101,206 research outputs found
Studies on the Marchenko–Pastur Law
No full textIn free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability that are defined by means of the exponential kernel. Within the context of CSK families, this article presents certain features of the Marchenko–Pastur law based on the Fermi convolution and the t-deformed free convolution. The Marchenko–Pastur law holds significant theoretical and practical implications in various fields, particularly in the analysis of random matrices and their applications in statistics, signal processing, and machine learning. In the specific context of CSK families, our study of the Marchenko–Pastur law is summarized as follows: Let K+(μ)={Qmμ(dx);m∈(m0μ,m+μ)} be the CSK family generated by a non-degenerate probability measure μ with support bounded from above. Denote by Qmμ•s the Fermi convolution power of order s>0 of the measure Qmμ. We prove that if Qmμ•s∈K+(μ), then μ is of the Marchenko–Pastur type law. The same result is obtained if we replace the Fermi convolution • with the t-deformed free convolution t
Redatuming and Quantifying Attenuation from Reflection Data Using the Marchenko Equation: A Novel Approach to Quantify Q-factor and Seismic Upscaling
No full textMarchenko Imaging is a new technology in geophysics which enables to retrieve Green's functions at any point in the subsurface having only reflection data. This method is based on the extension of the 1D Gelfand-Levitan-Marchenko equation to a 3D medium. One of the assumptions of the Marchenko method is that the medium is lossless. If the lossy reflection response is used in the Marchenko scheme, some artefacts in the Green's functions as well as in the seismic image are present. One way to circumvent this assumption is to find a compensation parameter for the lossy reflection series so that the lossless Marchenko scheme can be applied. The main tasks of this thesis are to: [1] use the Marchenko equation to estimate the attenuation in the subsurface, [2] find a compensation parameter for the lossy reflection series so that the lossless Marchenko scheme can be applied, and [3] to create an upscaling method for wave propagation. The Artefact Removal Method was created which makes it possible to calculate an effective temporal Q-factor of the medium between a virtual source in the subsurface and receivers at the surface. This method is based on the minimization of the artefacts produced by the lossless Marchenko scheme. The minimization was performed in three ways: [1] in the space-time domain, [2] in the frequency domain and [3] to the scales of the wavelet transform applied to the artefacts. This method can also be used to find the layers with high attenuation. The upscaling method which can be used to construct macro-scale homogenized viscoelastic properties of the medium from the micro-scale properties of a heterogeneous medium was developed. This is done through linking the macro- and micro- scale Lippmann-Schwinger equations which describe the wave field and the strain field scattering in an inhomogeneous medium, respectively. In this thesis, the macro-scale homogenized viscoelastic properties were calculated by using the T-matrix Approach and the Generalized Dvorkin-Mavko Attenuation Model. All theoretical results are supported by synthetic 1D modeling. The theoretical part of the thesis and the general work flow can be used for a very complex medium
Inverse scattering designs of dispersion-engineered single-mode planar waveguides
No full textWe use an inverse-scattering (IS) approach to design single-mode waveguides with controlled linear and higher-order dispersion. The technique is based on a numerical solution to the Gelfand-Levitan-Marchenko integral equation, for the inversion of rational reflection coefficients with arbitrarily large number of leaky poles. We show that common features of dispersion-engineered waveguides such as trenches, rings and oscillations in the refractive index profile come naturally from the IS algorithm without any a priori assumptions. Increasing the leaky-pole number increases the dispersion map granularity and allows design of waveguides with identical low order and differing higher order dispersion coefficients
On Green’s functions, propagator matrices, focusing functions and their mutual relations
No full textGreen’s functions and propagator matrices are both solutions of the wave equation, but whereas Green’s functions obey a causality condition in time (G = 0 for t < 0), propagator matrices obey a boundary condition in space. Marchenko-type focusing functions focus a wave field in space at zero time. We discuss the mutual relations between Green’s functions, propagator matrices and focusing functions, avoiding up-down decomposition and accounting for propagating and evanescent waves. We conclude with discussing a Marchenko-type Green’s function representation, which forms a basis for extending the Marchenko method to improve the imaging of steeply dipping flanks and to account for refracted waves.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic
A note on Marchenko-linearised full waveform inversion for imaging
No full textFull waveform inversion and least-squares reverse time migration are the leading technologies for imaging with seismic waves. Both of them usually rely (in one way or another) on a single-scattering approximation, i.e. the Born approximation, to compute gradients and obtain an updated model. This approximation linearises the relation between modelled data and model by ignoring multiple scattering. We propose to use the Marchenko integral, an equation originating from inverse scattering theory, to obtain an alternative linear equation. Using the Marchenko method we can retrieve Green's functions, including all orders of scattering, for virtual sources anywhere within the volume of interest - without prior knowledge of the high-wavelength model variations that induce scattering. Plugging these estimated Green's functions into the Lippmann-Schwinger integral delivers a Marchenko-linearised relation between the full waveform data and the model. We present this new linearisation strategy and illustrate its advantages and disadvantages by comparing numerical results for different inversion kernels. Our new linearisation is exact, i.e. it does not exclude any orders of scattering, however, it relies on the quality of the Marchenko-derived Green's functions. These Marchenko-based Green's functions require an estimate of the first arrivals of the Green's functions - commonly obtained by modelling in a background medium. Although these first arrival estimates strongly bias our results for inaccurate background models, we find the Marchenko-linearisation to deliver overall slightly better inverted models than the single-scattering approximation
Letter, [Author unclear] to Paulina T. Merritt
No full textHandwritten letter to Paulina Merritt from an unknown author, October 1, 1876.
Gamasiphis ochotensis Marchenko, 2013, sp. n.
No full textGamasiphis ochotensis sp. n. Diagnosis of adults (female and male). Anteromedial extension of epistome aciculate; all idiosomal setae aciculate; podonotal region of dorsal shield with 23 pairs of setae; opisthonotal region with 12 pairs of setae; seta j 4 about 0.9 times as long as distance between its base and base of j 5; seta z 6 about as long as j 6; setae s 3 and s 6 about 0.3 times as long as s 5; seta j 6 about 0.7 times as long as distance between its base and base of J 2; four pairs of J setae; two pairs of pre-sternal platelets; ventrianal shield with eight pairs of setae in addition to circum-anal setae (Jv 1 - Jv 5, Zv 1 - Zv 3); seta Zv 2 about 0.8 times as long as distance between its base and base of Zv 3; seta Jv 5 about 5 times as long as circum-anal setae; setae Jv 3 inserted at the level of unsclerotized line which partly separates the dorsal and ventrianal shields; seta Jv 5 inserted posterior to unsclerotized line which partly separates the dorsal and ventrianal shields; distance between ends of these unsclerotized lines equal to distance between bases of Jv 3; sclerotized diagonal section laterad of ventrianal shield is broad, with wide about 0.8 times as long as Zv 3 at the level of pore. Female. (Fig. 1–7) (five specimens measured). Gnathosoma: Fixed cheliceral digit 50–52 µm long with seven teeth in addition to apical tooth and a setiform pilus dentilis (Fig. 1). Movable cheliceral digit 48–50 µm long, with four teeth in addition to apical tooth. Dorsal cheliceral seta, lateral (antiaxial) and dorsal lyrifissures distinct. Epistome with anteromedian extension smooth and aciculate, with a pair of short anterolateral spines; some specimens with a pair of denticles between anteromedian extension and anterolateral spines (Fig. 2 A–B). Deutosternal groove of hypostome with eight rows of denticles, each bearing 6–14 denticles, except most basal row smooth (Fig. 3); anterior row V-shaped, followed by an inverted V-shaped row, subsequent rows roughly transverse; margins of groove not distinct. Setae h 1 and h 3 equal in length (25–30 µm), h 2 shorter (17–20 µm), Sc (h 4) (20–25 µm). Salivary styli well developed (Fig. 2 B). Internal malae fimbriate laterally. Corniculi 30–32 µm long, 12–15 µm wide at the widest point (Fig. 3). Palp chaetoxy 2-5 - 6-14 - 15; palp trochanter with one small ventral protuberance (Fig. 4); setae al 1 and al 2 of palp genu slightly stout; palp apotele 3 -tined. Dorsal idiosoma (Fig. 5): Dorsal shield entire, ovoid shape, smooth, totally covering dorsal surface; 410–430 µm long, 300–325 µm wide at level of coxa IV. Dorsal shield with 35 pairs of acicular setae. Podonotal region with 23 pairs of setae (j 1 - j 6, z 1 - z 6, s 1 - s 6, r 2 - r 6), 12 pairs of distinguishable lyrifissures (two pairs visible ventrally on mounted specimens) and two pairs of pores (mediad of r 3 and posterior to and mediad of r 6; visible ventrally on mounted specimens); with numerous sigilla posterior to j 5. Opisthonotal region with 12 pairs of setae (J 2 - J 5, Z 2 - Z 5, S 2 - S 3, R 2 - R 3); Z 5 slightly serrated; with 10 pairs of distinguishable lyrifissures (one pair visible ventrally on mounted specimens) and one pair of pores (gdZ 2, anterior and mediad to Z 2). Length of setae: j 1 (10–12), j 2 (25– 30), j 3 (40–45), j 4 (40–45), j 5 (45–50), j 6 (40–45), z 1 (7–10), z 2 (7–10), z 3 (35–40), z 4 (45–50), z 5 (40–45), z 6 (40–45), s 1 (7–10), s 2 (7–10), s 3 (10–12), s 4 (40–45), s 5 (40–45), s 6 (10–12), r 2 (7–10), r 3 (7–10), r 4 (7–10), r 5 (10–12), r 6 (7–10), J 2 (7–10), J 3 (7–10), J 4 (7–10), J 5 (7–10), Z 2 (7–10), Z 3 (7–10), Z 4 (7–10), Z 5 (60–62), S 2 (10–12), S 3 (10–12), R 2 (7–10), R 3 (10–12). Ventral idiosoma (Fig. 6): Base of tritosternum equal in length and wideth (12–17 µm), laciniae (70–75 µm) totally separated from each other, pilose. Pre-sternal area with two pairs of presternal platelets. Sternal shield reticulate anteriorly between st 1 and st 2, smooth posteriorly; 57–62 µm long at mid-line and 135–140 µm wide between coxae II and III; with four pairs of setae (st 1, st 2, st 4 acicular; st 3 stout), st 3 inserted about in transverse line and mediad to st 2; distance between st 3 – st 3 as long as st 3 seta (17–20 µm); and with four pairs of lyrifissures. Endopodal shields fused with and distinctly more sclerotised than sternal shield. Peritreme extending anteriorly to anterior margin of coxa I. Peritrematic shield fused with section of exopodal shield near to coxa IV, widest at level of posterior margin of coxa IV, with a lyrifissure posterior to stigma. Length of peritrematic-exopodal shield from stigma to posterior margin 70–75 µm, width 42–45 µm at level of posterior margin of coxa IV. Band of dorsal shield extending laterad to the fused peritrematic-exopodal shield ending sharply in posterior margin. Genital shield wider than long, 62–67 µm long and 100–102 µm wide, hyaline apex abutting the sternal shield; anterior margin rounded and posterior margin truncate, with a pair of setae st 5 and three pairs of sigilla; distance between st 5 - st 5 60–63 µm. Ventrianal shield with transverse striations anterior to Jv 4 and smooth posteriorly; 180–190 µm long from anterior margin to post-anal seta and 200–210 µm wide at widest point; with eight pairs of acicular setae (Jv 1 - Jv 5, Zv 1 - Zv 3) in addition to post-anal and para-anal setae; with five pairs of lyrifissures (antero-lateral margin of the shield, posterior to and laterad of Zv 1, posterior to and laterad of Zv 2, anterior to and mediad of Zv 3 and laterad of circum-anal seta); distance between Jv 5 and anterior margin of anal opening about 0.5–0.7 times as long as anal opening; seta Jv 5 about 5 times as long as circum-anal seta; post-anal seta about 4 times as long as para-anal setae, the latter situated at level of the posterior margin of anal opening. Dorsal and ventrianal shields partly separated by an unsclerotised line, the ends of this line reach the bases of Jv 3; seta Jv 3 situated at the level of this line; distance between Jv 3 and post-anal setae 70-80 µm. Sclerotised diagonal section laterad of ventrianal shield that connects the latter to the dorsal shield is broad, with one pair of pores; 18–20 µm wide at the level of pore; ending sharply at anterior part and ending broadly near of Zv 3 seta at posterior part. Length of ventral setae: st 1 (27–32), st 2 (25–30), st 3 (17–20), st 4 (25–27), st 5 (22–25), Jv 1 (20–25), Jv 2 (17–22), Jv 3 (20–25), Jv 4 (27–32), Jv 5 (50–55), Zv 1 (20–25), Zv 2 (20–25), Zv 3 (20–25), circum-anal (10–12) and post-anal seta (40–45). Spermatheca: Opening of spermathecal apparatus tubular, extending medially from base of coxa IV (Fig. 7). Other parts of spermatheca not clearly visible. Legs: Lengths: I: 320–330, II: 275–288, III: 230–250, IV: 325–345 µm. Chaetotaxy of legs I–IV: coxa 2, 2, 2, 1; trochanter 6, 5, 5, 5; femur (2 3 / 2 2 / 2 2), (2 3 / 1 2 / 2 1), (1 2 / 1 2 /0 0), (0 2 / 2 2 /0 0); genu (2 3 / 2 3 / 1 2), (2 3 / 1 2 / 1 2), (2 2 / 1 2 /0 1), (2 2 / 1 3 /0 0); tibia (2 3 / 2 3 / 2 2), (2 2 / 1 2 / 1 2), (2 1 / 1 2 / 1 1), (2 1 / 1 3 / 1 1). All leg setae acicular, except one antero-lateral pilose seta on trochanter II. All legs with pretarsus, each with elongate ambulacral stalk and a pair of strongly sclerotised claws, with three rounded pulvilli; claws of pretarsus I slightly smaller than others. Male. (Fig. 8–12) (five specimens measured). Gnathosoma: Fixed cheliceral digit 47–49 µm long, with six teeth in addition to apical tooth, with transverse line across the digit and a setiform pilus dentilis (Fig. 8 A–C). Movable cheliceral digit 45–47 µm long, with one tooth in addition to apical tooth. Spermatodactyl curved; with an internal canal along proximal part (2 / 3 length of spermatodactyl) and with distal part spatulate (1 / 3 length of spermatodactyl). Total length of spermatodactyl 65–70 µm, free process 30–35 µm long. Dorsal cheliceral seta, lateral (antiaxial) and dorsal lyrifissures distinct. Corniculi 25–27 µm long, 7–10 µm wide (Fig. 9). Epistome and hypostome as in female. Setae h 1 and h 3 equal length (25– 27 µm); setae h 1 and Sc equal length (20–25 µm) and slightly shorter than other. Palps as in female. Dorsal idiosoma: 375–400 µm long, 275–300 µm wide. Dorsal shield similar to that of female. Measurements of setae: j 1 (10–12), j 2 (25–30), j 3 (40–45), j 4 (40–45), j 5 (40–50), j 6 (35–40), z 1 (7–10), z 2 (7–10), z 3 (35–40), z 4 (40–50), z 5 (40–50), z 6 (40–50), s 1 (7–10), s 2 (7–10), s 3 (10–12), s 4 (40–50), s 5 (40–50), s 6 (10–12), r 2 (7–10), r 3 (7–10), r 4 (7–10), r 5 (10–12), r 6 (7–10), J 2 (7–10), J 3 (7–10), J 4 (7–10), J 5 (7–10), Z 2 (7–10), Z 3 (7–10), Z 4 (7– 10), Z 5 (55–65), S 2 (10–12), S 3 (10–12), R 2 (7–10), R 3 (7–10). Ventral idiosoma: Base of tritosternum 10–12 µm long and 15–18 µm wide proximally, lacinae (70–75 µm) totally separated from each other, pilose (Fig. 10). Except for the fusion of sternal and genital shields (sternogenital shield), shape, pattern and fusions of ventral shields as in female. Sternogenital shield reticulate between st 1 and st 2, smooth posteriorly; 100–110 µm long and 130–140 µm wide at widest point between coxae II and III; with five acicular setae (s t 1 – st 5), distance st 1 – st 1 45–50 µm, st 2 – st 2 70–75 µm, st 3 – st 3 80–85 µm, st 4 – st 4 80–85 µm and st 5 – st 5 70–75 µm; with four pairs of lyrifissures. Ventrianal shield 210–220 µm long from anterior margin to postanal seta and 200–210 µm wide at widest point; with eight pairs of setae (Jv 1 – Jv 5, Zv 1 – Zv 3) in addition to postanal and circum-anal setae; and with five pairs of lyrifissures (antero-lateral margin of the shield, posterior to and laterad of Zv 1, posterior to and laterad of Zv 2, anterior to and mediad of Zv 3 and laterad of circum-anal seta); postanal seta about 4 times as long as circum-anal seta. Length of ventral setae: st 1 (25–30), st 2 (25–30), st 3 (20–25), st 4 (25–30), st 5 (20–25), Jv 1 (20–25), Jv 2 (20–25), Jv 3 (20–25), Jv 4 (30–35), Jv 5 (45-50), Zv 1 (20–25), Zv 2 (20– 25), Z 3 (20–25), circum-anal (10–12) and post-anal seta (40–45). Legs: Lengths: I: 300–315, II: 260–275, III: 230–245, IV: 310–325 µm. Chaetotaxy of legs similar to that of female. Leg II with one antero-lateral pilose seta on trochanter (similar to female); femur with two ventral spur-like setae (one large spur 30–35 µm length and one small spur on elevated base); genu with two small ventral spur-like setae; tibia with one small ventral spur-like seta; tarsus with one acicular ventral seta on raised base (Fig. 11–12). All other setae of legs acicular. All legs with pretarsus, elongate ambulacral stalk, a pair of strongly sclerotised claws, with three rounded pulvillus; claws of pretarsus I slightly smaller than others, similar to those of female. Material examined. Holotype female, 33 paratype females and 11 paratype males from litter of forest with Betula ermanii —bamboo Sasa spp. and Abies sakhalinensis — Picea glehnii at Chekhov Mounting (47 °00' N, 142 ° 50 ' E), Susunaiskii Ridge, south of Sakhalin Island, Russia, 9 August 1990, collected by I. Volonikhina (Marchenko); 15 paratype females and 14 paratype males from litter at forest with Abies sakhalinensis; Querqus mongolica — Betula ermanii and forest with Ulmus spp. at south of Kunashir Island (43 ° 50 ' N, 145 ° 30 ' E), Russia, 18 July and 20 July 1989, collected by I. Volonikhina (Marchenko); two paratype females and three paratype males from bog with moss and Ledum palustre, in moss at environs of Yuzhno-Kurilsk, Kunashir Island, Russia, 4 August 1989, collected by I. Volonikhina (Marchenko); three paratype female and two paratype males in litter with bushes of Alnus spp. and Taxus cuspidate at Shikotan Island (43 ° 48 ' N, 146 ° 51 ' E), 30 October 1986, collected by S. Kalabin. Holotype and 51 paratypes (30 females and 21 males) deposited at Zoological Museum of the Institute of Systematics and Ecology of Animals, Novosibirsk, Russia; 32 paratypes (23 females and nine males) deposited at arthropod collection of Manchester Museum, Manchester, United Kingdom. Other examined material: 11 females and two males from mosses – lichens – blueberries (Vaccinum spp.) and in litter in a forest of Abies sakhalinensis – Picea glehnii and Betula ermanii –bamboo Sasa spp. at Chekhov Mounting, Susunaiskii Ridge, south of Sakhalin Island, Russia; five females from litter of mixed forest at environs of Ogonki, South Sakhalin, Russia; eight females and six males from litter in a forest of Abies sakhalinensis, in litter of mixed forest with Betula ermanii and Alnus spp., in a broadleaved forest, in a fumarole field with Pinus pumila, in bog with moss and Ledum palustre, at Kunashir Island, Russia; two females from bushes of Juniperus sargentii and Alnus spp. at Shikotan Island, Russia. Etymology. The name ochotensis refers to the name of Okhotsk Sea that bathes Sakhalin and Kuril Islands from the North. Remarks. Gamasiphis ochotensis sp. n. is most similar to Gamasiphis angaridis Marchenko, 2013, but females of the latter have setae s 3 and s 6 as long as s 5; distance between bases of st 3 – st 3 about 0.5 times as long as st 3; seta Jv 3 inserted posteriorly of unsclerotized line which separates partly the dorsal and ventrianal shields; sclerotised diagonal section laterad of ventrianal shield is narrow, with width at the level of pore about 0.3 times shorter than length of Zv 3; and males have spermatodactyl widest at proximal part and gradually narrowing apically, and tarsus II with a spur-seta. It is also similar to Gamasiphis lanceolatus Karg, 1987, but females of the latter have 22 pairs of podonotal setae (s 1 absent) and 13 pairs of opisthonotal setae (S 1 present); dorsal setae j 2 – j 6, z 3 – z 6, s 4 – s 5 and z 5 distally expanded; and males have spermatodactyl with very narrow distal part, about 0.5 times as long as total length of spermatodactyl.Published as part of Marchenko, Irina I., 2013, A new species of Gamasiphis Berlese (Acari: Ologamasidae) from Russia (Sakhalin and Kuril Islands) with a key to the Asian species, pp. 172-180 in Zootaxa 3741 (1) on pages 173-177, DOI: 10.11646/zootaxa.3741.1.6, http://zenodo.org/record/21923
Borg-Marchenko-type Uniqueness Results for CMV Operators
No full textWe prove local and global versions of Borg–Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velázquez [15]). While our half-lattice results are formulated in terms of Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s functions
Влияние психологического пола на самооценку физического развития школьников
No full textKrutsevych T. Yu. Psychological Gender Influence on Self-Esteem of Physical Development of Pupils / T. Yu. Krutsevych, O. Yu. Marchenko // British Medical Bulletin. – Issue 1 (2), (December), Volume 124. – Oxford University Press, 2017. – P. 856-861.Данная статья посвящена изучению взаимосвязи самооценки физического развития юношей и девушек с психологическим полом
The Marchenko-Ostrovski mapping and the trace formula for the Camassa-Holm equation
No full textWe consider the periodic weighted operator Ty---- _p-2(p2y,), q_ p-4 in L2(l,p2dx) where p is a 1-periodic positive function satisfying q -- p/p C L2(0, 1). The spec- trum of T consists of intervals separated by gaps. In the first part of the paper we construct the Marchenko-Ostrovski mapping q --> h(q) and solve the corresponding inverse problem. For our approach it is essential that the mapping h has the factoriza- tion h(q) = h(V(q)), where q --> V(q) is a certain nonlinear mapping and V --> h(V) is the Marchenko-Ostrovski mapping for the Hill operator. In the second part of this paper we derive the trace formula for T in the case q C L2(0, 1)
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