Search results

• Parallel external memory
  [math]\displaystyle{ M \lt B^{O(1)} }[/math] the I/O complexity is then: [math]\displaystyle{ O \left ( \frac{N}{PB} \log_{M/B} \frac{N}{B} \right ) }[/math]
  16 KB (1,823 words) - 18:07, 8 February 2024
• List of integrals of rational functions (section Integrands of the form (A + B x) (a + b x)m (c + d x)n (e + f x)p)
  \int (A\,a\,d\,f(m+n+p+2)-B (b\,c\,e\,m+a(d\,e(n+1)+c\,f(p+1)))+(A\,b\,d\,f(m+n+p+2)+B (a\,d\,f\,m-b(d\,e(m+n+1)+c\,f(m+p+1)))) x)(a+b\,x)^{m-1} (c+d\,x)^n(e+f\
  28 KB (6,644 words) - 07:43, 27 June 2023
• Modular arithmetic
  uint64_t b, uint64_t m) { long double x; uint64_t c; int64_t r; if (a >= m) a %= m; if (b >= m) b %= m; x = a; c = x * b / m; r = (int64_t)(a * b - c * m) %
  31 KB (3,899 words) - 23:05, 6 February 2024
• Bilinear map
  and for any m in M, n ↦ B(m, n) is an S-module homomorphism. This satisfies B(r ⋅ m, n) = r ⋅ B(m, n) B(m, n ⋅ s) = B(m, n) ⋅ s for all m in M, n in N, r
  9 KB (1,482 words) - 22:45, 6 February 2024
• Einstein–Infeld–Hoffmann equations
  \vec{a}_A & = \sum_{B \not = A} \frac{G m_B \vec{n}_{BA}}{r_{AB}^2} \\ & {} \quad{} + \frac{1}{c^2} \sum_{B \not = A} \frac{G m_B \vec{n}_{BA}}{r_{AB}^2}
  4 KB (600 words) - 23:18, 6 March 2023
• Confluent hypergeometric function
  \begin{align} z\frac{dM}{dz} = z\frac{a}{b}M(a+,b+) &=a(M(a+)-M)\\ &=(b-1)(M(b-)-M)\\ &=(b-a)M(a-)+(a-b+z)M\\ &=z(a-b)M(b+)/b +zM\\ \end{align} }[/math]
  24 KB (3,688 words) - 14:43, 6 February 2024
• Median (geometry)
  [math]\displaystyle{ a, b, c }[/math] and medians [math]\displaystyle{ m_a, m_b, m_c, }[/math] [math]\displaystyle{ \tfrac{3}{4}(a+b+c) \lt m_a + m_b + m_c \lt a+b+c \quad
  9 KB (1,317 words) - 05:56, 27 June 2023
• Caustic (mathematics)
  (π ○ i) : L ↪ M ↠ B; where i : L ↪ M is a Lagrangian immersion of a Lagrangian submanifold L into a symplectic manifold M, and π : M ↠ B is a Lagrangian
  5 KB (742 words) - 16:41, 6 February 2024
• Multiset
  In the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1. In the multiset {a, a, a, b, b, b}, a and b both have multiplicity
  36 KB (4,512 words) - 18:21, 6 February 2024
• Bernoulli number
  \frac{1}{m + 1} \sum_{k=0}^m \binom{m + 1}{k} B^+_k n^{m + 1 - k} = m! \sum_{k=0}^m \frac{B^+_k n^{m + 1 - k}}{k! (m+1-k)!} , }[/math] where (m + 1k) denotes
  92 KB (11,334 words) - 21:09, 8 February 2024
• Kaprekar number (section b = m2k + m2 − m + 1 and p = mn + m − 1)
  \begin{align} n^2 & = (b^p + m)^2 \\ & = b^{2p} + 2mb^p + m^2 \\ & = (b^p + 2m)b^p + m^2 \\ \end{align} }[/math] and [math]\displaystyle{ \beta = m^2 }[/math],
  17 KB (2,733 words) - 15:22, 6 February 2024
• Hypergeometric function
  [math]\displaystyle{ \lim_{c\to -m}\frac{{}_2F_1(a,b;c;z)}{\Gamma(c)}=\frac{(a)_{m+1}(b)_{m+1}}{(m+1)!}z^{m+1}{}_2F_1(a+m+1,b+m+1;m+2;z) }[/math] 2F1(z) is the
  39 KB (5,592 words) - 16:51, 6 February 2024
• Many-one reduction (section Many-one completeness (m-completeness))
  [math]\displaystyle{ B }[/math] and write [math]\displaystyle{ A \leq_1 B. }[/math] If [math]\displaystyle{ A \leq_{\mathrm{m}} B \, \mathrm{and} \, B \leq_{\mathrm{m}}
  7 KB (983 words) - 03:13, 27 October 2021
• Cancellation property
  in a magma (M, ∗) has the left cancellation property (or is left-cancellative) if for all b and c in M, a ∗ b = a ∗ c always implies that b = c. An element
  7 KB (710 words) - 17:50, 6 February 2024
• Newman–Penrose formalism
  [math]\displaystyle{ g_{ab}=-l_a n_b - n_a l_b +m_a \bar{m}_b +\bar{m}_a m_b\,, \quad g^{ab}=-l^a n^b - n^a l^b +m^a \bar{m}^b +\bar{m}^a m^b\,. }[/math] In keeping
  29 KB (4,824 words) - 19:29, 6 February 2024
• Coordinate vector
  &= \lbrack M\rbrack_C^B \lbrack M\rbrack_B^C = \lbrack M\rbrack_C^C \\[3pt] &= \lbrack M\rbrack_B^C \lbrack M\rbrack_C^B = \lbrack M\rbrack_B^B \end{align}
  7 KB (1,176 words) - 19:54, 8 February 2024
• Beta function
  \Beta(a,b)} \\ I_x(a,b+1) &= I_x(a,b)+\frac{x^a(1-x)^b}{b \Beta(a,b)} \\ \int B(x;a,b) \mathrm{d}x &= x B(x; a, b) - B(x; a+1, b) \\ \Beta(x;a,b)&=(-1)^{a}
  19 KB (2,980 words) - 00:08, 7 February 2024
• Five lemma
  there exists b′ in B′ with s(b′) = c′ − n(c). Since m is surjective, we can find b in B such that b′ = m(b). By commutativity, n(g(b)) = s(m(b)) = c′ − n(c)
  7 KB (920 words) - 00:08, 7 March 2023
• Perfect matrix
  equal to b, where b ≥ 2 there exists no row of the (m − k)-by-k submatrix formed by the rows not included in K with a row sum greater than b. The following
  1 KB (151 words) - 22:31, 6 March 2023
• Summation by parts
  \sum_{n=N}^{M-1} B_n (a_{n+1} - a_n)\\ &= (a_M-a) B_M - (a_N-a) B_N + a(B_M - B_N) - \sum_{n=N}^{M-1} B_n (a_{n+1} - a_n), \end{align} }[/math] where a is
  9 KB (1,660 words) - 21:12, 6 February 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)