• WordNet 3.6
    • n invariance the nature of a quantity or property or function that remains unchanged when a given transformation is applied to it "the invariance of the configuration under translation"
    • n invariance the quality of being resistant to variation
    • ***
Webster's Revised Unabridged Dictionary
    • n Invariance (Math) The property of remaining invariable under prescribed or implied conditions.
    • ***
Century Dictionary and Cyclopedia
    • n invariance In mathematics, the essential character of invariants; persistence after linear transformation.
    • ***


  • Edgar Allan Poe
    “Beauty of whatever kind, in its supreme development, invariably excites the sensitive soul to tears.”
  • John Wagstaff
    John Wagstaff
    “It is invariable found that a content man is usually a weak one.”
  • Karl Kraus
    “Corruption is worse than prostitution. The latter might endanger the morals of an individual, the former invariably endangers the morals of the entire country.”
  • Henry David Thoreau
    “There is no rule more invariable than that we are paid for our suspicions by finding what we suspect.”
  • Joe Gibbs
    Joe Gibbs
    “People who enjoy what they are doing invariably do it well.”
  • Baltasar Gracian
    “Never open the door to a lesser evil, for other ones invariably slink in after it.”


In literature:

Faith, invariably uniform, cannot be invested by fancy with decorations.
"Recreations of Christopher North, Volume 2" by John Wilson
Early morning invariably found the reunionists strengthening their acquaintance with the ocean.
"Grace Harlowe's Golden Summer" by Jessie Graham Flower
A few are in it as a rule, though not invariably.
"The Governments of Europe" by Frederic Austin Ogg
When, mentally, she compared the two men, the advantage invariably remained with the younger.
"The Easiest Way" by Eugene Walter and Arthur Hornblow
He invariably pitched his tent close to that of the doctor, who regularly dressed it for him.
"Great African Travellers" by W.H.G. Kingston
I invariably answer yes, if used judiciously.
"Your Plants" by James Sheehan
Our conceptions of things that we have not seen are almost invariably wrong.
"The Dog Crusoe and his Master" by R.M. Ballantyne
The phrase, and the smile which invariably accompanied it, were the main stock in trade of the monthly nurse.
"The Brentons" by Anna Chapin Ray
Andrea Amati invariably adopted this form.
"The Violin" by George Hart
For I beg the reader to observe that it is a very deeply-seated characteristic that whatever once takes root in my mind invariably grows.
"Memoirs" by Charles Godfrey Leland
It was always sunny and warm, and I invariably look back on that winter as spent in paradise.
"A Labrador Doctor" by Wilfred Thomason Grenfell
All Geometrae, whose larvae resemble twigs as they stand out from the plant on their anal prolegs, are invariably eaten.
"Contributions to the Theory of Natural Selection" by Alfred Russel Wallace
Others of a composite globular form had invariably been flattened into a slight curve on the side where they had come in contact with the soil.
"Across Unknown South America" by Arnold Henry Savage Landor
They are invariably assigned either to the lowest or topmost shelves of the library, and are, in fact, pariahs.
"The Book-Hunter at Home" by P. B. M. Allan
Eggs or very young animals seem generally to suffer most, but this is not invariably the case.
"On the Origin of Species by Means of Natural Selection" by Charles Darwin
I have tried a fruit-diet on many sickly people, invariably with great advantage.
"A Guide to Health" by Mahatma Gandhi
But Sunday evenings at Highland Hall were almost invariably harrowing.
"Girls of Highland Hall" by Carolyn Watson Rankin
In making these excavations, moreover, they invariably transfer the earth to the main sewers, and form obstructions to the flow.
"Curiosities of Civilization" by Andrew Wynter
The pericardial cavity contains almost invariably an increased quantity of fluid, which may be so great as to impede the heart's action.
"Scurvy Past and Present" by Alfred Fabian Hess
And then the electric light invariably went out.
"The Soul Stealer" by Cyril Arthur Edward Ranger Gull

In poetry:

How comes it, Flora, that, whenever we
Play cards together, you invariably,
However the pack parts,
Still hold the Queen of Hearts?
"The Queen Of Hearts" by Christina Georgina Rossetti
I've often wondered why
Old chaps who choose to die
In evil passes,
Before themselves they slay,
Invariably they
Take off their glasses?
"My Suicide" by Robert W Service
Devote thy heart, to worship and to love
The Lord — let it invariably adhere
Unto the great and glorious God above
With perfect trust, and confidence sincere.
"Advice To Serve God" by Rees Prichard
“That drink’s a curse that hangeth like a leech—
A sad but most indubitable fact is,
Mankind was meant to drink alone, I preach,
And what I preach invariably practise.
"Jimmy Wood" by Barcroft Henry Boake
"My capers," he cried, "are the kind that are
Invariably served with lamb.
Remember, this is a public bar,
And I'll do as I please. If your drink I mar,
I don't give a tinker's ——."
"The Inhuman Wolf And The Lamb Sans Gene" by Guy Wetmore Carryl

In news:

Invariably, I get a positive response.
When mired in melancholia, I often retreat into a self-created fantasy world to find magic and solace, and this world invariably involves an old house.
Invariably you notice someone with a keychain with more store loyalty cards on it than keys.
An invariable, and often feared, consequence of these seasonal indulgences is weight gain.
Whose name these days is invariably preceded by the title "troubled actress" -- is apparently in hot water again.
When I used to make my daily check-in phone call to my dear, now-departed mother, she would invariably say that my call was the first time the phone had rung all day, and that nothing had come in the mail, either.
While taking in both political conventions, I noticed that Republicans invariably use the word "Hispanics" while Democrats are far more likely to say "Latino/a".
" "What ends up happening, invariably, is we both grow.
It seems to be tradition that whenever a major hurricane is bearing down on NYC and the rest of the Eastern seaboard, memes and spoof Twitter accounts will invariable pop up.
When temperatures start flirting with the 50-degree mark, hemlines start rising, and I'm invariably overcome with shock.
With the semester creeping closer and closer and many of us frantically prepping new classes (or doing vital updates to existing classes), the topic of lecture slides invariably crops up.
There's the challenge of keeping hot foods hot and cold foods cold, the matter of transport from production site to consumption site, and dealing with the invariable stressful moment when you realize you forgot the damn corkscrew.
Biopics about artists, from Van Gogh the ear slicer to Basquiat the heroin casualty, invariably show painting as a bleeding art.
For it is the weak, the women, the sick, the elderly and the infants who invariably succumb to what Woodrow Wilson called "the silent, deadly remedy," not self-indulgent dictators like Saddam and Kim Jong-Il or their Praetorian Guard .
SAN DIEGO — Invariably, there is a local reporter who will approach Cole Hamels upon his return to this city, the place where he was born and raised, and ask him about how great it is to pitch at home.

In science:

If X ≤R M is fully invariant, then X ⊙M Y ≤R M is also fully invariant; and if Y ≤R M is fully invariant, then X + Y ⊆ X ⊙M Y .
A Dual Zariski Topology for Modules
This means that γ (H ) leaves the set of invariant elements in S (m) invariant, so if there is only one invariant spinor, γ (H ) maps it to a multiple of itself.
Homogeneous heterotic supergravity solutions with linear dilaton
We notice three types of invariance: scale invariance, translation invariance and invariance under the orthogonal (or unitary) group.
The mean value for infinite volume measures, infinite products and heuristic infinite dimensional Lebesgue measures
Through this concept of order by order gauge invariance, we can decompose any perturbation of Q into the gauge-invariant and gauge-variant parts, as shown in KN2003.11) In terms of these gauge-invariant variables, we can develop the gauge-invariant perturbation theory.
Decomposition of linear metric perturbations on generic background spacetime -- Toward higher-order general-relativistic gauge-invariant perturbation theory
An invariant measure νR for µR induces an invariant measure convergent subsequence is an invariant measure for µ. ∀ X ⊂ P Ck . ν (X ) = νR ( [θ∈T While invariant measures νz are hard to construct explicitly, their existence and certain properties can be established by analyzing hµz i.
Disordered Quantum Walks in one lattice dimension
One is a Mayer-Vietoris type formula for the GW invariants: a formula describing how the GW invariants behave when X degenerates into several components and that allows one to recover the invariants of X from those of the components of the limit.
GW Invariants Relative Normal Crossings Divisors
From expression of an invariant in terms of determinants of negativity fonts, one can easily read how subsystems invariants contribute to the composite system invariant.
Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
In this section, we list those invariants and identify two distinct types of three qubit invariants that constitute a four qubit invariant.
Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
The PBW isomorphism (of vector spaces) is obviously g-invariant, hence it is automatically k-invariant: therefore, β restricts to a k-invariant isomorphism of vector spaces from S(p) to β (S(p)) ⊆ U(g).
Biquantization of symmetric pairs and the quantum shift
We will say that π has almost invariant vectors if for every ε > 0 there exists uε ∈ H such that for every s ∈ S kπ(s)uε − uεk < εkuεk (call such uε ε-invariant). A vector u ∈ H is called invariant if π(g )u = u for every g ∈ Γ.
Random groups and Property (T): \.Zuk's theorem revisited
Note that ε-invariant vectors of π are also ε-invariant of π ′ , so if π has almost invariant vectors, so does π ′ .
Random groups and Property (T): \.Zuk's theorem revisited
Our initial experiments highlighted the power of HR as a tool for automating the discovery of both system and gluing invariants – system invariants introduce requirements of the system while gluing invariants relate the state of the refined model with the state of the abstract model.
Discovery of Invariants through Automated Theory Formation
The Gromov-Witten invariants (GW-invariants) are invariants of symplectic manifolds deduced from the structure of stable pseudoholomorphic maps from noded Riemann surfaces to the symplectic manifold.
Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory
On the other hand, any component C of the maximum locus of the invariant where either the invariant does not begin with Hp,q , for some p, q , or the invariant begins with some Hp,q but no point of C belongs to Σp,q , is a component of A.
Resolution of singularities of pairs preserving semi-simple normal crossings
We call a trace invariant whose associated graph is connected a connected trace invariant (or a single trace invariant).
Universality for Random Tensors