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Journal articles on the topic 'Filtration'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 October 2024

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1

Leiviskä, T., and J. Rämö. "Investigation of multimodal zeta potential and size distribution in chemical pulp process water." Water Science and Technology 56, no. 11 (December 1, 2007): 123–29. http://dx.doi.org/10.2166/wst.2007.770.

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Multimodal zeta potential distribution in chemical birch pulp process water was studied by filtrating the water into fractions and subsequently measuring zeta potential, charge quantity, turbidity and organic substances. Filtrations were made using 12 μm, 1.6 μm, 1.2 μm, 0.45 μm and 0.1 μm membranes. The number of populations with different zeta potentials diminished with filtration. With the unfiltrated water, 12 μm and 1.6 μm filtrates, three or four different zeta potentials were observed. When the filtration was performed with a 1.2 μm membrane or smaller, only two populations of different zeta potentials were detected. The charge quantity steadily approached zero from unfiltrated water towards a 1.6 μm fraction filtrate. After that, it remained constant. Turbidity constantly decreased when using smaller membranes. The amount of wood extractives decreased to half with 0.1 μm filtration. No significant difference in the amount of carbohydrates and lignin between the filtrated fractions and the unfiltrated water was detected. A comparison dealing with particle size analysis between two different apparatuses was also made.

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2

Parks, Allen D., and David J. Marchette. "Persistent homology in graph power filtrations." Royal Society Open Science 3, no. 10 (October 2016): 160228. http://dx.doi.org/10.1098/rsos.160228.

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The persistence of homological features in simplicial complex representations of big datasets in R n resulting from Vietoris–Rips or Čech filtrations is commonly used to probe the topological structure of such datasets. In this paper, the notion of homological persistence in simplicial complexes obtained from power filtrations of graphs is introduced. Specifically, the r th complex, r ≥ 1, in such a power filtration is the clique complex of the r th power G r of a simple graph G . Because the graph distance in G is the relevant proximity parameter, unlike a Euclidean filtration of a dataset where regional scale differences can be an issue, persistence in power filtrations provides a scale-free insight into the topology of G . It is shown that for a power filtration of G , the girth of G defines an r range over which the homology of the complexes in the filtration are guaranteed to persist in all dimensions. The role of chordal graphs as trivial homology delimiters in power filtrations is also discussed and the related notions of ‘persistent triviality’, ‘transient noise’ and ‘persistent periodicity’ in power filtrations are introduced.

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3

Forster, R. B. "Filtration and Filtration Plant." Journal of the Society of Dyers and Colourists 42, no. 11 (October 22, 2008): 333–43. http://dx.doi.org/10.1111/j.1478-4408.1926.tb01348.x.

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4

Arifjanov, Aybek. "Determination of Filtration Strength and Initial Filtration Gradient in Soil Constructions." Journal of Advanced Research in Dynamical and Control Systems 12, SP4 (March 31, 2020): 1860–64. http://dx.doi.org/10.5373/jardcs/v12sp4/20201672.

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5

Han, Chao, Hongping Xie, Bin Bai, Dongrui Liu, Yue Huang, and Rongjun Zhang. "Study on the Factors Affecting the Performance of a Pressure Filtration–Flocculation–Solidification Combined Method for Mud Slurry Treatment." Applied Sciences 13, no. 20 (October 14, 2023): 11299. http://dx.doi.org/10.3390/app132011299.

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A pressure filtration–flocculation–solidification combined treatment possesses great potential for the reutilization of the waste mud slurry generated from diverse construction projects as filling material due to its versatility and high efficiency. However, very limited existing studies have focused on the factors affecting pressure filtration’s efficiency. In this paper, a calculation model for compression filtration is established based on laboratory pressure filtration model tests and one-dimensional large-strain consolidation theory. The influence of various parameters on pressure filtration’s efficiency is analyzed, and favorable values for these parameters are recommended. The results show that an increased initial mud cake thickness significantly increases the dewatering time and reduces the treatment’s efficiency. A lower dewatering time and higher efficiency can be achieved by increasing the filtration pressure, but the efficiency improvements become limited after reaching the critical pressure threshold. For the mud slurry used in this study, the optimal values for the initial mud slurry bag thickness, filtration pressure, and dewatering time are 240 mm, 1.0 MPa, and 30 min, respectively, yielding a final mud cake water content of 58.7% after filtration.

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6

Yan, Guang Xu, Qian Zhang, Hui Li, and Yu Li. "Spinning Effluents Treatment from Dry-Spun Acrylic Fiber Producing by Integrated Membrane Filtration." Advanced Materials Research 476-478 (February 2012): 789–92. http://dx.doi.org/10.4028/www.scientific.net/amr.476-478.789.

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Spinning effluents (SE) from dry-spun acrylic fiber producing are hard to biodegrade for dimethyl formamide (DMF) and nitriles contained. Integrated membrane filtrations including micro-filtration (MF), ultra-filtration (UF) and nano-filtration (NF) were adopted to separate the pollutants in SE. Experiment showed that MF has weak capacity for the removal of organic pollutants, while NF and UF contributed to 49.49% and 31.51% to the initial COD removal rates of SE.

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7

Fedel, Tony. "Air filtration: Evaluating filtration efficiency." Filtration + Separation 49, no. 6 (November 2012): 37–39. http://dx.doi.org/10.1016/s0015-1882(12)70289-6.

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8

JENSEN, BERNT TORE, DAG OSKAR MADSEN, and XIUPING SU. "FILTRATIONS IN ABELIAN CATEGORIES WITH A TILTING OBJECT OF HOMOLOGICAL DIMENSION TWO." Journal of Algebra and Its Applications 12, no. 02 (December 16, 2012): 1250149. http://dx.doi.org/10.1142/s0219498812501496.

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We consider filtrations of objects in an abelian category [Formula: see text] induced by a tilting object T of homological dimension at most two. We define three extension closed subcategories [Formula: see text] and [Formula: see text] with [Formula: see text] for j > i, such that each object in [Formula: see text] has a unique filtration with factors in these categories. In dimension one, this filtration coincides with the classical two-step filtration induced by the torsion pair. We also give a refined filtration, using the derived equivalence between the derived categories of [Formula: see text] and the module category of [Formula: see text].

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9

Manish Chitnis, Aayush. "Nanotechnology for Water Filtration." International Journal of Science and Research (IJSR) 13, no. 5 (May 5, 2024): 1094–100. http://dx.doi.org/10.21275/sr24516215746.

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10

Kübel, Johannes. "From Jantzen to Andersen filtration via tilting equivalence." MATHEMATICA SCANDINAVICA 110, no. 2 (June 1, 2012): 161. http://dx.doi.org/10.7146/math.scand.a-15202.

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The space of homomorphisms between a projective object and a Verma module in category $\mathcal O$ inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Andersen filtration on the space of homomorphisms between a Verma module and a tilting module. Arkhipov's tilting functor, a contravariant self-equivalence of a certain subcategory of $\mathcal O$, which maps projective to tilting modules induces an isomorphism of these kinds of Hom-spaces. We show that this equivalence identifies both filtrations.

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11

Sutherland, Ken. "Water filtration: Bulk water filtration techniques." Filtration & Separation 45, no. 10 (December 2008): 17–19. http://dx.doi.org/10.1016/s0015-1882(08)70496-8.

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12

Holmes, Mark. "Filtration 2011: Filtration returns to Chicago." Filtration + Separation 48, no. 6 (November 2011): 14–16. http://dx.doi.org/10.1016/s0015-1882(11)70254-3.

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13

Sutherland, Ken. "Fine chemical filtration: Defining filtration processes." Filtration & Separation 44, no. 3 (April 2007): 38–39. http://dx.doi.org/10.1016/s0015-1882(07)70084-8.

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14

Dong, Xiu Ping, Ya Ting Huang, and Ming Ji Huang. "Mechanism Analysis and Dairy Filtration Experimental Research on Porous 1Cr18Ni9 Stainless Steel Components." Advanced Materials Research 668 (March 2013): 902–6. http://dx.doi.org/10.4028/www.scientific.net/amr.668.902.

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Cool-drawn 1Cr18Ni9 stainless steel wires of 0.1~0.5 mm can be woven and punched to prepare porous metal filters. There is certain amount of connected micron pores in the transformable components. Filtration mechanism of this porous material is investigated and three series of samples with different diameter of wires, porosities and filtrating ranges are prepared. Filtration performances compares experiments are carried out on a kind of chocolate milk with the brand of Sanyuan. Three-dimensional microscopy, KEYENCE VHX-600, is applied to investigate the diaphragms before and after filtrating. Portable contamination analysis kit, HPCA-2, is chosen to identify the degree of contaminating. Results indicate that these kind of porous metal filters have valid solid/fluid separating effects. Wires diameters and other preparation parameters will identify the porosity. Thinner wires contribute to more and tinier porous and will block particles effectively. Thickness of filters plays the similar role of filtration layer. Higher porosity will increase the cleanliness of the passing fluid and decrease the filtering efficiency. The data in this paper provide technical support to the application in dairy filtration industry.

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15

Greil, Peter, Ulrich Gruber, Nahum Travitsky, and Michael Kulig. "Pressure filtration of silicon nitride suspensions with constant filtrationn rate." Materials Science and Engineering: A 151, no. 2 (May 1992): 247–54. http://dx.doi.org/10.1016/0921-5093(92)90213-k.

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16

Atamanyuk, Volodymyr, Zoriana Gnativ, Diana Kindzera, Dauren Janabayev, Alisher Khusanov, and Botagoz Kaldybaeva. "Hydrodynamics of Cotton Filtration Drying." Chemistry & Chemical Technology 14, no. 3 (September 22, 2020): 426–32. http://dx.doi.org/10.23939/chcht14.03.426.

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17

Sutherland, Ken. "Membrane filtration: What's new in membrane filtration?" Filtration & Separation 46, no. 5 (September 2009): 32–35. http://dx.doi.org/10.1016/s0015-1882(09)70193-4.

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18

Bennett, Anthony. "Air filtration: Innovations in industrial air filtration." Filtration & Separation 47, no. 4 (July 2010): 20–23. http://dx.doi.org/10.1016/s0015-1882(10)70162-2.

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19

Padia, Jignesh, and Paul Huntington. "Gas filtration: sterile micro-filtration for bioreactors." Filtration & Separation 43, no. 4 (May 2006): 28–31. http://dx.doi.org/10.1016/s0015-1882(06)70866-7.

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20

Rognoni, M., and F. Volpe. "Flow inverted filtration (FIF) innovative filtration technology." Desalination 182, no. 1-3 (November 2005): 309–13. http://dx.doi.org/10.1016/j.desal.2005.04.018.

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21

Liu, Yunxia, Honghai Liu, and Zhongrong Shen. "Nanocellulose Based Filtration Membrane in Industrial Waste Water Treatment: A Review." Materials 14, no. 18 (September 18, 2021): 5398. http://dx.doi.org/10.3390/ma14185398.

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In the field of industrial wastewater treatment, membrane separation technology, as an emerging separation technology, compared with traditional separation technology such as precipitation, adsorption, and ion exchange, has advantages in separation efficiency, low energy consumption, low cost, simple operation, and no secondary pollution. The application has been expanding in recent years, but membrane fouling and other problems have seriously restricted the development of membrane technology. Natural cellulose is one of the most abundant resources in nature. In addition, nanocellulose has characteristics of high strength and specific surface area, surface activity groups, as well as being pollution-free and renewable, giving it a very wide development prospect in many fields, including membrane separation technology. This paper reviews the current status of nanocellulose filtration membrane, combs the widespread types of nanocellulose and its derivatives, and summarizes the current application of cellulose in membrane separation. In addition, for the purpose of nanocellulose filtration membrane in wastewater treatment, nanocellulose membranes are divided into two categories according to the role in filtration membrane: the application of nanocellulose as membrane matrix material and as a modified additive in composite membrane in wastewater treatment. Finally, the advantages and disadvantages of inorganic ceramic filtrations and nanocellulose filtrations are compared, and the application trend of nanocellulose in the filtration membrane direction is summarized and discussed.

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22

Rais, N. N. M., N. M. Noor, A. Hashim, D. A. Bradley, N. D. Osman, I. Ismail, and H. A. Hassan. "ESTABLISHMENT OF RQT BEAM QUALITY (100 TO 150 kV) FOR COMPUTED TOMOGRAPHY APPLICATIONS." Asian Journal Of Medical Technology 2, no. 2 (August 5, 2022): 1–14. http://dx.doi.org/10.32896/ajmedtech.v2n2.1-14.

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In Malaysia, the radiation beam qualities for calibration of dosimeters in computed tomography (RQT series) were established at the Secondary Standard Dosimetry Laboratory (SSDL) of the Malaysian Nuclear Agency by using a constant potential industrial X-ray machine and a 0.6 cc PTW UNIDOS ionization chamber calibrated at the International Atomic Energy Agency (IAEA). Through the experimental method of additional filtration determination, the results demonstrated that all measured first half-value layer (HVL) filtrations (mm Al) for each RQT 8 (100 kV), RQT 9 (120 kV) and RQT 10 (150 kV) comply with tolerance limits of ± 3% as recommended by the IEC-61676. For RQT 8, a repeated experiment to determine accurate additional filtration has to be done with different added filtration RQT (mm Cu) thickness as the value initially goes beyond the 3% difference. Compared to prior radiation quality series RQT determinations, the added filtration for RQT 8 changed from 0.1 mm Cu in 2019 to 0.2 mm Cu in 2020. When compared against values established over the previous three years, all three RQTs for 2020 exhibit differences in measured first HVL filtrations (mm Al), albeit remaining within the 3% difference standard recommended in the TRS 457 standard of the IAEA. This change arises from x-ray tube aging, anode roughening and inherent filtration alteration, leading to a perceived need for RQT trial and error re-evaluation to reduce the percentage decrement. Yearly monitoring of the beams should be performed to determine possible radiation quality changes, taking corrective action where necessary to remain within the prescribed tolerance limit. The standard radiation qualities should be maintained, allowing for calibration accuracy to confirm dosimeter readings.

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23

Crabb, M. C., and S. A. Mitchell. "The loops onU(n)/O(n) andU(2n)/Sp(n)." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 1 (July 1988): 95–103. http://dx.doi.org/10.1017/s0305004100065269.

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In [6] and [9] the second author and Bill Richter showed that the natural ‘degree’ filtration on the homology of ΩSU(n) has a geometric realization, and that this filtration stably splits (as conjectured by M. Hopkins and M. Mahowald). The purpose of the present paper is to prove the real and quaternionic analogues of these results. To explain what this means, consider the following two ways of viewing the filtration and splitting for ΩSU(n). Whenn= ∞, ΩSU=BU. The filtration isBU(1)⊆BU(2)⊆… and the splittingBU≅ V1≤<∞is a theorem of Snaith[14]. The result for ΩSU(n) may then be viewed as a ‘restriction’ of the result forBU. On the other hand there is a well-known inclusion ℂPn−1. This extends to a map ΩΣℂPn−1→ΩSU(n), and the filtration (or splitting) may be viewed, at least algebraically, as a ‘quotient’ of the James filtration (or splitting) of ΩΣℂPn−1. It is now clear what is meant by the ‘real and quaternionic analogues’. In the quaternionic case, we replaceBUbyBSp=Ω(SU/SP), ΩSU(n) by Ω(SU(2n)/SP(n))and ℂPn−1by ℍPn−1. The integral homology of Ω(SU(2n)/SP(n)) is the symmetric algebra on the homology of ℍPn−1, and may be filtered by the various symmetric powers. We show that this filtration can be realized geometrically, and that the spaces of the filtration are certain (singular) real algebraic varieties (exactly as in the complex case). The strata of the filtration are vector bundles over filtrations of Ω(SU(2n−2)/SP(n−1)), and the filtration stably splits. See Theorems (1·7) and (2·1) for the precise statement. In the real case we replaceBUby Ω(SU/SO), Ω(SU(n)/SO(n)) and ℂPn−1by ℝPn−1. Here integral homology must be replaced by mod 2 homology, and splitting is only obtained after localization at 2. (Snaith's splitting ofBOin [14] can be refined [2, 8] so as to be exactly analogous to the splitting ofBU:BO≅V1≤<∞MO(k).)

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24

Calzolari, Antonella, and Barbara Torti. "A Note on the Strong Predictable Representation Property and Enlargement of Filtration." Mathematics 10, no. 10 (May 23, 2022): 1783. http://dx.doi.org/10.3390/math10101783.

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The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration.

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25

Grbić, Jelena, Stephen Theriault, and Hao Zhao. "Properties of Selick's filtration of the double suspension E2." Journal of Topology and Analysis 06, no. 03 (June 16, 2014): 421–40. http://dx.doi.org/10.1142/s1793525314500150.

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To help study the double suspension [Formula: see text] when localised at a prime p, Selick filtered Ω2S2n+1 by H-spaces which geometrically realise a natural Hopf algebra filtration of H*(Ω2S2n+1;ℤ/p). Later, Gray showed that the fiber Wn of E2 has an integral classifying space BWn and there is a homotopy fibration [Formula: see text]. In this paper we correspondingly filter BWn in a manner compatible with Selick's filtration and the homotopy fibration [Formula: see text], study the multiplicative properties and homotopy exponents of the spaces in the filtrations, and use the filtrations to filter exponent information for the homotopy groups of S2n+1. Our results link three seemingly different in nature classical homotopy fibrations given by Toda, Selick and Gray and make them special cases of a systematic whole. In addition we construct a spectral sequence which converges to the homotopy groups of BWn.

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26

GRAHAM, NEIL. "CENTRIFUGAL FILTRATION." Industrial Lubrication and Tribology 38, no. 5 (May 1986): 174–80. http://dx.doi.org/10.1108/eb053336.

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27

Jacobsen, Erica K. "Water Filtration." Journal of Chemical Education 81, no. 2 (February 2004): 224A. http://dx.doi.org/10.1021/ed081p224a.

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28

Mikelborough, P. "Blood filtration." Anaesthesia 40, no. 2 (February 22, 2007): 204. http://dx.doi.org/10.1111/j.1365-2044.1985.tb10726.x.

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29

Duarte, Frederick F., Layton L. McCoy, and Frank D. Popp. "Microscale filtration." Journal of Chemical Education 69, no. 12 (December 1992): A314. http://dx.doi.org/10.1021/ed069pa314.1.

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30

Karger, Ralf, and Volker Kretschmer. "Inline-filtration." Transfusion and Apheresis Science 27, no. 2 (October 2002): 137–52. http://dx.doi.org/10.1016/s1473-0502(02)00036-8.

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31

Kozubov, A. V., A. A. Gaidash, A. D. Kiselev, and G. P. Miroshnichenko. "Filtration mapping as complete Bell state analyzer for bosonic particles." Scientific Reports 11, no. 1 (July 9, 2021). http://dx.doi.org/10.1038/s41598-021-93679-7.

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AbstractIn this paper, we present the approach to complete Bell state analysis based on filtering mapping. The key distinctive feature of this appoach is that it avoids complications related to using either hyperentanglement or representation of the Bell states as concatenated Greenber–Horne–Zeilinger (C-GHZ) state to perform discrimination procedure. We describe two techniques developed within the suggested approach and based on two-step algorithms with two different types of filtration mapping which can be called the non-demolition and semi-demolition filtrations. In the method involving non-demolition filtration measurement the filtration process employs cross-Kerr nonlinearity and the probe mode to distinguish between the two pairs of the Bell states. In the case of semi-demolition measurement, the two states are unambiguously discriminated and hence destroyed, whereas filtraton keeps the other two states intact. We show that the measurement that destroys the single photon subspace in every mode and preserves the superposition of zero and two photons can be realized with discrete photodetection based on microresonator with atoms.

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32

Bouaka, Aicha. "Sandwiched filtrations." Random Operators and Stochastic Equations, April 28, 2024. http://dx.doi.org/10.1515/rose-2024-2008.

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33

CUTKOSKY, STEVEN DALE. "ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS." Nagoya Mathematical Journal, November 23, 2022, 1–30. http://dx.doi.org/10.1017/nmj.2022.35.

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Abstract In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in a Noetherian local ring continues to be true for divisorial filtrations on a two-dimensional normal excellent local ring R, and that the Hilbert polynomial of the fiber cone of a divisorial filtration on R has a Hilbert function which is the sum of a linear polynomial and a bounded function. We prove these theorems by first studying asymptotic properties of divisors on a resolution of singularities of the spectrum of R. The filtration of the symbolic powers of an ideal is an example of a divisorial filtration. Divisorial filtrations are often not Noetherian, giving a significant difference in the classical case of filtrations of powers of ideals and divisorial filtrations.

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34

"Cattin Filtration acquires Dantherm Filtration's French activities." Filtration Industry Analyst 2010, no. 10 (October 2010): 16. http://dx.doi.org/10.1016/s1365-6937(10)70317-8.

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35

Li, Zhiyuan, and Ruxuan Zhang. "Beauville–Voisin Filtrations on Zero-Cycles of Moduli Space of Stable Sheaves on K3 Surfaces." International Mathematics Research Notices, June 13, 2022. http://dx.doi.org/10.1093/imrn/rnac161.

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Abstract The Beauville–Voisin conjecture predicts the existence of a filtration on a projective hyper-Kähler manifold opposite to the conjectural Bloch–Beilinson filtration, called the Beauville–Voisin filtration. In [13], Voisin has introduced a filtration on zero-cycles of an arbitrary projective hyper-Kähler manifold. On the moduli space of stable objects on a projective K3 surface, there are other candidates constructed by Shen–Yin–Zhao and Barros–Flapan–Marian–Silversmith in [1, 10] and more recently by Vial in [11] from a different point of view. According to the work in [11], all of them are proved to be equivalent except Voisin’s filtration. In this paper, we show that Voisin’s filtration is the same as the other filtrations. As an application, we prove a conjecture in [1].

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36

Mostinsky, I. L. "FILTRATION." A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering f (2006). http://dx.doi.org/10.1615/atoz.f.filtr.

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37

"Filtration." Nature Biotechnology 13, no. 6 (June 1995): 609. http://dx.doi.org/10.1038/nbt0695-609.

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38

"Filtration." Nature Biotechnology 11, no. 7 (July 1993): 846–47. http://dx.doi.org/10.1038/nbt0793-846.

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39

"Filtration." Nature Biotechnology 16, no. 3 (March 1998): 304. http://dx.doi.org/10.1038/nbt0398-304.

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40

Chase, George G., and Ernest Mayer. "Filtration." ChemInform 38, no. 42 (October 16, 2007). http://dx.doi.org/10.1002/chin.200742278.

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41

"Filtration." Journal - American Water Works Association 77, no. 12 (December 1985): 31. http://dx.doi.org/10.1002/j.1551-8833.1985.tb05653.x.

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42

"Filtration." Journal - American Water Works Association 78, no. 12 (December 1986): 25. http://dx.doi.org/10.1002/j.1551-8833.1986.tb02761.x.

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43

"Filtration." Journal - American Water Works Association 80, no. 12 (December 1988): 35. http://dx.doi.org/10.1002/j.1551-8833.1988.tb03146.x.

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44

"Haemo-filtration and plasma filtration devices." Membrane Technology 1999, no. 114 (October 1999): 12. http://dx.doi.org/10.1016/s0958-2118(00)88247-6.

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45

"Filtration cell for tangential flow filtration." Membrane Technology 2002, no. 4 (April 2002): 14. http://dx.doi.org/10.1016/s0958-2118(02)80148-3.

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46

"Crossflow filtration and cake filtration studied." Membrane Technology 1993, no. 44 (December 1993): 8. http://dx.doi.org/10.1016/0958-2118(93)90164-h.

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47

Karpenko, Nikita A. "Filtrations on the representation ring of an affine algebraic group." Quarterly Journal of Mathematics, January 10, 2023. http://dx.doi.org/10.1093/qmath/haac044.

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Abstract Let G be an affine algebraic group over a field. The representation ring $\mathrm{R}(G)$ has three standard filtrations, defining the same topology on $\mathrm{R}(G)$: augmentation, Chern and Chow, each of which contained in the next one. For split reductive G, motivated by potential applications related to spin groups, we introduce and study one more filtration, containing the previous ones, which we call induced because it is induced by any of the filtrations on the representation ring of a maximal split torus of G. In the case of semisimple simply connected G, this fourth filtration turns out to be equivalent (in the above topological sense) to the previous three. However, for the spin group $G=\operatorname{\mathrm{Spin}}(d)$ over the complex numbers with $d=7,8$, the new filtration is shown to be strictly larger than the others. It is also shown that for $G=\operatorname{\mathrm{Spin}}(d)$ over an arbitrary field and with any $d\geq7$, the Chern and Chow filtrations on $\mathrm{R}(G)$ are not the same, giving new counter-examples to an extension of Atiyah’s conjecture.

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48

"Membrane filtration: Managing aluminum in membrane filtration." Filtration + Separation 51, no. 4 (July 2014): 26–28. http://dx.doi.org/10.1016/s0015-1882(14)70145-4.

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"Enhancing filtration yields in tangential flow filtration." Filtration & Separation 39, no. 10 (December 2002): 17. http://dx.doi.org/10.1016/s0015-1882(02)80254-3.

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"95/04204 Modern filtration technologies — hyperbaric filtration." Fuel and Energy Abstracts 36, no. 4 (July 1995): 296. http://dx.doi.org/10.1016/0140-6701(95)95793-5.

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