This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on $$\\mathbb{R}^{n} \\times \\mathbb{R}^n$$ together with a functional form of Lozanovskii’s lemma. In...
Dirichlet convolution is often of interest in the context of multiplicative functions (i.e., functions such that f(a)f(b)=f(ab)f(a)f(b)=f(ab) for gcd(a,b)=1gcd(a,b)=1), as the result can be proven to also be a multiplicative function. Moreover, quite often functions of int...
The determination of a monotone nonincreasing and convex response function arising in reservoir mechanics is investigated from the computational point of v... B Hofmann,R Hausding,R Wolke - 《Computing》 被引量: 2发表: 1990年 THE GENERALIZED CROSS VALIDATION METHOD FOR THE SELECTION OF THE REGULA...
Find the derivative of the following function: y = 8. Find the derivative of the following function: f(x) = 10e^{-x/5}. Find the derivative of the following function: f(x) = 3 \: ln(x). Write the first derivative of the following funct...
convex objective function. This issue worsens when considering contact, which leads to abrupt, non-smooth kinks in the stress response. Our model, inspired by generative video modelling, is particularly suited to this nonlinear setting and overcomes many of these challenges, although being, from a ...
15.7). In inverse design problems, the methods based on the identification of the inverse function and its solutions are commonly known as backward methods. However, such an approach is seldom possible in many building physics models due to the nature of the physical–mathematical descriptions ...
Here, the increment of zot values is supplied by increasing Zoτ-1. Hence, due to Eq. (9), the initial stock input has to increase to Γoτ-1=Zoτ+T+∑t=ττ+Tρot. We need Conclusions In this paper, we extended the inverse DEA problems for input/output estimation under inter...
DL can learn highly non-linear functions mapping the inputs to the outputs in a training dataset by using deep artificial neural networks (NNs) with layer architectures that are amenable to training using convex optimization despite their depth. With a sufficient amount of training data and ...
Consider a producer in a perfectly competitive market with a strictly convex cost function. Assume there is no fixed cost (k = 0). For an output maximizer and a profit maximizer, analyze graphically (diagrammatically) the ...
The key is to find the specific dielectric structural distribution of ε and the EM fields (E, H) in the region of interest that allows the conversion. The main challenge here is that the optimization of ε, E and H at the same time is a highly non-convex problem intractable with tra...