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Artykuły w czasopismach na temat „Diffusion Equivalence”

Autor: Grafiati

Data publikacji: 27 lipca 2024

Data aktualizacji: 31 lipca 2025

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1

Derbez, Patrick, and Marie Euler. "Equivalence of Generalised Feistel Networks." IACR Transactions on Symmetric Cryptology 2024, no. 1 (2024): 412–40. http://dx.doi.org/10.46586/tosc.v2024.i1.412-440.

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This paper focuses on equivalences between Generalised Feistel Networks (GFN) of type-II. We introduce a new definition of equivalence which captures the concept that two GFNs are identical up to re-labelling of the inputs/outputs, and give a procedure to test this equivalence relation. Such two GFNs are therefore cryptographically equivalent for several classes of attacks. It induces a reduction o the space of possible GFNs: the set of the (k!)2 possible even-odd GFNs with 2k branches can be partitioned into k! different classes.This result can be very useful when looking for an optimal GFN r

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2

Goldberg, Maxim J., and Seonja Kim. "Equivalence of $$L_p$$ diffusion approximation and a function’s diffusion smoothness." Semigroup Forum 100, no. 3 (2019): 837–49. http://dx.doi.org/10.1007/s00233-019-10030-3.

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3

Harkola, Julia, and Arent Greve. "DIFFUSION OF TECHNOLOGY: COHESION OR STRUCTURAL EQUIVALENCE?" Academy of Management Proceedings 1995, no. 1 (1995): 422–26. http://dx.doi.org/10.5465/ambpp.1995.17536702.

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4

Malham, David G. "Toward Reality Equivalence in Spatial Sound Diffusion." Computer Music Journal 25, no. 4 (2001): 31–38. http://dx.doi.org/10.1162/01489260152815279.

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5

Iagar, Razvan Gabriel, Guillermo Reyes, and Ariel Sánchez. "Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations." Acta Applicandae Mathematicae 123, no. 1 (2012): 53–72. http://dx.doi.org/10.1007/s10440-012-9714-2.

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6

Skal, Asya S. "Equivalence in Mapping of Conductivity, Elasticity and Diffusion Equations Appears or Disappears." Modern Physics Letters B 12, no. 29n30 (1998): 1227–35. http://dx.doi.org/10.1142/s0217984998001451.

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Equivalence in mapping of diffusion and conductivity equations appears when diffusion and conductivity belong to the same universality class and disappears in the opposite case. For asymptotic long-time behavior one exponent of regular diffusion coefficient above the threshold [Formula: see text] and two below the threshold [Formula: see text] and [Formula: see text] are introduced, using the conductivity critical exponent (μ and s) and the Hall coeffcient critical exponent Re(p-pc)-g if R2/R1→1 and Re(p-pc)2s if R2/R1→1 and p<pc. In the first two cases equivalence between the diffusion and

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7

Yairi, Micah B., and David A. B. Miller. "Equivalence of diffusive conduction and giant ambipolar diffusion." Journal of Applied Physics 91, no. 7 (2002): 4374–81. http://dx.doi.org/10.1063/1.1453508.

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8

Popovych, Roman O., and Nataliya M. Ivanova. "Potential equivalence transformations for nonlinear diffusion–convection equations." Journal of Physics A: Mathematical and General 38, no. 14 (2005): 3145–55. http://dx.doi.org/10.1088/0305-4470/38/14/006.

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9

Kim, Heeyoun, and Juyoung Byun. "Development of HLB3-002 (recombinant human PH20 stand-alone) and its applicability as an anticancer diffusion agent." Journal of Clinical Oncology 42, no. 16_suppl (2024): e15195-e15195. http://dx.doi.org/10.1200/jco.2024.42.16_suppl.e15195.

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e15195 Background: HLB3-002 is a standalone of Halozyme's rHuPH20 (Original) and has the same amino acid sequence. HLB3-002 is being developed as a drug diffusion agent that decomposes subcutaneous hyaluronan, allowing substances such as anticancer drugs to be administered subcutaneously. This study was conducted to compare the in vivo efficacy and PK of original and HLB3-002 to confirm equivalence and thereby prove its applicability as a drug diffusion agent. Methods: In the in vivo efficacy test, Trypan blue was mixed with each original and HLB3-002 and administered subcutaneously to confirm

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10

Jespersen, Sune Nørhøj. "Equivalence of double and single wave vector diffusion contrast at low diffusion weighting." NMR in Biomedicine 25, no. 6 (2011): 813–18. http://dx.doi.org/10.1002/nbm.1808.

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11

Torrisi, Mariano, and Rita Tracinà. "An Application of Equivalence Transformations to Reaction Diffusion Equations." Symmetry 7, no. 4 (2015): 1929–44. http://dx.doi.org/10.3390/sym7041929.

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12

Fetthauer, F., S. Weissbach, and O. Bryngdahl. "Equivalence of error diffusion and minimal average error algorithms." Optics Communications 113, no. 4-6 (1995): 365–70. http://dx.doi.org/10.1016/0030-4018(94)00574-e.

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13

Genon-Catalot, Valentine, and Catherine Larédo. "Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments." Annals of Statistics 42, no. 3 (2014): 1145–65. http://dx.doi.org/10.1214/14-aos1216.

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14

Manea, Mihai. "Bottleneck links, essential intermediaries, and competing paths of diffusion in networks." Theoretical Economics 16, no. 3 (2021): 1017–53. http://dx.doi.org/10.3982/te4385.

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We investigate how information goods are priced and diffused over links in a network. A new equivalence relation between nodes captures the effects of network architecture and locations of sellers on the division of profits, and characterizes the topology of competing (and potentially overlapping) diffusion paths. Sellers indirectly appropriate profits over intermediation chains from buyers in their equivalence classes. Links within the same class constitute bottlenecks for information diffusion and confer monopoly power. Links that bridge distinct classes are redundant for diffusion and gener

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15

Ethier, S. N. "Equivalence of two descriptions of the ages of alleles." Journal of Applied Probability 29, no. 1 (1992): 185–89. http://dx.doi.org/10.2307/3214802.

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It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.

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16

Ethier, S. N. "Equivalence of two descriptions of the ages of alleles." Journal of Applied Probability 29, no. 01 (1992): 185–89. http://dx.doi.org/10.1017/s0021900200106734.

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It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.

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17

Freire, Igor Leite, and Mariano Torrisi. "Weak Equivalence Transformations for a Class of Models in Biomathematics." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/546083.

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A class of reaction-diffusion systems unifying severalAedes aegyptipopulation dynamics models is considered. Equivalence transformations are found. Extensions of the principal Lie algebra are derived for some particular cases.

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18

Liu, Zhi Bin, Jin Ma, Bing Shu Wang, and Xin Hui Duan. "The Study on Homogeneous Parameters of Light Water Reactor by the Nodal Diffusion Method." Applied Mechanics and Materials 666 (October 2014): 144–48. http://dx.doi.org/10.4028/www.scientific.net/amm.666.144.

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Recent progress in the development of coarse-mesh nodal methods for the numerical solution of the neutron diffusion and transport equations is reviewed. Compared with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships which are entirely consistent with the multi-group diffusion equation. These relationships most often are derived by developing approximations to the one-dimensional equations obtained by integrating the multidimensional diffusion equation over directions transverse to each coordinate axis

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19

Mariucci, Ester. "Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise." ESAIM: Probability and Statistics 19 (2015): 560–77. http://dx.doi.org/10.1051/ps/2015005.

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20

Iagar, Razvan Gabriel, Ariel Sánchez, and Juan Luis Vázquez. "Radial equivalence for the two basic nonlinear degenerate diffusion equations." Journal de Mathématiques Pures et Appliquées 89, no. 1 (2008): 1–24. http://dx.doi.org/10.1016/j.matpur.2007.09.002.

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21

Harutyunyan, Ani, and Ömer Özak. "Culture, diffusion, and economic development: The problem of observational equivalence." Economics Letters 158 (September 2017): 94–100. http://dx.doi.org/10.1016/j.econlet.2017.06.040.

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22

Gyimóthy, Szabolcs. "Modeling stationary moving medium by static magneto-electric material." European Physical Journal Applied Physics 85, no. 1 (2019): 10901. http://dx.doi.org/10.1051/epjap/2018180161.

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The electromagnetic equivalence of a stationary moving medium to magneto-electric materials is studied. The equivalent material characteristics of the medium at rest is obtained in terms of the diffusion tensor coefficient of the governing partial differential equation. Special attention is paid to the transition condition of field quantities on the boundary of the moving medium; it is found that the nonmoving magneto-electric equivalent model must be supplied with surface sources. The method is demonstrated through examples and verified by finite element simulation.

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23

Goldberg, Maxim J., and Seonja Kim. "A Natural Diffusion Distance and Equivalence of Local Convergence and Local Equicontinuity for a General Symmetric Diffusion Semigroup." Abstract and Applied Analysis 2018 (October 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/6281504.

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In this paper, we consider a general symmetric diffusion semigroup Ttft≥0 on a topological space X with a positive σ-finite measure, given, for t>0, by an integral kernel operator: Ttf(x)≜∫X‍ρt(x,y)f(y)dy. As one of the contributions of our paper, we define a diffusion distance whose specification follows naturally from imposing a reasonable Lipschitz condition on diffused versions of arbitrary bounded functions. We next show that the mild assumption we make, that balls of positive radius have positive measure, is equivalent to a similar, and an even milder looking, geometric demand. In the

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24

Zheng, Yang, Wei Liu, Xiaoqiang Li, et al. "Prediction and Analysis of Nuclear Explosion Radioactive Pollutant Diffusion Model." Pollutants 3, no. 1 (2023): 43–56. http://dx.doi.org/10.3390/pollutants3010004.

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This study presents a model for the dispersion of radioactive smoke clouds from a nuclear weapon explosion. A model based on a modified Settlement model is chosen to simulate the dispersion of radioactive contaminants from a nuclear explosion in the atmosphere. The arrival time and dose rate of radioactive fallout at various distances in the downwind direction are given for different equivalents of the surface explosion and typical meteorological conditions. Thus, the prediction of the dispersion of radioactive contaminants from a nuclear explosion can be achieved under the conditions of known

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25

Pérez-Pinacho, Claudia A., and Cristina Verde. "A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model." Mathematics 10, no. 5 (2022): 753. http://dx.doi.org/10.3390/math10050753.

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This note tackles the equivalence problem between the fractional and integer order diffusion models. Unlike existing approaches, the existence of a unique integral transformation mapping the solution of the integer order model to a solution of the fractional order model of α=1/2 is proven. Moreover, the corresponding inverse integral transformation is formally established to guarantee the equivalence and well-posedness of the solutions of these models. Finally, as an example, the solution of a fractional order diffusion model α=1/2, obtained through the solution of its integer order counterpar

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26

Özer, Saadet. "On the equivalence groups for (2+1) dimensional nonlinear diffusion equation." Nonlinear Analysis: Real World Applications 43 (October 2018): 155–66. http://dx.doi.org/10.1016/j.nonrwa.2018.02.010.

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27

Fresneda Portillo, Carlos, and Zenebe W. Woldemicheal. "Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 26. http://dx.doi.org/10.58997/ejde.2022.26.

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We obtain a system of boundary-domain integral equations (BDIE) equivalent to the Dirichlet problem for the diffusion equation in non-homogeneous media. We use an extended version of the boundary integral method for PDEs with variable coefficients for which a parametrix is required. We generalize existing results for this family of parametrices considering a non-smooth variable coefficient in the PDE and source term in \(H^{s-2}(\Omega)\), \(1/2< s <3/2\) defined on a Lipschitz domain. The main results concern the equivalence between the original BVP and the corresponding BDIE system, as

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28

Khushtova, F. G. "On the equivalence of two representations of Green's function of first boundary value problem for fractional-order diffusion equation." REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES 20, no. 2 (2020): 12–15. http://dx.doi.org/10.47928/1726-9946-2020-20-2-12-15.

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29

Vaneeva, Olena, and Alexander Zhalij. "Group classification of variable coefficient quasilinear reaction-diffusion equations." Publications de l'Institut Math?matique (Belgrade) 94, no. 108 (2013): 81–90. http://dx.doi.org/10.2298/pim1308081v.

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The group classification of variable coefficient quasilinear reaction diffusion equations ut = uxx + h(x)B(u) is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformations within the class.

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30

Lavenda, B. H. "Derivation of the Prior Distribution in Bayesian Analysis from the Principle of Statistical Equivalence." Open Systems & Information Dynamics 08, no. 02 (2001): 103–14. http://dx.doi.org/10.1023/a:1011910512406.

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The distinction between uniform and logarithmic uniform prior distributions is made in terms of the principle of statistical equivalence, consisting of two statistically equivalent experiments, where the variable and parameter of the distribution exchange their roles. The two choices of the prior correspond to two terms in the drift of a diffusion process, and the condition for a stationary solution eliminates the choice of the uniform prior. Parameter randomization gives rise to a new distribution where the parameter of the original distribution is replaced by a ‘hitting point’ value of the v

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31

Zhu, Yanjiao, Qilin Li, Wanquan Liu, Chuancun Yin, and Zhenlong Gao. "A Novel Exploration of Diffusion Process Based on Multi-Type Galton–Watson Forests." Mathematics 12, no. 22 (2024): 3462. http://dx.doi.org/10.3390/math12223462.

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Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. The multi-type Galton–Watson forest is a random model of population growth without space or any other resource constraints. In this paper, we use the degenerated multi-type Galton–Watson forest (MGWF) to interpret the diffusion process, corresponding vertices to types and establishing an equivalence relationship between them. With the two-phase setting of the MGWF, one can interpret the diffusion process and the Google PageRank system explicitly. It also

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32

Wang, Yu, and M. Douglas LeVan. "Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell−Stefan Approaches." Journal of Physical Chemistry B 112, no. 29 (2008): 8600–8604. http://dx.doi.org/10.1021/jp710570k.

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33

Genon-Catalot, Valentine, Catherine Laredo, and Michael Nussbaum. "Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift." Annals of Statistics 30, no. 3 (2002): 731–53. http://dx.doi.org/10.1214/aos/1028674840.

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34

Parviainen, Mikko, and Juan Luis Vázquez. "Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 1 (2020): 303–59. http://dx.doi.org/10.2422/2036-2145.201808_006.

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35

Chen, Jingrun, Jason D. A. Lin, and Thuc-Quyen Nguyen. "Towards a Unified Macroscopic Description of Exciton Diffusion in Organic Semiconductors." Communications in Computational Physics 20, no. 3 (2016): 754–72. http://dx.doi.org/10.4208/cicp.050615.010216a.

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AbstractWe study the exciton diffusion in organic semiconductors from a macroscopic viewpoint. In a unified way, we conduct the equivalence analysis between Monte-Carlo method and diffusion equation model for photoluminescence quenching and photocurrent spectrum measurements, in both the presence and the absence of Förster energy transfer effect. Connections of these two models to Stern-Volmer method and exciton-exciton annihilation method are also specified for the photoluminescence quenching measurement.

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36

Adam, Ahmed, Ayman Elbaz, Reo Kai, and Hiroaki Watanabe. "A Numerical Investigation of the Flame Characteristics of a CH4/NH3 Blend Under Different Swirl Intensity and Diffusion Models." Energies 18, no. 15 (2025): 3921. https://doi.org/10.3390/en18153921.

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This study investigates the effects of diffusion modeling and swirl intensity on flow fields and NO emissions in CH4/NH3 non-premixed swirling flames using large eddy simulations (LESs). Simulations are performed for a 50/50 ammonia–methane blend at three global equivalence ratios of 0.77, 0.54, and 0.46 and two swirl numbers of 8 and 12, comparing the unity Lewis number (ULN) and mixture-averaged diffusion (MAD) models against the experimental data includes OH-PLIF and ON-PLIF reported in a prior study by the KAUST group. Both models produce similar flow fields, but the MAD model alters the f

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37

Chaumont-Frelet, Théophile, Alexandre Ern, Simon Lemaire, and Frédéric Valentin. "Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods." ESAIM: Mathematical Modelling and Numerical Analysis 56, no. 1 (2022): 261–85. http://dx.doi.org/10.1051/m2an/2021082.

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We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. We also leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.

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38

KASSNER, K. "SIDEBRANCHING IN NOISELESS DIFFUSION-LIMITED AGGREGATION." Fractals 01, no. 02 (1993): 205–28. http://dx.doi.org/10.1142/s0218348x93000228.

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The equivalence between diffusion-limited aggregation (DLA) and growth in a Laplacian field is exploited to construct an algorithm for the simulation of DLA at large finite noise reduction. This algorithm allows performing of the limit towards infinite noise reduction, yielding a feasible prescription for the simulation of the noiseless, i.e., deterministic limit. Contrary to previous expectations as well as explicit predictions from an analytic theory, clusters grown without noise develop sidebranches. An explanation of this result in terms of the outer radius used in DLA simulations is sugge

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39

Whipham, James W., Gamal A. I. Moustafa, Mohamed Sabba, Weidong Gong, Christian Bengs, and Malcolm H. Levitt. "Cross-correlation effects in the solution NMR spectra of near-equivalent spin-1/2 pairs." Journal of Chemical Physics 157, no. 10 (2022): 104112. http://dx.doi.org/10.1063/5.0107221.

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The nuclear magnetic resonance (NMR) spectra of spin-1/2 pairs contain four peaks, with two inner peaks much stronger than the outer peaks in the near-equivalence regime. We have observed that the strong inner peaks have significantly different linewidths when measurements were performed on a 13C2-labelled triyne derivative. This linewidth difference may be attributed to strong cross-correlation effects. We develop the theory of cross-correlated relaxation in the case of near-equivalent homonuclear spin-1/2 pairs, in the case of a molecule exhibiting strongly anisotropic rotational diffusion.

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40

Tonarely, Michael E., Tommy Genova, Anthony J. Morales, Daniel Micka, Darin Knaus, and Kareem A. Ahmed. "Four-Line C2*/CH* Optical Sensor for Chemiluminescence Based Imaging of Flame Stoichiometry." Sensors 22, no. 15 (2022): 5665. http://dx.doi.org/10.3390/s22155665.

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In the present work, an optical sensor was developed and calibrated for the purpose of non-intrusive equivalence ratio measurements in combustion systems. The sensor incorporates a unique four-line, single-sensor chemiluminescence imaging-based approach, which relies on the ratio of C2* and CH* radical-species intensities to obtain measurements of equivalence ratios. The advantage of the four-line sensor is the use of additional filtering to mitigate broadband luminescence signals, and its improvements over conventional two-line chemiluminescence diagnostics are discussed. The sensor was calib

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41

Freire, Igor Leite, and Mariano Torrisi. "A review on symmetries for certain Aedes aegypti models." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560073. http://dx.doi.org/10.1142/s2010194515600733.

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We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

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42

Liu, Jun, Qing Zhu, and Lihong Zhou. "New Stability Results of the Modified Craig-Sneyd Scheme in a Multidimensional Diffusion Equation with Mixed Derivative Terms." Journal of Physics: Conference Series 2650, no. 1 (2023): 012002. http://dx.doi.org/10.1088/1742-6596/2650/1/012002.

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Abstract The time-dependent multidimensional diffusion equations with mixed derivative terms have been widely used in mathematics. Due to the mixed derivative terms, it is difficult to solve this pattern of multidimensional diffusion equations. The Modified Craig-Sneyd scheme (MCS), which has been applied to value the power derivatives, is one of the most promising methods for solving such equations. Therefore, it is of great importance to study its stability. The unconditional stability problem of MCS for a multidimensional diffusion equation with mixed derivative terms is investigated by tak

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43

Wassmer, Dominik, Bruno Schuermans, Christian Oliver Paschereit, and Jonas P. Moeck. "Measurement and modeling of the generation and the transport of entropy waves in a model gas turbine combustor." International Journal of Spray and Combustion Dynamics 9, no. 4 (2017): 299–309. http://dx.doi.org/10.1177/1756827717696326.

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Indirect combustion noise is caused by entropy spots that are accelerated at the first turbine stage. These so-called entropy waves originate from the equivalence ratio fluctuations in the air–fuel mixture upstream of the flame. As entropy waves propagate convectively through the combustion chamber, they are subject to diffusion and dispersion. Because of the inherent difficulty of accurately measuring the burned gas temperature with sufficient temporal resolution, experimental data of entropy waves are scarce. In this work, the transfer function between equivalence ratio fluctuations and entr

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44

Butterfield, David, Nicholas A. Martin, Georgie Coppin, and David E. Fryer. "Equivalence of UK nitrogen dioxide diffusion tube data to the EU reference method." Atmospheric Environment 262 (October 2021): 118614. http://dx.doi.org/10.1016/j.atmosenv.2021.118614.

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45

Mantegna, Michele, and Luigi Pietro Maria Colombo. "Diffusion through a half space: equivalence between different formulations of the unique solution." Applied Mathematical Sciences 8 (2014): 7727–48. http://dx.doi.org/10.12988/ams.2014.49723.

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46

Iagar, Razvan Gabriel, and Ariel Sánchez. "Radial equivalence and study of self-similarity for two very fast diffusion equations." Journal of Mathematical Analysis and Applications 351, no. 2 (2009): 635–52. http://dx.doi.org/10.1016/j.jmaa.2008.11.006.

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47

Khushtova, F. G. "On the equivalence of representations of Green’s functions of boundary value problems for the fractional diffusion equation." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 25, no. 1 (2025): 11–18. https://doi.org/10.47928/1726-9946-2025-25-1-11-18.

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In this paper, formulas for the integral Stankovich transforms of some elementary and special functions that are important in the theory of boundary value problems of mathematical physics are obtained. To prove the obtained formulas, integral representations, or expansions in power series, of the functions to which the transforms are applied are usedIn this paper, proves the equivalence of two expansions in series in some special functions. This paper is a continuation of the previously proven equivalence of two forms of the Green function of the first boundary value problem in a rectangular d

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48

Merkle, Ana. "Equivalence to uniqueness in the concept of predictability between filtrations." Filomat 37, no. 30 (2023): 10153–60. http://dx.doi.org/10.2298/fil2330153m.

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In this paper we develop the concept of dependence between filtrations given in [11], named causal predictability, which is based on the Granger?s definition of causality. Then, we provide some new properties of this concept and prove a result that consider equivalence to uniqueness of the given concept. Also, a few examples that illustrate applications of the given concept are given with the main focus on stochastic differential equations (SDE) and financial mathematics. The study of Granger?s causality has been defined in the context of time series. Since continuous time models become more a

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Wiegel, F. W., and J. R. Heringa. "Diffusion coefficient of a protein in a fluid membrane: numerical calculation." Canadian Journal of Physics 63, no. 1 (1985): 44–45. http://dx.doi.org/10.1139/p85-006.

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The drag force on an integral membrane protein is usually calculated with an asymptotic formula by Saffman. We have calculated this force by numerically solving the linearized Navier–Stokes equation. The results show that Saffman's formula is accurate within a few percent relative error for the usual range of parameter values. The mathematical equivalence of diffusion in an inhomogeneous membrane with the effective conduction of an inhomogeneous conductor is used to find a relation for the effective diffusion coefficient of a protein in an inhomogeneous membrane.

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50

ARAYA, RODOLFO, ABNER H. POZA, and ERNST P. STEPHAN. "A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM." Mathematical Models and Methods in Applied Sciences 15, no. 07 (2005): 1119–39. http://dx.doi.org/10.1142/s0218202505000674.

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In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

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