# monotonic

## Definitions

• WordNet 3.6
• adj monotonic sounded or spoken in a tone unvarying in pitch "the owl's faint monotonous hooting"
• adj monotonic of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value
• ***
Webster's Revised Unabridged Dictionary
• Monotonic (Math) Always increasing or always decreasing, as the value of the independent variable increases; -- of a function.
• Monotonic Of, pertaining to, or uttered in, a monotone; monotonous. "Monotonical declamation."
• ***
Century Dictionary and Cyclopedia
• monotonic Monotonous.
• monotonic Pertaining to a monotone; uttered in a monotone; also, capable of producing but a single tone, as a drum.
• monotonic Homogeneous; in marine zoölogy an aggregation of organisms is said to be monotonic if some one species, genus, or family forms more than one half of the total volume.
• ***
Chambers's Twentieth Century Dictionary
• adjs Monotonic uttered in one unvaried tone: marked by dull uniformity
• ***

## Quotations

• Mark Twain
“The human race was always interesting and we know by its past that it will always continue so, monotonously.”
• Mahatma Gandhi
“Monotony is the law of nature. Look at the monotonous manner in which the sun rises. The monotony of necessary occupation is exhilarating and life giving.”
• James Russell Lowell
“There is nothing so desperately monotonous as the sea, and I no longer wonder at the cruelty of pirates.”
• Mason Cooley
“The routines of tourism are even more monotonous than those of daily life.”

## Etymology

Chambers's Twentieth Century Dictionary
Gr. monos, alone, tonos, a tone.

## Usage

### In literature:

From the horse-stalls came the steady monotonous grind of the animals at feed.
"Ben Blair" by Will Lillibridge
His own was sometimes monotonous and a little dull.
"The Helpmate" by May Sinclair
She hardly recognized his voice, so gently monotonous were his phrases.
"Visionaries" by James Huneker
It appeared to me rather slow and monotonous.
"Round About the Carpathians" by Andrew F. Crosse
"Under Handicap" by Jackson Gregory
The interviews between Jeanie Trim and Kinnaird were not monotonous.
"A Dozen Ways Of Love" by Lily Dougall
The proceedings opened with the chairman holding forth in monotone German.
"Sixteen Months in Four German Prisons" by Henry Charles Mahoney
But my attention was attracted by a slight noise, a kind of soft and monotonous murmur, coming from the altar.
"In the Field (1914-1915)" by Marcel Dupont
Monotonous singing sounded from the roofs of the big house, from caves, and from slopes leading up to them.
"The Delight Makers" by Adolf Bandelier
When at last the two had the deck to themselves and Manhattan had become a shadowy and ragged monotone, she turned and smiled.
"The Lighted Match" by Charles Neville Buck
The view from the window was, on the whole, rather monotonous.
"The Land of Promise" by D. Torbett
My days have been sad and monotonous, but they are gone, and their flight brings me nearer to my happiness.
"The Continental Monthly, Volume V. Issue I" by Various
He still loved it, but certainty is monotonous, and his eyes wandered to other objects.
"The Damsel and the Sage" by Elinor Glyn
The mock-bird, perched upon the highest limb, was mimicking the monotonous tones of the parrot.
"The Rifle Rangers" by Captain Mayne Reid
This is especially true of a monotonous tone.
"Pushing to the Front" by Orison Swett Marden
The faint jarring of the wood, so monotonous and so persistent, never ceased.
"Before the Dawn" by Joseph Alexander Altsheler
It is the idea of the monotonous uniformity with which the Reviews will eulogize me.
"The Continental Monthly, Vol. 6, No 3, September 1864" by Various
Then, when life seemed to her unbearably monotonous, she went to a week-end party at the Brassfields' house in the country.
"Sacrifice" by Stephen French Whitman
In places this extended surface presents a somewhat monotonous aspect, though it is not so everywhere.
"The Death Shot" by Mayne Reid
It is its duty to be dull, it is monotonous by law: it cannot be correct and yet amusing.
"Lectures on Architecture and Painting" by John Ruskin
***

### In poetry:

Monotonously rolled
On the hills the broom
"Aftermath of Mining Days" by Clark Ashton Smith
Yea, and cold and heat,
And the sun and stars and moon,
Sea with her monotonous tune,
Rain and hail and sleet,
"St. Francis and the Birds" by Katharine Tynan
When that hour comes when I shall sit alone,
And ponder on the things that were, but are no more,
The while the weird night-breeze's dirge-like monotone
Is sobbing fitful anthems round the door;
"The Helping Hand" by John O Brien
It was a simple tale, a monotone:
She climbed one sunny hill, gazed once abroad,
Then wandered down, to pace a dreary plain;
Alas! how many such are told by night,
In fisher-cottages along the shore!
"A Story of the Sea-Shore" by George MacDonald
Yet, on and on till the land shall die,
And nothing save the sea and sky
Shall come within my vision's range;
Not e'en a bird to mar or change
E'en for a moment's space of time
The all monotonous, sublime!
"Valedictory On Leaving San Francisco, California." by James Madison Bell
Rich lay the sunlight far and near;
Through the great palms it shone;
Whispered the breeze upon his ear
Its tender monotone,
As, the fair fields the Lord had blest among,
Rose through the calm, sweet air the lone man's even-song.
"The Meditation Of Isaac" by Samuel John Stone

### In news:

'Game of Thrones': Great story brought down by monotonous voice-acting, weak gameplay.
Baseball players and coaches utter the phrase so often it becomes monotonous, even trite.
If a work place turns monotonous without giving compliments to its employees, productivity can suffer.
A Monotonic Cyborg Learns to Say 'Pantsuit'.
If you're wondering why a monotone man in a classroom keeps spouting the name "Bueller" in succession despite the man's clear absence, we've finally got an answer: he's busy on the set of 'Modern Family' season 4.
Jarol Boan, MD, MPH, gives patient Gregory Grogan some educational materials on diet choices -- he had a monotonous diet and needed variety in his food choices.
The essential assumption is that sensor distortions are strictly monotonous.
At Camp 14, prison life was a monotonous routine of hunger and hard work.
What I had anticipated would be a mundane, tedious and monotonous experience turned out to be interesting and very informative.
In the third webisode, the 'Love Story' singer gushes about how true love can light up even the most monotonous of days.
Parkinson 's changes voices into monotones, slows speech, robs facial expression and restricts the ability to blink.
The singing sounds very '90s — very dated — and it's also a little monotone.
The problem is that it's monotonously competent.
At the Great Escape yesterday, I wanted to see how many trips you had to take on The Comet before it started getting monotonous.
Shame cripples us and keeps us living a mundane, fruitless and monotonous life.
***

### In science:

In we used Loewner’s characterization of operator monotone functions, which shows in particular that an operator monotone function on (0, ∞) extends to an analytic function on a domain U containing (0, ∞) as in [9, p. 541].
Integrable operators and the squares of Hankel operators
The situation is slightly more complicated when p > 1 2 and G is not itself even, since the conditioned random-cluster measure used in Theorems 3.2 and 3.3 is neither monotone nor anti-monotone.
Random even graphs
We call µ monotone (respectively, anti-monotone ) if µ(1e | ξe ) is non-decreasing (respectively, non-increasing) in ξ ∈ Ω.
Random even graphs
It is standard that cftp may be used to sample from µ if µ is monotone (see [21, 28]), and it is explained in how to adapt this when µ is anti-monotone.
Random even graphs
The above recipe is exactly that of when µ is monotone, and that of when µ is anti-monotone.
Random even graphs
Suppose that Eσ (k) continuously and strictly monotonically increases from some value less than εf at k = 0 to +∞ at k = k⋆ and that it continuously and strictly monotonically increases from −∞ at k = k⋆ to +∞ at k = +∞.
On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions
We point out that since Φ+ (x) is a monotonically increasing and Φ− (x) a monotonically decreasing function of x (both functions are positive for x > 0), it follows that the RHS of Eq. (6.82) is a monotonically decreasing function of x.
On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions
Since G1 is a monotone class, it’s easy to check G2 is a monotone class.
Constituting Atoms of a $\sigma$ Algebra via Its Generator
The monotonicity of bξ and bγ follows from the branching process interpretations in Remark 3.5 together with the stochastic monotonicity Theorem 5.2(ii) (for both S and S − 1) and Theorem 4.5.
Random graphs with forbidden vertex degrees
The function r(x) can be chosen so that it is only eventually monotone increasing, and in the case where we are only considering a ﬁnite collection of random variables {Xi} it is suﬃcient to show that the chosen function is asymptotically equivalent to a monotone increasing function.
On Sums of Conditionally Independent Subexponential Random Variables
Then dim(X ) = 1 will follow from the fact that X is an inverse limit of one dimensional spaces. α , it suﬃces to ensure that each σα+1 For monotonicity of the σβ is monotone.
Aronszajn Compacta
Let f : Vn → R be a function functions that are -far from monotone are rejected with probability at least 2 that is -far from monotone.
Transitive-Closure Spanners
We have opted for Theorem 2.1 since it extensively uses the monotonicity (or “sandwiched ” monotonicity) to establish the stability of the converging eigenvalues and this ﬁts neatly into the perturbation framework of .
Relative convergence estimates for the spectral asymptotic in the Large Coupling Limit
T . hq − q ′ , r − r ′i ≥ 0, An operator T : X ⇒ X ∗ is maximal monotone (in X × X ∗ ) if it is monotone and maximal (whit respect to the inclusion) in the family of monotone operators of X into X ∗ .
On Gossez type (D) maximal monotone operators
An operator T : X ∗∗ ⇒ X ∗ is maximal monotone (in X ∗∗ × X ∗ ) if it is monotone and maximal (with respect to the inclusion) in the family of monotone operators of X ∗∗ into X ∗ .
On Gossez type (D) maximal monotone operators
***