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Journal articles on the topic 'Differential filtration'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Geiss, Hans C., Parhofer, Donner, and Schwandt. "Low Density Lipoprotein Apheresis by Membrane Differential Filtration (Cascade Filtration)." Therapeutic Apheresis 3, no. 3 (August 1999): 199–202. http://dx.doi.org/10.1046/j.1526-0968.1999.00157.x.

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2

von Baeyer, Hans, Frank Kochinke, Ingo Schwaner, Rainer Schwerdtfeger, and Wolfgang Schwarztkopff. "Fundamentals and application of differential filtration." Plasma Therapy and Transfusion Technology 8, no. 4 (December 1987): 273–82. http://dx.doi.org/10.1016/s0278-6222(87)80031-1.

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3

Nagase, Youichi, and Kenji Okada. "Experimental Verification of Governing Differential Equation for Filtration-Constant Pressure Cake Filtration-." Journal of the Society of Powder Technology, Japan 40, no. 11 (2003): 786–94. http://dx.doi.org/10.4164/sptj.40.786.

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4

Khodagholi, Mohammad, Mohammad Hemmati, and Ali Pour. "Efficient filtration system for paraffin-catalyst slurry separation." Chemical Industry and Chemical Engineering Quarterly 19, no. 2 (2013): 295–301. http://dx.doi.org/10.2298/ciceq120226063k.

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The filtration efficiency for separating liquid paraffin (or water) from a slurry consisting of 25 weight% spherical alumina in a Slurry Bubble Column Reactor (SBCR) comprised of a cylindrical tube of 10 cm diameter and 150 cm length was studied. Various differential pressures (?P) were applied to two separate tubular sintered metal stainless steel filter elements with nominal pore size of 4 and 16?m. The experimental results disclosed that the rate of filtrations increased on applying higher differential pressure to the filter element. Albeit this phenomenon is limited to moderate ?Ps and for ?P more than 1 bar is neither harmful nor helpful. The highest filtration rates at ?Ps higher than 1 bar were 170 and 248 ml/minute for 4 and 16?m respectively. Using water as the liquid in slurry the rate of filtration enhanced to 4 folds, and this issue reveals impact of viscosity on filtration efficiency clearly. In all situations, the total amount of particles present in the filtrate part never exceeded a few parts per million (ppm). The statistical analysis of the SEM image of the filtrate indicated that by applying higher pressure difference to the filter element the frequency percent of larger particle size increases. The operation of filter cake removing was performed with back flashing of 300 ml of clean liquid with pressures of 3-5 bar of N2 gas.

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5

Svalov, A. M. "Bottom-hole filtration at a positive differential pressure." Soviet Mining Science 25, no. 1 (January 1989): 56–60. http://dx.doi.org/10.1007/bf02528431.

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6

Atamanyuk, Volodymyr, and Yaroslav Gumnytskyi. "Mass Exchange Dynamics During the Second Filtration Drying Period." Chemistry & Chemical Technology 3, no. 2 (June 15, 2009): 129–37. http://dx.doi.org/10.23939/chcht03.02.129.

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The work is dedicated to theoretical and experimental investigations of kinetics and dynamics of filtration drying of capillary and pore materials, and mineral granulated fertilizers, in particular. The proposed physical model of a moist particle and the differential system of equations which describes heat exchange in the second drying period enables to determine the transfer velocity of mass-exchange zone in a dispersion layer of the material during filtration drying.

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7

Biswas, Indranil. "Differential operators and flat connections on a Riemann surface." International Journal of Mathematics and Mathematical Sciences 2003, no. 64 (2003): 4041–56. http://dx.doi.org/10.1155/s0161171203212187.

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We consider filtered holomorphic vector bundles on a compact Riemann surfaceXequipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. IfQis a stable vector bundle of rankrand degree(1−genus(X))nr, then any holomorphic connection on the jet bundleJn(Q)satisfies this transversality condition for the natural filtration ofJn(Q)defined by projections to lower-order jets. The vector bundleJn(Q)admits holomorphic connection. The main result is the construction of a bijective correspondence between the space of all equivalence classes of holomorphic vector bundles onXwith a filtration of lengthntogether with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of ordernwhose symbol is the identity map.

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8

Bierck, B. R., and R. I. Dick. "In Situ Examination of Effects of Pressure Differential on Compressible Cake Filtration." Water Science and Technology 22, no. 12 (December 1, 1990): 125–34. http://dx.doi.org/10.2166/wst.1990.0107.

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A synchrotron X-ray absorbance technique was used to monitor suspended solids concentration changes in compressible filter cakes formed at different constant pressure differentials. Results for a kaolin slurry and an activated sludge manifested the markedly higher compressibility of the latter sludge. A model developed to describe effects of pressure differential on filtrate production behavior of an ideal compressible slurry indicated that the kaolin slurry behaved as such. However, the activated sludge was not ideal because changes in pressure differential did not cause the idealized change in filtrate production rate. A thin skin of activated sludge solids at the filter medium accounted for the non-ideal compressive behavior. Porewater pressure data acquired 0.86 mm above the filter medium during activated sludge filtration provided evidence of skin formation and its effect - virtually the total pressure drop occurred within this 0.86 mm region throughout cake formation (after which shrinkage began). Hence, significant effective stresses required to consolidate the sludge cake did not develop in most of the cake until cake formation was complete and shrinkage began.

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9

Manolakos, Spiros, Francy Sinatra, Leila Albers, Kevin Hufford, James Alberti, Erkinjon Nazarov, and Theresa Evans-Nguyen. "Differential Mobility Spectrometry for Inorganic Filtration in Nuclear Forensics." Analytical Chemistry 88, no. 23 (November 7, 2016): 11399–405. http://dx.doi.org/10.1021/acs.analchem.6b01441.

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10

Ohkubo, Shun. "Logarithmic growth filtrations for -modules over the bounded Robba ring." Compositio Mathematica 157, no. 6 (June 2021): 1265–301. http://dx.doi.org/10.1112/s0010437x21007107.

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In the 1970s, Dwork defined the logarithmic growth (log-growth for short) filtrations for $p$-adic differential equations $Dx=0$ on the $p$-adic open unit disc $|t|<1$, which measure the asymptotic behavior of solutions $x$ as $|t|\to 1^{-}$. Then, Dwork calculated the log-growth filtration for $p$-adic Gaussian hypergeometric differential equation. In the late 2000s, Chiarellotto and Tsuzuki proposed a fundamental conjecture on the log-growth filtrations for $(\varphi ,\nabla )$-modules over $K[\![t]\!]_0$, which can be regarded as a generalization of Dwork's calculation. In this paper, we prove a generalization of the conjecture to $(\varphi ,\nabla )$-modules over the bounded Robba ring. As an application, we prove a generalization of Dwork's conjecture proposed by Chiarellotto and Tsuzuki on the specialization property for log-growth Newton polygons.

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11

Di Carlo, Dino, Jon F. Edd, Daniel Irimia, Ronald G. Tompkins, and Mehmet Toner. "Equilibrium Separation and Filtration of Particles Using Differential Inertial Focusing." Analytical Chemistry 80, no. 6 (March 2008): 2204–11. http://dx.doi.org/10.1021/ac702283m.

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12

Brunner, R., R. A. Widder, P. Walter, H. Borberg, and K. Oette. "Change in Hemorrheological and Biochemical Parameters following Membrane Differential Filtration." International Journal of Artificial Organs 18, no. 12 (December 1995): 794–98. http://dx.doi.org/10.1177/039139889501801208.

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Introduction: The elimination of high molecular weight proteins may have a positive influence on disorders of the microcirculation due to an improvement in rheological parameters. We therefore attempted to evaluate the rheological efficacy of membrane differential filtration (MDF). Patients and methods: Ten patients suffering from macular disease underwent MDF. Rheological and biochemical parameters as well as visual acuity were determined one day before and after therapy: The study aimed at a reduction in plasma viscosity, standardized whole blood viscosity at hematocrit 0.45 and erythrocyte aggregation at hematocrit 0.3. Results: Severe side-effects were not observed. The rheological parameters were significantly reduced. In detail the posttreatment values were reduced as compared to the pretreatment values as follows: plasma viscosity 85%, standardised whole blood viscosity 86% (hematocrit 0.45), erythrocyte aggregation 59% (hematocrit 0.3), total protein 81%, IgG 66%, IgA 59%, IgM 33%, alpha-2-macroglobulin 30%, triglycerides 102%, total cholesterol 47%, VLDL cholesterol 94%, LDL cholesterol 33%, HDL cholesterol 62%. Visual acuity was improved in 7/10 patients. Conclusions: MDF is a safe and highly effective method for lowering biochemical and improving rheological parameters which led to improvement in visual acuity. We have already replaced plasma exchange with MDF in our clinical practice of hemorrheological therapy.

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13

Lü, Qi, and Xu Zhang. "Well-posedness of backward stochastic differential equations with general filtration." Journal of Differential Equations 254, no. 8 (April 2013): 3200–3227. http://dx.doi.org/10.1016/j.jde.2013.01.010.

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14

Safina, Galina. "Numerical solution of filtration in porous rock." E3S Web of Conferences 97 (2019): 05016. http://dx.doi.org/10.1051/e3sconf/20199705016.

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The filtration problem is one of the most relevant in the design of retaining hydraulic structures, water supply channels, drainage systems, in the drainage of the soil foundation, etc. Construction of transport tunnels and underground structures requires careful study of the soil properties and special work to prevent dangerous geological processes. The model of particle transport in the porous rock, which is based on the mechanical-geometric interaction of particles with a porous medium, is considered in the paper. The suspension particles pass freely through large pores and get stuck in small pores. The deposit concentration increases, the porosity and the permissible flow of particles through large pores changes. The model of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and fractional flow through accessible pores is determined by the quasi-linear equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth. This complex system of differential equations has no explicit analytical solution. An equivalent differential equation is used in the paper. The solution of this equation by the characteristics method yields a system of integral equations. Integration of the resulting equations leads to a cumbersome system of transcendental equations, which has no explicit solution. The system is solved numerically at the nodes of a rectangular grid. All calculations are performed for non-linear filtration coefficients obtained experimentally. It is shown that the solution of the transcendental system of equations and the numerical solution of the original hyperbolic system of partial differential equations by the finite difference method are very close. The obtained solution can be used to analyze the results of laboratory research and to optimize the grout composition pumped into the porous soil.

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15

Kuzmina, Ludmila Ivanovna, and Yuri Viktorovich Osipov. "Asymptotic solution of the filtration equation." Vestnik MGSU, no. 2 (February 2016): 49–61. http://dx.doi.org/10.22227/1997-0935.2016.2.49-61.

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The problem of filtering a suspension of tiny solid particles in a porous medium is considered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles ahead of the front; behind the front of the fluid flow solid particles interact with the porous medium. The geometric model of filtration without effects caused by viscosity and electrostatic forces is considered. Solid particles in the suspension pass freely through large pores together with the fluid flow and are stuck in the pores that are smaller than the size of the particles. It is considered that one particle can clog only one small pore and vice versa. The precipitated particles form a fixed deposit increasing over time. The filtration problem is formed by the system of two quasi-linear differential equations in partial derivatives with respect to the concentrations of suspended and retained particles. The boundary conditions are set at the filter inlet and at the initial moment. At the concentration front the solution of the problem is discontinuous. By the method of potential the system of equations of the filtration problem is reduced to one equation with respect to the concentration of deposit with a boundary condition in integral form. An asymptotic solution of the filtration equation is constructed near the concentration front. The terms of the asymptotic expansions satisfy linear ordinary differential equations of the first order and are determined successively in an explicit form. For verification of the asymptotics the comparison with the known exact solutions is performed.

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16

Santos, Nathalia Fontes de Souto dos, Vanessa Viscardi, Anna Clara Porthun Caruso, Rodolpho de Almeida Torres Filho, Nayro Xavier de Alencar, and Daniel Augusto Barroso Lessa. "EQUINE TRACHEOBRONCHIAL WASH FILTRATION AND ITS EFFECTS ON DIFFERENTIAL CELL COUNT." Ciência Animal Brasileira 17, no. 2 (June 2016): 274–78. http://dx.doi.org/10.1590/1089-6891v17i231988.

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Abstract Tracheobronchial wash (TBW) is a method to recover cell samples from the airways. The cytology of TBW fluid is an important technique for the diagnosis of pulmonary diseases in horses. Excessive mucus in TBW may cause cell damage and morphological changes that hinder cell type recognition, resulting in a misdiagnosis. The aim of this study was to compare the results of differential cell count in a tracheobronchial wash of filtered and non-filtered samples. Endoscopy and TBW procedures were performed in thirty horses. Each TBW sample was split into two aliquots. Two groups were formed: non-filtrated aliquots (NF) and filtrated aliquots (F). The filtration was performed using a hydrophilic gauze pad. After centrifugation, the differential cell count was performed considering 300 nucleated cells. The filtrated aliquots results presented a significant increase of macrophages count and a significant decrease in neutrophils count comparing to the results of non-filtrated aliquots. These findings were consistent with results of filtered bronchoalveolar wash published studies. Therefore, the filtration of TBW is not an efficient method.

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17

Gard, M. F. "Measurement of X-ray tube accelerating potential by differential beam filtration." IEEE Transactions on Instrumentation and Measurement 45, no. 3 (June 1996): 745–49. http://dx.doi.org/10.1109/19.494592.

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18

Zhu, Minxian. "A Weyl module filtration for the vertex algebra of differential operators." Representation Theory of the American Mathematical Society 15, no. 10 (April 29, 2011): 370. http://dx.doi.org/10.1090/s1088-4165-2011-00381-2.

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19

Chen, Qiqi, Yujian Liu, Hangjun Deng, Tingting Lyu, Jing Tan, Weimin Yang, Haoyi Li, and Seeram Ramakrishna. "Melt differential electrospinning of polyphenylene sulfide nanofibers for flue gas filtration." Polymer Engineering & Science 60, no. 11 (October 15, 2020): 2887–94. http://dx.doi.org/10.1002/pen.25520.

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20

Nordén, Harry V., and Petteri Kauppinen. "Application of Volume Balances and the Differential Diffusion Equation to Filtration." Separation Science and Technology 29, no. 10 (June 1994): 1319–34. http://dx.doi.org/10.1080/01496399408006943.

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21

Lüke, C., R. A. Widder, F. Soudavar, P. Walter, R. Brunner, and H. Borberg. "Improvement of macular function by membrane differential filtration in diabetic retinopathy." Journal of Clinical Apheresis 16, no. 1 (2001): 23–28. http://dx.doi.org/10.1002/jca.1004.

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22

Shagapov, V. Sh, and Z. M. Nagaeva. "On elastic regime of filtration in hydraulic fracture." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 2 (2016): 156–66. http://dx.doi.org/10.21662/uim2016.2.023.

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Fluid recovery from a well in the modes of constant pressure drop and constant flow rate is considered basing on a theoretical model of filtration in a hydraulic fracture. Exact analytical solutions are obtained that allowed analyzing the effect of the reservoir and fracture properties (such as porosity, permeability and crack width) as well as the rheological properties of the saturating fluid upon: pressure evolution in the fracture, well flow rate at constant pressure drop, and pressure evolution in the wellbore. On the basis of theoretical models describing the filtration for a crack in an oil or gas reservoirs, the considered problem on the selection of fluids from the well in modes constant differential pressure and constant flow. For the considered tasks are received exact analytical solutions, based on which we analyzed the influence of reservoir characteristics of the formation and fractures (for example, their porosity, permeability and width of cracks) and the rheological properties of the saturating fluid on the evolution of the pressure in the fracture, the production rate at a constant differential to the dynamics of the pressure in the well.

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23

Ravshanov, Normakhmad, Nozim Kurbonov, and Abduvali Mukhamadiev. "An Approximate Analytical Solution of the Problem of Fluid Filtration in the Multilayer Porous Medium." International Journal of Computational Methods 13, no. 06 (November 2, 2016): 1650042. http://dx.doi.org/10.1142/s0219876216500420.

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This paper deals with a mathematical problem statement of unsteady fluid flow in heterogeneous porous media with various hydrogeological characteristics. In order to solve the problem the authors developed an approximate analytical method. The method allows multidimensional differential equation in partial derivatives describing the process of fluid filtration in layered porous media to become one-dimensional differential equation. There was obtained a calculation formula for determining the process of mass transfer between the layers, depending on the operating modes of production wells and hydrogeological parameters of filtration layers. The model and the algorithm can be used as a mathematical support for the processes of development of oil and gas fields.

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24

Agishi, T. "Selective Removal of Pathogenetic Macromolecules Directly from Whole Blood by Double Filtration Technique." International Journal of Artificial Organs 9, no. 5 (September 1986): 355–58. http://dx.doi.org/10.1177/039139888600900519.

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Double filtration plasmapheresis (DFPP) is a technique devised in an attempt to selectively remove pathogenetic macromolecules such as antibodies, immune complexes or viscosity-increasing substances directly from blood. In order to realize the differential filtration principle, two filters, one for separation of plasma and another for fractionation of plasma components, are installed in an extracorporeal circulation line. Selective separation of the plasma components is dependent on the filtration property of the two filters. Clinical experiences evidence the usefulness of this technique in regard to conservation of human blood products for supplementation.

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25

Gülle, Saniye, Mustafa Bak, Erkin Serdaroglu, Demet Can, and Ozalp Karabay. "Low-Density Lipoprotein Apheresis by Membrane Differential Filtration (Cascade Filtration) via Arteriovenous Fistula Performed in Children With Familial Hypercholesterolemia." Therapeutic Apheresis and Dialysis 14, no. 1 (February 2010): 87–92. http://dx.doi.org/10.1111/j.1744-9987.2009.00795.x.

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26

Selivyorstova, Tatjana, Vadim Selivyorstov, and Yuliia Mala. "Fractional-differential approach to describe the process of feeding metals and alloys solidifying under controlled gas pressure." System technologies 4, no. 135 (April 5, 2021): 149–55. http://dx.doi.org/10.34185/1562-9945-4-135-2021-15.

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To describe the processes of filtration in the folding dendritic-porous middle of the proponation, a number of fractional-differential mathematical models of the diffusion type. Described non-linear, how to take the shot of the abducted Riman-Leeuwill for an hour, as it can be stuck for a correct description of the single-phase filtration of not Newtonian age in the porous middle.The two-phase zone, which is established during the transition from melting from hard to hard mill, can often be characterized by abnormal kinetics of resistance. The peculiarities of kinetics in the whole range of winners are related to the issues of widespread nonlocality, in a number of types, memory defects, which adhere to the progressive laws. The mathe-?atical apparatus, which allows to adequately describe such processes, is the theory of integration-differentiation of the fractional order.Victorians in robotic thinking have a phenomenological character, so the possibility of their dependence in a specific, practical dermal condition is blamed on the basis of experimental results, so that the validity of other differences is confirmed. Stagnation of the given approach for describing the dynamics of the process of vitality of the two-phase zones and metals and alloys, which solidifies in the minds of a regulated gas vice. Presented in the fractional-differential robotic model of filtration are classified as abnormal diffusion. A characteristic feature of the ryvnyan, which is derived from different types of differential models of filtration, is not the same. With a whole model, they preserve the structure of the classical lines of filtration in the whole order and pass into them in boundary drops, if the order of the other differentiation is old.Vivchennya yakіsnyh authorities otrimanih іvnyans, and also prompts їh numerical decisions є to finish nontrivial zavdannyi, as vimagayut in the skin okremomu vampad of independent thought.

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27

Krupp, A. U., I. M. Griffiths, and C. P. Please. "Stochastic modelling of membrane filtration." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160948. http://dx.doi.org/10.1098/rspa.2016.0948.

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Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances and deposition on the membrane surface. In this paper, we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function , which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.

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28

Bondarko, M. V. "Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura." Journal of the Institute of Mathematics of Jussieu 8, no. 1 (October 16, 2008): 39–97. http://dx.doi.org/10.1017/s147474800800011x.

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AbstractWe describe explicitly the Voevodsky's triangulated category of motives $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$ (and give a ‘differential graded enhancement’ of it). This enables us to able to verify that DMgm ℚ is (anti)isomorphic to Hanamura's $\mathcal{D}$(k).We obtain a description of all subcategories (including those of Tate motives) and of all localizations of $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$. We construct a conservative weight complex functor $t:\smash{\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}}\to\smash{K^{\mathrm{b}}(\operatorname{Chow}^{\mathrm{eff}})}$; t gives an isomorphism $K_0(\smash{\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}})\to\smash{K_0(\operatorname{Chow}^{\mathrm{eff}})}$. A motif is mixed Tate whenever its weight complex is. Over finite fields the Beilinson–Parshin conjecture holds if and only if tℚ is an equivalence.For a realization D of $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$ we construct a spectral sequence S (the spectral sequence of motivic descent) converging to the cohomology of an arbitrary motif X. S is ‘motivically functorial’; it gives a canonical functorial weight filtration on the cohomology of D(X). For the ‘standard’ realizations this filtration coincides with the usual one (up to a shift of indices). For the motivic cohomology this weight filtration is non-trivial and appears to be quite new.We define the (rational) length of a motif M; modulo certain ‘standard’ conjectures this length coincides with the maximal length of the weight filtration of the singular cohomology of M.

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29

KEDLAYA, KIRAN S. "LOCAL MONODROMY OF p-ADIC DIFFERENTIAL EQUATIONS: AN OVERVIEW." International Journal of Number Theory 01, no. 01 (March 2005): 109–54. http://dx.doi.org/10.1142/s179304210500008x.

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This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent ∇-modules, the Christol–Mebkhout construction of the ramification filtration, and the Christol–Dwork Frobenius antecedent theorem. We also briefly discuss the p-adic local monodromy theorem without proof.

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30

Bogaenko, V. A., and V. M. Bulavatsky. "Computer modeling of the fractional-differential dynamics of some filtration-consolidation processes." Reports of the National Academy of Sciences of Ukraine, no. 4 (April 28, 2018): 16–24. http://dx.doi.org/10.15407/dopovidi2018.04.016.

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31

Nagase, Youichi, Kenji Okada, and Shaoxiang Qian. "Constitutive Equation and Governing Differential Equation for Filtration Expressed in Moving Coordinate." Journal of the Society of Powder Technology, Japan 40, no. 10 (2003): 712–19. http://dx.doi.org/10.4164/sptj.40.712.

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32

Prabu, G. R., P. G. Kawar, and D. Theertha Prasad. "Differential filtration approach for isolation and enrichment of Sugarcane Grassy Shoot phytoplasma." Sugar Tech 10, no. 3 (October 2008): 274–77. http://dx.doi.org/10.1007/s12355-008-0049-2.

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33

Hall, Adam B., Stephen L. Coy, Amol Kafle, James Glick, Erkinjon Nazarov, and Paul Vouros. "Extending the Dynamic Range of the Ion Trap by Differential Mobility Filtration." Journal of The American Society for Mass Spectrometry 24, no. 9 (June 25, 2013): 1428–36. http://dx.doi.org/10.1007/s13361-013-0655-4.

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34

Maximova, N. O. "On nonnegative solutions of differential inequalities connected with the nonstationary filtration equation." Journal of Mathematical Sciences 80, no. 5 (July 1996): 2108–12. http://dx.doi.org/10.1007/bf02362516.

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35

Freeman, Charles, Reuben Burch, Lesley Strawderman, Catherine Black, David Saucier, Jaime Rickert, John Wilson, Holli Seitz, and Jeffrey Stull. "Do They Really Work? Quantifying Fabric Mask Effectiveness to Improve Public Health Messaging." International Journal of Environmental Research and Public Health 19, no. 11 (May 24, 2022): 6372. http://dx.doi.org/10.3390/ijerph19116372.

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The purpose of this study is to compare masks (non-medical/fabric, surgical, and N95 respirators) on filtration efficiency, differential pressure, and leakage with the goal of providing evidence to improve public health messaging. Masks were tested on an anthropometric face filtration mount, comparing both sealed and unsealed. Overall, surgical and N95 respirators provided significantly higher filtration efficiency (FE) and differential pressure (dP). Leakage comparisons are one of the most significant factors in mask efficiency. Higher weight and thicker fabric masks had significantly higher filtration efficiency. The findings of this study have important implications for communication and education regarding the use of masks to prevent the spread of COVID-19 and other respiratory illnesses, specifically the differences between sealed and unsealed masks. The type and fabric of facial masks and whether a mask is sealed or unsealed has a significant impact on the effectiveness of a mask. Findings related to differences between sealed and unsealed masks are of critical importance for health care workers. If a mask is not completely sealed around the edges of the wearer, FE for this personal protective equipment is misrepresented and may create a false sense of security. These results can inform efforts to educate health care workers and the public on the importance of proper mask fit.

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36

Аlexeev, B. V. "ANALYTIC SOLUTION OF NONLINEAR LEYBENSON EQUATION IN THE THEORY OF FILTRATION." Fine Chemical Technologies 11, no. 1 (February 28, 2016): 34–39. http://dx.doi.org/10.32362/2410-6593-2016-11-34-39.

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Analytic solution of nonlinear Leybenson equation in the theory of filtration is obtained. Analytical solutions of the partial differential equations are presented in the explicit algebraic form. The integral surfaces in three dimensions are presented.

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37

CORNEA, O., K. A. DE REZENDE, and M. R. DA SILVEIRA. "Spectral sequences in Conley’s theory." Ergodic Theory and Dynamical Systems 30, no. 4 (October 13, 2009): 1009–54. http://dx.doi.org/10.1017/s0143385709000479.

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AbstractIn this paper, we analyse the dynamics encoded in the spectral sequence (Er,dr) associated with certain Conley theory connection maps in the presence of an ‘action’ type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Δ to provide a system that spans Er in terms of the original basis of C and to identify all of the differentials drp:Erp→Erp−r. In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E0p and E0p−r in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications.

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KAPLUNOV, D. R., A. N. KACHURIN, G. V. FRIDLENDER, and M. P. GANIN. "CALCULATING FILTRATION AIR FLOW IN THE BLOCK OF GASIFIED COAL BED." News of the Tula state university. Sciences of Earth 2, no. 1 (2020): 283–89. http://dx.doi.org/10.46689/2218-5194-2020-2-1-283-289.

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The mathematical model for calculating the filtration air flow in the block of gasified coal bed is substantiated. It is proved that the rate of filtration of the air flow in the block of gasified coal bed will depend on the gas permeability of coal and the difference between the squares of the air pressure on the lines of injection and production wells. It is shown that the filtration rate of the air flow in the block of gasified coal bed is one of the main physical parameters of the process of underground coal gasification. Obviously, the efficiency of underground coal gasification can be controlled by changing the rate of filtration of the air flow, by changing the gas permeability of the coal bed and the differential pressure of air on the lines of injection and production wells.

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Freeman, Charles, Reuben Burch, Lesley Strawderman, Catherine Black, David Saucier, Jaime Rickert, John Wilson, et al. "Preliminary Evaluation of Filtration Efficiency and Differential Pressure ASTM F3502 Testing Methods of Non-Medical Masks Using a Face Filtration Mount." International Journal of Environmental Research and Public Health 18, no. 8 (April 13, 2021): 4124. http://dx.doi.org/10.3390/ijerph18084124.

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Research surrounding the mandated use of non-medical fabric masks is inconsistent and often confusing when compared to the standard N95. A recently published standard from ASTM International and the Centers for Disease Control and Prevention attempts to normalize evaluation procedures. The purpose of this study is to conduct a preliminary evaluation of the new methods for testing filtration efficiency of masks outlined by ASTM International F3502, where results can be directly compared to standards outlined for non-medical fabric masks. Eleven consumer non-medical fabric masks were tested for filtration efficiency and airflow resistance using a face filtration mount in accordance with the newly released ASTM International standard for facial barriers. The mean FE% (SD) ranged from 0.46% (0.44) to 11.80% (2.76) with the 3-layer athletic mesh having the highest performance and the highest deviations. All the masks tested following the procedure failed to meet to minimum FE of 20%; however all masks performed below the minimum upper limits for airflow resistance. Using a non-medical fabric masks as the sole mitigation strategy may not be as effective, as previously reported. With efforts to standardize and regulate the non-medical fabric mask market, this study demonstrates a variety of currently available consumer mask products do not meet the minimum standards nor are these remotely close to the standards of surgical or N95 masks.

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Topolewski, Mateusz. "Reflected BSDEs with general filtration and two completely separated barriers." Probability and Mathematical Statistics 39, no. 1 (June 10, 2019): 199–218. http://dx.doi.org/10.19195/0208-4147.39.1.13.

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We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right-continuity and completeness. As for barriers, we assume that there are càdlàg processes of class D that are completely separated. We prove the existence and uniqueness of solutions for an integrable final condition and an integrable monotone generator. An application to the zero-sum Dynkin game is given.

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Alimbekova, N. B., D. R. Baigereyev, and M. N. Madiyarov. "Study of a Numerical Method for Solving a Boundary Value Problem for a Differential Equation with a Fractional Time Derivative." Izvestiya of Altai State University, no. 4(114) (September 9, 2020): 64–69. http://dx.doi.org/10.14258/izvasu(2020)4-10.

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Recently, there has been an increased interest in the problem of numerical implementation of multiphase filtration models due to its enormous economic importance in the oil industry, hydrology, and nuclear waste management. In contrast to the classical models of filtration, filtration models in highly porous fractured formations with the fractal geometry of wells are not fully understood. The solution to this problem reduces to solving a system of differential equations with fractional derivatives. In the paper, a finite-difference scheme is constructed for solving the initial-boundary value problem for the convection-diffusion equation with a fractional time derivative in the sense of Caputo-Fabrizio. A priori estimates are obtained for solving a difference problem under the assumption that there is a solution to the problem in the class of sufficiently smooth functions that prove the uniqueness of the solution and the stability of the difference scheme. The convergence of the solution of the difference problem to the solution of the original differential problem with the second order in time and space variables is shown. The results of computational experiments confirming the reliability of theoretical analysis are presented.

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Li, Yan Xia, Hao Hu, Mao Zhong Hu, Liang Yin, Dan Yang, and Shi Qiu. "Air Filtration and Pressure Boost Technique for the Operating Room of Construction Machinery." Advanced Materials Research 468-471 (February 2012): 168–72. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.168.

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An air filtration and pressure boost technique for the operating room was brought forward to the construction machinery working in dust atmosphere. The constitution, rationale and design method of the air filtration and pressure boost system was introduced in details. The method was successfully used to the operating room upgrade for a small scoop-tram. A certain positive pressure differential was maintained between the upgraded operating room and the outside, which preventing the access of the outside dust to the interior room and protecting the operator.

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Bulavatskiy, Vladimir M., and Iuriy G. Kryvonos. "On the Modeling of Fractional-Differential Dynamics of Some Processes of Relaxational Filtration." Journal of Automation and Information Sciences 47, no. 7 (2015): 4–14. http://dx.doi.org/10.1615/jautomatinfscien.v47.i7.20.

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Klingel, Reinhard, Thurid Fassbender, Cordula Fassbender, and Britta Gohlen. "From Membrane Differential Filtration to Lipidfiltration: Technological Progress in Low-density Lipoprotein Apheresis." Therapeutic Apheresis and Dialysis 7, no. 3 (June 2003): 350–58. http://dx.doi.org/10.1046/j.1526-0968.2003.00062.x.

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Miller, G. B., and A. R. Pankov. "Filtration of a random process in a statistically uncertain linear stochastic differential system." Automation and Remote Control 66, no. 1 (January 2005): 53–64. http://dx.doi.org/10.1007/s10513-005-0006-4.

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Miller, G. B., and A. R. Pankov. "Filtration of a random process in a statistically uncertain linear stochastic differential system." Automation and Remote Control 66, no. 1 (January 2005): 53–64. http://dx.doi.org/10.1007/s10513-005-0058-5.

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Bulavatsky, V. M. "Mathematical Models and Problems of Fractional-Differential Dynamics of Some Relaxation Filtration Processes." Cybernetics and Systems Analysis 54, no. 5 (September 2018): 727–36. http://dx.doi.org/10.1007/s10559-018-0074-4.

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Baigereyev, Dossan, Dinara Omariyeva, Nurlan Temirbekov, Yerlan Yergaliyev, and Kulzhamila Boranbek. "Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation." Mathematics 10, no. 8 (April 15, 2022): 1319. http://dx.doi.org/10.3390/math10081319.

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In this paper, we propose an efficient numerical method for solving an initial boundary value problem for a coupled system of equations consisting of a nonlinear parabolic partial integro-differential equation and an elliptic equation with a nonlinear term. This problem has an important applied significance in petroleum engineering and finds application in modeling two-phase nonequilibrium fluid flows in a porous medium with a generalized nonequilibrium law. The construction of the numerical method is based on employing the finite element method in the spatial direction and the finite difference approximation to the time derivative. Newton’s method and the second-order approximation formula are applied for the treatment of nonlinear terms. The stability and convergence of the discrete scheme as well as the convergence of the iterative process is rigorously proven. Numerical tests are conducted to confirm the theoretical analysis. The constructed method is applied to study the two-phase nonequilibrium flow of an incompressible fluid in a porous medium. In addition, we present two examples of models allowing for prediction of the behavior of a fluid flow in a porous medium that are reduced to solving the nonlinear integro-differential equations studied in the paper.

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QADERMARZI, AMIR, MOJTABA POULADI, ALI REZAMAND, SEYED HOSSEIN HOSEINIFAR, and ALI AKBAR HEDAYATI. "Investigation of sub-acute levels of zinc oxide nanoparticles on the filtration rate of Mytilaster lineatus and Dressina polymorpha in the short term." Nusantara Bioscience 10, no. 1 (February 1, 2018): 53–57. http://dx.doi.org/10.13057/nusbiosci/n100108.

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Qadermarzi A, Pouladi M, Rezamand A, Hoseinifar SH, Hedayati AA. 2018. Investigation of sub-acute levels of zinc oxide nanoparticles on the filtration rate of Mytilaster lineatus and Dressina polymorpha in the short term. Nusantara Bioscience 10: 53-57. The filtration rate is one of the physiological indices in the bivalves which indicate the degree of efficacy of the filtration function in the exposure to contaminants. In this study, changes in the filtration rate of freshwater bivalves (D. polymorpha and M. lineatus) were investigated after exposure periods of 5 and 10 days with nanoparticles. Bivalves were transferred from the natural environment to the laboratory. The distribution of nanoparticles was measured by differential light scattering (DLS). Bivalves were exposed to 2.5, 25 and 50 ppm nanoparticles for ten days in water reservoirs. The filtration rates were significantly different in the treatments compared to the control samples, with the highest filtration rate was observed in the control group. On the fifth day, the highest filtration rate was obtained in the first treatment of M. lineatus and the lowest filtration rate was obtained in the third treatment of D. polymorphia. The highest filtration rates were observed in the first and second treatments and the lowest filtration rate was observed in the third treatment. Also, there was no significant difference in the filtration rate of M. lineatus in the 1st treatment with control (P> 0.05) on the 5th day, but filtration rate was significantly (P <0.05) less than other concentrations and control group in the third treatment. On the other hand, the filtration rates on the 10th day showed similar differences compared to the 5th day. It could be concluded that the changes infiltration rate are an appropriate indicator for the measurement of contamination in nanoparticles.

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FAIDI, WAHID, ANIS MATOUSSI, and MOHAMED MNIF. "OPTIMAL STOCHASTIC CONTROL PROBLEM UNDER MODEL UNCERTAINTY WITH NONENTROPY PENALTY." International Journal of Theoretical and Applied Finance 20, no. 03 (April 24, 2017): 1750015. http://dx.doi.org/10.1142/s0219024917500157.

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In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type [Formula: see text]-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty is studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.

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