Journal articles: 'Maps over finite fields'

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de Cataldo, Mark Andrea A. "Proper Toric Maps Over Finite Fields." International Mathematics Research Notices 2015, no. 24 (2015): 13106–21. http://dx.doi.org/10.1093/imrn/rnv094.

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Berson, Joost. "Linearized polynomial maps over finite fields." Journal of Algebra 399 (February 2014): 389–406. http://dx.doi.org/10.1016/j.jalgebra.2013.10.013.

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Misiurewicz, Michał, John G. Stevens, and Diana M. Thomas. "Iterations of linear maps over finite fields." Linear Algebra and its Applications 413, no. 1 (February 2006): 218–34. http://dx.doi.org/10.1016/j.laa.2005.09.002.

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Vivaldi, F. "Geometry of linear maps over finite fields." Nonlinearity 5, no. 1 (January 1, 1992): 133–47. http://dx.doi.org/10.1088/0951-7715/5/1/005.

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Küçüksakallı, Ömer. "Value sets of Lattès maps over finite fields." Journal of Number Theory 143 (October 2014): 262–78. http://dx.doi.org/10.1016/j.jnt.2014.04.014.

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DEMPWOLFF, U., J. CHRIS FISHER, and ALLEN HERMAN. "SEMILINEAR TRANSFORMATIONS OVER FINITE FIELDS ARE FROBENIUS MAPS." Glasgow Mathematical Journal 42, no. 2 (May 2000): 289–95. http://dx.doi.org/10.1017/s0017089500020164.

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Mullen, G. L., D. Wan, and Q. Wang. "VALUE SETS OF POLYNOMIAL MAPS OVER FINITE FIELDS." Quarterly Journal of Mathematics 64, no. 4 (October 17, 2012): 1191–96. http://dx.doi.org/10.1093/qmath/has026.

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Morton, Patrick. "Periods of Maps on Irreducible Polynomials over Finite Fields." Finite Fields and Their Applications 3, no. 1 (January 1997): 11–24. http://dx.doi.org/10.1006/ffta.1996.0168.

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Küçüksakallı, Ömer. "Value sets of bivariate Chebyshev maps over finite fields." Finite Fields and Their Applications 36 (November 2015): 189–202. http://dx.doi.org/10.1016/j.ffa.2015.08.005.

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FLYNN, RYAN, and DEREK GARTON. "GRAPH COMPONENTS AND DYNAMICS OVER FINITE FIELDS." International Journal of Number Theory 10, no. 03 (March 18, 2014): 779–92. http://dx.doi.org/10.1142/s1793042113501224.

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For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of components of their functional graphs as well as the average number of periodic points of their associated dynamical systems.

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Kuhlmann, Franz-Viktor. "Elementary properties of power series fields over finite fields." Journal of Symbolic Logic 66, no. 2 (June 2001): 771–91. http://dx.doi.org/10.2307/2695043.

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AbstractIn spite of the analogies between ℚp and which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for ℚp, to the case of does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on . We formulate an elementary property expressing this action and show that it holds for all maximal valued fields. We also derive an example of a rather simple immediate valued function field over a henselian defectless ground field which is not a henselian rational function field. This example is of special interest in connection with the open problem of local uniformization in positive characteristic.

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Lima, Juliano B., and Ricardo M. Campello de Souza. "Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields." IEEE Transactions on Circuits and Systems II: Express Briefs 67, no. 4 (April 2020): 775–79. http://dx.doi.org/10.1109/tcsii.2019.2923879.

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Roberts, John A. G., and Franco Vivaldi. "A combinatorial model for reversible rational maps over finite fields." Nonlinearity 22, no. 8 (June 29, 2009): 1965–82. http://dx.doi.org/10.1088/0951-7715/22/8/011.

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Panario, Daniel, and Lucas Reis. "The functional graph of linear maps over finite fields and applications." Designs, Codes and Cryptography 87, no. 2-3 (September 3, 2018): 437–53. http://dx.doi.org/10.1007/s10623-018-0547-5.

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Scowcroft, Philip, and Lou van den Dries. "On the structure of semialgebraic sets over p-adic fields." Journal of Symbolic Logic 53, no. 4 (December 1988): 1138–64. http://dx.doi.org/10.1017/s0022481200027973.

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In his Singular points of complex hypersurfaces Milnor proves the following “curve selection lemma” [10, p. 25]:Let V ⊂ Rm be a real algebraic set, and let U ⊂ Rm be an open set defined by finitely many polynomial inequalities:Lemma 3.1. If U ∩ V contains points arbitrarily close to the origin (that is if 0 ∈ Closure (U ∩ V)) then there exists a real analytic curvewith p(0) = 0 and with p(t) ∈ U ∩ V for t > 0.Of course, this result will also apply to semialgebraic sets (finite unions of sets U ∩ V), and by Tarski's theorem such sets are exactly the sets obtained from real varieties by means of the finite Boolean operations and the projection maps Rn+1 → Rn. If, in this tiny extension of Milnor's result, we replace ‘R’ everywhere by ‘Qp’, we obtain a p-adic curve selection lemma, a version of which we will prove in this essay. Semialgebraic sets, in the p-adic context, may be defined just as they are over the reals: namely, as those sets obtained from p-adic varieties by means of the finite Boolean operations and the projection maps . Analytic maps are maps whose coordinate functions are given locally by convergent power series.

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Wang, Hong-Li, Gang Wang, and You Gao. "Subspace Codes Based on Partial Injective Maps of Vector Spaces Over Finite Fields." IEEE Access 8 (2020): 192608–15. http://dx.doi.org/10.1109/access.2020.3032552.

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Szabo, Steve, and Felix Ulmer. "Duality preserving Gray maps for codes over rings." Journal of Algebra and Its Applications 16, no. 09 (September 9, 2016): 1750161. http://dx.doi.org/10.1142/s0219498817501614.

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Given a finite ring [Formula: see text] which is a free left module over a subring [Formula: see text] of [Formula: see text], two types of [Formula: see text]-bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric bases, are defined which in turn are used to define duality preserving maps from codes over [Formula: see text] to codes over [Formula: see text]. Both types of bases are generalizations of similar concepts for fields. Many illustrative examples are given to shed light on the advantages to such mappings as well as their abundance.

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Mérai, László, and Igor E. Shparlinski. "Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields." Acta Arithmetica 188, no. 4 (2019): 401–11. http://dx.doi.org/10.4064/aa180307-20-8.

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Borisov, Alexander, and Mark Sapir. "Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms." Inventiones mathematicae 160, no. 2 (December 30, 2004): 341–56. http://dx.doi.org/10.1007/s00222-004-0411-2.

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Cocke, William. "Size of free groups in varieties generated by finite groups." International Journal of Algebra and Computation 29, no. 08 (October 24, 2019): 1419–30. http://dx.doi.org/10.1142/s0218196719500565.

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The number of distinct [Formula: see text]-variable word maps on a finite group [Formula: see text] is the order of the rank [Formula: see text] free group in the variety generated by [Formula: see text]. For a group [Formula: see text], the number of word maps on just two variables can be quite large. We improve upon previous bounds for the number of word maps over a finite group [Formula: see text]. Moreover, we show that our bound is sharp for the number of 2-variable word maps over the affine group over fields of prime order and over the alternating group on five symbols.

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BENTMANN, RASMUS. "CLASSIFICATION OF CERTAIN CONTINUOUS FIELDS OF KIRCHBERG ALGEBRAS." International Journal of Mathematics 25, no. 01 (January 2014): 1450004. http://dx.doi.org/10.1142/s0129167x14500049.

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We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational K-theory groups satisfying the universal coefficient theorem. We provide a range result for fields in this class with finite-dimensional K-theory. There are versions of both results for unital continuous fields.

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Ugolini, S. "Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields." Periodica Mathematica Hungarica 77, no. 2 (May 17, 2018): 237–60. http://dx.doi.org/10.1007/s10998-018-0242-3.

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KARHUMÄKI, ULLA. "DEFINABLY SIMPLE STABLE GROUPS WITH FINITARY GROUPS OF AUTOMORPHISMS." Journal of Symbolic Logic 84, no. 02 (April 10, 2019): 704–12. http://dx.doi.org/10.1017/jsl.2019.29.

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AbstractWe prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble the Frobenius maps, and allow us to classify definably simple stable groups in the specific case when they admit such automorphisms.

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Aceves, Kelly, and Manfred Dugas. "Local multiplication maps on F[x]." Journal of Algebra and Its Applications 14, no. 03 (November 7, 2014): 1550029. http://dx.doi.org/10.1142/s0219498815500292.

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Let F be a field and A a F-algebra. The F-linear transformation φ : A → A is a local multiplication map if for all a ∈ A there exists some ua ∈ A such that φ(a) = aua. Let [Formula: see text] denote the F-algebra of all local multiplication maps of A. If F is infinite and F[x] is the ring of polynomials over F, then it is known Lemma 1 in [J. Buckner and M. Dugas, Quasi-Localizations of ℤ, Israel J. Math.160 (2007) 349–370] that [Formula: see text]. The purpose of this paper is to study [Formula: see text] for finite fields F. It turns out that in this case [Formula: see text] is a "very" non-commutative ring of cardinality 2ℵ0 with many interesting properties.

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Gowers, W. T., and L. Milićević. "A note on extensions of multilinear maps defined on multilinear varieties." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (April 30, 2021): 148–73. http://dx.doi.org/10.1017/s0013091521000055.

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AbstractLet $G_1, \ldots , G_k$ be finite-dimensional vector spaces over a prime field $\mathbb {F}_p$. A multilinear variety of codimension at most $d$ is a subset of $G_1 \times \cdots \times G_k$ defined as the zero set of $d$ forms, each of which is multilinear on some subset of the coordinates. A map $\phi$ defined on a multilinear variety $B$ is multilinear if for each coordinate $c$ and all choices of $x_i \in G_i$, $i\not =c$, the restriction map $y \mapsto \phi (x_1, \ldots , x_{c-1}, y, x_{c+1}, \ldots , x_k)$ is linear where defined. In this note, we show that a multilinear map defined on a multilinear variety of codimension at most $d$ coincides on a multilinear variety of codimension $O_{k}(d^{O_{k}(1)})$ with a multilinear map defined on the whole of $G_1\times \cdots \times G_k$. Additionally, in the case of general finite fields, we deduce similar (but slightly weaker) results.

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García, Darío, Dugald Macpherson, and Charles Steinhorn. "Pseudofinite structures and simplicity." Journal of Mathematical Logic 15, no. 01 (June 2015): 1550002. http://dx.doi.org/10.1142/s0219061315500026.

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We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted.

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Javanpeykar, Ariyan, and Ljudmila Kamenova. "Demailly’s notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps." Mathematische Zeitschrift 296, no. 3-4 (February 26, 2020): 1645–72. http://dx.doi.org/10.1007/s00209-020-02489-6.

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Abstract Demailly’s conjecture, which is a consequence of the Green–Griffiths–Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence for Demailly’s conjecture by verifying several predictions it makes. We first define what an algebraically hyperbolic projective variety is, extending Demailly’s definition to (not necessarily smooth) projective varieties over an arbitrary algebraically closed field of characteristic zero, and we prove that this property is stable under extensions of algebraically closed fields. Furthermore, we show that the set of (not necessarily surjective) morphisms from a projective variety Y to a projective algebraically hyperbolic variety X that map a fixed closed subvariety of Y onto a fixed closed subvariety of X is finite. As an application, we obtain that $${{\,\mathrm{Aut}\,}}(X)$$ Aut ( X ) is finite and that every surjective endomorphism of X is an automorphism. Finally, we explore “weaker” notions of hyperbolicity related to boundedness of moduli spaces of maps, and verify similar predictions made by the Green–Griffiths–Lang conjecture on hyperbolic projective varieties.

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Geyer, Wulf-Dieter, Moshe Jarden, and Aharon Razon. "On stabilizers of algebraic function fields of one variable." Advances in Geometry 17, no. 2 (March 28, 2017): 131–74. http://dx.doi.org/10.1515/advgeom-2016-0026.

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AbstractLet $\tilde K$ be a fixed algebraic closure of an infinite field K. We consider an absolutely integral curve Γ in $\mathbb{P}_{K}^{n}$ with n ≥ 2. The curve $\it\Gamma_{\tilde{K}}$ should have only finitely many inflection points, finitely many double tangents, and there exists no point in $\mathbb{P}_{\tilde{K}}^{n}$ through which infinitely many tangents to $\it\Gamma_{\tilde{K}}$ go. In addition there exists a prime number q such that $\it\Gamma_{\tilde{K}}$ has a cusp of multiplicity q and the multiplicities of all other points of $\it\Gamma_{\tilde{K}}$ are at most q. Under these assumptions, we construct a non-empty Zariski-open subset O of $\mathbb{P}_{\tilde{K}}^{n}$ such that if n ≥ 3, the projection from each point o ∈ O(K) birationally maps Γ onto an absolutely integral curve Γ′ in $\mathbb{P}_{K}^{n-1}$ with the same properties as Γ (keeping q unchanged). If n = 2, then the projection from each o ∈ O(K) maps Γ onto $\mathbb{P}_{K}^{1}$ and leads to a stabilizing element t of the function field F of Γ over K. The latter means that F/K(t) is a finite separable extension whose Galois closure ${\hat F}$ is regular over K.

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Arruda, J. R. F., and P. Mas. "Localizing Energy Sources and Sinks in Plates Using Power Flow Maps Computed From Laser Vibrometer Measurements." Shock and Vibration 5, no. 4 (1998): 235–53. http://dx.doi.org/10.1155/1998/738387.

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This paper presents an experimental method especially adapted for the computation of structural power flow using spatially dense vibration data measured with scanning laser Doppler vibrometers. In the proposed method, the operational deflection shapes measured over the surface of the structure are curve-fitted using a two-dimensional discrete Fourier series approximation that minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. Divergence plots are then obtained from the computed intensity fields. An example consisting of a rectangular aluminum plate supported by rubber mounts and excited by a point force is used to appraise the proposed method. The proposed method is compared with more traditional finite difference methods. The proposed method was the only to allow the localization of the energy source and sinks from the experimental divergence plots.

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Beacom, Jamie. "Computation of the unipotent Albanese map on elliptic and hyperelliptic curves." Annales mathématiques du Québec 44, no. 2 (December 26, 2019): 201–59. http://dx.doi.org/10.1007/s40316-019-00129-y.

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AbstractWe study the unipotent Albanese map appearing in the non-abelian Chabauty method of Minhyong Kim. In particular we explore the explicit computation of the p-adic de Rham period map $$j^{dr}_n$$ j n dr on elliptic and hyperelliptic curves over number fields via their universal unipotent connections $${\mathscr {U}}$$ U . Several algorithms forming part of the computation of finite level versions $$j^{dr}_n$$ j n dr of the unipotent Albanese maps are presented. The computation of the logarithmic extension of $${\mathscr {U}}$$ U in general requires a description in terms of an open covering, and can be regarded as a simple example of computational descent theory. We also demonstrate a constructive version of a lemma of Hadian used in the computation of the Hodge filtration on $${\mathscr {U}}$$ U over affine elliptic and odd hyperelliptic curves. We use these algorithms to present some new examples describing the co-ordinates of some of these period maps. This description will be given in terms iterated p-adic Coleman integrals. We also consider the computation of the co-ordinates if we replace the rational basepoint with a tangential basepoint, and present some new examples here as well.

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Galassi, Alessio, José D. Martín-Guerrero, Eduardo Villamor, Carlos Monserrat, and María José Rupérez. "Risk Assessment of Hip Fracture Based on Machine Learning." Applied Bionics and Biomechanics 2020 (December 22, 2020): 1–13. http://dx.doi.org/10.1155/2020/8880786.

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Identifying patients with high risk of hip fracture is a great challenge in osteoporosis clinical assessment. Bone Mineral Density (BMD) measured by Dual-Energy X-Ray Absorptiometry (DXA) is the current gold standard in osteoporosis clinical assessment. However, its classification accuracy is only around 65%. In order to improve this accuracy, this paper proposes the use of Machine Learning (ML) models trained with data from a biomechanical model that simulates a sideways-fall. Machine Learning (ML) models are models able to learn and to make predictions from data. During a training process, ML models learn a function that maps inputs and outputs without previous knowledge of the problem. The main advantage of ML models is that once the mapping function is constructed, they can make predictions for complex biomechanical behaviours in real time. However, despite the increasing popularity of Machine Learning (ML) models and their wide application to many fields of medicine, their use as hip fracture predictors is still limited. This paper proposes the use of ML models to assess and predict hip fracture risk. Clinical, geometric, and biomechanical variables from the finite element simulation of a side fall are used as independent variables to train the models. Among the different tested models, Random Forest stands out, showing its capability to outperform BMD-DXA, achieving an accuracy over 87%, with specificity over 92% and sensitivity over 83%.

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Wojtczak, Erwin, and Magdalena Rucka. "Wave Frequency Effects on Damage Imaging in Adhesive Joints Using Lamb Waves and RMS." Materials 12, no. 11 (June 6, 2019): 1842. http://dx.doi.org/10.3390/ma12111842.

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Structural adhesive joints have numerous applications in many fields of industry. The gradual deterioration of adhesive material over time causes a possibility of unexpected failure and the need for non-destructive testing of existing joints. The Lamb wave propagation method is one of the most promising techniques for the damage identification of such connections. The aim of this study was experimental and numerical research on the effects of the wave frequency on damage identification in a single-lap adhesive joint of steel plates. The ultrasonic waves were excited at one point of an analyzed specimen and then measured in a certain area of the joint. The recorded wave velocity signals were processed by the way of a root mean square (RMS) calculation, giving the actual position and geometry of defects. In addition to the visual assessment of damage maps, a statistical analysis was conducted. The influence of an excitation frequency value on the obtained visualizations was considered experimentally and numerically in the wide range for a single defect. Supplementary finite element method (FEM) calculations were performed for three additional damage variants. The results revealed some limitations of the proposed method. The main conclusion was that the effectiveness of measurements strongly depends on the chosen wave frequency value.

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Su, Bingzhi, Y. C. Lee, and Martin L. Dunn. "Die Cracking at Solder (In60-Pb40) Joints on Brittle (GaAs) Chips: Fracture Correlation Using Critical Bimaterial Interface Corner Stress Intensities." Journal of Electronic Packaging 125, no. 3 (September 1, 2003): 369–77. http://dx.doi.org/10.1115/1.1602702.

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We study cracking from the interface of an In60-Pb40 solder joint on a brittle GaAs die when the joint is subjected to a uniform temperature change. Our primary objective is to apply and validate a fracture initiation criterion based on critical values of the stress intensities that arise from an analysis of the asymptotic elastic stress fields at the interface corner. In some regards the approach is similar to interface fracture mechanics; however, it differs in that it is based on a singular field other than that for a crack. We begin by determining the shape that the solder bump will assume after reflow when constrained by a fixed diameter wetting pad on the GaAs. To simplify the interpretation of the results, we focus on a class of solder bumps of various sizes, but with a self-similar shape. The approach, though, can be applied to different size and shape solder bumps. We then compute the asymptotic interface corner fields when the system is subjected to a uniform temperature change. The asymptotic structure (radial and angular dependence) of the elastic fields is computed analytically, and the corresponding stress intensities that describe the scaling of the elastic fields with geometry and loading are computed by axisymmetric finite element analysis. In order to assess the validity of fracture correlation using critical stress intensities, we designed and fabricated a series of test structures consisting of In60-Pb40 solder bumps on a GaAs chip. The test structures were subjected to uniform temperature drops from room temperature to induce cracking at the interface corner. From the tests we determined the relationship between the solder bump size and the temperature change at which cracking occurred. Not unexpectedly, smaller bumps required larger temperature changes to induce cracking. The observed scaling between solder bump size and temperature change is well described by the critical stress intensity failure criterion based on only a single parameter, the critical value of the mode 1 stress intensity, K1crn. Interestingly, this is because over a significant region, the mode 2 and constant terms in the asymptotic expansion cancel each other. This failure criterion provides the necessary machinery to construct failure maps in terms of geometry and thermomechanical loading. We conclude by describing how to apply the approach in more general and more practical settings that are possibly applicable to a wide range of problems in microelectronics, optoelectronics, and microelectromechanical systems packaging.

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Adhikari, Surendra, Erik R. Ivins, Thomas Frederikse, Felix W. Landerer, and Lambert Caron. "Sea-level fingerprints emergent from GRACE mission data." Earth System Science Data 11, no. 2 (May 9, 2019): 629–46. http://dx.doi.org/10.5194/essd-11-629-2019.

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Abstract. The Gravity Recovery and Climate Experiment (GRACE) mission data have an important, if not revolutionary, impact on how scientists quantify the water transport on the Earth's surface. The transport phenomena include land hydrology, physical oceanography, atmospheric moisture flux, and global cryospheric mass balance. The mass transport observed by the satellite system also includes solid Earth motions caused by, for example, great subduction zone earthquakes and glacial isostatic adjustment (GIA) processes. When coupled with altimetry, these space gravimetry data provide a powerful framework for studying climate-related changes on decadal timescales, such as ice mass loss and sea-level rise. As the changes in the latter are significant over the past two decades, there is a concomitant self-attraction and loading phenomenon generating ancillary changes in gravity, sea surface, and solid Earth deformation. These generate a finite signal in GRACE and ocean altimetry, and it may often be desirable to isolate and remove them for the purpose of understanding, for example, ocean circulation changes and post-seismic viscoelastic mantle flow, or GIA, occurring beneath the seafloor. Here we perform a systematic calculation of sea-level fingerprints of on-land water mass changes using monthly Release-06 GRACE Level-2 Stokes coefficients for the span April 2002 to August 2016, which result in a set of solutions for the time-varying geoid, sea-surface height, and vertical bedrock motion. We provide both spherical harmonic coefficients and spatial maps of these global field variables and uncertainties therein (https://doi.org/10.7910/DVN/8UC8IR; Adhikari et al., 2019). Solutions are provided for three official GRACE data processing centers, namely the University of Texas Austin's Center for Space Research (CSR), GeoForschungsZentrum Potsdam (GFZ), and Jet Propulsion Laboratory (JPL), with and without rotational feedback included and in both the center-of-mass and center-of-figure reference frames. These data may be applied for either study of the fields themselves or as fundamental filter components for the analysis of ocean-circulation- and earthquake-related fields or for improving ocean tide models.

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Parshall, Hans. "Simplices over finite fields." Proceedings of the American Mathematical Society 145, no. 6 (January 25, 2017): 2323–34. http://dx.doi.org/10.1090/proc/13493.

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Esnault, Hélène. "Coniveau over -adic fields and points over finite fields." Comptes Rendus Mathematique 345, no. 2 (July 2007): 73–76. http://dx.doi.org/10.1016/j.crma.2007.05.017.

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Loureiro, B. V., P. R. de Souza Mendes, and L. F. A. Azevedo. "Taylor-Couette Instabilities in Flows of Newtonian and Power-Law Liquids in the Presence of Partial Annulus Obstruction." Journal of Fluids Engineering 128, no. 1 (September 29, 2005): 42–54. http://dx.doi.org/10.1115/1.2136930.

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The flow inside a horizontal annulus due to the inner cylinder rotation is studied. The bottom of the annular space is partially blocked by a plate parallel to the axis of rotation, thereby destroying the circumferential symmetry of the annular space geometry. This flow configuration is encountered in the drilling process of horizontal petroleum wells, where a bed of cuttings is deposited at the bottom part of the annulus. The velocity field for this flow was obtained both numerically and experimentally. In the numerical work, the equations which govern the three-dimensional, laminar flow of both Newtonian and power-law liquids were solved via a finite-volume technique. In the experimental research, the instantaneous and time-averaged flow fields over two-dimensional meridional sections of the annular space were measured employing the particle image velocimetry (PIV) technique, also both for Newtonian and power-law liquids. Attention was focused on the determination of the onset of secondary flow in the form of distorted Taylor vortices. The results showed that the critical rotational Reynolds number is directly influenced by the degree of obstruction of the flow. The influence of the obstruction is more perceptible for Newtonian than for non-Newtonian liquids. The more severe is the obstruction, the larger is the critical Taylor number. The height of the obstruction also controls the width of the vortices. The calculated steady-state axial velocity profiles agreed well with the corresponding measurements. Transition values of the rotational Reynolds number are also well predicted by the computations. However, the measured and predicted values for the vortex size do not agree as well. Transverse flow maps revealed a complex interaction between the Taylor vortices and the zones of recirculating flow, for moderate to high degrees of flow obstruction.

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Angel, Jeff. "Finite Upper Half Planes over Finite Fields." Finite Fields and Their Applications 2, no. 1 (January 1996): 62–86. http://dx.doi.org/10.1006/ffta.1996.0005.

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Yang, Li, Xuezhi Ben, Ming Zhang, and Chongguang Cao. "Induced Maps on Matrices over Fields." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/596756.

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Suppose that𝔽is a field andm,n≥3are integers. Denote byMmn(𝔽)the set of allm×nmatrices over𝔽and byMn(𝔽)the setMnn(𝔽). Letfij(i∈[1,m],j∈[1,n]) be functions on𝔽, where[1,n]stands for the set{1,…,n}. We say that a mapf:Mmn(𝔽)→Mmn(𝔽)is induced by{fij}iffis defined byf:[aij]↦[fij(aij)]. We say that a mapfonMn(𝔽)preserves similarity ifA~B⇒f(A)~f(B), whereA~Brepresents thatAandBare similar. A mapfonMn(𝔽)preserving inverses of matrices meansf(A)f(A-1)=Infor every invertibleA∈Mn(𝔽). In this paper, we characterize induced maps preserving similarity and inverses of matrices, respectively.

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40

Wamelen, Paul van. "Jacobi sums over finite fields." Acta Arithmetica 102, no. 1 (2002): 1–20. http://dx.doi.org/10.4064/aa102-1-1.

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Koike, Masao. "Hypergeometric polynomials over finite fields." Tohoku Mathematical Journal 51, no. 1 (1999): 75–79. http://dx.doi.org/10.2748/tmj/1178224854.

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Poonen, Bjorn. "Bertini theorems over finite fields." Annals of Mathematics 160, no. 3 (November 1, 2004): 1099–127. http://dx.doi.org/10.4007/annals.2004.160.1099.

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43

Greene, John. "Lagrange inversion over finite fields." Pacific Journal of Mathematics 130, no. 2 (December 1, 1987): 313–25. http://dx.doi.org/10.2140/pjm.1987.130.313.

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Ghorpade, S., and G. Lachaud. "Singular Varieties over Finite Fields." Moscow Mathematical Journal 2, no. 3 (2002): 589–631. http://dx.doi.org/10.17323/1609-4514-2002-2-3-589-631.

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Coulter, Robert S., and Rex W. Matthews. "Bent polynomials over finite fields." Bulletin of the Australian Mathematical Society 56, no. 3 (December 1997): 429–37. http://dx.doi.org/10.1017/s000497270003121x.

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The definition of bent is redefined for any finite field. Our main result is a complete description of the relationship between bent polynomials and perfect non-linear functions over finite fields: we show they are equivalent. This result shows that bent polynomials can also be viewed as the generalisation to several variables of the class of polynomials known as planar polynomials. An explicit method for obtaining large sets of not necessarily distinct maximal orthogonal systems using bent polynomials is given and we end with a short discussion on the existence of bent polynomials over finite fields.

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Coons, Jane Ivy, Jack Jenkins, Douglas Knowles, Rayanne A. Luke, and Patrick X. Rault. "Numerical ranges over finite fields." Linear Algebra and its Applications 501 (July 2016): 37–47. http://dx.doi.org/10.1016/j.laa.2016.03.024.

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Lyall, Neil, Ákos Magyar, and Hans Parshall. "Spherical configurations over finite fields." American Journal of Mathematics 142, no. 2 (2020): 373–404. http://dx.doi.org/10.1353/ajm.2020.0010.

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Masuda, Ariane M., and Michael E. Zieve. "Permutation binomials over finite fields." Transactions of the American Mathematical Society 361, no. 08 (March 17, 2009): 4169–80. http://dx.doi.org/10.1090/s0002-9947-09-04578-4.

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Winterhof, Arne. "Polynomial spaces over finite fields." Linear Algebra and its Applications 295, no. 1-3 (July 1999): 223–29. http://dx.doi.org/10.1016/s0024-3795(99)00102-0.

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Hong, J., and M. Vetterli. "Hartley transforms over finite fields." IEEE Transactions on Information Theory 39, no. 5 (1993): 1628–38. http://dx.doi.org/10.1109/18.259646.

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Journal articles on the topic 'Maps over finite fields'

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