Advances In Geometry Research Articles

Technology Focus: Artificial Lift (March 2023)

Selecting artificial lift papers for the Tech Focus feature of JPT can be a daunting exercise when technologies and innovations abound, more so post-pandemic, with 157 submitted abstracts covering 2021–2022. In narrowing the offerings to three, the criteria of conformance to guidelines and novelty of information, technical equipment, and application were considered. Industry indicators and interest were also factors. Gas lift remains of high global interest, whether in long horizontal shale oil wells or vertical ones because of the cost to operate lower lifting. Declining production and high gas/oil ratios (GORs) present a challenge for conversion to secondary lift forms. Paper SPE 209721 provides an innovative solution combining gas lift with sucker rod lift to enhance and exploit low-productivity wells in high-GOR fields. Permanent magnet motors (PMMs) have made quite the technical splash in the industry over the past decade. PMMs are one-third shorter and result in higher power densities and power savings of up to 18% just by changing out the induction motor. PMMs are again grabbing attention for the direct 1:1 ratio of electrical to carbon footprint. Current environmental, social, and governance concerns are placing demands on all operators, and PMMs are positioned to help with carbon reduction as a low-hanging fruit in paper SPE 209736. In paper SPE 209763, we look at all-metal progressing cavity pumps (aka M2M), which consist of a metal rotor and metal stator. Incremental advances in geometry and materials continue to see operators use high-temperature fluids with low operational expenditure in mind. Reliability is always a concern, and now a novel condition indicator has been developed and tested that offers a better indicator than pump efficiency alone. Recommended additional reading at OnePetro: www.onepetro.org. SPE 206909 Successful Progressing Cavity Pump Reliability Improvement Project in an Oman Steamflood by Shauna Noonan, Oxy, et al. SPE 211782 Maximizing Marginal Fields Profitability Through Drilling Multilateral Wells To Reduce Well Count and Well Cost: Dual Lateral Well With Single ESP and Smart Lower Completion by Mahmoud Mohamed Abdelhay Mostafa, ADNOC, et al. SPE 209748 Gas Pump—A Gas-Driven Positive Displacement Pump Artificial Lift System by Stephen W. Turk, ELC Energy Services, et al.

Erratum for "Tropical superelliptic curves"

Abstract We correct two errors in our paper Tropical superelliptic curves published in Advances in Geometry 20 (2020), 527–551. These corrections do not change the main results of the paper.

Science on Stage in Early Modern Spain ed. by Enrique García Santo-Tomás

Reviewed by: Science on Stage in Early Modern Spain ed. by Enrique García Santo-Tomás Shifra Armon Science on Stage in Early Modern Spain. Edited by Enrique García Santo-Tomás. U OF TORONTO P, 2019. 296 PP. IN ELEVEN ESAYS BY SCHOLARS from North America and Spain, this volume investigates the dynamic interplay between early modern science and comedia. Taken in its entirety, Science on Stage refutes the view that Counter-Reformation Spain spurned the epistemic paradigm shifts loosely referred to as the “Scientific Revolution.” The traditionalist disparagement of Spain’s contributions to science, as García Santo-Tomás recounts in his introduction, derives both from vestiges of anti-Spanish sentiment among Anglo-American historians and from the belief that Spain’s economic and political losses during this period precipitated intellectual decline as well. Science on Stage is divided into three parts comprised of three chapters each. Part 1, “Technologies of Knowledge,” recognizes comedia stagecraft’s debt to Spain’s legacy of Islamic science and to contemporaneous advances in geometry and engineering. Part 2, “Stages of Science,” highlights dramatic works that wove innovations in medicine, pharmacology, and warcraft into their dramatic plots. The third trio of essays, “Performing Numbers,” inquires into the “challenges of uncertainty” (Jeremy Robbins, The Challenges of Uncertainty. An Introduction to Seventeenth-Century Spanish Literature, Rowman & Littlefield Publishers, 1998) posed by rapidly changing commercial, mechanical, dramatic, and pictorial practices; the common theme here is not numbers per se, but new habits of thought (quantification, skepticism, circumspection, empirical observation, and so forth) required to navigate illusive new topographies of knowledge. To do justice to the diversity of critical approaches that the nine core chapters of Science on Stage represent, it will be useful to offer a synopsis of each. Ryan Szpiech’s essay, “From Mesopotamia to Madrid: The Legacy of Ancient and Medieval Science in Early Modern Spain,” aptly opens part [End Page 149] 1 by exploring myths and frameworks that have encumbered the study of Spain’s scientific past. Szpiech eschews the Western bias implicit in elevating Greek science above its Sumerian, Babylonian, and Egyptian precursors as well as the Enlightenment bias favoring post-Cartesian science above earlier admixtures of physics and metaphysics. Notational systems, both mathematical and alphabetical, or “technolog[ies] of information storage” (31), developed in several ancient civilizations, thereby facilitating the accumulation and diffusion of knowledge. Later, the Baghdad and Andalusian caliphates and the great Library of Alexandria became sites of knowledge translation, transmission, and refinement. This archive nourished Iberian scientia more thoroughly than its non-Arabized neighbors to the north. Szpiech highlights numerous Golden Age comedias that registered the ongoing prestige that Islamic mathematics, medicine, and science enjoyed even in inquisitorial Spain. Following Szpiech’s essay, Alejandro García-Reidy’s contribution on the materiality of staging, “The Technological Environment of the Early Modern Spanish Stage,” provides a helpful update to John Jay Allen and José María Ruano de la Haza’s Los teatros comerciales del siglo XVII y la escenificación de la comedia (Castalia, 1994) and José María Díez Borque’s Teatro cortesano en la España de los Austrias (Cuadernos de teatro clásico, 10, 1998). Rounding out part 1, John Slater discerns the same mathematizing zeal that was breathing new life into Renaissance engineering, gardening, and fencing in both the built space of the corrales and in comedia plotlines that pitted erotic chaos against geometric order. Geometric or “gridded” conceptualization informed many facets of theatrical culture. Slater notes for example that Lope de Vega composed a sonnet for Ginés Rocamora y Torrano’s Sphera del Universo of 1599 that illustrates the dramatist’s keen awareness of contemporary geometric thought (81–82). Part 2 turns to dramatic works that drew upon the poetic power of early modern medical science and technology. Leading off this part, Julio Vélez-Sainz assembles eclogues and plays by Juan del Enzina, Lucas Fernández, and Torres Naharro, all of which approached lovesickness as a physiological condition that demanded specialized medical intervention. Next, Lourdes Albuixech’s chapter focuses on poison, a morbidly fascinating pharmacological subfield, to be sure, but also an ideologically charged signifier associated with...

ON SOME ALGEBRAIC AND COMBINATORIAL PROPERTIES OF DUNKL ELEMENTS

We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147–182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371–383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248].Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang–Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan–Robbins polytope.

Contemporary Geometry For The Built Design?

I explore the terrain that lies between architecture and geometry, from the perspective of a structural scientist with no professional architectural expertise. The divide between these disciplines perhaps stems from an ancient dichotomy between the art versus engineering schools of architecture, fertilised by the current dogma that art and science can never meet. Architects stand to gain much from study of the spectacular advances in geometry in recent decades, such as the growing understanding of cellular patterns in space, tiles, nets and curved surfaces. Some examples of those advances are discussed in detail. I conclude that both architecture and geometry would benefit from a renewed mutual interest.

Latin bitrades derived from groups

A Latin bitrade is a pair of partial Latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. In [A. Drápal, On geometrical structure and construction of Latin trades, Advances in Geometry (in press)] it is shown that a Latin bitrade may be thought of as three derangements of the same set, whose product is the identity and whose cycles pairwise have at most one point in common. By letting a group act on itself by right translation, we show how some Latin bitrades may be derived directly from groups. Properties of Latin bitrades such as homogeneity, minimality (via thinness) and orthogonality may also be encoded succinctly within the group structure. We apply the construction to some well-known groups, constructing previously unknown Latin bitrades. In particular, we show the existence of minimal, k -homogeneous Latin bitrades for each odd k ≥ 3 . In some cases these are the smallest known such examples.

ESPACES DE MODULES DE SYSTÈMES COHÉRENTS

Etant donne un polynome > 0 a coefficients rationnels, nous definissons la notion de systeme coherent -semi-stable sur une variete algebrique projective lisse. Sur p#2(c), nous montrons l'irreductibilite et la normalite des espaces de modules s# de systemes coherents -semi-stables a = (,f(l)), ou f est un faisceau algebrique coherent de rang 2 sur le plan projectif p#2(c), de classes de chern (0,n), l un entier 1, et h#0(f(l)) un sous-espace vectoriel de rang 1. Quand n'est pas valeur critique, nous definissons ici sur chaque variete s# les fibres determinants, et l'integrale correspondante. La description du saut des espaces de modules de systemes coherents -semi-stables au passage d'une valeur critique, est analogue a celle des flips de thaddeus, avec la difficulte supplementaire due au fait que les espaces de modules ne sont pas forcement lisses. En etudiant le saut de ces integrales au passage d'une valeur critique, nous obtenons des relations entre les nombres de donaldson sur p#2(c) et certains nombres d'intersection sur le schema de hilbert hilb#n#+#l#2 (p#2) (3 n 11)

Managing geometric information with a database management system

Current database management systems do not meet the needs of CAD/CAM users. Boeing's Integrated Programs for Aerospace-Vehicle Design (IPAD) project strikes at the heart of the problem-moving data across heterogeneous distributed systems. A fundamental goal of IPAD is increased industrial productivity. The key to this increase is the concept of integration. The project does not pursue new advances in geometry or graphics, but focuses on the problem of managing information flow in the engineering/manufacturing environment. The creation and use of effective tools for this purpose will reduce the manual intervention in the data flow, speed up the interactions in the process, and make the information more readily available to those who need it.