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Let G be a finite abelian group. The Davenport con-stant D(G) is the smallest integer l ∈ N such that every sequence S over G of length |S| ≥ l has a nontrivial zero-sum subsequence. This invariant has been studied since the 196...
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Let G be a finite abelian group. The Davenport con-stant D(G) is the smallest integer l ∈ N such that every sequence S over G of length |S| ≥ l has a nontrivial zero-sum subsequence. This invariant has been studied since the 1960s, and it naturally occurs in various branches of combinatorics, number theory and geometry. Its precise value in terms of the group invariants is known for p-groups and for groups of rank at most two, among others. On the other hand, it is still unknown, for example, even for groups of the form C_n~3. The reader may want to consult one of the surveys [10, 13] for more information.
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Let K be an algebraic number field with non-trivial class group G and let O_k be its ring of integers. For k ∈ N and some real x ≥ 1, let F_k(x) denote the number of nonzero principal ideals aO_k with norm bounded by x such that...
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Let K be an algebraic number field with non-trivial class group G and let O_k be its ring of integers. For k ∈ N and some real x ≥ 1, let F_k(x) denote the number of nonzero principal ideals aO_k with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that F_k(x) behaves, for x→∞, asymptotically like x(logx)~(-1+1/∣G∣) (log logx)~(N_k(G)). We study N_k(G) with new methods from Combinatorial Number Theory.
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In this article, we consider a single unmanned aerial vehicle (UAV)-assisted heterogeneous network in a disaster area, which includes a UAV, ground cellular users, and ground sensor users. The cellular data and sensing data are tr...
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In this article, we consider a single unmanned aerial vehicle (UAV)-assisted heterogeneous network in a disaster area, which includes a UAV, ground cellular users, and ground sensor users. The cellular data and sensing data are transmitted to UAVs by cellular users and sensor users, due to the outage of the ground wireless network caused by the disaster. In this scenario, we aim to minimize the energy consumption of all the users, to extend their communication time and facilitate rescue. At the same time, cellular users and sensor users have different rate requirements, hence the quality of service (QoS) of the users should be guaranteed. To solve these challenges, we propose an energy-effective relay selection and resource-allocation algorithm. First, to solve the problem of insufficient coverage of the single UAV network, we propose to perform multi-hop transmission for the users outside the UAV’s coverage by selecting suitable relays in an energy-effective manner. Second, for the cellular users and sensor users inside the coverage of the UAV but with different QoS requirements, we design a non-orthogonal multiple access (NOMA)-based transmission scheme to improve spectrum efficiency. Deep reinforcement learning is exploited to dynamically adjust the power level and allocated sub-bands for inside users to reduce energy consumption and improve QoS satisfaction. The simulation results show that the proposed NOMA transmission scheme can achieve 9–17% and 15–32% performance gain on the reduction of transmit power and the improvement of QoS satisfaction, respectively, compared with state-of-the-art NOMA transmission schemes and orthogonal multiple access scheme.
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Millimeter-wave (mmWave) communication is considered a promising technology for fifth-generation (5G) wireless communications systems since it can greatly improve system throughput. Unfortunately, because of extremely high frequen...
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Millimeter-wave (mmWave) communication is considered a promising technology for fifth-generation (5G) wireless communications systems since it can greatly improve system throughput. Unfortunately, because of extremely high frequency, mmWave transmission suffers from the signal blocking problem, which leads to the deterioration of transmission performance. In this paper, we solve this problem by the combination of ultra-dense network (UDN) and user-centric virtual cell architecture. The deployment of dense small base stations (SBSs) in UDN can reduce transmission distance of signals. The user-centric virtual cell architecture mitigates and exploits interference to improve throughput by using coordinated multipoint (CoMP) transmission technology. Nonetheless, the backhaul burden is heavy and interbeam interference still severe. Therefore, we propose a novel iterative backhaul capacity-limited joint user association and power allocation (JUAPA) scheme in ultra-dense mmWave networks under user-centric virtual cell architecture. To mitigate interference and satisfy quality of service (QoS) requirements of users, a nonconvex system throughput optimization problem is formulated. To solve this intractable optimization problem, we divide it into two alternating optimization subproblems, i.e., user association and power allocation. During each iteration, a many-to-many matching algorithm is designed to solve user association. Subsequently, we perform power allocation optimization using a successive convex approximation (SCA) algorithm. The results confirm that the performance of the proposed scheme is close to that of the exhaustive searching scheme, which greatly reduces complexity, and clearly superior to that of traditional schemes in improving system throughput and satisfying QoS requirements.
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The geographical environment adaptation of the resettled population is a deep-seated problem that determines whether the goal of the poverty alleviation resettlement (PAR) policy can be achieved. Scientific assessment of adaptive ...
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The geographical environment adaptation of the resettled population is a deep-seated problem that determines whether the goal of the poverty alleviation resettlement (PAR) policy can be achieved. Scientific assessment of adaptive capacity (AC) and adaptation level (AL) provides a basis for subsequent policy formulation, which is of practical significance. This study took the poverty-stricken areas of northwest Yunnan as the study area and calculated the adaptive capacity index (ACI) and adaptation level index (ALI) based on survey data of 1002 resettled households and regional socioeconomic statistics by constructing the vulnerability as expected poverty (VEP) model and multi-factor analysis model. The results showed that (1) The ACI and ALI were 0.660 and 61.2 respectively, indicating that the resettled population has obvious environment adaptation barriers and a relatively high risk of returning to poverty. (2) The AC and AL of the resettled population had significant geographical differentiation. In general, Diqing Prefecture was significantly better than Nujiang Prefecture and the problems in Gongshan County, Fugong County and Lanping County were more prominent. (3) AC is a determinant of AL. However, these two indices in Gongshan and Lanping counties deviated from the general trend due to different policy effects. Based on the evaluation results and differentiation mechanism analysis, the study finally emphasized the importance of formulating and implementing the follow-up development plan of the resettled population and put forward measures to promote the resettled population to adapt to the geographical environment around the three core tasks of employment income increase, public service and bottom guarantee.
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Since stating carbon peak goal, Shandong has garnered widespread concern over its large GHG emissions. Based on the latest emission factors and detailed activity data, a comprehensive high-resolution GHG emission inventory of Shan...
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Since stating carbon peak goal, Shandong has garnered widespread concern over its large GHG emissions. Based on the latest emission factors and detailed activity data, a comprehensive high-resolution GHG emission inventory of Shandong Province for 2020 was established by updating estimation methods and allocation profiles. The results indicated that the emissions of CO_2, CH_4, N_2O, HFCs, PFCs and SF_6 had reached 1233.46, 36.49, 45.79, 74.27, 6.21 and 0.56 Mt CO_(2eq), respectively. Specifically, CO_2 emissions mainly originated from fossil fuel consumption (81.83%); the major sources of CH_4 emissions were mining industries and agriculture, contributing 1.40% and 0.81% of the total GHG emissions, respectively; industry processes and product use discharged the largest amount of N_2O (1.92%) and were responsible for all of the fiuorinated greenhouse gas emissions. To obtain more accurate GHG emission information, GHG emissions were spatially allocated to grid cells with a resolution of 0.05°×0.05° according to appropriate surrogates and results showed that most of the emissions are concentrated over a small number of grid cells, specifically, 10% of grid cells accounts for 73% of GHG, 75% of CO_2, 88% of CH_4 and 40% of N_2O emission. Spatially, the GHG emissions were mainly distributed in eastern and central cities of Shandong and decreased radially from urban centres to the surrounding areas.
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Let G be an additive finite abelian group. For a sequence T over G and g ∈ G, let v_g(T ) denote the multiplicity of g in T. Let B(G) denote the set of all zero-sum sequences over G. For ? ? B(G), let d_?(G) be the smallest integ...
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Let G be an additive finite abelian group. For a sequence T over G and g ∈ G, let v_g(T ) denote the multiplicity of g in T. Let B(G) denote the set of all zero-sum sequences over G. For ? ? B(G), let d_?(G) be the smallest integer t such that every sequence S overG of length |S| ≥ t has a subsequence in ?. The invariant d_?(G) was formulated recently in [3] to take a unified look at zero-sum invariants, it led to the first results there, and some open problems were formulated as well. In this paper, we make some further study on d_?(G). Let q'(G) be the smallest integer t such that every sequence S over G of length |S| ≥ t has two nonempty zero-sum subsequences, say T_1 and T_2, having different forms, i.e., v_g(T_1) ≠ v_g(T_2) for some g ∈ G. Let q(G) be the smallest integer t such that ∩ d_?(G)=t ? = ?. The invariants q(G) and q'(G) were also introduced in [3]. We prove, among other results, that q(G) = q'(G) in fact.
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Nonwovens are ideal materials for use as noise control elements because of their unique physical structure and special acoustic behaviors, especially when their structures are complicatedly designed. In this paper, we first deduce...
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Nonwovens are ideal materials for use as noise control elements because of their unique physical structure and special acoustic behaviors, especially when their structures are complicatedly designed. In this paper, we first deduce a sound absorption model for dual-layered porous nonwovens by extending the Zwikker and Kosten theory. Then a theoretical analysis and a numerical simulation of the impact of thickness and porosity of outer and inner layers on the sound absorption coefficient are followed by an experiment designed to compare the calculated sound absorption coefficients and the measured ones. Experiment results indicate that the measured and the calculated sound absorption coefficients are very similar in trend with change of thickness, porosity and sound frequency, apart from the obvious difference at low frequency. Finally, the main reasons for the differences between the theoretic data and the experimental ones are also explored.
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Let G be an additive finite Abelian group. In the last decades group algebras R[G]-over suitable commutative rings R-have turned out to be powerful tools for a growing variety of questions from combinatorics and number theory.
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Analysis of urban area function is crucial for urban development. Urban area function features can help to conduct better urban planning and transportation planning. With development of urbanization, urban area function becomes co...
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Analysis of urban area function is crucial for urban development. Urban area function features can help to conduct better urban planning and transportation planning. With development of urbanization, urban area function becomes complex. In order to accurately extract function features, researchers have proposed multisource data mining methods that combine urban remote sensing and other data. Therefore, the research of efficient multisource data analysis tools has become a new hot topic. In this paper, a novel urban data analysis method combining spatiotemporal wireless network data and remote sensing data was proposed. First, a Voronoi-diagram-based method was used to divide the urban remote sensing images into zones. Second, we combined period and trend components of wireless network traffic data to mine urban function structure. Third, for multisource supported urban simulation, we designed a novel spatiotemporal city computing method combining graph attention network (GAT) and gated recurrent unit (GRU) to analyze spatiotemporal urban data. The final results prove that our method performs better than other commonly used methods. In addition, we calculated the commuting index of each zone by wireless network data. Combined with the urban simulation conducted in this paper, the dynamic changes of urban area features can be sensed in advance for a better sustainable urban development.
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