For, if so, the path leads through a complex process of parliamentary diplomacy which adds still another dimension to the problem.

The quest for holism leads most anthropologists to study a particular place, problem or phenomenon in detail, using a variety of methods, over a more extensive period than normal in many parts of academia.

Obesity, a serious problem in the western world, leads to higher chances of developing heart disease, diabetes, and many other diseases.

" The Earned income tax credit ( EITC ) is a wage supplement for low-income workers, but the problem is the EITC is not for married couples because they have to combine their wages, which again leads to " the marriage penalty.

In this pamphlet, Bukharin explains and embraces Trotsky's theory of permanent revolution, writing: " The Russian proletariat is confronted more sharply than ever before with the problem of the international revolution … The grand total of relationships which have arisen in Europe leads to this inevitable conclusion.

He also occasionally drinks to excess and has a gambling problem, which leads to the second gag: every time Parker tries to profit from gambling on events he recalls from the future, he picks the losing side ( the lone exception to this is when he gambles to get a bankroll for a charitable purpose ).

Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and others ; and bearing their names in various combinations in various contexts.

This rarely leads to syncope unless the patient has developed true autonomic failure or has an unrelated cardiac problem.

Perturbation theory leads to an expression for the desired solution in terms of a formal power series in some " small " parameter – known as a perturbation series – that quantifies the deviation from the exactly solvable problem.

# Positive affect leads to defocused attention and a more complex cognitive context, increasing the breadth of those elements that are treated as relevant to the problem ;

When T is the empty set, a smallest T-join leads to a solution of the postman problem.

This leads to the problem of transposing an n × m matrix in-place, with O ( 1 ) additional storage or at most storage much less than mn.

But this leads to a substantial problem for Cartesian dualism: How can an immaterial mind cause anything in a material body, and vice-versa?

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense, since it focuses on the lack of justification for either:

" This relates to the problem of depressed wages in female-dominated industries, and whether using such jobs as an equivalent leads to the undervaluing of unpaid work.

This sometimes leads people to believe that eventually, computers will be able to solve any mathematical problem, no matter how complicated ( See Turing Test ).

Duska states that doing so leads to a problem that Ladd overlooks.

Since the entity is separate and distinct from others, if a problem occurs which leads to a massive liability, the individual is protected from losing more than the value of that one property.

Solving an interpolation problem leads to a problem in linear algebra where we have to solve a system of linear equations.

Solving an interpolation problem leads to a problem in linear algebra where we have to solve a matrix.

In his description of the first two, the pious and the impious, Saadia devotes himself in the main to the problem of the sufferings of the pious and the good fortune of the impious, while the description of the last class, that of the contrite, leads him to detailed considerations, based upon the Bible, of repentance, prayer, and other evidences of human piety.

This refutation leads to what later became known as the transformation problem.

The equation is used for the mathematical process of solving the problem.

In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand ; in practice, this is not possible except for very small systems.

Because of the absence of a net force in the azimuthal direction, conservation of angular momentum allows the radial component of this equation to be expressed solely with respect to the radial coordinate, r, and the angular momentum, yielding the radial equation ( a " fictitious one-dimensional problem " with only an r dimension ):

Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

If I told you my son's age, then there would no longer be two unknowns ( variables ), and the problem becomes a linear equation with just one variable, that can be solved as described above.

In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem.

At this stage in the algorithm, it is required that terms with zero-valued coefficients are dropped, so that only binary coefficients equal to one are counted, thus the problem of multiplication or division by zero is not an issue, despite this implication in the factored equation:

Archimedes ' cattle problem ; its solution ( absent from the manuscript ) requires solving an indeterminate quadratic equation ( which reduces to what would later be misnamed Pell's equation ).

For instance, Archimedes ' cattle problem may be solved using a Pell equation, the fundamental solution of which has 206545 digits if written out explicitly.

The first step in solving a quantum chemical problem is usually solving the Schrödinger equation ( or Dirac equation in relativistic quantum chemistry ) with the electronic molecular Hamiltonian.

The equation alone does not specify a solution ; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the value and velocity of the wave.

The solution of the initial-value problem for the wave equation in three space dimensions can be obtained from the solution for a spherical wave.

These formulas provide the solution for the initial-value problem for the wave equation.

One method to solve the initial value problem ( with the initial values as posed above ) is to take advantage of the property of the wave equation that its solutions obey causality.

He shows how to convert a problem stated verbally into a system of polynomial equations ( up to 14th order ), by using up to four unknowns: 天Heaven, 地Earth, 人Man, 物Matter, and then how to reduce the system to a single polynomial equation in one unknown by sucessive elimination of unknowns.

The Dirichlet problem for Laplace's equation consists of finding a solution on some domain such that on the boundary of is equal to some given function.

Since the Laplace operator appears in the heat equation, one physical interpretation of this problem is as follows: fix the temperature on the boundary of the domain according to the given specification of the boundary condition.

replace p by its operator equivalent, expand the square root in an infinite series of derivative operators, set up an eigenvalue problem, then solve the equation formally by iterations.

His most original contribution is the elementary solution he provided for the Riemann – Hilbert problem f < sub >+</ sub > = g f < sub >−</ sub > about the existence of a differential equation with given monodromy group.

If the problem is cylindrically symmetric, the natural solutions of the paraxial wave equation are Laguerre-Gaussian modes.

The Cauchy – Kowalevski theorem states that the Cauchy problem for any partial differential equation whose coefficients are analytic in the unknown function and its derivatives, has a locally unique analytic solution.