'definite relations' is correct and can be used in written English.
You can use it to refer to relationships that are specific, definite, and certain. For example, "The mayor and city council have definite relations when it comes to creating and enforcing laws."
None of these measurements are static, but their changes bear definite relations to changes in the wind, the depth of the water, and many other matters.
The upwelling of deep water, rising to displace the upper layers, bears certain definite relations to the pattern of the currents.
There are definite relations between the reductive peak value of Au and the concentration of dsDNA.
Drug-related eruptions were defined as skin reactions with a probable or definite relation to the use of TNF-α-blocking agents, based on a time relation with the administration of the agent, morphological pattern, and/or histological information.
Furthermore, doctors will tell you that there is a definite relation between anger and ulcers.
In definite relation to the increased difficulties attendant upon the practice of murder, music has become more and more sadistic.
The definite relation that may or may not exist between an object and a set is called the membership relation.
Best results are apparently obtained when the air swirl bears a definite relation to the fuel-injection rate.
Divorce: Finding a Figure The insight of mediation is that neither party's satisfaction bears a definite relation to the settlement's dollar amount, and therefore the mediator should not focus on a monetary figure -- as litigators do -- but on how money figures.
I'm a great believer in salt, and I hate this government anti-salt thing: a decent sea salt contains lots of good minerals such as magnesium and zinc, which women are often lacking in, and if you talk to a doctor who actually knows their stuff, there is no definite relation between high blood pressure and salt.
All such studies clearly revealed specific results of exertion and disclosed evidence for the burning of food materials (metabolites); taken by themselves, the data provided a picture of the human organism as an energy-converting system and showed a definite relation of this process to energetic (work) performance.
