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Communications in Algebra, ISSN 0092-7872, 05/2018, Volume 46, Issue 5, pp. 2073 - 2082
The Nagata ring R(X) and the Serre's conjecture ring R⟨X⟩ are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic... 
Prüfer ring | Arithmetical ring | weak dimension | 13F20 | 13B25 | 13C10 | 13F30 | semihereditary ring | 13D05 | Serre's conjecture ring | Gaussian ring | Nagata ring | Prüfer domain | fqp-ring | R(X) | INTEGRAL-DOMAINS | LEMMA | KRONECKER FUNCTION RING | IDEALS | POLYNOMIALS | MATHEMATICS | Prufer ring | Prufer domain | DIMENSION | PROJECTIVE MODULES | Polynomials
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 4, pp. 681 - 731
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a... 
Tutte-Grothendieck ring | Matroid | Arithmetic matroid | Arithmetic Tutte polynomial | Module over Dedekind ring | Valuated matroid | Tropical flag Dressian | MATHEMATICS | MATHEMATICS, APPLIED | tropical flag Dressian | module over Dedekind ring | arithmetic Tutte polynomial | arithmetic matroid | valuated matroid
Journal Article
Computer Physics Communications, ISSN 0010-4655, 02/2019, Volume 235, pp. 400 - 413
In this paper we briefly discuss — an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gröbner... 
Commutative algebra | Polynomial arithmetic | Computer algebra | FACTORIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FACTORING POLYNOMIALS | ALGORITHM | COMPUTATION | PHYSICS, MATHEMATICAL
Journal Article
Communications in Algebra, ISSN 0092-7872, 07/2015, Volume 43, Issue 7, pp. 2863 - 2874
Let A be a commutative ring and E a nonzero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either... 
Arithmetical ring | 13E05 | Bézout ring | Gaussian ring | 13F30 | 13C11 | Chain ring | MATHEMATICS | Bezout ring | Commutative Algebra | Mathematics | Rings and Algebras
Journal Article
Advances in Mathematics, ISSN 0001-8708, 03/2018, Volume 327, pp. 470 - 623
We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring classifying deformations of a fixed Galois representation to... 
Cohomology of arithmetic groups | Automorphic form | Derived algebraic geometry | Galois deformation | LIE-ALGEBRAS | MATHEMATICS | REPRESENTATIONS | PRODUCTS | FUNCTORS | MODEL CATEGORIES | SPECTRA | HOMOLOGY | Mathematics - Number Theory
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2018, Volume 46, Issue 5, pp. 2073 - 2082
Journal Article
Wuhan University Journal of Natural Sciences, ISSN 1007-1202, 8/2018, Volume 23, Issue 4, pp. 277 - 282
For a prime p, let $${E_{P,{P^m}}} = \left\{ {\left( {\begin{array}{*{20}{c}} aamp;b \\ {{p^{m – 1}}c}amp;d \end{array}} \right)\left| {a,b,c \in {Z_p},d}... 
Life Sciences | Life Sciences, general | invertible element | Materials Science, general | endomorphism ring | O 157.4 | Computer Science, general | minimal polynomials | Bisphenol-A
Journal Article
2010, Fields Institute communications, ISBN 0821843117, Volume 58, iv, 133
Book
Journal Article
Optics Communications, ISSN 0030-4018, 06/2014, Volume 321, pp. 38 - 46
An all-optical reconfigurable logic operation essentially constitutes a key technology for performing various processing tasks with ultrafast signal-processing... 
Logic gates | Micro-ring resonator | Multiplexer | Reconfigurable logic | FIBER LASER | BOOLEAN XOR | MACH-ZEHNDER INTERFEROMETER | ARITHMETIC OPERATIONS | BRIGHT SOLITON CONVERSION | XOR GATE | WAVE-GUIDES | ASYMMETRIC-DEMULTIPLEXER | TREE ARCHITECTURE | ASSISTED SAGNAC SWITCH | OPTICS | Network switches | Computer simulation | Circuit design | Multiplexers | Optical switching | Pumps | Circuits | Logic | Resonators
Journal Article
IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 01/2009, Volume 57, Issue 1, pp. 256 - 260
Journal Article
2015, Mathematical surveys and monographs, ISBN 147042214X, Volume no. 204., xiii, 518 pages
Book
Medical Physics, ISSN 0094-2405, 11/2014, Volume 41, Issue 11, pp. 111912 - n/a
Purpose: Compressed sensing (CS)‐based iterative reconstruction (IR) techniques are able to reconstruct cone‐beam CT (CBCT) images from undersampled noisy... 
Computed radiography | iterative reconstruction | Tissues | parallel processing | GPU | CBCT | Digital computing or data processing equipment or methods, specially adapted for specific applications | artifact | Computed tomography | Medical X‐ray imaging | Computerised tomographs | medical image processing | Artifacts and distortion | Reconstruction | Combinations of two or more digital computers each having at least an arithmetic unit, a programme unit and a register, e.g. for a simultaneous processing of several programmes | diagnostic radiography | image reconstruction | graphics processing units | Image sensors | computerised tomography | Cone beam computed tomography | Image data processing or generation, in general | radiation therapy | Image guided radiation therapy | Medical image reconstruction | Therapeutic applications, including brachytherapy | Processor architectures; Processor configuration, e.g. pipelining | low‐dose | Medical image artifacts | low-dose | RISKS | QUALITY | SCATTER CORRECTION | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | COMPUTED-TOMOGRAPHY | PROJECTION DATA | Artifacts | Computer Graphics | Head and Neck Neoplasms - radiotherapy | Algorithms | Time Factors | Head and Neck Neoplasms - diagnostic imaging | Humans | Image Processing, Computer-Assisted - methods | Radiation Dosage | Radiotherapy, Image-Guided | Phantoms, Imaging | Cone-Beam Computed Tomography | INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY | HEAD | PATIENTS | DESIGN | CONES | BEAMS | RESOLUTION | IMPLEMENTATION | CONTAMINATION | PLANT TISSUES | ANIMAL TISSUES | COMPARATIVE EVALUATIONS | 60 APPLIED LIFE SCIENCES | ACCELERATION | DOSES | IMAGES | PELVIS | PHANTOMS | ITERATIVE METHODS | NECK | RADIOTHERAPY | EFFICIENCY | Radiation Imaging Physics
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2016, Volume 445, pp. 232 - 243
Tits has defined Kac–Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley–Demazure group schemes. Here... 
Hyperbolic Kac–Moody group | Finite presentation | Hyperbolic Kac-Moody group | MATHEMATICS | ARITHMETIC GROUPS | FIELDS | THEOREM
Journal Article
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