# resolvent

## Definitions

• WordNet 3.6
• n resolvent a liquid substance capable of dissolving other substances "the solvent does not change its state in forming a solution"
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Webster's Revised Unabridged Dictionary
• Resolvent (Math) An equation upon whose solution the solution of a given pproblem depends.
• a Resolvent Having power to resolve; causing solution; solvent.
• Resolvent (Med) That which has power to disperse inflammatory or other tumors; a discutient; anything which aids the absorption of effused products.
• Resolvent That which has the power of resolving, or causing solution; a solvent.
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Century Dictionary and Cyclopedia
• resolvent Having the power to resolve or dissolve; causing solution; solvent.
• n resolvent That which has the power of causing solution.
• n resolvent In medicine, a remedy which causes the resolution of a swelling; a discutient.
• n resolvent In algebra, an equation formed to aid the resolution of a given equation having for its roots known functions of the roots of the given equation. Thus, if x, x′ , x″, x‴ are the roots of a biquadratic, one method of solution begins by solving the cubic whose roots are of the form xx′ + x″ x‴.
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Chambers's Twentieth Century Dictionary
• adj Resolvent having power to resolve
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## Quotations

• Ivan Benson
“Resolve to make each day the very best and don't let anyone get in your way. If they do, step on them.”
• Edward G. Bulwer-Lytton
“Every man who observes vigilantly and resolves steadfastly grows unconsciously into genius.”
• Jean Baudrillard
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
• Dwight L. Moody
“No man can resolve himself into Heaven.”
• Wayne Dyer
“There's no scarcity of opportunity to make a living at what you love. There is only a scarcity of resolve to make it happen.”
• George Eliot
“The sons of Judah have to choose that God may again choose them. The divine principle of our race is action, choice, resolved memory.”

## Etymology

Webster's Revised Unabridged Dictionary
L. resolvens, p. pr. of resolvere,: cf. F. résolvant,. See Resolve
Chambers's Twentieth Century Dictionary
Fr.,—L. resolvĕre, resolutumre-, inten., solvĕre, to loose.

## Usage

### In literature:

I resolved to go to the harbor in search of medical aid.
"Vendetta" by Marie Corelli
"The Ordeal of Richard Feverel, Complete" by George Meredith
He resolved that he would study for this Cambridge Local Examination, and have a try for the scholarship.
"Born in Exile" by George Gissing
Accordingly they resolved to put some men on board a boat, and send them without a herald's wand to the Athenians, as an experiment.
"The History of the Peloponnesian War" by Thucydides
He resolves to propose to a woman, or proposes without resolving, because she is close to him.
"The Eustace Diamonds" by Anthony Trollope
So firmly resolved to have his own way, so thoroughly dauntless, and such a grand beard!
"Springhaven" by R. D. Blackmore
I resolved at length, after many conscientious scruples, to endeavor to satisfy a curiosity excused by its motives.
"The Caxtons, Complete" by Edward Bulwer-Lytton
The step treads firmer; this time it halts more resolved.
"Lucretia, Complete" by Edward Bulwer-Lytton
He resolved that the battle should be fought out, even in the absence of the candidate, and at his own expense.
"My Novel, Complete" by Edward Bulwer-Lytton
You can ill afford my schooling, and I am resolved that at school I will not stay.
"Godolphin, Complete" by Edward Bulwer-Lytton
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### In poetry:

Should he resolve the rainbow's hues,
Into their prime and simple forms,
And thus the charm dispel, unloose,
Which gladdens us, amid the storms?
"How Nature's Beauties Should Be Viewed" by Thomas Frederick Young
If such a dreamy touch should fall,
O turn thee round, resolve the doubt;
My guardian angel will speak out
In that high place, and tell thee all.
"In Memoriam A. H. H.: 44" by Alfred Lord Tennyson
So he resolved at once to train,
And walked and walked with all his main;
For years he paced this mortal earth,
To bring himself to decent girth.
"The Perils of Invisibility" by William Schwenck Gilbert
"This is the man she loves!" said he,
And, searching in the noble face,
"This saint," he cried, "usurps my place!"
"The Lovers" by C J Dennis
Never, on Right and Providence relying,
Fail'd of success, while duteously trying,
He, who resolves and wrestles like a Roman,
Yielding to no man!
"Confidence (In Sapphics.)" by Martin Farquhar Tupper
"Your oath on the four gospels sworn?
What oath can bind resolves unborn?
You lose that far eternal life?
Is it yours to lose? Is it child and wife?
"The Last Word" by Sir Henry Newbolt

### In news:

Yes, it's raining again in Peoria, which is going to cause problems with a full-squad workout, but nothing the Seattle Mariners won't resolve.
Navy works to resolve toilet problems on new carrier.
Pharmaceutical manufacturers look to various solutions to resolve the challenge of poorly soluble drugs.
Whoever gets the nod will have to resolve the church's split on gay marriage.
The Celtics had more energy, more zip, more resolve, and more of just about everything on Friday night.
Defiant Tuheitia lays down challenge to PM as hui resolves to back Maori Council over Mighty River sale.
Both sides in a lawsuit over dredging the Savannah River are set to sit down next week and try to resolve their issues.
A judge asks Twinkies maker Hostess and union lawyers to participate in mediation Tuesday to resolve their differences.
The promoters of Saturday night's middleweight title fight between WBC champion Julio Cesar Chavez Jr and challenger Andy Lee are certain that any controversy surrounding the venue in El Paso, Texas, has been resolved.
The US Environmental Protection Agency has reached a settlement with El Paso Midstream Group, LLC resolving Clean Air Act violations at the Blue Bell Gas Plant near Roosevelt in Duchesne County, Utah.
This New Year's I've resolved to become more in tune with modern young people.
Consider how the NHL dispute was resolved.
Austin says it resolved homeowner's mixed-up water bill.
Special master ordered to resolve UPMC, West Penn legal morass .
One of the first things we resolved to do when we launched "60 Minutes Overtime" was hang out with Morley Safer in that wonderfully cluttered office of his and ask him to tell some stories from his 42 years as a correspondent on "60 Minutes".
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### In science:

Let X be a resolving subcategory of mod R. (1) For each p ∈ Spec R, the subcategory add Xp of mod Rp is resolving. (2) Let Z be a nonempty ﬁnite subset of Spec R.
Classification of resolving subcategories and grade consistent functions
Hence their components α and β in the invariant chart (z , u, v) are differential invariants as well assuming that all vector ﬁelds ¯Z , ¯W resolving relations (36) can be lifted to vector ﬁelds Z, W on M that resolve relations (34) and (35).
Assembling Lie Algebras from Lieons
Our proof of the existence of such a partition relies heavily on a number of properties of s-resolving factor maps; a factor map between two Smale spaces is s-resolving if it is injective on the local stable sets of its domain.
Smale Spaces via Inverse Limits
For each R-module M the smallest resolving subcategory containing M is called the resolving closure of M .
Modules that detect finite homological dimensions
Relation generated by pair of differential expressions one of which depends on spectral parameter in nonlinear manner, non-injective resolvent, generalized resolvent, eigenfunction expansion.
Analogs of generalized resolvents and eigenfunction expansions of relations generated by pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner
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