Reduction (mathematics)

Abstract: 1 Introduction.- 2 Representative problems: analysis and (high-fidelity) approximation.- 3 Getting parameters into play.- 4 RB method: basic principle, basic properties.- 5 Construction of reduced basis spaces.- 6 Algebraic and geometrical structure.- 7 RB method in actions.- 8 Extension to nonaffine problems.- 9 Extension to nonlinear problems.- 10 Reduction and control: a natural interplay.- 11 Further extensions.- 12 Appendix A Elements of functional analysis.

Abstract: Previous research has established that surfaces with tiny ribs (riblets) aligned in the streamwise direction can reduce the turbulent wall-shear stress below that of a smooth surface. Typical skin-friction reductions have been found to be about 5%. The results of the present investigation, however, demonstrate a considerable improvement over this value. This improvement is achieved by a systematic experimental optimization which has been guided by theoretical concepts.A key feature of our experiments is the utilization of an oil channel. Previous experiments in wind tunnels had to contend with very small riblet dimensions which typically had a lateral rib spacing of about 0.5 mm or less. By contrast, in our oil channel, the ribs can have a lateral spacing of between about 2 and 10 mm. This increased size of the surface structures enables test surfaces to be manufactured with conventional mechanical methods, and it also enables us to build test surfaces with adjustable geometry. In addition, the Berlin oil channel has a novel shear stress balance with an unprecedented accuracy of ±0.3%. This latter feature is a prerequisite for a systematic experimental optimization.In the present investigation, surfaces with longitudinal ribs and additional slits are studied. The experiments cover a fairly large range of parameters so that the drag reduction potential of a surface with ribs and/or slits is worked out conclusively. A large parameter range is made possible because of the adjustability of the surfaces as well as the automatic operation of the oil channel. In particular, the following tests were run:(i) Shear stress measurements with conventional riblet configurations, i.e. with triangular and semi-circular grooves, have been carried out. These measurements were necessary in order to establish the connection between our oil channel data and previous data from wind tunnels. As was previously established, we found a drag reduction of about 5%.(ii) An adjustable surface with longitudinal blade ribs and with slits was built and tested. Both groove depth and slit width could be varied separately and continuously during the experiment. It turned out, that slits in the surface did not contribute to the drag reduction. Nevertheless, these investigations show how perforated surfaces (e.g. for boundary-layer control) can be designed for minimal parasitic drag. On the other hand, with closed slits, an optimal groove depth for the rib surface could be determined, i.e. half of the lateral rib spacing. For this configuration, we found an 8.7% skin-friction reduction. By carefully eliminating deleterious effects (caused by little gaps, etc.), the skin-friction reduction could be improved to a record value of 9.9%.(iii) A quantitative comparison between theory and experiment was carried out. The theory is based on the assumption that riblets impede the fluctuating turbulent crossflow near the wall. In this way, momentum transfer and shear stress are reduced. The simplified theoretical model proposed by Luchini (1992) is supported by the present experiments.(iv) For technological applications of riblets, e.g. on long-range commercial aircraft, the above thin-blade ribs are not practical. Therefore, we have devised a surface that combines a significantly improved performance (8.2 %) with a geometry which exhibits better durability and enables previously developed manufacturing methods for plastic riblet film production to be used. Our riblet geometry exhibits trapezoidal grooves with wedge-like ribs. The flat floor of the trapezoidal grooves permits an undistorted visibility through the transparent riblet film which is essential for crack inspection on aircraft.

Abstract: Nowadays mobile usage is the essential need of humans. To provide the mobile network services, the Telecommunication companies propose the installation of Base Transceiver Station over large populated and industrial areas. The radiations emit from these BTS may give rise to various electromagnetic and ecological compatibility issues [1]. The radiation power of these BTS is up to 5-10 KiloWatts (up to 320-350 W per channel), which can be detrimental for the human beings, if they are installed in populated areas. The purpose of this paper is to reduce the transmission power of the BTS which is possible through the usage of Self-phased array antenna. Self-phasing array antenna through the use of pilot carrier in Telecommunication systems can degrade the Tx upto10-20dB

Abstract: To design fast neural networks, many works have been focusing on reducing the number of floating-point operations (FLOPs). We observe that such reduction in FLOPs, however, does not necessarily lead to a similar level of re-duction in latency. This mainly stems from inefficiently low floating-point operations per second (FLOPS). To achieve faster networks, we revisit popular operators and demonstrate that such low FLOPS is mainly due to frequent memory access of the operators, especially the depthwise con-volution. We hence propose a novel partial convolution (PConv) that extracts spatial features more efficiently, by cutting down redundant computation and memory access simultaneously. Building upon our PConv, we further propose FasterNet, a new family of neural networks, which attains substantially higher running speed than others on a wide range of devices, without compromising on accuracy for various vision tasks. For example, on ImageNet-lk, our tiny FasterNet-TO is 2.8×, 3.3×, and 2.4× faster than MobileViT-XXS on GPU, CPU, and ARM processors, respectively, while being 2.9% more accurate. Our large FasterNet-L achieves impressive 83.5% top-1 accuracy, on par with the emerging Swin-B, while having 36% higher inference throughput on GPU, as well as saving 37% compute time on CPU. Code is available at https://github.com/JierunChen/FasterNet.