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[[File:Offset (union-of-balls) filtration.png|thumb|upright=1.2|The offset filtration at six scale parameters on a point cloud sampled from two circles of differ ...002-2885-2 |issn=0179-5376|doi-access=free }}</ref> Since then, the offset filtration has become a primary example in the study of computational topology and dat ...

==Experimental techniques== ...age that the deposition of particles can be followed in real time by video techniques and the sequence of images can be analyzed quantitatively.<ref>Y. Luthi, J. ...

.../math> is an increasing <math>\mathbb{Z}</math>-[[Filtration (mathematics)|filtration]] on <math>H_\mathbb{Q} = H_\mathbb{Z}\otimes\mathbb{Q}</math>, <math>\cdot # <math>F^\bullet</math> is a decreasing <math>\mathbb{N}</math>-filtration on <math>H_\mathbb{C}</math>, <math>H_\mathbb{C} = F^0 \supset F^1 \supset ...

...tion of [[linear map]]s induced by the [[Inclusion map|inclusions]] of the filtration. The concept of a persistence module was first introduced in 2005 as an app ...cture of a [[vector space]]. Therefore, given a [[Filtration (mathematics)|filtration]] of spaces <math>F:P \to \mathbf{Top} </math>, by applying the homology [[ ...

...le systems with specific boundary conditions, but in most cases, numerical techniques like finite element analysis (FEA) or finite difference methods (FDM) are u ...forces vary spatially or temporally. These require more advanced numerical techniques to solve. ...

...|title=A review of the function of using carbon nanomaterials in membrane filtration for contaminant removal from wastewater |journal=Materials Research Express ...into a circular configuration. In recent developments, surface patterning techniques have allowed for the integration of permeable feed spacers directly into th ...

...the mechanical separation of gas and liquid streams. In the simplest case, filtration is achieved when the pores of the membrane are smaller than the diameter of ...Database|Nano-Mem-Pro IPPC Database]]). Even in modern [[energy recovery]] techniques, membranes are increasingly used, for example in [[fuel cell]]s and in [[os ...

...([[Infrared spectroscopy|IR]]).<ref name=":2" /> Several other analytical techniques such as [[High-performance liquid chromatography|high performance liquid ch ...issue=9|pages=249–256|doi=10.1016/S0273-1223(99)00663-0}}</ref> A two step filtration process consists of two GAC filters in series. The first filter is loaded w ...

Polymeric coatings are another area of applied grafting techniques. In the formulation of water-borne paint, [[latex]] particles are often sur ...azardous nature of remnant ozone after corona treatment stipulates careful filtration and ventilation during processing, restricting its implementation to applic ...

...rocess (as well as many other continuous processes adapted to the Brownian filtration) is a <math>\mathbb{P}_{\theta^*}</math>-martingale.<ref>{{Cite book|last=A ...g time for <math>X_1, X_2</math>, . . . is then a stopping time w.r.t. the filtration <math> \{\mathfrak{F}_n\}</math>, . . . Let further <math> \mathfrak{G}</ma ...

* Filtration of emitted light: optical filters ensure that reflected and scattered light A different array of microscope techniques can be employed to change the visualization and contrast of an image. Each ...

...rify the K-stability of Fano varieties. For example using purely algebraic techniques it can be proven that all Fermat hypersurfaces<blockquote><math>F_{n,d} = \ === Filtration K-Stability === ...

...lygon mesh|meshes]], and [[molecule]]s, resulted in the development of new techniques, culminating in the field of [[Graph neural network|geometric deep learning ...vector machine]]s or [[random forest]]s. Such descriptors ranged from new techniques for [[feature engineering]] over new ways of providing suitable [[coordinat ...

...nium chloride is removed by filtration from the reaction mass. Because the filtration step is both time-consuming and cost-intensive, several production methods ...c binders added to ceramic powders, [[injection molding]] or other casting techniques are possible, but removal of the organics (“debinding”) is expensive and re ...

...mimic, the endogenously found cellular components. On the other hand, such techniques are also available to create receptor antagonists in order to prevent furth Historically, ligand binding assay techniques were used extensively to quantify hormone or hormone receptor concentration ...

...rationTechniquesforSurfaceMetrology.pdf ''New 3D parameters and filtration techniques for surface metrology'', François Blateyron, Quality Magazine White Paper] ...

A distinct difference to other techniques is that the gyratory motion applied here depends on eccentric [[wikt:weight ...ry separators still make the grade for screening dry bulk powders |journal=Filtration & Separation |date=January–February 2004 |volume=41 |issue=1 |pages=20–21|d ...

...rmite–Einstein metrics, as well as her contributions to the key analytical techniques that underpin the proof of the theorem.<ref name="uhlenbeckprize">{{cite we ...c coherent subsheaf with which slope-destabilises the vector bundle. These techniques were built on by Buchdahl and Li–Yau in the setting where the 2-form <math> ...

...are capable of radiative relaxation, thus limiting fluorescence microscopy techniques such as one-photon and [[two-photon microscopy]].<ref name=Zhou_2016 /> Cur ...fiber output end coaxially aligned with the focused ultrasound transducer. Filtration of ballistic light relies on the altered shape of the excitation laser beam ...

...non-financial entities and by extending existing accounting principles and techniques to these entities. Once the impacts of an organisation on its human and nat ...f an organisation. However, for historians and anthropologists, accounting techniques play a central organising role in the development and complexification of c ...