China
Africa
Explore chapters and articles related to this topic
Backwater and drawdown curves in stepped spillway flow
Published in H.-E. Minor, W.H. Hager, Hydraulics of Stepped Spillways, 2020
Willi H. Hager, Robert M. Boes
where tanh is the tangent hyperbolic function. Further Y90=h90/h90u with h90=hm(C=0.9) as mixture flow depth with a surface air concentration of 90%, and χm=x/xm, where xm=hc3/(h90u2sinϕ) is the mixture normalizing length. In order to plot all data on one curve, one will again select an abscissa χ(Y90=Y90i)= χo at the inception point and then move in the downstream direction. Figure 5 compares the data with Eq.(6) and agreement is again noted. A typical standard deviation is ±5% for φ=30° and ±2% for φ=50°. These deviations are so small for air-water flows that one can talk of almost perfect agreement.
Introduction and Review
Published in Russell L. Herman, A Course in Mathematical Methods for Physicists, 2013
We finally note that there is a simple relationship between hyperbolic functions and trigonometric functions. Recall that coshx=ex+e−x2.Hyperbolic functions and trigonometric functions are intimately related: cos(ix)=coshx,sin(ix)=−isinhx.
Calculating
Published in Victor A. Bloomfield, Using R for Numerical Analysis in Science and Engineering, 2018
R can be used, without any programming, as a powerful calculator. It has all the standard arithmetic operators and functions, which operate on numeric or complex vectors (including scalars, which are vectors of length 1). Arithmetic operators: The binary arithmetic operators are +, -, *, /, ^ (exponentiation), %% (mod), and %/% (integer division).Logarithms and exponentials: log (natural log), log10, (base 10 log), log2 (base 2 log), log (x,b) (log of x to base b). log1p(x) computes log(1+x) accurately for |x| << 1.exp computes the exponential function, and expm1 computes exp(x)-1 accurately for |x| << 1.Trigonometric functions : cos(x), sin(x), tan(x), acos(x), asin(x), atan(x), atan2(y,x) where angles are in radians and x and y are numeric or complex scalars or vectors. atan2(y,x) = atan(y/x) for positive arguments. The pracma package, to which we will refer later, adds more trigonometric functions: cot(x), csc(x), sec(x), acot(x), acsc(x), asec(x).Hyperbolic functions : cosh(x), sinh(x), tanh(x), acosh(x), asinh(x), atanh(x). pracma adds coth(x), csch(x), sech(x), acoth(x), acsch(x), asech(x).Miscellaneous mathematical functions: abs(x), sqrt(x).
Hybrid Attention-based Approach for Arabic Paraphrase Detection
Published in Applied Artificial Intelligence, 2021
For each time step t, is fed through a fully connected network to get as a hidden representation. It is based on a Tangent Hyperbolic function (Tanh). It helps to identify relevant features by generating high scores for them. It is the core idea of the attention mechanism. Then, weights are calculated by applying Softmax function on the scores, which are called attention weights representing the relevance of each word in the sentence. After that, a context vector is constructed applying a multiplication of weights and the features generated from the CNN. Finally, a fixed representation of the whole sentence is computed as the weighted sum of all hidden states using the attention weights . Formally, the attention mechanism process is denoted in Equations (5)–(7):
Search for parking: A dynamic parking and route guidance system for efficient parking and traffic management
Published in Journal of Intelligent Transportation Systems, 2019
Huajun Chai, Rui Ma, H. Michael Zhang
This is a hyperbolic function. When the parking occupancy approaches 100%, the searching cost becomes extremely large so that it penalizes vehicles from parking in this parking garage. Such a setting fits the reality, as the time needed to find an available parking slot increases dramatically when the parking garage is almost fully occupied.Expected parking fees —the monetary cost charged by the parking service provider. As dynamic parking pricing schemes are emerging to better coordinate the parking demand and supply in some pioneering projects such as SFPark, we define the parking fee as a function of current occupancy of the parking garage. In this article, we apply a hyperbolic function, which is similar to the in-garage searching time function.