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Journal articles on the topic 'Ideal Computing'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Sreeramana, Aithal, and Pai T. Vaikunth. "Opportunity for Realizing Ideal Computing System using Cloud Computing Model." International Journal of Case Studies in Business, IT and Education (IJCSBE) 1, no. 2 (2017): 60–71. https://doi.org/10.5281/zenodo.1094995.

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An ideal computing system is a computing system with ideal characteristics. The major components and their performance characteristics of such hypothetical system can be studied as a model with predicted input, output, system and environmental characteristics using the identified objectives of computing which can be used in any platform, any type of computing system, and for application automation, without making modifications in the form of structure, hardware, and software coding by an external user. In this paper, we have proposed cloud computing service model to be used as a part of comput

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2

Keppens, R., and J. W. S. Blokland. "Computing Ideal Magnetohydrodynamic Equilibria." Fusion Science and Technology 49, no. 2T (2006): 131–38. http://dx.doi.org/10.13182/fst06-a1112.

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3

Dung, P. M., P. Mancarella, and F. Toni. "Computing ideal sceptical argumentation." Artificial Intelligence 171, no. 10-15 (2007): 642–74. http://dx.doi.org/10.1016/j.artint.2007.05.003.

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4

AL-AYYOUB, IBRAHIM. "AN ALGORITHM FOR COMPUTING THE RATLIFF–RUSH CLOSURE." Journal of Algebra and Its Applications 08, no. 04 (2009): 521–32. http://dx.doi.org/10.1142/s0219498809003473.

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Let I ⊂ K[x, y] be a 〈x, y〉-primary monomial ideal where K is a field. This paper produces an algorithm for computing the Ratliff–Rush closure Ĩ for the ideal I = 〈m0, …, mn〉 whenever mi is contained in the integral closure of the ideal 〈xan, yb0〉. This generalizes of the work of Crispin [2]. Also, it provides generalizations and answers for some questions given in [6], and enables us to construct infinite families of Ratliff–Rush ideals.

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Sadik, Brahim. "Computing Characteristic Sets of Ordinary Radical Differential Ideals." gmj 13, no. 3 (2006): 515–27. http://dx.doi.org/10.1515/gmj.2006.515.

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Abstract We give upper bounds for the order of the elements in a characteristic set of a regular differential ideal or a radical of a finitely generated differential ideal with respect to some specific orderings. We then show how to compute characteristic sets of these ideals using algebraic methods.

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Creado, Orhio Mark, Bala Srinivasan, Phu Dung Le, and Jeff Tan. "The Ideal Computing System Framework – A Novel Security Paradigm." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 02, no. 04 (2014): 94–103. http://dx.doi.org/10.9756/sijcsea/v2i4/0203270402.

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Hashemi, Amir, Martin Kreuzer, and Samira Pourkhajouei. "Computing all border bases for ideals of points." Journal of Algebra and Its Applications 18, no. 06 (2019): 1950102. http://dx.doi.org/10.1142/s0219498819501020.

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In this paper, we consider the problem of computing all possible order ideals and also sets connected to 1, and the corresponding border bases, for the vanishing ideal of a given finite set of points. In this context, two different approaches are discussed: based on the Buchberger–Möller Algorithm [H. M. Möller and B. Buchberger, The construction of multivariate polynomials with preassigned zeros, EUROCAM ’82 Conf., Computer Algebra, Marseille/France 1982, Lect. Notes Comput. Sci. 144, (1982), pp. 24–31], we first propose a new algorithm to compute all possible order ideals and the correspondi

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Heuberger, Clemens, and Roswitha Rissner. "Computing J-ideals of a matrix over a principal ideal domain." Linear Algebra and its Applications 527 (August 2017): 12–31. http://dx.doi.org/10.1016/j.laa.2017.03.028.

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9

Smith, N. P. "Janus: The Ideal Patron For Computing." Computing in Science and Engineering 2, no. 6 (2000): 106–7. http://dx.doi.org/10.1109/mcise.2000.881714.

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10

Bouziane, Driss, and Abdelilah Kandri Rody. "On the resolvent of an ideal and some applications." International Journal of Mathematics and Mathematical Sciences 2003, no. 70 (2003): 4421–34. http://dx.doi.org/10.1155/s0161171203205378.

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We give an algorithm to compute a resolvent of an algebraic variety without computing its irreducible components; we decompose the radical of an ideal into prime ideals and we test the primality of a regular ideal.

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11

Yang, Zhuoran, and Chang Tan. "Computing Independent Variable Sets for Polynomial Ideals." Journal of Mathematics 2022 (September 19, 2022): 1–6. http://dx.doi.org/10.1155/2022/7049980.

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Computing independent variable sets for polynomial ideals plays an important role in solving high-dimensional polynomial equations. The computation of a Gröbner basis for an ideal, with respect to a block lexicographical order in classic methods, is huge, and then an improved algorithm is given. Based on the quasi-Gröbner basis of the extended ideal, a criterion of assigning independent variables is gained. According to the criteria, a maximal independent variable set for a polynomial ideal can be computed by assigning indeterminates gradually. The key point of the algorithm is to reduce dimen

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Devineni, Sreenath, and Bhargavi Gorantla. "Energy-Efficient Computing and Green Computing Techniques." 4 1, no. 4 (2023): 37–45. http://dx.doi.org/10.46632/cset/1/4/5.

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Energy-efficient computing and strategies for environmentally sustainable computing have become indispensable in the contemporary world, given the escalating demand for computing power and the growing emphasis on ecological conservation. This summary delves into diverse facets of energy efficient computing and green computing methodologies, elucidating their significance, hurdles, and potential remedies. The primary objective of energy-efficient computing is to curtail the energy consumption of computing systems while either maintaining or enhancing their performance. This proves pivotal in al

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13

Pacetti, Ariel, and Nicolás Sirolli. "Computing ideal classes representatives in quaternion algebras." Mathematics of Computation 83, no. 289 (2014): 2479–507. http://dx.doi.org/10.1090/s0025-5718-2014-02796-8.

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14

KESH, DEEPANJAN, and SHASHANK K. MEHTA. "GENERALIZED REDUCTION TO COMPUTE TORIC IDEALS." Discrete Mathematics, Algorithms and Applications 02, no. 01 (2010): 45–59. http://dx.doi.org/10.1142/s1793830910000462.

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Toric ideals have many applications including solving integer programs. Several algorithms for computing the toric ideal of an integer matrix are available in the literature. Since it is an NP hard problem the present approaches can only solve relatively small problems. We propose a new approach which improves upon a well known technique to compute ideal saturation, which leads to a faster algorithm to compute toric ideals.

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15

Bykovskih, D. A., and V. A. Galkin. "On a computing test of an ideal non-interacting gas model." Computational Mathematics and Information Technologies 2, no. 1 (2018): 9–16. http://dx.doi.org/10.23947/2587-8999-2018-2-1-9-16.

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16

Ndungi, Rebeccah, and Bambang Sugiantoro. "THE FUTURE OF FOG COMPUTING IN KENYA." American Journal of Computing and Engineering 4, no. 2 (2021): 1–9. http://dx.doi.org/10.47672/ajce.857.

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The study, titled "The Future of Fog Computing in Kenya," discusses fog computing, computing evolution, and the Internet of Things. It has layers ideal for fog networks. The architecture depicts the functions performed by each layer, the protocols, devices, and their functionality at various layers. Fog computing extends cloud computing and helps mitigate its difficulties. The study also goes forth to explain the various sectors where fog-computing technology is applied and the various merits associated with it. In order to improve present technology, this article will greatly help researchers

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Jiang, Xue, and Yihe Gong. "Algorithms for computing Gröbner bases of ideal interpolation." AIMS Mathematics 9, no. 7 (2024): 19459–72. http://dx.doi.org/10.3934/math.2024948.

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<abstract><p>This paper proposes algorithms for computing the reduced Gröbner basis of the vanishing ideal of a finite set of points in the frame of ideal interpolation. We also consider the case that the points have multiplicity conditions. First, we introduce the definition of "reverse" reduced team and compute the interpolation monomial basis of a single point ideal interpolation problem; then we translate the interpolation condition functionals into formal power series via Taylor expansion; this will help convert the general ideal interpolation problem to a single point ideal i

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18

Sreeramana, Aithal. "Review on Various Ideal System Models Used to Improve the Characteristics of Practical Systems." International Journal of Applied and Advanced Scientific Research, ISSN (Online): 2456 – 3080 1, no. 1 (2016): 47–56. https://doi.org/10.5281/zenodo.159770.

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Ideal properties of a device or a system can be used to upgrade or improve its properties towards reaching 100% efficiency. By comparing the properties/characteristics of a practical device/system with its ideal counterpart, one can find out the possible modifications in that device /system towards reaching the objective of achieving such an ideal system. Even though ideal systems are hypothetical systems, which cannot be realized completely in practice, gives a broad idea on how the practical systems can be improved continuously to reach ideal system characteristics. The ideal system characte

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Dr., P. S. Aithal. "REVIEW ON VARIOUS IDEAL SYSTEM MODELS USED TO IMPROVE THE CHARACTERISTICS OF PRACTICAL SYSTEMS." International Journal of Applied and Advanced Scientific Research 1, no. 1 (2016): 47–56. https://doi.org/10.5281/zenodo.159749.

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Ideal properties of a device or a system can be used to upgrade or improve its properties towards reaching 100% efficiency. By comparing the properties/characteristics of a practical device/system with its ideal counterpart, one can find out the possible modifications in that device /system towards reaching the objective of achieving such an ideal system. Even though ideal systems are hypothetical systems, which cannot be realized completely in practice, gives a broad idea on how the practical systems can be improved continuously to reach ideal system characteristics. The ideal system characte

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20

M K Kanna Babu, A., and M. Sree Latha. "Efficient Ideal Algorithm for Task Scheduling in Cloud Computing." International Journal of Engineering & Technology 7, no. 3.12 (2018): 5. http://dx.doi.org/10.14419/ijet.v7i3.12.15852.

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Present days cloud computing is one of the best raising technologies in distributed computing sectors which permits pays in line with model as per customer demand and requirements.Cloud includes a set of virtual machines which incorporates each persistent andcomputational facility. Providing efficient access of any data to the remote area through network is the primary motto of the cloud computing. Day by day cloud is facing many demanding situations. In which it is facing scheduling is the key one. The process through which the task can be done in certain order via pc device is called schedul

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21

Marseglia, Stefano. "Computing the ideal class monoid of an order." Journal of the London Mathematical Society 101, no. 3 (2019): 984–1007. http://dx.doi.org/10.1112/jlms.12294.

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22

Lee, Wanbil William. "Ethical Computing for Mitigating Hyperconnectivity Threats." International Journal of Hyperconnectivity and the Internet of Things 5, no. 1 (2021): 25–43. http://dx.doi.org/10.4018/ijhiot.2021010102.

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Many of the problems arising from a technology-driven information-intensive environment that could have been avoided occur because we are either insensitive to or ignorant of their ethical implications. Consequently, data protection remains a chronic, expensive nightmare despite the big speeding on cybersecurity. Ethical computing can play a role in identifying the ethical issues, key stakeholders, and reaching a near-ideal solution vis-à-vis an ideal solution. Hyperconnectivity threats that inherit all the IoT threats plus all the vulnerabilities of the physical objects and virtual subsystems

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23

Norton, Graham H., and Ana Sǎlǎgean. "Strong Gröbner bases for polynomials over a principal ideal ring." Bulletin of the Australian Mathematical Society 64, no. 3 (2001): 505–28. http://dx.doi.org/10.1017/s0004972700019973.

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Gröbner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Gröbner bases, also known as D-bases. Several authors have shown that strong Gröbner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Gröbner bases and strong Gröbner bases when A is a principal ideal ring. We also give algorithms for computing Gröbner bases and strong Gröbner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computin

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24

Matsumoto, Ryutaroh. "Computing the Radical of an Ideal in Positive Characteristic." Journal of Symbolic Computation 32, no. 3 (2001): 263–71. http://dx.doi.org/10.1006/jsco.2001.0446.

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25

Mircea, Cimpoeaș, and Bălănescu Silviu. "Remarks on the Hilbert depth of powers of the maximal graded ideal." Annals of the University of Craiova Mathematics and Computer Science Series 51, no. 2 (2024): 540–50. https://doi.org/10.52846/ami.v51i2.1911.

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Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of $S:=K[x_1,\ldots,x_n]$. We present a new method for computing the Hilbert depth of $\mathbf m^t$, using the polarization and a combinatorial characterization of the Hilbert depth of a quotient of squarefree monomial ideals.

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26

Kaish, Md, Kusum Sharma, and Dr Shikha Pandey. "Large-Scale Multimedia Communication on A Cloud Computing Platform." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (2022): 1293–98. http://dx.doi.org/10.22214/ijraset.2022.46405.

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Abstract: This research examines the creation of a multimedia communication platform to expand the size of multimedia communication based on cloud computing (CC). The research focuses on high-quality material, multimedia profit avenues, and copyright awareness. Big data diversion under cloud computing optimizes data grouping and pattern identification. Cloud computing's typical large data shunting technology uses open-source embedded system architecture. The connecting coil ties the shunting system's switch to the cloud computing platform's switch, resulting in data loss and corruption. Using

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27

Sadiku, Matthew N. O., Mahamadou Tembely, and Sarhan M. Musa. "Fog Computing: A Primer." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 7 (2017): 405. http://dx.doi.org/10.23956/ijarcsse.v7i7.165.

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Fog computing (FC) was proposed in 2012 by Cisco as the ideal computing model for providing real-time computing services and storage to support the resource-constrained Internet of Things (IoT) devices. Thus, FC may be regarded as the convergence of the IoT and the Cloud, combining the data-centric IoT services and pay-as-you-go characteristics of clouds. This paper provides a brief introduction of fog computing.

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28

Lesavourey, Andrea, Thomas Plantard, and Willy Susilo. "Short Principal Ideal Problem in multicubic fields." Journal of Mathematical Cryptology 14, no. 1 (2020): 359–92. http://dx.doi.org/10.1515/jmc-2019-0028.

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AbstractOne family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices. Ideal lattices can be seen as ideals in a number field. However recent progress in both quantum and classical computing showed that such cryptosystems can be cryptanalysed efficiently over some number fields. It is therefore important to study the security of such cryptosystems for other number fields in order to have a better understanding of

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29

Biasse, Jean-François, Claus Fieker, and Michael J. Jacobson. "Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation." LMS Journal of Computation and Mathematics 19, A (2016): 371–90. http://dx.doi.org/10.1112/s1461157016000358.

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In this paper, we present novel algorithms for finding small relations and ideal factorizations in the ideal class group of an order in an imaginary quadratic field, where both the norms of the prime ideals and the size of the coefficients involved are bounded. We show how our methods can be used to improve the computation of large-degree isogenies and endomorphism rings of elliptic curves defined over finite fields. For these problems, we obtain improved heuristic complexity results in almost all cases and significantly improved performance in practice. The speed-up is especially high in situ

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30

Robinson, E. Richard, and David H. Wood. "Computing ideal starting fields for parabolic equations: Approach and examples." Journal of the Acoustical Society of America 83, S1 (1988): S118. http://dx.doi.org/10.1121/1.2025177.

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31

Montes, Antonio. "Software for computing the Gröbner cover of a parametric ideal." ACM Communications in Computer Algebra 45, no. 3/4 (2012): 180–82. http://dx.doi.org/10.1145/2110170.2110178.

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32

López, Hiram H., and Rafael H. Villarreal. "Computing the degree of a lattice ideal of dimension one." Journal of Symbolic Computation 65 (November 2014): 15–28. http://dx.doi.org/10.1016/j.jsc.2014.01.002.

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33

Chen, Franklin M. C. "Computing Liquid–Vapor Phase Diagrams for Non-Ideal Binary Mixtures." Journal of Chemical Education 82, no. 7 (2005): 1100. http://dx.doi.org/10.1021/ed082p1100.1.

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Wozny, Janusz, Andrii Kovalchuk, Jacek Podgorski, and Zbigniew Lisik. "Extended Hückel Semi-Empirical Approach as an Efficient Method for Structural Defects Analysis in 4H-SiC." Materials 14, no. 5 (2021): 1247. http://dx.doi.org/10.3390/ma14051247.

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This paper presents an efficient method to calculate the influence of structural defects on the energy levels and energy band-gap for the 4H-SiC semiconductor. The semi-empirical extended Hückel method was applied to both ideal 4H-SiC crystal and different structures with defects like vacancies, stacking faults, and threading edge dislocations. The Synopsys QuatumATK package was used to perform the simulations. The results are in good agreement with standard density functional theory (DFT) methods and the computing time is much lower. This means that a structure with ca. 1000 atoms could be ea

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35

Bouazizi, Faïçal. "Algebraic certification of numerical algorithms computing Lagrange resolvents." Journal of Algebra and Its Applications 17, no. 01 (2018): 1850007. http://dx.doi.org/10.1142/s021949881850007x.

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36

Srikanth, Kandragula. "Cloud Computing in IoT Applications." European Journal of Advances in Engineering and Technology 7, no. 1 (2020): 70–72. https://doi.org/10.5281/zenodo.13950929.

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The burgeoning Internet of Things (IoT) landscape, with its ever-increasing network of interconnected devices, generates a massive and ever-expanding stream of data. This data deluge necessitates robust solutions for storage, processing, and analysis. Cloud computing emerges as the ideal platform, offering unparalleled scalability, security, and real-time analytics capabilities. This paper explores the symbiotic relationship between cloud computing and IoT applications, highlighting the key advantages cloud computing offers and showcasing its transformative impact across various IoT domains.

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Rehman, Fazal Ur, Hasan Mahmood, Thai Thanh Nguyen, and Muhammad Ahsan Binyamin. "Generalization of f -Graphs and Their Algebraic Aspects." Journal of Mathematics 2023 (February 28, 2023): 1–9. http://dx.doi.org/10.1155/2023/7984489.

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The notion of f -graphs and f -ideals are relatively new and have been studied in many papers. In this paper, we have generalized the idea of f -graphs and f -ideals to quasi f -graphs and quasi f -ideals, respectively. We have characterized all quasi f -graphs and quasi f -ideals of degree 2 and determined all the minimal primes ideals of these ideals. Furthermore, construction of quasi f -ideals of degree 2 has been described; the formula for computing Hilbert function and Hilbert series of the polynomial ring modulo the edge ideal of the quasi f -graph has been provided.

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Greenberg, Noam, Joseph S. Miller, and André Nies. "Computing from projections of random points." Journal of Mathematical Logic 20, no. 01 (2019): 1950014. http://dx.doi.org/10.1142/s0219061319500144.

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We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call [Formula: see text]-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the [Formula: see text]-trivial sets. We characterize [Formula: see text]-bases as the sets computable from both halves of Chaitin’s [Formula: see text], and as the sets that obey the cost function [Formula: see text]. Generalizing these results yields a dense hierarchy of subideals in the [Formula: see text]-trivial de

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Kirshanova, E. A., E. S. Malygina, S. A. Novoselov, and D. O. Olefirenko. "AN ALGORITHM FOR COMPUTING THE STICKELBERGER IDEAL FOR MULTIQUADRATIC NUMBER FIELDS." Prikladnaya Diskretnaya Matematika, no. 51 (2021): 9–30. http://dx.doi.org/10.17223/20710410/51/1.

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We present an algorithm for computing the Stickelberger ideal for multiquadratic fields K = Q(√d1,√d2, . . . , √dn), where the integers di ≡ 1 mod 4 for i ∈ {1, . . . , n} or dj ≡ 2 mod 8 for one j ∈ {1, . . . , n}; all di’s are pairwise co-prime and squarefree. Our result is based on the paper of Kuˇcera [J. Number Theory, no. 56, 1996]. The algorithm we present works in time O(lg ∆K • 2n• poly(n)), where ∆K is the discriminant of K. As an interesting application, we show a connection between Stickelberger ideal and the class number of a multiquadratic field

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García-Marco, Ignacio, Irene Márquez-Corbella, Edgar Martínez-Moro, and Yuriko Pitones. "Computing generalized hamming weights of binary linear codes via free resolutions." ACM Communications in Computer Algebra 56, no. 2 (2022): 19–24. http://dx.doi.org/10.1145/3572867.3572868.

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In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support that provides us some information about the GHWs. We prove that the first and second generalized Hamming weight of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated to a binomial ideal related with the code. Moreover, the remaining weights are bounded by the Betti numbers for that set.

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Torrente, Maria-Laura, and Matteo Varbaro. "Computing the Betti table of a monomial ideal: A reduction algorithm." Journal of Symbolic Computation 87 (July 2018): 87–98. http://dx.doi.org/10.1016/j.jsc.2017.06.001.

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Abdalhaq, Baker, Ana Cortés, Tomàs Margalef, Germán Bianchini, and Emilio Luque. "Between classical and ideal: enhancing wildland fire prediction using cluster computing." Cluster Computing 9, no. 3 (2006): 329–43. http://dx.doi.org/10.1007/s10586-006-9745-4.

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43

Ballico, E., and F. Orecchia. "Computing minimal generators of the ideal of a general projective curve." Journal of Symbolic Computation 37, no. 3 (2004): 295–304. http://dx.doi.org/10.1016/j.jsc.2003.04.001.

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Blanco, Cristina, Gabriela Jeronimo, and Pablo Solernó. "Computing generators of the ideal of a smooth affine algebraic variety." Journal of Symbolic Computation 38, no. 1 (2004): 843–72. http://dx.doi.org/10.1016/j.jsc.2004.02.002.

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Öztürk Sözen, Esra, Turki Alsuraiheed, Cihat Abdioğlu, and Shakir Ali. "Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings." Symmetry 15, no. 12 (2023): 2133. http://dx.doi.org/10.3390/sym15122133.

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Let n≥1 be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of Zn, where n=pα,p2q,p2q2,pqr,p3q,p2qr, and pqrs for the different prime integers p,q,r, and s. Moreover, we construct M-polynomials and CoM-polynomials using the PIS-graph structure of Zn to avoid the difficulty of computing the descriptors via formulas directly. Furthermore, we present a geometric comparison for representations of each surface obtained by M-polynomials and CoM-polynomials. Finally, we di

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Randriamaro, Hery. "The Tutte polynomial of ideal arrangements." Discrete Mathematics, Algorithms and Applications 12, no. 02 (2020): 2050017. http://dx.doi.org/10.1142/s1793830920500172.

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The Tutte polynomial was originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning subgraphs, and of acyclic orientations. In 2007, Ardila extended the notion of Tutte polynomial to hyperplane arrangements, and computed the Tutte polynomials of the classical root systems for certain prime powers of the first variable at the same time. In this paper, we compute the Tutte polynomial of ideal arrangements. These arrangements were introduced in 2006 by Sommers and

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47

Marais, Magdaleen S., and Yue Ren. "Mora’s holy graal: Algorithms for computing in localizations at prime ideals." International Journal of Algebra and Computation 25, no. 07 (2015): 1125–43. http://dx.doi.org/10.1142/s0218196715500332.

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This paper discusses a computational treatment of the localization [Formula: see text] of an affine coordinate ring [Formula: see text] at a prime ideal [Formula: see text] and its associated graded algebra [Formula: see text] with the means of computer algebra. Building on Mora’s paper [T. Mora, La queste del Saint [Formula: see text]: A computational approach to local algebra, Discrete Appl. Math. 33 (1991) 161–190], we present shorter proofs on two of the central statements and expand on the applications touched by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials,

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48

Finlay, Janet. "Academic background: a predictor of computing aptitude?" ITNOW 30, no. 3 (1988): 36–40. https://doi.org/10.1093/combul/30.3.36.

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Abstract It is a commonly held assumption that the ‘ideal’, if not essential academic background to success in understanding and using computers, and particularly programming, is a combination of mathematics and physics. This paper reports on a statistical experiment to examine this assumption; there is no evidence to suggest that alternative educational backgrounds do not provide as useful a preparation to such activity.

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Li, Huishi. "Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras." Georgian Mathematical Journal 25, no. 3 (2018): 451–59. http://dx.doi.org/10.1515/gmj-2017-0006.

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AbstractLet {K\langle X\rangle=K\langle X_{1},\ldots,X_{n}\rangle} be the free algebra generated by {X=\{X_{1},\ldots,X_{n}\}} over a field K. It is shown that, with respect to any weighted {\mathbb{N}}-gradation attached to {K\langle X\rangle}, minimal homogeneous generating sets for finitely generated graded two-sided ideals of {K\langle X\rangle} can be algorithmically computed, and that if an ungraded two-sided ideal I of {K\langle X\rangle} has a finite Gröbner basis {{\mathcal{G}}} with respect to a graded monomial ordering on {K\langle X\rangle}, then a minimal standard basis for I can

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50

Shmueli, Uri. "INSTAT: a program for computing non-ideal probability density functions of |E|." Journal of Applied Crystallography 46, no. 5 (2013): 1521–22. http://dx.doi.org/10.1107/s0021889813021390.

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The purpose of this program is to evaluate probability density functions (p.d.f.s) of the magnitude of the normalized structure factor |E| for the space groups of the triclinic, monoclinic and orthorhombic systems, and for any chemical composition of the asymmetric unit, assuming that the atoms are located in general positions. The p.d.f.s are computed by the Fourier and Fourier–Bessel methods [seee.g.Shmueli (2012).J. Appl. Cryst.45, 389–392]. The p.d.f.s evaluated are scaled together with the histogram of observed |E| values and discrepancy criteria are computed. In addition to the above non

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