Likewise, if Q ( x, n ) denotes the number of n-free integers ( e. g. 3-free integers being cube-free integers ) between 1 and x, one can show

Likewise, a function is called monotonically decreasing ( also decreasing, or non-increasing ) if, whenever x ≤ y, then f ( x ) ≥ f ( y ), so it reverses the order ( see Figure 2 ).

Likewise, a variable y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x, that is if there exist non-zero constants k and a

Likewise, the question of whether " y is in f ( x )" cannot actually be physically computed.

Likewise, a 3-form f ( x, y, z ) dx ∧ dy ∧ dz represents something that can be integrated over a region of space.

Likewise, if more than one root is known, a linear factor ( x – r ) in one of them ( r ) can be divided out to obtain Q ( x ), and then a linear term in another root, s, can be divided out of Q ( x ), etc.

Likewise, a loop in X is one that is based at x < sub > 0 </ sub >.

Likewise, if x is greater than x_center, we know that all intervals in S_center must begin before x, so we find those intervals that end after x using the list sorted by interval endings.

If the positive axis is also directed rightward, then F is represented by the vector 15 N, and if positive points leftward, then the vector for F is − 15 N. In either case, the magnitude of the vector is 15 N. Likewise, the vector representation of a displacement Δs of 4 meters to the right would be 4 m or − 4 m, and its magnitude would be 4 m regardless.

Likewise the unitary group U ( n ) acts transitively on V < sub > k </ sub >( C < sup > n </ sup >) with stabilizer subgroup U ( n − k ) and the symplectic group Sp ( n ) acts transitively on V < sub > k </ sub >( H < sup > n </ sup >) with stabilizer subgroup Sp ( n − k ).

Likewise, a change in is not necessary to change y, because a change in y could be caused by something implicit in the error term ( or by some other causative explanatory variable included in the model ).

Likewise, we can also express dx in terms of dy and solve for y in terms of θ:

Likewise, a legend from Pont y Wern says that in the 13th or 14th century, the inhabitants of the town of Corwrion watched fairies dancing in a ring around a glow worm every Sunday after church at a place called Pen y Bonc.

Likewise, a change in is not necessary to change y, because a change in y could be caused by something implicit in the error term ( or by some other causative explanatory variable included in the model ).

Likewise the letters g, w, and y are also pronounced a bit harder as a terminal letter of a word with a grave accent mark.

Likewise, he was President of the Coordinating Committee of Agricultural, Trade, Industry and Financial Associations ( In Spanish, Comité Coordinador de Asociaciones Agrícolas, Comerciales, Industriales y Financieras – CACIF -) Director of the Hemispheric Congress of the Chambers of Commerce of Latin America, President of the Permanent Secretary of Chambers of Commerce and Industries of Latin America ( In Spanish, Secretaría Permanente de Cámaras de Comercio e Industrias Latinas – CAMACOL -) and Vice-president of the Permanent Committee of Expositions ( In Spanish, Comité Permantente de Exposiciones – COPEREX -)

Likewise, in the theory of the firm, the lemma gives a similar formulation for the conditional factor demand for each input factor: the derivative of the cost function c ( w, y ) with respect to the factor price:

Likewise, and equally fascinating, is the news that such unlikely synonyms as `` pratakku '', `` sweathruna '', and the tongue-twister `` nnuolapertar-it-vuh-karti-birifw- '' all originated in the same village in Bathar-on-Walli Province and are all used to express sentiments concerning British `` imperialism ''.

Likewise, tan (), tan (), tan (), tan () all satisfy the irreducible polynomial, and so are conjugate algebraic integers.

Likewise a popular Hindu ritual form of worship of North Malabar in Kerala, India is the Tabuh Rah blood offering to Theyyam gods, despite being forbidden in the Vedic philosophy of sattvic Hinduism, Jainism and Buddhism, Theyyam deities are propitiated through the cock sacrifice where the religious cockfight is a religious exercise of offering blood to the Theyyam gods.

Likewise during early spring orchard blossoms, bumblebee populations are limited to only a few queens, and thus are not significant pollinators of early fruit.

Likewise, a type collection might focus on an unusual design feature such as coins with a hole in the middle, coins that are not circular in shape or coins with brockage.

Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can tend to the missing point without tending to any point within the space.

Likewise, all bank accounts are linked to the national identification of the owner ( companies and institutions all have their own identification numbers ).

Likewise, it is unclear whether prophylactic treatment of chronic infection is beneficial in persons who will undergo immunosuppression ( for example, organ transplant recipients ) or in persons who are already immunosuppressed ( for example, those with HIV infection ).

Likewise, other DNA sequences have structural purposes, or are involved in regulating the use of this genetic information.

Likewise, in the sentence, " here, there is a pot ", " here " is the bearer of the property " pot-existence " – this shows that the categories of property and property-bearer are closer to those of a logical predicate and its subject-term, and not to a grammatical predicate and subject.

Likewise, Jesus Christ proclaims in the Gospel of Matthew that one should " Render unto Caesar the things which are Caesar's "; that is at first, literally, the payment of taxes as binding those who use the imperial currency, but more widely interpreted as the offer of obedience and submission to the proclaimed worldly king () in matters not contrary to conscience.

Likewise, in Eastern Christianity, both meat and dairy are prohibited during the Lenten fast, and eggs are seen as " dairy " ( a foodstuff that could be taken from an animal without shedding its blood ).

Likewise, “ where ” and “ when ” question types are very closely linked.

Likewise other popular sizes are 90mm, 120mm and almost every increment in between.

Hiragana is used to write native words for which there are no kanji, including particles such as から kara " from ", and suffixes such as さん ~ san " Mr., Mrs., Miss, Ms ." Likewise, hiragana is used to write words whose kanji form is obscure, not known to the writer or readers, or too formal for the writing purpose.

Likewise, the pitcher is recorded as having given up a hit, a run for each runner that scores including the batter, and an earned run each for the batter and for all baserunners who did not initially reach base on error, except that the runs scored by any runners who reached base while facing an earlier pitcher are charged to that pitcher.

Likewise, schooling attainment is often persistent across generations and families with higher amounts of inheritance are able to acquire and transmit higher amounts of human capital.

Likewise, every hominid species found on the Ringworld is descended from Pak breeders, and all are susceptible to the virus of Tree-of-life.

Likewise, the Al-Masjid al-Nabawi and the city of Medina that surrounds it are also off-limits to those who do not practice Islam.

Likewise, cold-cathode gauges may be reluctant to start at very low pressures, in that the near-absence of a gas makes it difficult to establish an electrode current-in particular in Penning gauges, which use an axially symmetric magnetic field to create path lengths for ions that are of the order of metres.

Likewise outside of that gate are an old house for the servants, a good table, long and divided, and to the east of the principal building, beyond the smaller stable, a solar for the use of the servants.

Likewise, most cases of sciatica and other mechanical radiculopathies are treated by general practitioners, though they may be referred to neurologists or a surgeon ( neurosurgeons or orthopedic surgeons ).

Likewise, the outgoing Eddington – Finkelstein coordinates are obtained by replacing t with u.

Likewise, Kant formulated the nebular hypothesis, according to which the solar system was evolved from a rotating mass of incandescent gas, nearly a half century before its scientific value was made plain by Laplace in his Systeme Du Monde.

Likewise, the ecumenist may become so absorbed in the conflict of the church with the totalitarian state in East Germany, the precarious situation of the church in revolutionary China, and the anguish of the church over apartheid in South Africa that he loses close contact with the parish church in its unspectacular but indispensable ministry of worship, pastoral service and counseling, and Christian nurture for a face-to-face group of individuals.

Likewise, in Toronto, the Prince Edward Viaduct has five lanes of motor traffic, bicycle lanes, and sidewalks on its upper deck ; and a pair of tracks for the Bloor – Danforth subway line on its lower deck.

Likewise, a continuous-time filter is minimum-phase if the zeros of its transfer function fall in the left half of the complex s-plane.

Less formally, the equivalence relation ker on X, takes each function f: X → X to its kernel ker f. Likewise, ker ( ker ) is an equivalence relation on X ^ X.

Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:

Likewise, the map which sends every differentiable manifold to its cotangent bundle and every smooth map to its pullback is a contravariant functor.

Likewise the Ruhr steel industry went into sharp decline, as its prices were undercut by lower-cost suppliers such as Japan.

Likewise, a hyperbola with its transverse axis aligned with the y-axis is called a " North-South opening hyperbola " and has equation

Likewise, the tradename Hycodan points to its relationship with oxycodone ( Percodan ) hy-for hydrogen, per-for oxygen ( as in potassium permanganate ) -- this can also be seen with other trade names for other drugs, like Permonid ( desomorphine ) and Hydal ( hydromorphone ).

Likewise, Mande is often assumed to be the second-most distant branch based on its lack of the noun-class system prototypical of the Niger – Congo family.

Likewise if John says he has a flush, but in fact he does not, his hand is judged on its actual merits, not his verbal declaration.

Likewise, a project slogan is to " break down the bars of ignorance and illiteracy ", because its volunteers aim to continue spreading public literacy and appreciation for the literary heritage just as public libraries began to do in the late 19th century .< ref >

Likewise, the development of a series of hydroelectric plants along the Río Paraná linked Paraguay to its neighbors and provided it access to cherished energy resources and badly needed export revenues.

Likewise, to say of an interface or language feature that it is pythonic is to say that it works well with Python idioms, that its use meshes well with the rest of the language.

Likewise, the Cáin Adomnáin ( Law of Adomnán, Lex Innocentium ) counts Nechtan's brother Bridei among its guarantors.

Likewise, Hawaiian Creole English is commonly referred to by its speakers as " Pidgin ".

Likewise in Cabinda, " Lemba is the spirit of peace, as its name indicates.

Likewise, Manchuria was also governed by military generals until its division into provinces, though some areas of Xinjiang and Manchuria were lost to the Russian Empire in the mid-19th century.