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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

MicroRNA-425 facilitates pathogenic Th17 cell differentiation by targeting forkhead box O1 (Foxo1) and is associated with inflammatory bowel disease

Highlights: • MiR-425 expression is significantly increased in patients with IBD. • MiR-425 promotes pathogenic Th17 cell differentiation. • Foxo1 is a novel target of miR-425. • In vivo inhibition of miR-425 alleviates TNBS-induced colitis in mice. Inflammatory bowel disease (IBD) is a chronic autoimmune disease, and its pathogenesis remains mostly unknown. MicroRNAs (miRs) has drawn much attention as a crucial regulator of autoimmune diseases. In this study, we demonstrated, for the first time, that miR-425 was significantly up-regulated in peripheral blood mononuclear cells (PBMC) and mucosa of patients with IBD. In note, T helper (Th) 17 cells were found to be the major source of miR-425 expression. Using gain-of-function approaches, we demonstrated that miR-425 could facilitate the differentiation of CD4{sup +} T cells into Th17 lineage. In addition, forkhead box O1 (Foxo1) was identified as a novel target gene of miR-425, which was able to inhibit Th17 cell differentiation, and it was observed to be markedly decreased in PBMC and mucosa of patients with IBD. Notably, in vivo inhibition of miR-425 significantly alleviated the disease severity of TNBS-induced colitis in mice, with down-regulated levels of IL-17A. Our data reveal a novel mechanism in which the elevated miR-425 in IBD mediates pathogenic Th17 cell generation through down-regulation of Foxo1. In vivo blockade of miR-425 may serve as a novel therapeutic approach in the treatment of IBD.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

CTLA-4 regulates T follicular regulatory cell differentiation and participates in intestinal damage caused by spontaneous autoimmunity

Highlights: • CTLA-4 deficiency leads to spontaneous humoural autoimmune intestinal injury. • CTLA-4 deficiency leads to differentiation obstacles in Tfr cells. • A Tfr shortage leads to non-specific humoural immunity enhancement. Cytotoxic T lymphocyte-associated protein 4 (CTLA-4) is a co-inhibitory molecule expressed by T cells and is required for immune regulation and inflammation prevention. In clinical patients, the CTLA-4 mutation causes spontaneous immune-related early-onset Crohn's disease; however, its potential mechanism is still unknown. In the current study, we found that defects in CTLA-4 in CD4 cells lead to limited differentiation of T follicular regulatory (Tfr) cells and relatively increased T follicular helper (Tfh) cells and spontaneous B cell germinal centres (GCs) responses that trigger the accumulation of autoantibodies in intestinal epithelial cells. In addition, the deficiency of Tfr cells caused by defects in CTLA-4 causes these cells to lose their function of inhibiting the non-specific immune response produced during the specific humoural immune response induced by MCMV (mouse cytomegalovirus), resulting in acute intestinal injury and death in mice. The lack of Tfr cells may be responsible for the immunosuppressive disorder of inflammatory bowel disease caused by CTLA-4 deficiency. In conclusion, we verified that CTLA-4 may be required for Tfr cell differentiation and production. Tfr cells inhibit B cell responses and prevent humoural autoimmune-mediated intestinal damage by regulating Tfh-dependent GC responses.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2023

Learning subgrid-scale models with neural ordinary differential equations

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The early differentiation of Mars inferred from Hf–W chronometry

Mars probably accreted within the first 10 million years of Solar System formation and likely underwent magma ocean crystallization and crust formation soon thereafter. In this study, to assess the nature and timescales of these large-scale mantle differentiation processes we applied the short-lived 182 Hf– 182 W and 146 Sm– 142 Nd chronometers to a comprehensive suite of martian meteorites, including several shergottites, augite basalt NWA 8159, orthopyroxenite ALH 84001 and polymict breccia NWA 7034. Compared to previous studies the 182 W data are significantly more precise and have been obtained for a more diverse suite of martian meteorites, ranging from samples from highly depleted to highly enriched mantle and crustal sources. Our results show that martian meteorites exhibit widespread 182 W/ 184 W variations that are broadly correlated with 142 Nd/ 144 Nd, implying that silicate differentiation (and not core formation) is the main cause of the observed 182 W/ 184 W differences. The combined 182 W– 142 Nd systematics are best explained by magma ocean crystallization on Mars within ~20–25 million years after Solar System formation, followed by crust formation ~15 million years later. Finally, these ages are indistinguishable from the I–Pu–Xe age for the formation of Mars' atmosphere, indicating that the major differentiation of Mars into mantle, crust, and atmosphere occurred between 20 and 40 million years after Solar System formation and, hence, earlier than previously inferred based on Sm–Nd chronometry alone.

58 GEOSCIENCES↗
DOE OSTI2013

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, the computational cost for stiff systems is significantly reduced, while keeping the computational algorithm fully explicit and easy to implement. Numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized MLMC method and corroborate our theoretical findings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improved evaluation of safeguards parameters from spent fuel measurements with the Differential Die-Away (DDA) instrument

The Differential Die-Away (DDA) technique is a highly sensitive non-destructive assay method for characterizing and detecting the presence of fissile material within an item of interest. DDA utilizes a series of pulses from a neutron generator (NG) to actively interrogate an item of interest. The die-away time of the neutron population induced by this active interrogation and the integral of the total differential die-away signal can be used to characterize items such as nuclear waste drums and spent nuclear fuel assemblies. In this work, Los Alamos National Laboratory (LANL) conceptualized, designed, and fabricated a DDA instrument that was deployed for field test measurements at the Central Interim Storage Facility for Spent Nuclear Fuel (Clab) in Oskarshamn, Sweden. The instrument performed multiple static measurements at fixed locations and dynamic axial scans of 15 pressurized water reactor (PWR) and 10 boiling water reactor (BWR) spent fuel assemblies, collecting both passive and active measurement data. The static assays of the assemblies measured the differential die-away signal, die-away time, and total passive neutron emission rate to create calibration curves for the evaluation of assembly multiplication, burnup, initial enrichment, effective fissile mass, and total elemental plutonium mass. Each calibration curve was optimized by minimizing the relative root mean square error (RRMSE) of assembly assay results compared to declared assembly parameters. The same quantities were also measured with the axial scans, and the resulting data were applied in two ways: (1) in the creation of calibration curves to improve evaluation of the same safeguards parameters as static assays, and (2) for comparison to simulation. In most cases, across both PWR and BWR assemblies, axial scan data improved the estimation of the above parameters, quantified by decreasing the calibration curve RRMSE. These axial scan results demonstrate the ability of the DDA instrument and analysis method to characterize spent PWR and BWR fuel as well as, or better than, a static assay of the same assembly. Furthermore, the DDA instrument’s unique ability to obtain both active and passive data in a single, axial scan of an entire spent fuel assembly represents a more efficient and accurate way of assaying spent fuel for verification purposes. These results represent a significant advancement for characterizing spent nuclear fuel compared to current technologies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Azimuthally differential pion femtoscopy relative to the second and third harmonic in Pb–Pb 2.76 TeV collision from ALICE

Azimuthally differential femtoscopic measurements, being sensitive to spatio-temporal characteristics of the source as well as to the collective velocity fields at freeze-out, provide very important information on the nature and dynamics of the system evolution. While the HBT radii modulations relative to the second harmonic event plane reflect mostly the spatial geometry of the source, the third harmonic results are mostly defined by the velocity fields. Radii variations with respect to the third harmonic event plane unambiguously signal a collective expansion and anisotropy in the flow fields. Event shape engineering (ESE) is a technique proposed to select events corresponding to a particular shape. Azimuthally differential HBT combined with ESE allows for a detailed analysis of the relation between initial geometry, anisotropic flow and the deformation of source shape. We present azimuthally differential pion femtoscopy with respect to second and third harmonic event planes as a function of the pion transverse momentum for different collision centralities in Pb–Pb collisions at $\sqrt{S_{NN}}$ = 2.76 TeV. All these results are compared to existing models. Thus, the effects of the selection of the events with high elliptic or triangular flow are also presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Fibroblasts maintained in 3 dimensions show a better differentiation state and higher sensitivity to estrogens

Cell differentiation and response to hormonal signals were studied in a 3D environment on an in-house generated mouse fibroblast cell line expressing a reporter gene under the control of estrogen responsive sequences (EREs). 3D cell culture conditions were obtained in a Rotary Cell Culture System; (RCCS™), a microgravity based bioreactor that promotes the aggregation of cells into multicellular spheroids (MCS). In this bioreactor the cells maintained a better differentiated phenotype and more closely resembled in vivo tissue. The RCCS™ cultured fibroblasts showed higher expression of genes regulating cell assembly, differentiation and hormonal functions. Microarray analysis showed that genes related to cell cycle, proliferation, cytoskeleton, migration, adhesion and motility were all down-regulated in 3D as compared to 2D conditions, as well as oncogene expression and inflammatory cytokines. Controlled remodeling of ECM, which is an essential aspect of cell organization, homeostasis and tissue was affected by the culture method as assessed by immunolocalization of β-tubulin. Markers of cell organization, homeostasis and tissue repair, metalloproteinase 2 (MMP2) and its physiological inhibitor (TIMP4) changed expression in association with the relative formation of cell aggregates. The fibroblasts cultured in the RCCS™ maintain a better responsiveness to estrogens, measured as expression of ERα and regulation of an ERE-dependent reporter and of the endogenous target genes CBP, Rarb, MMP1 and Dbp. Our data highlight the interest of this 3D culture model for its potential application in the field of cell response to hormonal signals and the pharmaco-toxicological analyses of chemicals and natural molecules endowed of estrogenic potential. - Highlights: • We here characterized the first cell line derived from an estrogen reporter mouse. • In the RCCS cells express an immortalized behavior but not a transformed phenotype. • The RCCS provides a system for maintaining cells in more physiological conditions. • RCCS-cultured fibroblasts showed higher hormonal sensitivity to estradiol. • This bioreactor is a novel 3D model to be applied to pharmacotoxicological studies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Dimethyl sulfoxide inhibits spontaneous diabetes and autoimmune recurrence in non-obese diabetic mice by inducing differentiation of regulatory T cells

Type 1 diabetes mellitus (T1D) is caused by the destruction of insulin-producing β cells in pancreatic islets by autoimmune T cells. Islet transplantation has been established as an effective therapeutic strategy for T1D. However, the survival of islet grafts can be disrupted by recurrent autoimmunity. Dimethyl sulfoxide (DMSO) is a solvent for organic and inorganic substances and an organ-conserving agent used in solid organ transplantations. DMSO also exerts anti-inflammatory, reactive oxygen species scavenger and immunomodulatory effects and therefore exhibits therapeutic potential for the treatment of several human inflammatory diseases. In this study, we investigated the therapeutic potential of DMSO in the inhibition of autoimmunity. We treated an animal model of islet transplantation (NOD mice) with DMSO. The survival of the syngeneic islet grafts was significantly prolonged. The population numbers of CD8, DC and Th1 cells were decreased, and regulatory T (Treg) cell numbers were increased in recipients. The expression levels of IFN-γ and proliferation of T cells were also reduced following DMSO treatment. Furthermore, the differentiation of Treg cells from naive CD4 T cells was significantly increased in the in vitro study. Our results demonstrate for the first time that in vivo DMSO treatment suppresses spontaneous diabetes and autoimmune recurrence in NOD mice by inhibiting the Th1 immune response and inducing the differentiation of Treg cells. - Highlights: • We report a therapeutic potential of DMSO in autoimmune diabetes. • DMSO exhibits an immune modulatory effect. • DMSO treatment increases regulatory T cell differentiation. • The increase in STAT5 signaling pathway explains the effect of DMSO in Tregs.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

ERα inhibited myocardin-induced differentiation in uterine fibroids

Uterine fibroids, also known as uterine leiomyomas, are a benign tumor of the human uterus and the commonest estrogen-dependent benign tumor found in women. Myocardin is an important transcriptional regulator in smooth and cardiac muscle development. The role of myocardin and its relationship with ERα in uterine fibroids have barely been addressed. We noticed that the expression of myocardin was markedly reduced in human uterine fibroid tissue compared with corresponding normal or adjacent myometrium tissue. Here we reported that myocardin induced the transcription and expression of differentiation markers SM22α and alpha smooth muscle actin (α-SMA) in rat primary uterine smooth muscle cells (USMCs) and this effect was inhibited by ERα. Notably, we showed that, ERα induced expression of proliferation markers PCNA and ki-67 in rat primary USMCs. We also found ERα interacted with myocardin and formed complex to bind to CArG box and inhibit the SM22α promoter activity. Furthermore, ERα inhibited the transcription and expression of myocardin, and reduced the levels of transcription and expression of downstream target SM22α, a SMC differentiation marker. Our data thus provided important and novel insights into how ERα and myocardin interact to control the cell differentiation and proliferation of USMCs. Thus, it may provide potential therapeutic target for uterine fibroids.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

An siRNA-based screen in C2C12 myoblasts identifies novel genes involved in myogenic differentiation

Myogenesis is a highly regulated multi-step process involving myoblast proliferation and differentiation. Although studies over the last decades have identified several factors governing these distinct major phases, many of them are not yet known. In order to identify novel genes, we took advantage of the C2C12 myoblastic line to establish a functional siRNA screen combined with quantitative-imaging analysis of a large amount of differentiated myoblasts. We knocked down 100 preselected mouse genes without a previously characterized role in muscle. Using image analysis, we tracked gene-silencing phenotypes by quantitative assessment of cellular density, myotube quantity, myotube morphology and fusion index. Our results have revealed six genes involved in both stages of C2C12 myogenesis and 13 genes specific to the differentiation stage. These findings prove that our RNAi-based screen could be an efficient tool to detect clear and subtle phenotypes allowing the identification of new myogenic regulators in mammals. - Highlights: • A new optimized protocol to perform a functional siRNA based screen. • 100 preselected genes knocked-down in C2C12 myoblastic cell line. • 19 candidates genes identified as novel myogenic actors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Optimized simple and affordable procedure for differentiation of monocyte-derived dendritic cells from LRF: An accessible and valid alternative biological source

Dendritic cells are one of the most popular immune cells, which plays a remarkable role in both immunotherapy and tolerance induction. Due to unwanted side effects of leukocyte presence in donated blood, the policy of blood service is the pre-storage reduction of leukocytes, which today, filtration is the most common method for this purpose. The filtration method has led to diminished access to Buffy coat as a generally used conventional source of biological cells. We developed a simple, affordable, and reproducible method for dendritic cell differentiation from filter-derived monocytes and, the results of the filter study were compared with differentiated DCs from the conventional buffy coat-derived monocytes. The Monocytes were recovered from leukoreduction filter using an optimized protocol with supplemented PBS buffer. Following the adhesion method, CD14{sup +} Monocyte-enriched population with the purity of 94 % was obtained. After cytokine stimulation over a 6-day period and maturation induction by LPS, differentiated DCs were evaluated for morphology, surface markers (CD86, CD40, CD83 and, HLA-DR), antigen uptake potency and IL-12 secretion. Analysis and comparison of the results represented no significant difference between the two groups. Accordingly, we conclude that leukoreduction filters could be introduced as a reliable and research-grade source of monocyte for DC generation in biological research.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation

We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion (FWI), subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) At the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in automatic differentiation operators from the TensorFlow backend; (3) at the flow physics level, we implemented customized partial differential equation (PDE) operators for the multiphase flow equations. The three-level coupled inversion strategy strikes a good balance between computational efficiency and programming efforts, and when the gradients are chained together, it constitutes a coupled inverse system. Our numerical experiments demonstrate that the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy. Additionally, our method is able to simultaneously invert for parameters in empirical relationships such as the rock physics models. Our proposed inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Rotationally inelastic scattering of NO(A{sup 2}Σ{sup +}) + Ar: Differential cross sections and rotational angular momentum polarization

We present the implementation of a new crossed-molecular beam, velocity-map ion-imaging apparatus, optimized for collisions of electronically excited molecules. We have applied this apparatus to rotational energy transfer in NO(A{sup 2}Σ{sup +}, v = 0, N = 0, j = 0.5) + Ar collisions, at an average energy of 525 cm{sup −1}. We report differential cross sections for scattering into NO(A{sup 2}Σ{sup +}, v = 0, N′ = 3, 5, 6, 7, 8, and 9), together with quantum scattering calculations of the differential cross sections and angle dependent rotational alignment. The differential cross sections show dramatic forward scattered peaks, together with oscillatory behavior at larger scattering angles, while the rotational alignment moments are also found to oscillate as a function of scattering angle. In general, the quantum scattering calculations are found to agree well with experiment, reproducing the forward scattering and oscillatory behavior at larger scattering angles. Analysis of the quantum scattering calculations as a function of total rotational angular momentum indicates that the forward scattering peak originates from the attractive minimum in the potential energy surface at the N-end of the NO. Deviations in the quantum scattering predictions from the experimental results, for scattering at angles greater than 10°, are observed to be more significant for scattering to odd final N′. We suggest that this represents inaccuracies in the potential energy surface, and in particular in its representation of the difference between the N- and O-ends of the molecule, as given by the odd-order Legendre moments of the surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Theoretical and experimental study on electron interactions with chlorobenzene: Shape resonances and differential cross sections

In this work, we report theoretical and experimental cross sections for elastic scattering of electrons by chlorobenzene (ClB). The theoretical integral and differential cross sections (DCSs) were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR). The calculations with the SMCPP method were done in the static-exchange (SE) approximation, for energies above 12 eV, and in the static-exchange plus polarization approximation, for energies up to 12 eV. The calculations with the IAM-SCAR method covered energies up to 500 eV. The experimental differential cross sections were obtained in the high resolution electron energy loss spectrometer VG-SEELS 400, in Lisbon, for electron energies from 8.0 eV to 50 eV and angular range from 7{sup ∘} to 110{sup ∘}. From the present theoretical integral cross section (ICS) we discuss the low-energy shape-resonances present in chlorobenzene and compare our computed resonance spectra with available electron transmission spectroscopy data present in the literature. Since there is no other work in the literature reporting differential cross sections for this molecule, we compare our theoretical and experimental DCSs with experimental data available for the parent molecule benzene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Geometric properties of commutative subalgebras of partial differential operators

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k[u,t] is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗