On the mean value of Dedekind sum weighted by the quadratic Gauss sum

summary:Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it

Modeling Multi-interest News Sequence for News Recommendation

A session-based news recommender system recommends the next news to a user by modeling the potential interests embedded in a sequence of news read/clicked by her/him in a session. Generally, a user's interests are diverse, namely there are multiple interests corresponding to different types of news, e.g., news of distinct topics, within a session. %Modeling such multiple interests is critical for precise news recommendation. However, most of existing methods typically overlook such important characteristic and thus fail to distinguish and model the potential multiple interests of a user, impeding accurate recommendation of the next piece of news. Therefore, this paper proposes multi-interest news sequence (MINS) model for news recommendation. In MINS, a news encoder based on self-attention is devised on learn an informative embedding for each piece of news, and then a novel parallel interest network is devised to extract the potential multiple interests embedded in the news sequence in preparation for the subsequent next-news recommendations. The experimental results on a real-world dataset demonstrate that our model can achieve better performance than the state-of-the-art compared models

Generation of Intense High-Order Vortex Harmonics

This paper presents the method for the first time to generate intense high-order optical vortices that carry orbital angular momentum in the extreme ultraviolet region. In three-dimensional particle-in-cell simulation, both the reflected and transmitted light beams include high-order harmonics of the Laguerre-Gaussian (LG) mode when a linearly polarized LG laser pulse impinges on a solid foil. The mode of the generated LG harmonic scales with its order, in good agreement with our theoretical analysis. The intensity of the generated high-order vortex harmonics is close to the relativistic region, and the pulse duration can be in attosecond scale. The obtained intense vortex beam possesses the combined properties of fine transversal structure due to the high-order mode and the fine longitudinal structure due to the short wavelength of the high-order harmonics. Thus, the obtained intense vortex beam may have extraordinarily promising applications for high-capacity quantum information and for high-resolution detection in both spatial and temporal scales because of the addition of a new degree of freedom

Design and Optimization of the Vertical Plate Metering Device for Alfalfa Seeds Precision Based on Engineering Discrete Element Method (EDEM)

The research is financed by China Agriculture Research System (CARS34) Abstract The vertical plate seed metering device enhancement and constraints mass flow rate when added to the device improve mass flow performance of alfalfa vertical plate device. Alfalfa forage crop is a potential feeding nutrient and the backbone of dairy production success in China. Engineering discrete element method EDEM was adopted for simulation computing and analysis of the seed-filling performance of the vertical plate metering device with three cell shapes under desired rotational speeds. The results showed significant differences at P< 0.05 of seed filing performance in relation to the rotational speed and cell shapes. Triangular cell shape had indicated the lower mass flow at 8x10-5 kg/s compared to the V-shape of 12x10-4 kg/s and U-shape of 8x10-3 kg/s, 20 to 30% reduction, respectively. The rotational velocity of the vertical plate exceeded 30rpm the cell units reach the optimum seed filling efficiency resulted in 30% decrease of the mass flow rate, the results indicated more seeds disturbance, reduces seed filling by enhancing seeds accessibility and falling, from cells. Furthermore, the T-shape had a lower seed filling and higher seeds releasing in comparison to the V-shape and U-shape cells. The lower seed filling found to be the higher filling efficiency while the higher seed filling leads to the lower filling efficiency. Keywords: Alfalfa seed model, cell, filling performance, mass flow, simulation EDE

Effects of Moisture Content on Selected Physical and Mechanical Properties of Alfalfa Seeds

Alfalfa is one of the most widely planted forage legume in the world and that because of its tolerance, adaptation, high yield and nutritious value. Physico-mechanical properties of alfalfa seed are very crucial in the machine designing and processing operations. In this study, some of the physical and mechanical properties of alfalfa seed cultivar were investigated under laboratory condition, as desired for the design of a metering device.  Seven moisture contents were introduced to the initial content of 7.98%, d.b. The geometric and gravimetric characteristics were determined. Correlation equation models were developed based on the function of moisture contents. The means average parameter values of the length, width, thickness, aspect ratio, seed mass, arithmetic, geometric mean diameter, true and bulk density, porosity seed volume, and surface area ranged between 2.356 to 2.718mm, 1.390 to 1.473mm, 1.071 to 1.345mm, 0.68 to 0.776%, 1.7968 to 2.295g, 1.466 to 1.589mm, 1.141 to 1.517mm and 1.466 to 1.589g/cm31.199 to 0.830g/cm3, 0.10 to 0.44%, 0.7383 to 0.79426, and 6.305 to 7.2438mm2, respectively. While, the plywood surface had the highest value of the coefficient of friction as the roughest, followed by polished steel and rubber, glass the least surface roughness. However, the germination rate (%) increased as seed damages decreased, as the coefficient of internal friction decreases from 0.127 to 0.095, while the cohesion increasing from 2.11 to 5.95. The angle of repose resulted in a non-linear increase from 27.05o to 28.68o, 28.86o to 29.86o, 31.49o to 32.35o, and 32.47o to 33.21o as moisture content increased from7.98 to 22.12% d.b. Keywords: alfalfa seed, moisture content, mechanical property, physical propert