In effect, a new conceptual approach to the calculus of variations is provided, with no reference made to Euler equations, the fundamental lemma, Bellman's principle, or the maximum principle of Pontryagin. It i
Smart beam design even allows for rather complex shapes, demonstrated as a proof of principle by imprinting the word ‘LIGHT’ into the light field, as shown in Fig. 3m. The quality of these complex intensity profiles can be further improved by engineering the interference more rigorously, i....
In this case, too much is as bad as too little. The study emphasizes the similarity of all works in order to form the common PDO principle, and it will not cover all of the possible implementations. The primary PDO techniques that will be reviewed in this paper are categorized as shown ...
Ahuja, K., et al.: Invariance principle meets information bottleneck for out-of-distribution generalization. NeurIPS 34, 3438–3450 (2021) Google Scholar Arjovsky, M., Bottou, L., Gulrajani, I., Lopez-Paz, D.: Invariant risk minimization. arXiv preprint arXiv:1907.02893 (2019) Atzmon, ...
First, this typically requires a case-by-case analysis, and in this paper, we try to focus on highlighting a general principle that can be applied to a wide number of settings. Secondly, ultimately the number of separating invariants is not likely to be smaller than the dimension of \math...
This issue has been discussed from the results of realistic data in the Results section. Principle of the alternative 2D FFT method The 2D FFT method can be employed for the boundary value problems to determine the gravity field from the third invariant efficiently. As mentioned above, this ...
An invariant variational principle for canonical flows on Lie groups In this paper we examine the existence of Lie groups, whose canonical geodesic flows are variational with respect to a left-invariant regular—but not nece... Muzsnay,Zolta?n - 《Journal of Mathematical Physics》 被引量: 5发...
Pressure can never be allowed to be infinite, it means that the celestial bodies cannot exist, and (2GM/R) is in principle arbitrary, which at least should not be restricted by general relativity. Pressure appears infinite which shows our theory is not perfect yet, and this is the reason ...
The problems with this kind of inheritance can be avoided by observing the Liskov Substitution Principle (LSP) [Liskov93, Martin96a] for the creation of subtypes when we build inheritance hierarchies. This principle states that an object of a subtype—and thus also an instance of a subclass—mu...
On the other hand, the molecular elasticity theory, supplemented by a simple non-Gaussian term whose molecular origin is in principle within reach, seems able to account for the observed behavior at small and moderate strains with comparable success. At moderate strains, the value of J2 is ...