the equivalent problem of

USAGE SUMMARY

The phrase "the equivalent problem of" is correct and usable in written English.
It can be used when discussing a problem that has a similar nature or structure to another problem, often in mathematical or theoretical contexts. Example: "In order to solve the complex equation, we first need to address the equivalent problem of simplifying the variables involved."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

The algorithm serves also to solve the equivalent problem of computing invariant tori and action-angle variables for a one-dimensional time-dependent numerically specified Hamiltonian (or a two-dimensional time-independent Hamiltonian).

Journal of Computational Physics

The equivalent problem of the original one is approximated to a new convex problem, which is solved efficiently by the dual-based decomposition approach.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

Most previous systems for adaptive drawing [Hop97] state the viewpoint problem in terms of camera location, but for convenience in our case we consider instead the mathematically equivalent problem of an object position with respect to a fixed camera.

Stanford University

Thus, in this paper, the generalized sidelobe canceler (GSC) structure is used, which can be thought as an updating rule of the equivalent problem without constraints.

EURASIP Journal on Wireless Communications and Networking

For example, while the S measures consider the differences in eigenstructure between two matrices, the RS procedure focuses on the related, but not equivalent problem of the differences between the evolutionary responses generated by these matrices.

BMC Evolutionary Biology

Nevertheless, we note that the equivalent problem (see [26], p. 67) for the definition of equivalent problems), obtained considering the change of variables P S, DT ( k ) = ( 2 b S, DT ( k ) − 1 ) / η S, D ( k ), where b S, DT ( k ) = lo g 2 1 + P S, DT ( k ) η S, D ( k ), is a convex optimization problem.

EURASIP Journal on Advances in Signal Processing

In such a way, we have transformed the problem of finding a control u(t) for the system (2.30) steering from the start point (2.31) to the final point (2.32), into an equivalent problem of finding a control v t) for system (2.35) steering from the start point (2.36) to the final point (2.37), which has already been explained in Sect.

Advances in Difference Equations

Hence, by denoting f i,j =π i p i,j, we can get the equivalent optimization problem of P- 1 as: begin{array}{*{20}l} textrm{P-}textbf{2}: quad max &;;;sumlimits_{i = 0}^{N} {sumlimits_{j = 0}^{i} {{f_{i,j}}{u_{i-j}}} } end{array} (12a).

EURASIP Journal on Wireless Communications and Networking

In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist.

Journal of Inequalities and Applications

The organization of this paper is as follows: In a preliminary section, Section 2, we describe the appropriate functional setting for the study of the problem (1.1) or (1.2), including the definition of an equivalent problem.

Boundary Value Problems

The problem of the global phase synchronization for the complex networks is equivalent to the problem of the asymptotical stability for the corresponding error dynamical networks.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "the equivalent problem of", ensure that the equivalence is clearly defined and relevant to the context. Providing a brief explanation of why the problems are considered equivalent can enhance clarity.

Common error

Avoid using "the equivalent problem of" if the problems are only superficially similar. A false equivalence can mislead your audience and weaken your argument.

Linguistic Context

The phrase "the equivalent problem of" functions as a prepositional phrase that introduces a problem which is mathematically, logically, or computationally similar to another, as shown in the Ludwig examples. It is typically used to reframe a complex issue in a more accessible or solvable way.

Expression frequency: Rare

Frequent in

Science

66%

Academia

33%

News & Media

0%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "the equivalent problem of" is a prepositional phrase used to highlight the similarity between two distinct problems. As Ludwig AI confirms, this phrase is grammatically correct and finds its primary use in scientific and academic contexts. While its frequency is rare, using this phrase effectively requires ensuring that the equivalence is clearly defined. Remember that using alternative phrasing like "the analogous problem of" or "the related problem of" can, in certain situations, be more appropriate depending on context. When you apply it, think of it as creating a link between two situations that can use the same solving methods, and remember to be accurate in your assertion that there is, in fact, an equivalence.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the analogous problem of

Replaces 'equivalent' with 'analogous', implying a similarity rather than exact equivalence.

the isomorphic problem of

Emphasizes a structural equivalence, particularly in mathematical or logical contexts.

the corresponding problem of

Replaces 'equivalent' with 'corresponding', highlighting a direct relationship or match.

the parallel problem of

Substitutes 'equivalent' with 'parallel', suggesting problems that run alongside each other.

the interchangeable problem of

Indicates that the two problems can be swapped without affecting the outcome.

the twin problem of

Implies that both problems are very similar and can be treated together.

the related problem of

Uses 'related' instead of 'equivalent', indicating a connection but not necessarily identity.

the mirrored problem of

Suggests a problem that reflects another in its structure or solution.

the alternative formulation of the problem of

Highlights that it's a different way of stating the same underlying issue.

the alternative representation of the problem of

Focuses on a different way of expressing the same problem.

FAQs

How can I use "the equivalent problem of" in a sentence?

Use "the equivalent problem of" to introduce a problem that can be solved using the same methods or principles as another problem. For example, "Solving this differential equation is the equivalent problem of finding the area under the curve".

What are some alternatives to "the equivalent problem of"?

Alternatives include "the analogous problem of", "the related problem of", or "the parallel problem of", depending on the specific nuance you want to convey.

Is it always accurate to claim two problems are "the equivalent problem of" each other?

No, ensure the problems truly share a mathematical or logical equivalence. Superficial similarities don't warrant using this phrase; instead, consider alternatives like "the related problem of".

In what contexts is "the equivalent problem of" most appropriate?

This phrase is most appropriate in technical fields like mathematics, physics, or computer science, where problems can be rigorously transformed into equivalent forms. It's less suitable for informal or subjective contexts.