law of the solution

USAGE SUMMARY

The phrase "law of the solution" is correct and usable in written English.
It can be used in scientific or technical contexts, particularly in chemistry or physics, to refer to a principle governing the behavior of solutions. Example: "According to the law of the solution, the solubility of a substance increases with temperature."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

15 human-written examples

Let pt,x y) be the density of the law of the solution u t,x) of such an equation at points (t,x ∈]0,T]×R3.

Journal of Functional Analysis

We prove that the law of the solution immediately has a density in some Besov space, under some non-degeneracy condition on the driving Lévy process and some very light Hölder-continuity assumptions on the drift and diffusion coefficients.

Journal of Functional Analysis

Using Malliavin Calculus, we give sufficient conditions ensuring the smoothness of the density for the law of the solution to a Stratonovich stochastic differential equation with anticipating initial condition.

Journal of Functional Analysis

We show that the solution is Hölder continuous and the probability law of the solution admits a smooth density with respect to the Lebesgue measure.

Boundary Value Problems

Let us point out the fact that the right-hand side of Equations 22 and 23 depends on the law of the solution; this fact is sometimes referred to as 'the process X ¯ is attracted by its own law'.

The Journal of Mathematical Neuroscience

The fact that the McKean-Vlasov equations involve an expectation of a certain function under the law of the solution of the equation makes them particularly hard to simulate directly.

The Journal of Mathematical Neuroscience

Human-verified similar examples from authoritative sources

Similar Expressions

45 human-written examples

In [5], Malliavin calculus is applied to study the absolute continuity of the law of the solutions of stochastic reaction diffusion equations driven by Poisson random measures.

Advances in Difference Equations

The probability laws of the solutions of such SPDEs are given by Girsanov probability measures, that are non-linearly transformed measures of the probability law of Nelson's free field defined on subspaces of Schwartz space of tempered distributions.

Journal of Functional Analysis

Lyapunov design is used to develop the adaptation law of the proposed solution.

Control Engineering Practice

The rule of law is the solution.

Forbes

The McCain-Feingold law remains part of the solution to our campaign finance problems, not part of the problem.

Huffington Post

Expert writing Tips

Best practice

When using the phrase "law of the solution", ensure that the context is clearly scientific or technical to avoid ambiguity. Be explicit about what aspect of the solution the law governs.

Common error

Avoid applying the "law of the solution" in contexts where a more general principle or heuristic would be more appropriate. This phrase is specific to scenarios with solutions, particularly in chemistry or physics.

Linguistic Context

The phrase "law of the solution" functions as a noun phrase that identifies a specific principle or rule governing the properties or behavior of a solution, often within a scientific context. Ludwig examples show it related to probability, smoothness, and density in relation to equations and processes.

Expression frequency: Common

Frequent in

Science

70%

News & Media

15%

Academia

10%

Less common in

Encyclopedias

3%

Formal & Business

2%

Reference

0%

Ludwig's WRAP-UP

In summary, "law of the solution" is a noun phrase primarily employed in scientific and technical contexts to denote a governing principle for solutions. Ludwig AI analysis shows that it is grammatically sound and often found in academic and scientific literature. While primarily used in Science, it also appears in News & Media. Remember to use this phrase when referring to established principles in chemistry or physics. When writing consider that alternative phrasings like "principle governing the solution" might offer a different emphasis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

principle governing the solution

Focuses on a guiding principle instead of a strict law related to the solution.

rule dictating the solution's behavior

Emphasizes the prescriptive nature of the rule on the solution's behavior.

governing equation for the solution

Highlights the mathematical equation that describes the solution's properties.

solution's underlying principle

Shifts the focus to a foundational principle that influences the solution.

solution's defining characteristic

Focuses on identifying key characteristic of the solution.

regulation affecting the solution

Emphasizes the regulatory effect on the solution instead of its intrinsic properties.

theory behind the solution

Broadens the perspective to the overall theory that explains the solution's behaviour.

solution's standard practice

Refers to conventional methodology for approaching the solution

protocols for the solution

Emphasizes specific steps or processes for handling the solution.

formula governing the solution

Highlights the formula that governs the behaviours in a solution.

FAQs

How is "law of the solution" typically used in scientific writing?

In scientific writing, "law of the solution" refers to a principle that governs the behavior or properties of a solution. For example, it could relate to solubility, concentration gradients, or chemical reactions within the solution.

What are some alternative ways to refer to the "law of the solution"?

Depending on the context, you could use alternatives such as "principle governing the solution", "governing equation for the solution", or "solution's underlying principle".

Is "law of the solution" applicable in non-scientific contexts?

While technically correct, using "law of the solution" outside of scientific or technical discussions may sound unusual or overly formal. It's best reserved for contexts where it accurately describes a governing principle of a solution.

How does "law of the solution" differ from a general "principle"?

A "law" in this context implies a more rigorous, experimentally verified relationship, whereas a "principle" can be a broader, more conceptual guideline. A law of the solution has a mathematical relationship but not necessarily a general principle.