To enhance the sound insulation performance of double panel partitions at their mass-air-mass resonance frequency, novel compact and low-mass solutions are sought. This paper investigates the use of ...the locally resonant vibro-acoustic metamaterial concept as a possible solution. The metamaterial solution is applied to one panel of a double panel partition in order to enhance the sound transmission loss at the mass-air-mass resonance. To design the metamaterial solution and predict its sound transmission loss performance, an extension of the multiple reflection theory is proposed, incorporating the dynamic mass of a metamaterial panel. The latter is obtained from the metamaterial plate dispersion curves, calculated using finite element based unit cell modeling. The designed metamaterial solution is manufactured and its insertion loss is measured. The novel design outperforms the original double panel and an equivalent total mass double panel configuration in the targeted mass-air-mass resonance frequency region. The predictions obtained with the proposed method are in good agreement with the experimentally obtained results. This demonstrates the potential of the metamaterial solution to enhance the acoustic insulation at the mass-air-mass resonance and indicates that the proposed method allows a fast, simple and representative indication of their acoustic insulation performance.
•Double panel STL is enhanced at the mass-air-mass frequency using locally resonant metamaterials.•A unit cell based dynamic mass calculation based on the dispersion curves is proposed.•Fast STL prediction method is proposed using the multiple reflection theory combined with the dynamic mass.•A transparent metamaterial double panel partition is designed, manufactured and tested experimentally.•Good agreement between proposed method and experimental results.
We investigate the parity of the coefficients of certain eta-quotients, extensively examining the case of m-regular partitions. Our theorems concern the density of their odd values, in particular ...establishing lacunarity modulo 2 for specified coefficients; self-similarities modulo 2; and infinite families of congruences in arithmetic progressions. For all m≤28, we either establish new results of these types where none were known, extend previous ones, or conjecture that such results are impossible.
All of our work is consistent with a new, overarching conjecture that we present for arbitrary eta-quotients, greatly extending Parkin-Shanks' classical conjecture for the partition function. We pose several other open questions throughout the paper, and conclude by suggesting a list of specific research directions for future investigations in this area.
Weighted cylindric partitions Bridges, Walter; Uncu, Ali K.
Journal of algebraic combinatorics,
2022/12, Letnik:
56, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. ...Here, we extend this framework to include very general product-sides coming from work of Han and Xiong. In doing so, we are led to consider structures such as weighted cylindric partitions, symmetric cylindric partitions and weighted skew double-shifted plane partitions. We prove some new identities and obtain new proofs of known identities, including the Göllnitz–Gordon and Little Göllnitz identities as well as some beautiful Schmidt-type identities of Andrews and Paule.
In the shallow lakes, the partitioning of organic contaminants into the water phase from the solid phase might pose a potential hazard to both benthic and planktonic organisms, which would further ...damage aquatic ecosystems. This study determined the concentrations of polycyclic aromatic hydrocarbons (PAHs), organochlorine pesticides (OCPs), and phthalate esters (PAEs) in both the sediment and the pore water from Lake Chaohu and calculated the sediment – pore water partition coefficient (KD) and the organic carbon normalized sediment – pore water partition coefficient (KOC), and explored the effects of particle size, organic matter content, and parallel factor fluorescent organic matter (PARAFAC-FOM) on KD. The results showed that log KD values of PAHs (2.61–3.94) and OCPs (1.75–3.05) were significantly lower than that of PAEs (4.13–5.05) (p < 0.05). The chemicals were ranked by log KOC as follows: PAEs (6.05–6.94) > PAHs (4.61–5.86) > OCPs (3.62–4.97). A modified MCI model can predict KOC values in a range of log 1.5 at a higher frequency, especially for PAEs. The significantly positive correlation between KOC and the octanol – water partition coefficient (KOW) were observed for PAHs and OCPs. However, significant correlation was found for PAEs only when excluding PAEs with lower KOW. Sediments with smaller particle sizes (clay and silt) and their organic matter would affect distributions of PAHs and OCPs between the sediment and the pore water. Protein-like fluorescent organic matter (C2) was associated with the KD of PAEs. Furthermore, the partitioning of PARAFAC-FOM between the sediment and the pore water could potentially affect the distribution of organic pollutants. The partitioning mechanism of PAEs between the sediment and the pore water might be different from that of PAHs and OCPs, as indicated by their associations with influencing factors and KOW.
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•A modified MCI model predicts the KOC with high frequency, especially for PAEs.•PAHs’ and OCPs’ KOC correlated with their KOW, which was not found for PAEs.•Sediments’ clay, slit, and TOC affected the partitioning of PAHs and OCPs.•Protein-like fluorescent organic matter associated with the PAEs’ partitioning.•The sediment-pore water partitioning of PAEs was different from PAHs and OCPs.
The partition mechanism of PAEs in the sediment – pore water system in a eutrophic Chinese lake was found to be different from that of PAHs and OCPs.
Uptake kinetics of semi‐volatile organic compounds (SVOCs) present indoors, namely phthalates and halogenated flame retardants (HFRs), were characterized for cellulose‐based cotton and rayon fabrics. ...Cotton and rayon showed similar accumulation of gas‐ and particle‐phase SVOCs, when normalized to planar surface area. Accumulation was 3–10 times greater by rayon than cotton, when normalized to Brunauer–Emmett–Teller (BET) specific surface area which suggests that cotton could have a longer linear uptake phase than rayon. Linear uptake rates of eight consistently detected HFRs over 56 days of 0.35–0.92 m3/day.dm2 planar surface area and mass transfer coefficients of 1.5–3.8 m/h were statistically similar for cotton and rayon and similar to those for uptake to passive air sampling media. These results suggest air‐side controlled uptake and that, on average, 2 m2 of clothing typically worn by a person would sequester the equivalent of the chemical content in 100 m3 of air per day. Distribution coefficients between fabric and air (K′) ranged from 6.5 to 7.7 (log K′) and were within the range of partition coefficients measured for selected phthalates as reported in the literature. The distribution coefficients were similar for low molecular weight HFRs, and up to two orders of magnitude lower than the equilibrium partition coefficients estimated using the COSMO‐RS model. Based on the COSMO‐RS model, time to reach 95% of equilibrium for PBDEs between fabric and gas‐phase compounds ranged from 0.1 to >10 years for low to high molecular weight HFRs.
A convex fair partition of a convex polygonal region is defined as a partition on which all regions are convex and have equal area and equal perimeter. In this article we describe an algorithm that ...finds such fair partition.
•The Fair Partitions method finds a fair partition for any given convex polygon and any given number of regions.•Our method relies on two well-known methods: Lloyd's algorithm and the Normal Flow Algorithm.•The method proposed in this article can be used in various contexts and many real-world applications.
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The occurrence of sixteen pharmaceutically active compounds in influent and effluent wastewater and in primary, secondary and digested sludge in one-year period has been evaluated. Solid–water ...partition coefficients (Kd) were calculated to evaluate the efficiency of removal of these compounds from wastewater by sorption onto sludge. The ecotoxicological risk to aquatic and terrestrial ecosystems, due to wastewater discharges to the receiving streams and to the application of digested sludge as fertilizer onto soils, was also evaluated. Twelve of the pharmaceuticals were detected in wastewater at mean concentrations from 0.1 to 32μg/L. All the compounds found in wastewater were also found in sewage sludge, except diclofenac, at mean concentrations from 8.1 to 2206μg/kg dm. Ibuprofen, salicylic acid, gemfibrozil and caffeine were the compounds at the highest concentrations. LogKd values were between 1.17 (naproxen) and 3.48 (carbamazepine). The highest ecotoxicological risk in effluent wastewater and digested sludge is due to ibuprofen (risk quotient (RQ): 3.2 and 4.4, respectively), 17α-ethinylestradiol (RQ: 12 and 22, respectively) and 17β-estradiol (RQ: 12 and 359, respectively). Ecotoxicological risk after wastewater discharge and sludge disposal is limited to the presence of 17β-estradiol in digested-sludge amended soil (RQ: 2.7).
An internal or friendly partition of a graph is a partition of the vertex set into two nonempty sets so that every vertex has at least as many neighbours in its own class as in the other one. It has ...been shown that apart from finitely many counterexamples, every 3, 4 or 6-regular graph has an internal partition. In this note we focus on the 5-regular case and show that among the subgraphs of minimum degree at least 3 of 5-regular graphs, there are some which have small intersection. We also discuss the existence of internal partitions in some families of Cayley graphs, notably we determine all 5-regular Abelian Cayley graphs which do not have an internal partition.
Beck introduced two partition statistics NT(r,m,n) and Mω(r,m,n), which denote the total number of parts in the partition of n with rank congruent to r modulo m and the total number of ones in the ...partition of n with crank congruent to r modulo m, respectively. In recent years, a number of congruences and identities on NT(r,m,n) and Mω(r,m,n) for some small m have been established. In this paper, we prove an identity on NT(r,8,n) and Mω(r,4,n) which confirm a conjecture given by Mao.
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