Journal articles: 'Weighted sequences'

1

Garn, Bernhard, and Dimitris E. Simos. "Weighted t-way Sequences." Electronic Notes in Discrete Mathematics 70 (December 2018): 43–48. http://dx.doi.org/10.1016/j.endm.2018.11.007.

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Mathew, Jill K., and Sunil Mathew. "Special sequences in weighted graphs." International Journal of Computing Science and Mathematics 8, no. 4 (2017): 313. http://dx.doi.org/10.1504/ijcsm.2017.085851.

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Mathew, Jill K., and Sunil Mathew. "Special sequences in weighted graphs." International Journal of Computing Science and Mathematics 8, no. 4 (2017): 313. http://dx.doi.org/10.1504/ijcsm.2017.10006755.

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Totura, Ümit, and İbrahim Çanak. "On regularly weighted generated sequences." Filomat 31, no. 7 (2017): 2167–73. http://dx.doi.org/10.2298/fil1707167t.

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We introduce a new concept which is called a regularly weighted generated sequence for sequences of real numbers. Moreover, we obtain some Tauberian conditions in terms of regularly weighted generated sequences for the power series method of summability, and generalize some classical Tauberian theorems given by Tietz [Acta Sci. Math. 54 (3-4) 355-365 (1990)].

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Corcino, R. B., K. J. M. Gonzales, M. J. C. Loquias, and E. L. Tan. "Dually weighted Stirling-type sequences." European Journal of Combinatorics 43 (January 2015): 55–67. http://dx.doi.org/10.1016/j.ejc.2014.06.010.

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Pessoa, Bruno Jefferson de S., Daniel Aloise, and Lucidio A. F. Cabral. "The Weighted Fair Sequences Problem." Computers & Operations Research 91 (March 2018): 121–31. http://dx.doi.org/10.1016/j.cor.2017.11.008.

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Das Adhikari, Sukumar, David J. Grynkiewicz, and Zhi-Wei Sun. "On weighted zero-sum sequences." Advances in Applied Mathematics 48, no. 3 (March 2012): 506–27. http://dx.doi.org/10.1016/j.aam.2011.11.007.

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Nakazi, Takahiko. "Weighted interpolation of weighted ℓ^p sequences and Carleson inequality." Journal of Mathematical Inequalities, no. 2 (2012): 161–66. http://dx.doi.org/10.7153/jmi-06-16.

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9

Strand, Robin. "Weighted distances based on neighbourhood sequences." Pattern Recognition Letters 28, no. 15 (November 2007): 2029–36. http://dx.doi.org/10.1016/j.patrec.2007.05.016.

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10

Barton, Carl, Tomasz Kociumaka, Chang Liu, Solon P. Pissis, and Jakub Radoszewski. "Indexing weighted sequences: Neat and efficient." Information and Computation 270 (February 2020): 104462. http://dx.doi.org/10.1016/j.ic.2019.104462.

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11

Eisner, Tanja. "Linear Sequences and Weighted Ergodic Theorems." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/815726.

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We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .

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Kongpromsuk, Sutasinee, Nantaporn Pitakvej, Nutchawan Jittapiromsak, and Supada Prakkamakul. "Detection of brain metastases using alternative magnetic resonance imaging sequences: a comparison between SPACE and VIBE sequences." Asian Biomedicine 14, no. 1 (July 13, 2020): 27–35. http://dx.doi.org/10.1515/abm-2020-0005.

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AbstractBackgroundAccurate identification of brain metastases is crucial for cancer treatment.ObjectivesTo compare the ability to detect brain metastases of two alternative types of contrast-enhanced three-dimensional (3D) T1-weighted sequences called SPACE (Sampling Perfection with Application optimized Contrasts using different flip angle Evolutions) and VIBE (Volumetric Interpolated Brain Sequence) on magnetic resonance imaging (MRI) at 3 tesla.MethodsBetween April 2017 and February 2018, 27 consecutive adult Thai patients with a total number of 424 brain metastases were retrospectively included. The patients underwent both contrast-enhanced 3D T1-weighted SPACE and 3D T1-weighted VIBE MRI sequences at 3 tesla. Two neuroradiology experts independently reviewed the images to determine the number of enhancing lesions on each sequence. Wilcoxon signed rank test was used to compare the difference between the numbers of detectable parenchymal enhancing lesions. Interobserver reliability was calculated using intraclass correlation.Results3D T1-weighted SPACE detected more parenchymal enhancing lesions than 3D T1-weighted VIBE (424 vs. 378 lesions, median 6 vs. 5, P = 0.008). Fifteen patients (55.6%) had equal number of parenchymal enhancing lesions between two sequences. 3D T1-weighted SPACE detected more parenchymal enhancing lesions (up to 9 more lesions) in 10 patients (37%), while 3D T1-weighted VIBE detected more enhancing lesions (up to 2 more lesions) in 2 patients (7.4%). Interobserver reliability between the readers was excellent.ConclusionContrast-enhanced 3D T1-weighted SPACE sequence demonstrates a higher ability to detect brain metastases than contrast-enhanced 3D T1-weighted VIBE sequence at 3 tesla.

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13

FAN, AI-HUA. "Weighted Birkhoff ergodic theorem with oscillating weights." Ergodic Theory and Dynamical Systems 39, no. 5 (September 25, 2017): 1275–89. http://dx.doi.org/10.1017/etds.2017.81.

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We consider sequences of Davenport type or Gelfond type and prove that sequences of Davenport exponent larger than$\frac{1}{2}$are good sequences of weights for the ergodic theorem, and that the ergodic sums weighted by a sequence of strong Gelfond property are well controlled almost everywhere. We prove that for any$q$-multiplicative sequence, the Gelfond property implies the strong Gelfond property and that sequences realized by dynamical systems can be fully oscillating and have the Gelfond property.

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FRANTZIKINAKIS, NIKOS, and BERNARD HOST. "Weighted multiple ergodic averages and correlation sequences." Ergodic Theory and Dynamical Systems 38, no. 1 (July 4, 2016): 81–142. http://dx.doi.org/10.1017/etds.2016.19.

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We study mean convergence results for weighted multiple ergodic averages defined by commuting transformations with iterates given by integer polynomials in several variables. Roughly speaking, we prove that a bounded sequence is a good universal weight for mean convergence of such averages if and only if the average of this sequence times any nilsequence converges. Two decomposition results of independent interest play key roles in the proof. The first states that every bounded sequence in several variables satisfying some regularity conditions is a sum of a nilsequence and a sequence that has small uniformity norm (this generalizes a result of the second author and Kra); and the second states that every multiple correlation sequence in several variables is a sum of a nilsequence and a sequence that is small in uniform density (this generalizes a result of the first author). Furthermore, we use these results in order to establish mean convergence and recurrence results for a variety of sequences of dynamical and arithmetic origin and give some combinatorial implications.

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Decorato, Douglas R., Neil M. Rofsky, James P. Earls, Glenn A. Krinsky, and Jeffery C. Weinreb. "T-1 weighted sequences for hepatic mri." Clinical Imaging 23, no. 1 (January 1999): 26–31. http://dx.doi.org/10.1016/s0899-7071(98)00075-8.

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Rahman, Md Mahmudur, Chowdhury Farhan Ahmed, and Carson Kai-Sang Leung. "Mining weighted frequent sequences in uncertain databases." Information Sciences 479 (April 2019): 76–100. http://dx.doi.org/10.1016/j.ins.2018.11.026.

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17

Ibadov, Nadir V., and Il'dar Kh Musin. "Difference equations in weighted spaces of sequences." Functiones et Approximatio Commentarii Mathematici 49, no. 2 (December 2013): 357–70. http://dx.doi.org/10.7169/facm/2013.49.2.13.

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18

Serra, António. "Interpolating sequences in harmonically weighted Dirichlet spaces." Proceedings of the American Mathematical Society 131, no. 9 (January 2, 2003): 2809–17. http://dx.doi.org/10.1090/s0002-9939-03-06846-1.

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19

Chacón, Gerardo R. "Interpolating Sequences in Harmonically Weighted Dirichlet Spaces." Integral Equations and Operator Theory 69, no. 1 (July 16, 2010): 73–85. http://dx.doi.org/10.1007/s00020-010-1820-9.

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20

Exner, George R., Joo Young Jin, Il Bong Jung, and Mi Ryeong Lee. "Weighted shifts induced by Hamburger moment sequences." Journal of Mathematical Analysis and Applications 427, no. 2 (July 2015): 581–99. http://dx.doi.org/10.1016/j.jmaa.2015.02.033.

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21

Kim, T. K., B. I. Choi, J. K. Han, H. J. Jang, and M. C. Han. "Optimal MR Protocol for Hepatic Hemangiomas." Acta Radiologica 38, no. 4 (July 1997): 565–71. http://dx.doi.org/10.1080/02841859709174388.

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Purpose: To compare conventional spin-echo (SE) sequences with T2-weighted turbo SE and serial gadolinium-enhanced T1-weighted FLASH sequences in the detection and characterization of hepatic hemangiomas, and to describe the enhancement characteristics of the lesions on dynamic MR imaging. Material and Methods: Forty-two patients with 66 hemangiomas were studied at 1.0 T or 1.5 T by using conventional SE sequences (T1-weighted, T2-weighted, and heavily T2-weighted), T2-weighted turbo SE sequences, and breath-hold T1-weighted FLASH sequences acquired before, immediately after, and 1, 2, 3, 5, and 10 min after injection of a bolus of gadopentetate dimeglumine. Images were quantitatively analyzed for lesion-to-liver contrast-to-noise (C/N) ratios, and qualitatively analyzed for lesion conspicuity. The enhancement pattern and the rapidity of enhancement were analyzed in small (<15 mm), medium (15-39 mm), and large (>39 mm) hemangiomas. Results: In T2-weighted images, T2-weighted turbo SE and heavily T2-weighted SE images had higher C/N ratios than T2-weighted SE images (p=0.003). Lesion conspicuity was not significantly different in these 3 sequences (p=0.307). In T1-weighted images, T1-weighted FLASH images had higher C/N (p<0.001) and also better lesion conspicuity (p<0.001) than T1-weighted SE images. Immediate uniform enhancement was seen in 43% of small hemangiomas (9 of 21 lesions), and persistent central hypo-intensity was seen in 73% of large hemangiomas (11 of 15 lesions). Rapid enhancement was seen in 62% of small hemangiomas (13 of 21 lesions) and in 31% of medium or large hemangiomas (14 of 45 lesions). Conclusion: Further clinical study is needed for evaluating the differential diagnostic advantages of turbo SE T2-weighted imaging compared to the calculation of T2-values by means of a SE T2-weighted sequence. However, the results of the present study suggest that T2-weighted turbo SE imaging and precontrast and serial gadolinium-enhanced FLASH imaging have the potential to replace conventional SE imaging in the evaluation of hepatic hemangiomas.

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22

Yang, Ming Shi, He Jiang, Hong Jun Yu, Xiu Fang Li, and Da Ding. "An Algorithm for Mining Weighted Negative Sequence Pattern." Applied Mechanics and Materials 644-650 (September 2014): 1717–20. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.1717.

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.For the purpose of showing the importance of certain items in the negative sequences and make negative sequences have more practicality, this paper presents a method for mining weighted negative sequence pattern. Set the weight value to calculate the weighted support and prune the weighted negative sequences which don’t meet conditions. We use IRIS data set which belongs to UCI data sets to verify the new algorithm. Comparing with Neg-GSP algorithm, showing the benefit of the weighted concept.

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23

Nagy, Benedek. "Generalised distances of sequences II: B-distances with weight sequences." Filomat 33, no. 18 (2019): 5803–12. http://dx.doi.org/10.2298/fil1918803n.

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In this paper, we investigate the weighted B-distances of infinite sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Zn), and the theory was recently extended for application to sequences. By assigning various weights to the elements of the sequences the concept is further generalized. An algorithm is presented which provides a shortest path between two sequences. Formula is also provided to calculate the weighted B-distance of any two sequences with a neighbourhood sequence B and a weight sequence. There are several neighbourhood sequences, which do not generate metrics. We prove a necessary and sufficient condition for a B-distance to define a generalized metric space above the sequences. Moreover, our results can be applied if the elements of the sequences used with various weights. In case of weight functions used B-distances we present also the metric conditions.

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Barton, Carl, Chang Liu, and Solon P. Pissis. "Fast Average-Case Pattern Matching on Weighted Sequences." International Journal of Foundations of Computer Science 29, no. 08 (December 2018): 1331–43. http://dx.doi.org/10.1142/s0129054118430062.

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A weighted string is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices, weighted sequences or uncertain sequences, naturally arise in many contexts. In this paper, we study the problem of weighted string matching with a special focus on average-case analysis. Given a weighted pattern string [Formula: see text] of length [Formula: see text], a text string [Formula: see text] of length [Formula: see text], both on a constant-sized alphabet of size [Formula: see text], and a cumulative weight threshold [Formula: see text], defined as the minimal probability of occurrence of factors in a weighted string, we present an on-line algorithm requiring average-case search time [Formula: see text] for pattern matching for weight ratio [Formula: see text]. For a pattern string [Formula: see text] of length [Formula: see text], a weighted text string [Formula: see text] of length [Formula: see text], both on a constant-sized alphabet, and a cumulative weight threshold [Formula: see text], we present an on-line algorithm requiring average-case search time [Formula: see text] for the same weight ratio. The importance of these algorithms lies on the fact that, for these ratios, they can work in sublinear search time in the size of the input text, and in linear preprocessing costs in the size of the pattern.

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Cai, Guang-hui. "Chover-type laws of the iterated logarithm for weighted sums of NA sequences." Mathematica Bohemica 132, no. 1 (2007): 27–33. http://dx.doi.org/10.21136/mb.2007.133994.

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Batta, Akash, Karthik Vinay Mahesh, Nandita Prabhat, Ritu Shree, Manoj K. Goyal, Chirag K. Ahuja, Alex Rebello, et al. "Newer magnetic resonance imaging techniques in neurocysticercosis." Neuroradiology Journal 33, no. 6 (August 26, 2020): 538–44. http://dx.doi.org/10.1177/1971400920949394.

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Introduction The definitive diagnosis of neurocysticercosis continues to be challenging. We evaluate the role of newer magnetic resonance imaging techniques including constructive interference in steady state, susceptibility-weighted imaging, arterial spin labelling and magnetic resonance spectroscopy in the diagnosis of neurocysticercosis. Aims and objectives To study the utility of newer magnetic resonance imaging sequences in the diagnosis of neurocysticercosis. Patients and methods Eighty-five consecutive patients with neurocysticercosis attending a tertiary care hospital and teaching centre in northern India were included in the study. The diagnosis of neurocysticercosis was made by the Del Brutto criteria. All patients received treatment according to standard guidelines and were followed at 3-month intervals. The following magnetic resonance sequences were performed at baseline: T1 and T2-weighted axial sequences; T2 fluid-attenuated inversion recovery axial sequences; diffusion-weighted imaging; susceptibility-weighted imaging; pre and post-contrast T1-weighted imaging; heavily T2-weighted thin sections (constructive interference in steady state); arterial spin labelling ( n = 19); and magnetic resonance spectroscopy ( n = 24). Results The mean (±SD) age was 29.4 ± 12.9 years and 76.5% were men. Seizures were the commonest symptom (89.4%) followed by headache (24.3%), encephalitis (9.4%) and raised intracranial pressure (9.4%). Scolex could be visualised in 43.7%, 55.5% and 61.2% of neurocysticercosis patients using conventional, susceptibility-weighted angiography and constructive interference in steady state imaging sequences, respectively. Susceptibility-weighted angiography and constructive interference in steady state images resulted in significantly higher ( P < 0.01) visualisation of scolex compared to conventional sequences. Conclusion Newer magnetic resonance imaging modalities have a lot of promise for improving the radiological diagnosis of neurocysticercosis.

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Rhoades, B. E. "The Spectrum of Weighted Mean Operators." Canadian Mathematical Bulletin 30, no. 4 (December 1, 1987): 446–49. http://dx.doi.org/10.4153/cmb-1987-065-9.

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AbstractRecently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on c0, the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on c0, obtaining the result of Reade as a special case.

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Vellmer, Sebastian, Rüdiger Stirnberg, Daniel Edelhoff, Dieter Suter, Tony Stöcker, and Ivan I. Maximov. "Comparative analysis of isotropic diffusion weighted imaging sequences." Journal of Magnetic Resonance 275 (February 2017): 137–47. http://dx.doi.org/10.1016/j.jmr.2016.12.011.

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29

Liang, Han-Ying, and Chun Su. "Complete convergence for weighted sums of NA sequences." Statistics & Probability Letters 45, no. 1 (October 1999): 85–95. http://dx.doi.org/10.1016/s0167-7152(99)00046-2.

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30

Zhang, Hui, Qing Guo, and Costas S. Iliopoulos. "Locating tandem repeats in weighted sequences in proteins." BMC Bioinformatics 14, Suppl 8 (2013): S2. http://dx.doi.org/10.1186/1471-2105-14-s8-s2.

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31

Lasser, Rupert, and Josef Obermaier. "Weighted shift operators, orthogonal polynomials and chain sequences." Acta Scientiarum Mathematicarum 86, no. 12 (2020): 331–42. http://dx.doi.org/10.14232/actasm-019-152-4.

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32

Ohkubo, Yukio. "The Weighted Discrepancies of Some Slowly Increasing Sequences." Mathematische Nachrichten 174, no. 1 (1995): 239–51. http://dx.doi.org/10.1002/mana.19951740117.

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Hu, Xiaoping, Peter Erhard, Tuang Huu Le, Seong-Gi Kim, Ravi Menon, Peter Andersen, Gregor Adriany, John P. Strupp, and Kâmil U??urbil. "Comparison of T2*-weighted sequences for functional MRI." International Journal of Imaging Systems and Technology 6, no. 2-3 (1995): 184–90. http://dx.doi.org/10.1002/ima.1850060208.

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34

Gao, Peng. "On weighted Hardy inequalities for non-increasing sequences." Journal of Mathematical Inequalities, no. 2 (2018): 551–57. http://dx.doi.org/10.7153/jmi-2018-12-41.

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35

Fan, Aihua. "Fully oscillating sequences and weighted multiple ergodic limit." Comptes Rendus Mathematique 355, no. 8 (August 2017): 866–70. http://dx.doi.org/10.1016/j.crma.2017.07.008.

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Stadtmüller, U., and У. Щтадтмуллер. "Tauberian theorems for weighted means of double sequences." Analysis Mathematica 25, no. 1 (December 1999): 57–68. http://dx.doi.org/10.1007/bf02908426.

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Iliopoulos, C., K. Perdikuri, E. Theodoridis, A. Tsakalidis, and K. Tsichlas. "Algorithms for extracting motifs from biological weighted sequences." Journal of Discrete Algorithms 5, no. 2 (June 2007): 229–42. http://dx.doi.org/10.1016/j.jda.2006.03.018.

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38

Bennett, G., and K. G. Grosse-Erdmann. "Weighted Hardy inequalities for decreasing sequences and functions." Mathematische Annalen 334, no. 3 (February 3, 2006): 489–531. http://dx.doi.org/10.1007/s00208-005-0678-7.

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Chakraborty, Mithun, Ulrike Schmidt-Kraepelin, and Warut Suksompong. "Picking sequences and monotonicity in weighted fair division." Artificial Intelligence 301 (December 2021): 103578. http://dx.doi.org/10.1016/j.artint.2021.103578.

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Cinar, Muhammed, and Mikail Et. "Generalized weighted statistical convergence of double sequences and applications." Filomat 30, no. 3 (2016): 753–62. http://dx.doi.org/10.2298/fil1603753c.

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In this paper we introduce the concept generalized weighted statistical convergence of double sequences. Some relations between weighted (?,?)-statistical convergence and strong (N???,p,q,?,?)-summablity of double sequences are examined. Furthemore, we apply our new summability method to prove a Korovkin type theorem.

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Ben Taher, R., and M. Rachidi. "The Near Subnormal Weighted Shift and Recursiveness." International Journal of Analysis 2013 (March 27, 2013): 1–4. http://dx.doi.org/10.1155/2013/397262.

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We aim at studying the near subnormality of the unilateral weighted shifts, whose moment sequences are defined by linear recursive relations of finite order. Using the basic properties of recursive sequences, we provide a natural necessary condition, that ensure the near subnormality of this important class of weighted shifs. Some related new results are established; moreover, applications and consequences are presented; notably the notion of near subnormal completion weighted shift is implanted and explored.

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Hu, Xun Yang, Luckshi Rajendran, Emmanuelle Lapointe, Roger Tam, David Li, Anthony Traboulsee, and Alexander Rauscher. "Three-dimensional MRI sequences in MS diagnosis and research." Multiple Sclerosis Journal 25, no. 13 (May 22, 2019): 1700–1709. http://dx.doi.org/10.1177/1352458519848100.

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The most recent guidelines for magnetic resonance imaging (MRI) in multiple sclerosis (MS) recommend three-dimensional (3D) MRI sequences over their two-dimensional (2D) counterparts. This development has been made possible by advances in MRI scanner hardware and software. In this article, we review the 3D versions of conventional sequences, including T1-weighted, T2-weighted and fluid-attenuated inversion recovery (FLAIR), as well as more advanced scans, including double inversion recovery (DIR), FLAIR2, FLAIR*, phase-sensitive inversion recovery, and susceptibility weighted imaging (SWI).

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Sparacia, G., T. Angileri, M. Accardi, S. Pappalardo, C. Sarno, and M. De Maria. "Valutazione comparativa delle sequenze fast Spin-echo e Spin-echo T2-dipendenti nella dimostrazione delle lesioni demielinizzanti encefaliche in corso di sclerosi multipla." Rivista di Neuroradiologia 10, no. 2_suppl (October 1997): 233–35. http://dx.doi.org/10.1177/19714009970100s2106.

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We compared T2-weighted fast spin-echo (FSE) magnetic resonance (MR) imaging and conventional spin-echo (CSE) T2-weighted imaging in the detection of brain lesions of multiple sclerosis (MS). 20 patients with clinically definite MS underwent brain imaging with both FSE and CSE T2-weighted imaging. There was no significant difference in total number of lesions detected on FSE vs CSE (1354 vs 1378). Slightly more periventricular and subcortical lesions were detected using CSE than FSE, whereas more posterior cranial fossa lesions were detected by FSE. There was no statistically significant difference in the signal intensity (SI) ratio of MS lesions to that of surrounding normal white matter on FSE vs CSE, however the SI ratio of MS lesions was lower on FSE T2-weighted images (FSE ? 1.87 ± 0.39 vs CSE = 2.09 ± 0.36). Considerable time savings can accrue when substituting FSE for CSE sequences in T2-weighted imaging, and this is a compelling reason to employ such sequence in clinical practice. Our results suggest that although CSE sequences are required to confirm the diagnosis of brain involvement of MS lesions, T2-weighted FSE sequences can replace CSE sequences in long term monitoring especially when patient's movements preclude useful investigation and when optional scanning planes are required.

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Guo, Mingle. "Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random Variables." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/425969.

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The complete convergence for weighted sums of sequences of negatively dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence for weighted sums of sequences of negatively dependent random variables are established. These results not only extend the corresponding results obtained by Li et al. (1995), Gut (1993), and Liang (2000) to sequences of negatively dependent random variables, but also improve them.

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Konca, Şükran. "Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces." Filomat 30, no. 3 (2016): 621–29. http://dx.doi.org/10.2298/fil1603621k.

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Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.

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Peyrot, Hélène, Pierre-François Montoriol, and Michel Canis. "Spontaneous T1-Hyperintensity within an Ovarian Lesion: Spectrum of Diagnoses." Canadian Association of Radiologists Journal 66, no. 2 (May 2015): 115–20. http://dx.doi.org/10.1016/j.carj.2014.07.006.

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Whenever elevated signal intensity is displayed at magnetic resonance imaging (MRI) within an ovarian lesion on unenhanced T1-weighted sequences, some specific diagnoses should be considered because only 3 main components may be responsible for this T1-hyperintensity at MRI: fat, blood products, and proteinaceous or mucinous material. The associated clinical data and concomitant use of T2-weighted sequences and fat-saturation techniques is mandatory to make this tissue characterization possible. The goal of this pictorial review is to provide a simple radiologic reasoning and the differential diagnoses to consider in the presence of spontaneous elevated signal intensity on T1-weighted sequences within a cystic or solid ovarian tumour.

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Kumar Raghuvanshi, Aditya, B. K. Singh, and Ripendra Kumar. "ON DOUBLE WEIGHTED MEAN STATISTICAL CONVERGENCE." International Journal of Research -GRANTHAALAYAH 5, no. 2 (February 28, 2017): 279–83. http://dx.doi.org/10.29121/granthaalayah.v5.i2.2017.1739.

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In this paper, we have established some new theorems on double weighted mean statistical convergence of double sequences, which gives some new results and generalizes the some previous known results of Karakaya.

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Sui, Binbin, Xiaoyan Bai, Peiyi Gao, Yan Lin, Yisen Zhang, Jia Liang, and Xinjian Yang. "High-resolution vessel wall magnetic resonance imaging for depicting imaging features of unruptured intracranial vertebrobasilar dissecting aneurysms." Journal of International Medical Research 49, no. 2 (February 2021): 030006052097738. http://dx.doi.org/10.1177/0300060520977388.

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Objective To demonstrate the application value of high-resolution vessel wall magnetic resonance imaging (HR-VW-MRI) for depicting the imaging features of unruptured intracranial vertebrobasilar dissecting aneurysms (VBDAs). Methods HR-VW-MRI data of 49 patients with suspected unruptured VBDAs were retrospectively analyzed. The presence of intramural hematomas (IMH), double lumens, intimal flaps, and outer diameter enlargements were recorded. Specificity and sensitivity were calculated for both two-dimensional (2D) and three-dimensional (3D) sequences. Additionally, IMH volumes were measured and posterior inferior cerebellar artery (PICA) involvement was analyzed. Results Thirty-five VBDAs were confirmed in 34 patients. The overall sensitivity and specificity were 0.889 (95% confidence interval [CI]: 0.730–0.964) and 0.769 (95% CI: 0.460–0.938) for 2D sequences, and 0.917 (95% CI: 0.764–0.978) and 0.846 (95% CI: 0.537–0.973) for 3D sequences, respectively. Intimal flaps were detected in 57.1%, 87.5%, and 71.4% of all cases on 2D pre-contrast T1-weighted, contrast-enhanced T1-weighted, and 3D T1-weighted black-blood (BB) images, respectively. There was no significant difference in IMH volume between 3D T1-weighted BB and magnetization-prepared rapid gradient-echo sequences. PICA involvement was best visualized using 3D T1 sequences. Conclusion 3D T1-weighted BB MRI provided good visualization of VBDA features, with large coverage, and was useful for detecting dissection flaps.

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49

Tryba, Jacek. "Weighted uniform density ideals." Mathematica Slovaca 68, no. 4 (August 28, 2018): 717–26. http://dx.doi.org/10.1515/ms-2017-0139.

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Abstract Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of weighted uniform density ideals and consider the topological complexity of these ideals as well as when they have certain analytical properties related to the ideal convergence of sequences and series. Furthermore, we prove some inequalities between different upper and lower weighted uniform densities and give the answer to the problem concerning the Darboux property of these densities.

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50

Wang, C., H. Ahlström, S. Ekholm, H. Fagertun, M. Hellström, A. Hemmingsson, S. Holtås, et al. "Diagnostic efficacy of MnDPDP in MR imaging of the liver." Acta Radiologica 38, no. 5 (September 1997): 643–49. http://dx.doi.org/10.1080/02841859709172395.

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Purpose: To assess the diagnostic efficacy, safety and tolerability of mangafodipir trisodium (MnDPDP, Teslascan) in MR imaging of the liver. Material and Methods: Eighty-two patients from 4 centres underwent MR imaging with pre-contrast sequences including T1-weighted SE and GRE, and T2-weighted turbo SE sequences. MnDPDP at a dose of 5 μmol/kg b.w. was administered by slow i.v. infusion, and 20–60 min after infusion the T1-weighted SE and GRE sequences were repeated. Diagnostic efficacy was evaluated by counting the number of lesions and by evaluating whether more information for lesion characterisation was available in post-contrast images. Safety and tolerability were assessed by recording adverse events and infusion-related discomfort. Results: Significantly more lesions were found in MnDPDP-enhanced T1-weighted SE and GRE images than in unenhanced images of the same sequences. More lesions were also found in these images compared with T2-weighted images at a level of marginal significance. More information was obtained from MnDPDP-enhanced images in 40 cases. Mild to moderate adverse events were experienced by 17% of the patients. Conclusion: MnDPDP-enhanced images can improve lesion detection in the liver and are helpful for lesion characterisation. To obtain optimal diagnostic information of liver lesions T2-weighted images are also valuable. MnDPDP is a safe contrast agent for MR imaging of liver lesions.

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Journal articles on the topic 'Weighted sequences'

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