Wikipedia, the world largest encyclopedia contains a lot of knowledge that is expressed as formulae exclusively. Unfortunately, this knowledge is currently not fully accessible by intelligent information retrieval systems. This immense body of knowle...
We reduce Boyer-Finley equation to a family of compatible systems of hydrodynamic type, with characteristic speeds expressed in terms of spaces of rational functions. The systems of hydrodynamic type are then solved by the generalized hodograph met...
A solar radius is a unit of distance, commonly understood as 695,700 km and expressed as R ⊙ {\displaystyle R_{\odot }} , used mostly to express the size
The Mertens function, $M(x) := \sum_{n \leq x} μ(n)$, is defined as the summatory function of the classical Möbius function. The Dirichlet inverse function $g(n) := (ω+1)^{-1}(n)$ is defined in terms of the shifted strongly additive function $ω(n...
Are there difference between those sentences? Alex is getting married next month. Alex will get married next month. Seems that the first one is expressed in present continues, and the s...
Sentiment analysis (SA) plays a vital role in Natural Language Processing (NLP) by ~identifying sentiments expressed in text. Although significant advances have been made in SA for widely spoken languages, low-resource languages such as Hausa face un...
adverb in such a condition or manner, especially as expressed or implied “They're happy and I hope they will remain so ” “ so live your life that old age will bring no regrets” adverb in the way indicated …
Warning: Contents of this paper may be upsetting. Public attitudes towards key societal issues, expressed on online media, are of immense value in policy and reform efforts, yet challenging to understand at scale. We study one such social issue: home...
The roots of a monic polynomial expressed in a Chebyshev basis are known to be the eigenvalues of the so-called colleague matrix, which is a Hessenberg matrix that is the sum of a symmetric tridiagonal matrix and a rank-1 matrix. The rootfinding prob...
The Alexander polynomials Δ_{n,3}(t) and Δ_{n,4}(t) are presented as a sum of the Alexander polynomials Δ_{k,2}(t). These polynomials are also expressed in the form of a sum of Chebyshev polynomials of the second kind. These expansions allow one t...
Mar 25, 2025 · Is it impossible to build the project without changing the code in the dependencies? If your project's dependencies can be expressed as pre-installed libraries, then you could just build …
Dec 4, 2024 · Following Iran’s ballistic missile attack on Israel on October 1, defense analysts have expressed concerns about the U.S. use of about a dozen Standard Missile-3 (SM-3) interceptors. …
Self-ownership, also known as sovereignty of the individual or individual sovereignty, is the concept of property in one's own person, expressed as the
The Beckenstein-Hawking black hole entropy in string theory and its extensions, as expressed in terms of charges that correspond to central extensions of the supersymmetry algebra, has more symmetries than U-duality. It is invariant under transform...
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Dec 31, 2014 · equationï¼çå¼ï¼æ¹ç¨å¼ è±è±éä¹ï¼ An assertion that two expressions are , expressed by writing the two expressions separated by an equal sign; from which one is to determine a â¦
music depicted them with huge eyeballs, very wide noses, and thick-lipped mouths that hung open or grinned foolishly; one character expressed his love for
Passive-aggressive behavior is a communication that in the mind of the speaker is based on a strong, negative emotion such as anger but is expressed using
In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving th...