generalized versions

USAGE SUMMARY

The phrase "generalized versions" is correct and usable in written English.
It can be used when referring to broader or more inclusive forms of specific concepts, ideas, or items. Example: "The study presents generalized versions of the theories to make them applicable across various disciplines."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

38 human-written examples

In many generalizations, approximate convexity and invexity are two significant generalized versions of convexity, which tried to weaken the convexity hypotheses thus to study the relations between vector variational-like inequalities and multi-objective programming problems.

Journal of Inequalities and Applications

Among other things, we generalize a recent result of Altun, Sola and Simsek, and we give some generalized versions of the fixed point theorem of Matthews, and the main result of Ćirić is also recovered.

Fixed Point Theory and Applications

Results show that single RF chain schemes have better performance while generalized versions have better spectral efficiency.

Ingeniería, Investigación y Tecnología

We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramér-von Mises tests.

Yale University

Using a particular kernel function, the classes based on integrated measures provide generalized versions of the classical Box Pierce/Ljung Box test statistics, which are popular procedures among practitioners.

Computers & Operations Research

We also show that no deterministic on-line algorithm can have competitive ratio better than 3. Then we study generalized versions of our model, these are the case of an asymmetric setup cost function and the case of multiple SEs.

Theoretical Computer Science

Human-verified similar examples from authoritative sources

Similar Expressions

22 human-written examples

It is shown that the proposed adjacency is a generalized version of the traditional adjacency.

Journal of Manufacturing Systems

A generalized version of logistic function was successfully used for modelling the oxidation curve of liposomes.

Food Chemistry

A unique contribution of the paper is formulating a generalized version of the poverty segregation curve.

World Development

Tolerance neurons form a generalized version of intervals (sets) arising in a form of fuzzy intervals.

Neurocomputing

While the Riemann hypothesis does not have very many applications, the generalized version, if true, would solve hundreds of important mathematical problems.

The New York Times - Science

Expert writing Tips

Best practice

When using "generalized versions", ensure the context clearly indicates what the original form is and how the generalized version expands upon it. This clarifies the relationship and avoids ambiguity.

Common error

Avoid using "generalized versions" without providing specific details about the generalization. Vague references can make your writing less informative and harder to understand.

Linguistic Context

The phrase "generalized versions" typically functions as a noun phrase, often used as the subject or object of a sentence or clause. It describes forms or adaptations that have been broadened or extended from an original concept or model. Ludwig AI confirms this usage through its examples.

Expression frequency: Common

Frequent in

Science

62%

Academia

30%

Formal & Business

8%

Less common in

News & Media

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "generalized versions" is a noun phrase commonly used in academic and scientific contexts to describe adaptations or expansions of original concepts, models, or methods. As Ludwig AI points out, it signifies an evolution or broadening of scope. When using this phrase, ensure you clearly define the original form and the specific aspects that have been generalized to avoid vagueness. Alternatives like "extended forms" or "broader interpretations" may also be suitable depending on the specific context. This phrase is considered grammatically correct and sees frequent use in scientific literature.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

generalized forms

Replaces "versions" with "forms" maintaining a similar meaning.

extended forms

Focuses on the act of making something longer or more comprehensive.

broader interpretations

Emphasizes the wider scope of understanding or meaning.

modified iterations

Highlights changes and adaptations from an original form.

adapted variants

Suggests a form that has been altered to suit a new purpose or condition.

expanded renditions

Implies a more detailed or elaborate presentation.

revised editions

Highlights that the forms are edited or modified.

advanced implementations

Focuses on progress to higher or more developed stage.

enhanced modifications

Stresses improvements made to the original.

comprehensive adaptations

Emphasizes thoroughness and inclusivity in the changes.

FAQs

How do I use "generalized versions" in a sentence?

You can use "generalized versions" to describe adaptations or expansions of existing concepts, models, or methods. For example, "The paper presents "generalized versions" of the original algorithm to handle more complex data sets."

What can I say instead of "generalized versions"?

Alternatives include "extended forms", "broader interpretations", or "modified iterations", depending on the specific context.

When is it appropriate to use "generalized versions" in academic writing?

It's appropriate when discussing adaptations or extensions of established theories, models, or methods. Be sure to specify what aspects have been generalized or extended.

What is the difference between "generalized versions" and "revised editions"?

"Generalized versions" typically refer to adaptations that expand the scope or applicability of something, while "revised editions" usually imply updates or corrections within the same scope.