Examples of using Varphi in English and their translations into Russian
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Here φ{\displaystyle\varphi} denotes Euler's totient function.
This is the mathematical coincidence π≈ 4/ φ{\displaystyle\pi\approx 4/{\sqrt{\varphi.
The image φ( T i){\displaystyle\varphi(T_{i})} is called the placement's region.
The point is that Wiener's attack does not apply here because the value of d mod φ( N){\displaystyle d{\bmod{\varphi}}(N)} can be large.
Let φ{\displaystyle\varphi} be a conformal map of W onto the open unit disk.
There is auseful categorical interpretation of the map φ: G→ G ab{\displaystyle\ varphi:G\rightarrow G^{\operatorname{ab.
The rotation φ{\displaystyle\varphi} and the transverse shear force Q x{\displaystyle Q_{x}} are not specified.
The“bandwidth parameter” h controls how fast we try to dampen the function φ^( t){\displaystyle\scriptstyle{\widehat{\varphi}}t.
The Hodge theorem states that φ{\displaystyle\varphi} is an isomorphism of vector spaces.
Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function φ{\displaystyle\varphi} the Greek letter phi.
The golden ratio φ{\displaystyle\varphi} may be defined as the root of the polynomial x 2- x- 1{\displaystyle x^{2}-x-1.
In LaTeX, the math symbols are\Phi( Φ{\displaystyle\Phi\,\!}),\phi( ϕ{\displaystyle\phi\,\!}), and\varphi φ{\displaystyle\varphi\,\!
Furthermore, there is often no need to compute φ{\displaystyle\varphi} directly during computation, as is the case with support vector machines.
Common knowledge is thought of as the fixed point of the"equation" C G φ φ∧ E G( C G φ){\displaystyle C_{G}\varphi=\varphi\wedge E_{ G} C_{ G}\ varphi.
The states φ 0( mod 2 π){\displaystyle\varphi =0\,({\textrm{mod}}\, 2\pi)} are known as vacuum states as they are constant solutions of zero energy.
Clamped beams: The displacement w{\displaystyle w} andthe rotation φ{\displaystyle\varphi} are specified to be zero at the clamped end.
There is φ( 2)1{\displaystyle\varphi(2)=1} character modulo 2: Note that χ is wholly determined by χ(1) since 1 generates the group of units modulo 2.
Although the attacker does not know φ( N){\displaystyle\varphi(N)}, he may use N{\displaystyle N} to approximate it.
One difficulty with applying this inversion formula is that it leadsto a diverging integral, since the estimate φ^( t){\displaystyle\scriptstyle{\widehat{\varphi}}(t)} is unreliable for large t's.
On the other hand,an explicit representation for φ{\displaystyle\varphi} is not necessary, as long as V{\displaystyle{\mathcal{V}}} is an inner product space.
Some algorithms that depend on arbitrary relationships in the native space X{\displaystyle{\mathcal{X}}} would, in fact,have a linear interpretation in a different setting: the range space of φ{\displaystyle\varphi.
The gravitational potential created by the mass m{\displaystyle m},at this length is φ G m/ l{\displaystyle\varphi=Gm/l}, where G{\displaystyle G} is the constant of universal gravitation.
There are φ( 6)2{\displaystyle\varphi(6)=2} characters modulo 6: Note that χ is wholly determined by χ(5) since 5 generates the group of units modulo 6.
In every one of the above-mentioned works, some restrictions on the functions φ( x){\displaystyle\varphi(x)} and f( x){\displaystyle f(x)} were imposed.
Poisson's equation is Δ φ f{\displaystyle\Delta\varphi=f} where Δ{\displaystyle\Delta} is the Laplace operator, and f{\displaystyle f} and φ{\displaystyle\varphi} are real or complex-valued functions on a manifold.
Choosing large public key:Replace e{\displaystyle e} by e′{\displaystyle e'}, where e′ e+ k⋅ φ( N){\displaystyle e'=e+k\cdot\varphi(N)} for some large of k{\displaystyle k.
In the Kepler triangle with sides 1, φ,φ,{\displaystyle 1,{\sqrt{\varphi}},\varphi,} consider: the circle that circumscribes it, and a square with side equal to the middle-sized edge of the triangle.
In particular when h is small, then ψh(t) will be approximately one for alarge range of t's, which means that φ^( t){\displaystyle\scriptstyle{\widehat{\varphi}}(t)} remains practically unaltered in the most important region of t's.
The alternative follows from Mercer's theorem: an implicitly defined function φ{\displaystyle\varphi} exists whenever the space X{\displaystyle{\mathcal{X}}} can be equipped with a suitable measure ensuring the function k{\displaystyle k} satisfies Mercer's condition.
In the above, the value m is a free parameter, usually taken to be real, 0≤ m≤ 1, and so the elliptic functions can be thought of as beinggiven by two variables, the amplitude φ{\displaystyle\varphi} and the parameter m.