A recent numerical study observed that neural network classifiers enjoy a large degree of symmetry in the penultimate layer. Namely, if h(x) = Af(x) + b where A is a linear map and f is the output of the penultimate l...
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This study aimed to determine the potential of coffee skin waste (Coffea robusta L) as a superior compost innovation for the growth of pepper-cutting seedlings (Piper nigrum L). This study used an experimental method ...
This study aimed to determine the potential of coffee skin waste (Coffea robusta L) as a superior compost innovation for the growth of pepper-cutting seedlings (Piper nigrum L). This study used an experimental method with a completely randomized design using five treatments and five repeats, variations in the dose of coffee skin waste used P0 (control), P1 (90 g), P2 (135 g), P3 (180 g), and P4 (225 g). The shoot height, number of leaves, number of roots, and length of roots were measured. The results showed that coffee skin waste compost significantly affected shoot height, especially at P1 (90 g), resulting in an average growth height of 7.24 cm. In addition, the highest number of leaves was found at a concentration of P1 (90 g), with an average of two leaves. Although there was no significant effect on the number of roots, the concentration of P1 (90 g) yielded the best results, with an average of 33 root blades, and the best root length was obtained at the concentration of P1 (90 g), with an average of 44.6 cm. Therefore, coffee skin waste significantly influenced shoot height and the number of leaves on pepper-cut seedlings (Piper nigrum L.) in the P1 treatment (90 g).
A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequ...
A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequence of period doublings leading to chaos according to the Feigenbaum scenario [J. Statis. Phys. 19, 25 (1978); Phys. Lett. 74 A, 375 (1979)].
We develop Banach spaces for ReLU neural networks of finite depth L and infinite width. The spaces contain all finite fully connected L-layer networks and their L2-limiting objects under bounds on the natural path-nor...
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We will prove an analogue of Landauʼs necessary conditions [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52] for spaces of functions w...
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We will prove an analogue of Landauʼs necessary conditions [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52] for spaces of functions whose Hankel transform is supported in a measurable subset S of the positive semi-axis. As a special case, necessary density conditions for the existence of Fourier–Bessel frames are obtained.
We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such function spaces. Consequently, these solut...
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＜正＞Accessing precisely to the phase variation of electronic wavepacket（EWP）provides unprece dented s patiotemporal information of microworld.A radial interference pattern at near zero energy has been widely obser...
＜正＞Accessing precisely to the phase variation of electronic wavepacket（EWP）provides unprece dented s patiotemporal information of microworld.A radial interference pattern at near zero energy has been widely observed in experiments of strong field ***,the underlying physical picture of this in terference pattern is still debated and remains *** we report an experimental and theoretical ver
We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and direct approximation theorems to obtain ...
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The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400...
The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400. The process has been documented in several eXperimental mvestigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the NavierStokes equations at representative Reynolds numbers, up to 500. A high-order timeaccurate, miXed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vorteX street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vorteX filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vorteX filaments. Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance intermittent phenomena. It is concluded that the wake undergoes transit
In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with varia...
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In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum *** two methods can preserve the intrinsic properties of original problems as much as *** splitting technique increases the computational ***,the error estimation and some conservative properties are *** is proved to preserve the charge conservation *** global energy and momentum conservation laws can be preserved under several *** experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.
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