic forms of representation -- algebraic representations , equations , codes .

By means of the numerical solution to deal with the systematical equations, the important flow laws to actual engineering are obtained.

On a small scale, they now have the equations to simulate neurons and the electro-chemical reactions between them.

Some of the comments are well taken , but let me restate my argument in a slightly more formal way , although I will still avoid equations .

In this fashion, this paper presents a simple method used to establish reentry motion equations of a satellite.

A set of equations was drawn up that represented the interactions of these different factors in mathematical form, leading to. . . Ding!

Still, once all its equations have been solved, a simple fact remains: Most women enter prostitution for the money.

We do advise, however, against getting any of these equations tattooed on your body, much less branded.

We would expect to see detailed sketches, major equations and plots which demonstrate that you are on the right track.

He made notes in the margins and corrected some of the equations.

Data-flow analysis is typically path-insensitive, though it is possible to define data-flow equations that yield a path-sensitive analysis.

When he put together the equations of general relativity back in 1916, Einstein applied them to the universe as a whole.

It is an important method that the exact solutions of the heat conduction equations test the correctness of the numerical solutions.

The differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential.

The broad question of which equations are solvable by algebraic operations was definitely and comprehensively answered by Galois.

These have been developed by the numerical integration of the differential equations of gas motion for a spherical blast wave in air.

This is China, remember. The economic equations that may seem to work obviously elsewhere, do not necessarily do the trick here.

Builds the performance curve regression equations of two types of pumps with the least square method, and gains the fitted curve equations.

The general dynamical equations of the system are derived using the concepts of path vectors and augmented bodies.

The first "computers" were indeed people. The word originally meant an individual who solved equations, often using a mechanical calculator.

Also we point out that this kind of variational equations has a main theoretical meaning in the study of stochastic controls.

Firstly, the statics model of the bearing is established and a set of equilibrium equations are obtained.

He developed a mathematical model that produces precise analytical solutions by solving of a set of mathematical equations.

by vibration differential equations, crack deformation equation is derived by the concept of mobility.

Exponential, hyperbolic, and harmonic curve equations are often used to mathematically express the decline curve.

Finally, we used the obtained results to discuss the existence of multiple solutions of differential equations and a difference equation.

During his time at Oxford he published the economic models and equations for which he would eventually be awarded his Nobel Prize.

The governing boundary layer equations were written into a dimensionless form by similarity transformations.

Ideally, the air both inside and outside the ball should be included, and the viscosities modelled using Navier-Stokes equations.

The Jacobian matrix of the 2-DOF parallel manipulator used in kinematics is derived by means of derivation of constraint equations.

The subject of differential and difference equations is an old and much-honored chapter in science.

Solution of a class of second-order vibration matrix equations is investigated, which are widely used in vibration control fields.

Precisely, as you are undoubtedly gathering, the anomaly is systemic-creating fluctuations in even the most simplistic equations.

And some equations were got to control correlation parameter in hydrocyclone for intensifying heat and mass transfer.

Could Einstein's Theory of Relativity be a few mathematical equations away from being disproved?

In the model the complex computation due to various equations in earlier works can be avoided with the number of components unlimited.

The undisturbed electron density distribution, calculated from the quantum mechanical equations of motion is shown in yellow.

There was a serendipitous second advantage to working with a library of equations.

But during the election process and after the assassination of Benazir Bhutto, the political equations seemed to have changed clearly.

One of the main topics of the soliton theory is to search for the soliton solutions of nonlinear evolution equations (NLEEs).

There would be a set of equations relating supply and demand for each product to incomes and prices.

The other is the initial value problem about the general, the non-autonomous singular perturbation of fractional differential equations.

Einstein is up at the board writing his equations and trying to describe his problem.

A set of simultaneous, linear algebraic equations results for the entire structure, in which the structural displacements are unknowns.

These equations are called differential equations, and their study forms one of the most challenging branches of mathematics.

A method of constructing the basic set of solutions of a system of homogeneous constant-coefficient differential equations is introduced.

This method basically consists in formulating the power flow problem as a set of autonomous ordinary differential equations.

We're going to use, very heavily, the equations that you see here that are so familiar with us.

The extra dimensions introduce a correction term into the equations, which ensures that the curvature of an empty brane is not zero .

There is no general method for solving the equations that you get from this method. You just have to think about them.

It is one of the important research fields to apply the methods of wavelet analysis and partial differential equations in image processing.

The Gauss truncation theory is used to linearize the nonlinear equations when taking account of the non-linearity of guys.

The nonlinear coupled equations of the perturbed magnetic field and the perturbed temperature are derived in the beginning.

The book begins with a basic overview of the field, essential equations, and core concepts of compressible turbulence.

The equations derived by the eccentric genius are still used to design cars, build bridges and send spacecraft into the cosmos.

MathML lets you model mathematical equations -- imagine all the different equations you could create.

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations.

To be useful in solving engineering problems, the differential equations must be integrated.

graphic technology - graphic arts transmission densitometry measurements - terminology , equations , image elements , and procedures.

To solve the set of governing equations , initial conditions have to be properly represented and set up using the latest information .

The heat conduction equations considering heat resource are established, and the corresponding boundary conditions are given.

Furthermore, a forest competition algorithm was proposed. To verify the algorithm, it was applied to solve transcendental equations.

The gained results are very important to help ones understand and apply Maxwell's equations of time-varying electromagnetic field.

This paper deals with the general boundary value problem for nonlinear elliptic equations of second order.

For most matrix of A, the linear differentiable equations with quasi-periodic finitely differentiable coefficients are reducible.

Predict the temperature usually require only two consecutive months of the establishment of equations and can be recursive relationship.

Correlation coefficient, r, was inappropriately used to describe the significance of curve regression equations.

Partial differential equations are solved by first discretizing the equation, bringing it into a finite-dimensional subspace.

Equations of SBFEM for a seepage problem are derived with a transformation from Cartesian coordinates to scaled coordinates.

And that is in the case of the circular orbit, square root of two So these are the numbers that we are going to use today, the equations.

The blow-up theory of the solutions for nonlinear evolution equations is an important aspect of partial differential equation.

At a rigid joint of a space frame, three resolution and three moment equations can be written.

graphic technology - graphic arts reflection densitometry measurements - terminology , equations , image elements and procedures.

The solution of the set of second- order linear differential equations ( 6. 10 ) depends on the eigenvalues of A .

The performance of logical networks is expressed in terms of equations that are governed by special theorems and rules.

Results A recursion formula to the solutions of a class of linear ordinary differential equations with constant coefficients is given.

The coefficient functions of the hyperbolic equations considered are assumed to be piecewise constant.

Even though the entire imagery had to be changed, the validity of those equations persisted.

This theory received support in the 1870s from James Clerk Maxwell's equations showing that light was a form of electromagnetic wave.

Consider the nonlinear delay partial difference equations with continuous arguments Some oscillation criteria of this equation are obtained.

The solution of equations are obtained by means of both Green function method and natural boundary conditions.

The oscillation of a class of nonlinear hyperbolic equations with continuous distributed deviating arguments is studied.

To estimate the unknown parameters of the equations, the least square parameters estimation method was employed.

The elementary equations of pressure and open-channel unsteady flow are the essential theory of hydraulic transients of hydropower station.

A study of the stability of the compressible single-stream shear mixing layers is performed by using parabolized stability equations (PSE).

We consider the initial boundary value problem for a class of nonlinear degenerate wave equations in a bounded domain.

The weak nonlinear instability of a nonparallel boundary layer is studied by nonlinear parabolized stability equations(PSE).

Kepler s equations can be solved with the gradual approach, which can be further extended to the solution of the non-linear equations.

I've spent the past three and a half years staring at grease boards full of equations. Before that, I spent four years working on my thesis.

By using EH11 mode, we have numerically solved the rate equations of a three-level pumping scheme for a fiber laser.

Conjugate conditions equations are established on the basis of conjugate conditions of two curved surface and meshing theory of gears.

The remarks below the diagrams should be observed; they concern the applicability of the equations to the various operating ranges.

The theory of the solution of partial differential equations remained to be fashioned .

Uses a reduced-Newton algorithm with a weak line search to solve a set of non-linear algebraic equations.

One approach would be, following Newton, to write down the equations for the evolution of the biosphere and solve them.

Unlike Einstein's equations, ECKS gravity takes account of the spin or angular momentum of elementary particles.

Since the equations are nonlinear, one has to resort to a numerical solution scheme except for relatively simple problems.

A note on paper "a simple fast method in finding the analytical solutions to a class of nonlinear partial differential equations"

According to the static balance principle, the general equations for solving the describing parameters are derived and proved reliable.

From that moment on, all other classical laws or equations of these disciplines became simplified cases of Maxwell's equations.

The remainder of the book is devoted to the numerical solutions of these equations.

Initially, the equations generated by the program failed to explain the data, but some failures were slightly less wrong than others.

In this study, these problems refer to a standard form of minimizing a single parameter subject to parameterized linear equations.

To derive mathematical model, dynamic characteristic equations are obtained and the pulse amplitude and time of input shaper was calculated.

Measured in the least squares adjustment of the function model to solve problems, eventually reduced to the problem of linear equations.

A Beautiful Mind It is only in the mysterious equations of love that any logical reasons can be found.

The kinematic analysis of the planar four-bar linkage and dimensional six-bar linkage can be done by building up the structural equations.

The borehole trajectory design to be drilled well with defined direction needs to solve a set of 7-element nonlinear equations.

Maxwell's equations actually tell you about div and curl of these fields.

By test, the variations calculated with the equations are in conformity with the actual values and can be used in engineering calculation.

It is sometime necessary to have the stresses at directions other than those given by the equations.

The solution is verified with a numerical example, its results without extraneous roots agree with the original equations.

The whole flow is divided into three different regions, each being subject to a treatment by the basic aerodynamic flow equations .

The global existence and blow up time problem for solutions of a parabolic equations with nonlinear boundary conditions are studied.

The fourth one is to determine differential equations which sum functions satisfy, then solve the differential equations.

The slipper motion equations are established, and the relationship between the time constant of the motor and the displacement is given.

The imaginary inputs satisfying all the compatibility equations are the true kinetostatics parameters.

The description of a plane wave diffracted by a circular aperture is directly started from the Maxwell's equations.

These equations may be used for heavy oil reservoir in development design and evaluation.

And that's exactly what you see comes out of these equations whether you go to the center of mass or whether you do it from 26. 100.

With the symmetry applied to the solution process, the matrix equations were simplified, and the amount of calculation was reduced greatly.

For the case of sinusoidal pulsation, the linear equations have been solved.

Even if there is only one, unique set of possible laws, it is only a set of equations.

The sets of nonlinear synthesis equations are solved by using chaos optimization method, and a numerical example is given for illustration.

Function to calculate the Jacobian matrix for a set of nonlinear algebraic equations. A simple central differencing scheme is used.

Mathematical equations are used to fit the experimental data if the mechanical models have not been clearly invented.

This means that the empirical equations cannot be raised into an universal abstract form by themselves.

Compressible miscible displacement in porous medium is modeled by a nonlinear system of two coupled partial differential equations.

Consider the chemical reactions described earlier. Word equations are a useful way of describing these chemical reaction.

Due to the complexity of the nonlinear partial differential equations, the matching conditions simplified and solved.

It includes basic information, thermodynamic and thermophysical properties and temperature-dependent correlation equations.

Add Zeeman coupling to external magnetic field, , and obtain Bloch equations as a saddle point approximation to this path integral.

The OCP is governed by a set of nonlinear partial differential equations and involves control constraints.

For your enjoyment, the Wired Science team has gathered nine of our favorite equations.

The equations can be used to calculate the solubility parameters of alkyd resin prepared from various plant oils and polyols.

In besides, The series equations about transformer-core arc snubber operation also is derived and analyzed on the basis of a ideal model.

The nonlinear motion equations of the systems are derived and the journal orbits are determined as aPProximate solution of those equations.

Using maximum principle and mountain pass lemma to a class of nonlinear elliptic equations, two different positive solutions are obtained.

Relations between physical quantities are usually given in the form of equations.

The nonlinear complementarity problem can be reformulated as the solution to a nonsmooth system of equations with FB-NCP function.

They exist in solutions to Einstein's equations, and are thought to be extremely unstable, and would instantly fall apart once created.

Derive and the equations of motion for a multibody dynamic system and apply the equations in a simulation of limb motion.

Numerical solution of these equations yields the intensity factors and the energy release rate at the crack tip.

RARELY has a report with so many charts and equations in it caused such a stir.

Two are still unemployed which basically means that getting a girlfriend will prove to be difficult given the current equations.

The equations describing these curves are known as Bezier curves or paths, named after the mathematician Pierre Bezier.

On the contrary, only through calculate a set of linear algebraic equations can obtain the explicit composite Lyapunov function.

The remaining four parameters can be calculated by solving a special set of linear equations.

The field equations of his theory of relativity imply that a large star or cloud of gas would collapse in on itself and form a black hole.

a condition specified for the solution to a set of differential equations.

The integral equations for determining the unknown forces can be transformed into algebraic equations and solved numerically.

This can take the form of prototypes, mathematical equations, or interaction diagrams.

In this paper the computational techniques for the approximative solution of equations are discussed, and a practical method is given.

Therefore, these equations with vanishing body forces cannot admit plane wave solutions under an arbitrary initial state of stress.

Also, we study the existence of global attractors for a class of semilinear hyperbolic equations.

This led physicists to think that the equations of the subatomic world would not look the same if time were reversed .

The energy integral and cyclic integral are involved in the first integration of the Lagrange's equations for a potential system.

The solvability of such equations in space L2(G) is solved by means of utilizing the normal solvability of integral operator.

Remarks on the Paper "The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations"

Finally, it is presented that the error distribution of the roots from complex coefficient higher-order algebraic equations is not even.

A set of nonlinear equations of precise synthesis of each linkage are established.

A class of singularly perturbed initial boundary value problems for reaction diffusion equations in a part of domain are considered.

Like most books on control system design, this book presents tools that can be reduced to mathematical equations: analysis and simulation.

A transient process simulation model with open structure can be obtained from the above voltage equations and magnetic linkage equations.

Linear differential equations are, generally speaking, among the simplest to solve.

The inverse transfer function matrix of attitude dynamics is derived from the hybrid coordinates equations, and its normality is analyzed.

In this paper we consider the singularly perturbed boundary value problems for a class of quasilinear difference equations.

In this paper, two equations which can be used to fit the efficiency curves of coaxial Germanium detectors are introduced.

Many practical problems in engineering and science can be classified as inverse problems of partial differential equations.

This paper establishes an extended system of a system of differential equations by introducing some supplementary variables.

The generalization is quite similar to the corresponding one in the theory of differential equations.

Assume the parameter uncertainty is norm-bounded and the system dynamic is modeled by Ito-type stochastic differential equations.

Engineering geometric constraint problem is equivalent to the problem of solving a set of nonlinear equations substantially.

Based on the force transferring through the components, mathematical equations among the related dimensions are derived.

This paper introduces a simple solution to the homogeneous linear difference equations with constant coefficients.

In natural science and engineering technology, the resolutions of many problems are reduced to solving linear algebraic equations.

Using energy equations the characteristic equations are established, which are the energy characteristic model of gear trains.

In this paper, we consider the anti-periodic boundary value problem for a class of nonlinear second order differential equations.

condition of a kind of jump Vandermonde matrix through linear equations, and recursion formula and the expression of its inverse Matrix.

Matrix differential equations appear frequently in a wide variety of models in physics and engineering.

Time-dependent electromagnetic fields and Maxwell's equations. Electromagnetic waves, emission, absorption, and scattering of radiation.

The dynamic model of the system is developed, and the numerical results of the dynamic equations are obtained.

The oscillation of ordinary differential equation is one of important branche of Differential equations.

The dynamic equations of a human body and a railway vehicle are setup based on study on human body vibration model.

The experimental results were verified by using computer simulation through the rate equations of passively Q-switched laser.

It is only in the mysterious equations of love that any logic or reasons can be found.

There have been many studies of continuous epidemic model through differential equations, but little research on discrete models.

The cut joints constraint equations are founded and a new direct violation correction method is utilized.

A set of non-linear network equations of the multi-branch complex network system is established by using a mesh method.

Separable variables are a special class of first order differential equations, which has a wide range of uses in practice.

The dynamic model of the system was developed, and the numerical results of the dynamic equations were gained.

The researchers showed how the equations describing fluid flow in the rock always contain a mathematical instability.

According to electromagnetic theory of waveguides, the coupled-mode equations for the interactions between the modes are deduced.

As well as the traditional topics of analysis and differential equations, the degree offers newer topics as well.

The approximate numerical method to deal with the coupled mode equations is presented in detail and the rationality of the method is given.

A new pattern of structures, combined isolation structure, was presented, and its vibration and control equations were derived.

It might ask you to just set up the equations, or it might ask you to solve them.

We will focus on some problems for the existence and non-existence of solutions for a class of nonlinear elliptic equations.

It is only in the mysterious equations of love that any logic reason can be found.

The assumed linearity of these equations can be related to the uniformity of space and time.

his primary research is nonlinear partial differential equations , in particular , equations arising from physical and biological sciences.

For the next four decades, no scientist could find an exact solution to the equations.

An example shows that some of these results have important applications in difference equations.

Onedimensional partial parabolic equations can be solved by high precision integration method.

Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations.

The Laguerre spectral and pseudo spectral methods for multiple-dimensional nonlinear partial differential equations are investigated.

These leveraging equations describe how the two types of leverage affect book rates of return on equity.

Many problems in the engineering practice may be transformed as boundary value problems about elliptic differential equations.

spurious unstable modes are avoided by choosing available form of stability equations in the present research.

In this paper, a parallel iterative algorithm for linear equations is given by approximating inverse of a matrix.

The Existence of viscosity solutions of initial problem is proved for second order parabolic equations under certain conditions.

Firstly, the directional-lateral motion equations and transfer functions suited for the certain third generation fighter were deduced .

Moreover, the corresponding velocity equations of hydraulic characteristic flows are deduced with certain simplification.

a scheme of diagrammatic representation of fundamental dependent equations relating thermodynamic functions is suggested.

By iterating or repeating fractal-generating equations many times random outputs create beautiful patterns that are unique yet recognizable.

Then the stress-strain and mixed fluid pressure can be computed by mixed fluid continuity equations and balanced equations.

Method of substitution of constants is an important method for solving nonhomogeneous linear differential equations.

True, he minimises the use of equations and has dreamt up some imaginative metaphors to help make complex notions more accessible.

In this paper, the interval wavelets methods of differential and integral equations are studied and a series of results are obtained.

By these equations, the air temperature within greenhousein different season can be estimated and analyzed.

Two-dimensional, steady-state axial momentum equations were solved with a two-layer turbulence model.

At last, this scheme is used for constructing an adaptive orthonormal collocation method for differential equations.

The stable temperature field of the spindle system was rebuilt through solving the heat balance equations by MATLAB.

We shall now formulate these integral equations and discuss some of their consequences.

In this paper, we discuss the boundary value problems for a class of second order functional differential equations.

Needless to say, the method of integral equations and the Green's function technique can also be developed.

The solution procedures for nonlinear equilibrium equations in structural analysis were systematically summarized.

Secondly, the component structural model is proposed, which consists of dynamic differential equations and interface algebraic equations.