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Journal articles on the topic 'Field of two elements'

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Published: 4 June 2021

Last updated: 2 February 2022

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1

Judd, B. R. "Quasi-spin for two-electron crystal-field matrix elements." Journal of Physics C: Solid State Physics 20, no. 32 (November 20, 1987): L903—L906. http://dx.doi.org/10.1088/0022-3719/20/32/005.

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2

De Seguins Pazzis, Clément. "Range-compatible homomorphisms over the field with two elements." Electronic Journal of Linear Algebra 34 (February 21, 2018): 71–114. http://dx.doi.org/10.13001/1081-3810.2982.

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Let U and V be finite-dimensional vector spaces over a field K, and S be a linear subspace of the space L(U, V ) of all linear operators from U to V. A map F : S â V is called range-compatible when F(s) â Im s for all s â S. Previous work has classified all the range-compatible group homomorphisms provided that codimL(U,V )S â¤ 2 dim V â 3, except in the special case when K has only two elements and codimL(U,V )S = 2 dim V â 3. This article gives a thorough treatment of that special case. The results are partly based upon the recent classification of vector spaces of matrices with rank at most 2 over F2. As an application, the 2-dimensional non-reflexive operator spaces are classified over any field, and so do the affine subspaces of Mn,p(K) with lower-rank at least 2 and codimension 3.

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3

Kawahito, S., S. O. Choi, M. Ishida, and T. Nakamura. "Micromachined hall elements for two-dimensional magnetic-field sensing." Sensors and Actuators A: Physical 40, no. 2 (February 1994): 141–46. http://dx.doi.org/10.1016/0924-4247(94)85020-8.

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4

Wannamaker, Philip E., John A. Stodt, and Luis Rijo. "Two‐dimensional topographic responses in magnetotellurics modeled using finite elements." GEOPHYSICS 51, no. 11 (November 1986): 2131–44. http://dx.doi.org/10.1190/1.1442065.

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We simulate the magnetotelluric response to two‐dimensional earth topography using finite elements. Linear interpolation of the secondary field parallel to strike over triangular elements allows accurate modeling of inclined resistivity boundaries, including topographic surfaces. To avoid discontinuities in field derivatives or resistivity, care must be taken that the nodal values of the field parallal to strike used to obtain the auxiliary secondary fields are kept within uniform earth media. The nodal locations may be shifted, but the derivatives still are evaluated at the field points of interest. Correct values may be returned at gentle breaks in slope as well as along straight surfaces. The finite‐element program is verified by comparison with the analytic transverse magnetic response of a hemicylindrical depression and with Rayleigh scattering and transmission surface results for transverse electric and transverse magnetic polarization. Agreement with the other methods generally is excellent, with the exception of some results of the transmission surface technique (especially the transverse magnetic mode). A result presented shows that placing the H-field sensors horizontally reduces topographic anomalies compared to locating sensors parallel to the slope. Moreover, if earth resistivity increases with elevation, the apparent resistivity is relatively nonanomalous near the base of the topography.

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5

Knabe, Władyslaw, JarosWław Przewłócki, and Grzegorz Róźyński. "Spatial averages for linear elements for two-parameter random field." Probabilistic Engineering Mechanics 13, no. 3 (July 1998): 147–67. http://dx.doi.org/10.1016/s0266-8920(97)00015-5.

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6

Judd, B. R., and L. Zing. "Two-electron crystal-field matrix elements for half-filled shells." Journal of Physics C: Solid State Physics 21, no. 22 (August 10, 1988): 4071–81. http://dx.doi.org/10.1088/0022-3719/21/22/020.

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7

Hubrig, S., S. P. Järvinen, H. Korhonen, I. Ilyin, M. Schöller, E. Niemczura, and S. D. Chojnowski. "Detection of weak magnetic fields in two HgMn stars." Monthly Notices of the Royal Astronomical Society: Letters 495, no. 1 (April 16, 2020): L97—L101. http://dx.doi.org/10.1093/mnrasl/slaa064.

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ABSTRACT The main-sequence mercury–manganese (HgMn) stars are known to exhibit large overabundances of exotic elements and, similar to magnetic Ap/Bp stars, are spectrum variables, implying the presence of an inhomogeneous element distribution over the stellar surface. A number of magnetic field studies have been attempted in the last decades, indicating that magnetic fields in HgMn stars, if they exist, should be rather weak. The presence of tangled magnetic fields was suggested by several authors who detected quadratic magnetic fields using the moment technique. We employ the least-squares deconvolution technique to carry out a sensitive search for weak magnetic fields in spectropolarimetric observations of three HgMn stars, HD 221507, HD 65949, and HD 101189, which have different fundamental parameters and spectral characteristics. A definite weak longitudinal field is discovered in HD 221507 and HD 65949 on single epochs, while only marginal field detections were achieved for HD 101189. The new measurements indicate that the structure of the magnetic fields is probably rather complex: our analysis reveals the presence of reversed Stokes V profiles at the same observational epoch if individual elements are used in the measurements. This is the first observational evidence that individual elements sample distinct local magnetic fields of different polarity across the stellar surface.

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8

Jokinen, Eric P., and Andrew Scanlon. "Field measured two-way slab deflections." Canadian Journal of Civil Engineering 14, no. 6 (December 1, 1987): 807–19. http://dx.doi.org/10.1139/l87-119.

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Results of a survey of two-way slab deflections both during and after construction of a 28-storey office tower are presented. A comparison is made between measured deflections and deflections computed using a finite element program that includes the effects of cracking. Effects of construction loading and time-dependent deformations are included in the calculations. The measured and calculated deflections illustrate the high variability that can be expected in two-way slab deflections. Key words: concrete construction, deflection, finite elements, loads, multistorey construction, two-way slabs, variability.

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9

de Seguins Pazzis, Clément. "Primitive spaces of matrices with upper rank two over the field with two elements." Linear and Multilinear Algebra 64, no. 7 (September 11, 2015): 1321–53. http://dx.doi.org/10.1080/03081087.2015.1083526.

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10

Herrera-Fernandez, Jose Maria, Luis Miguel Sanchez-Brea, and Eusebio Bernabeu. "Near-field shaping with two binary diffractive optical elements in tandem." Optics Communications 297 (June 2013): 182–89. http://dx.doi.org/10.1016/j.optcom.2013.01.059.

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11

PINTO, TIAGO, and JEAN-PIERRE COYETTE. "CONJUGATED INFINITE ELEMENTS FOR TWO-DIMENSIONAL TIME-HARMONIC ELASTODYNAMICS." Journal of Computational Acoustics 08, no. 03 (September 2000): 473–93. http://dx.doi.org/10.1142/s0218396x00000327.

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Wave propagation problems in unbounded domains require the handling of appropriate radiation conditions (Sommerfeld). Various absorbing boundary conditions are available for that purpose. In a discrete finite element context, local and global Dirichlet-to-Neumann (DtN) and infinite element methods have shown their efficiency for the scalar wave equation. The paper concentrates on the extension of an infinite element method to the elastodynamic vector wave equation. The extension is developed in the frequency domain for 2-D problems. The paper focuses on the development of a conjugated formulation using the Helmholtz decomposition theorem of smooth vector fields. The accuracy of the developed formulation is assessed through the study of benchmarks. The computed results are shown to be in good agreement with the analytical solution for a multi-pole field along a circular cavity and with the results produced by other numerical methods.

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12

REZAIEE-PAJAND, MOHAMMAD, MAJID YAGHOOBI, and MOHAMMAD KARKON. "HYBRID TREFFTZ FORMULATION FOR THIN PLATE ANALYSIS." International Journal of Computational Methods 09, no. 04 (December 2012): 1250053. http://dx.doi.org/10.1142/s0219876212500533.

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In this paper, two efficient elements are proposed by utilizing hybrid Trefftz method for the analysis of thin plate bending. The triangular element, THT, and the quadrilateral element, QHT, which have 9 and 12 degrees of freedom, respectively. Two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a way that it satisfies the governing equation of the thin plate. Boundary field is dependent on the nodal degrees of freedom via boundary interpolation functions. For deriving boundary interpolation functions, element's edges are assumed to deform like a beam, and the related interpolation functions are used for the boundary fields. The solution accuracies of the famous and hard bench mark problems, such as circular and skew plates, prove the justification of suggested elements. Based on the various test problems, QHT in comparison to other four-sided elements, and THT in comparison to triangular ones, show better results and rapider convergence rate.

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13

Rezaiee-Pajand, Mohammad, Nima Gharaei-Moghaddam, and Mohammadreza Ramezani. "Two Triangular Membrane Elements Based on Strain." International Journal of Applied Mechanics 11, no. 01 (January 2019): 1950010. http://dx.doi.org/10.1142/s1758825119500108.

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The strain formulation approach improves accuracy and removes complications, such as shear parasitic errors and sensitivity to mesh distortions. For analyzing plane stress and strain problems, two new strain-based triangular elements are proposed. Both compatibility and equilibrium conditions are imposed to these elements. Contrary to the quadrilateral shape, triangular element facilitates proper meshing of various geometries. To formulate these elements, the linear strain field is assumed. The first element is a five-node triangular element, in which each node has two degrees of freedom. In the second one, which is a four-node element, drilling degrees of freedom are added to improve applicability of the element for bending problems. Various numerical examples and patch tests verify high accuracy and efficiency of the suggested elements in comparison with the other existing plane elements.

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14

Mohtar, Rabi H., and Larry J. Segerlind. "Dynamic time-step estimates for two-dimensional transient field problems using square elements." International Journal for Numerical Methods in Engineering 42, no. 1 (May 15, 1998): 1–14. http://dx.doi.org/10.1002/(sici)1097-0207(19980515)42:1<1::aid-nme302>3.0.co;2-q.

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15

Yong-woo, Kim, and Min Oak-key. "Optimal strain locations of two-dimensional continuum elements in terms of field-consistency." Computers & Structures 59, no. 6 (June 1996): 1121–38. http://dx.doi.org/10.1016/0045-7949(95)00305-3.

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16

Pilkey, Walter D., and Yongquan Liu. "Field theory: A two-dimensional case for not using finite or boundary elements." Finite Elements in Analysis and Design 13, no. 2-3 (June 1993): 127–36. http://dx.doi.org/10.1016/0168-874x(93)90052-r.

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17

Shlepkin, А. А., and I. V. Sabodakh. "On Two Properties of Shunkov Group." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 103–19. http://dx.doi.org/10.26516/1997-7670.2021.35.103.

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One of the interesting classes of mixed groups ( i.e. groups that can contain both elements of finite order and elements of infinite order) is the class of Shunkov groups. The group $G$ is called Shunkov group if for any finite subgroup $H$ of $G$ in the quotient group $N_G(H)/H$, any two conjugate elements of prime order generate a finite group. When studying the Shunkov group $G$, a situation often arises when it is necessary to move to the quotient group of the group $G$ by some of its normal subgroup $N$. In which cases is the resulting quotient group $G/N$ again a Shunkov group? The paper gives a positive answer to this question, provided that the normal subgroup $N$ is locally finite and the orders of elements of the subgroup $N$ are mutually simple with the orders of elements of the quotient group $G/N$. Let $ \mathfrak{X}$ be a set of groups. A group $G$ is saturated with groups from the set $ \mathfrak{X}$ if any finite subgroup of $G$ is contained in a subgroup of $ G$ that is isomorphic to some group of $\mathfrak{X}$ . If all elements of finite orders from the group $G$ are contained in a periodic subgroup of the group $G$, then it is called the periodic part of the group $G$ and is denoted by $T(G)$. It is proved that the Shunkov group saturated with finite linear and unitary groups of degree 3 over finite fields has a periodic part that is isomorphic to either a linear or unitary group of degree 3 on a suitable locally finite field. \end{abstracte}

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18

DRENSKY, VESSELIN, and JIE-TAI YU. "PRIMITIVE ELEMENTS OF FREE METABELIAN ALGEBRAS OF RANK TWO." International Journal of Algebra and Computation 13, no. 01 (February 2003): 17–33. http://dx.doi.org/10.1142/s021819670300133x.

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Let F(x,y) be a relatively free algebra of rank 2 in some variety of algebras over a field K of characteristic 0. In this paper we consider the problem whether p(x,y) ∈ F(x,y) is a primitive element (i.e. an automorphic image of x): (i) If F(x,y)/(p(x,y)) ≅ F(z), the relatively free algebra of rank 1 (ii) If p(f,g) is primitive for some injective endomorphism (f,g) of F(x,y) (iii) If p(x,y) is primitive in a relatively free algebra of larger rank. These problems have positive solutions for polynomial algebras in two variables. We give the complete answer for the free metabelian associative and Lie algebras and some partial results for free associative algebras.

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19

Bell, Jason, Daryl Funk, Byoung Du Kim, and Dillon Mayhew. "Effective Versions of Two Theorems of RADO." Quarterly Journal of Mathematics 71, no. 2 (March 17, 2020): 599–618. http://dx.doi.org/10.1093/qmathj/haaa001.

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20

Feinstein, Jonathan S. "Optimal Learning Patterns for Creativity Generation in a Field." American Economic Review 101, no. 3 (May 1, 2011): 227–32. http://dx.doi.org/10.1257/aer.101.3.227.

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I present a model of optimal learning for creativity generation in a field. The field is defined as a knowledge structure. A creative contribution is based on combining two previously unconnected elements, generating a new element. Individuals may possess private information/intuition about new combinations. Individuals contribute the maximum creative contribution they are able to produce based on the set of elements they have learned. In equilibrium individuals learn different elements, with some degree of overlap, effectively pursuing distinct creative interests. The model illustrates a general approach for analyzing the creative development of fields and, in a broader sense, cultural innovation.

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21

Wang, Hui, and Qing-Hua Qin. "Voronoi Polygonal Hybrid Finite Elements with Boundary Integrals for Plane Isotropic Elastic Problems." International Journal of Applied Mechanics 09, no. 03 (April 2017): 1750031. http://dx.doi.org/10.1142/s1758825117500314.

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Polygonal finite elements with high level of geometric isotropy provide greater flexibility in mesh generation and material science involving topology change in material phase. In this study, a hybrid finite element model based on polygonal mesh is constructed by centroidal Voronoi tessellation for two-dimensional isotropic elastic problems and then is formulated with element boundary integrals only. For the present [Formula: see text]-sided polygonal finite element, two independent fields are introduced: (i) displacement and stress fields inside the element; (ii) frame displacement field along the element boundary. The interior fields are approximated by fundamental solutions so that they exactly satisfy the governing equations to convert element domain integral in the two-field functional into element boundary integrals to reduce integration dimension. While the frame displacement field is approximated by the conventional shape functions to satisfy the conformity requirement between adjacent elements. The two independent fields are coupled by the weak functional to form the stiffness equation. This hybrid formulation enables the construction of [Formula: see text]-sided polygons and extends the potential applications of finite elements to convex polygons of arbitrary order. Finally, five examples including patch tests in square domain, thick cylinder under internal pressure, beam bending and composite with clustered holes are provided to illustrate convergence, accuracy and capability of the present Voronoi polygonal finite elements.

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22

Petrenko, B. V. "On the sum of two primitive elements of maximal subfields of a finite field." Finite Fields and Their Applications 9, no. 1 (January 2003): 102–16. http://dx.doi.org/10.1016/s1071-5797(02)00014-x.

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23

Petrenko, B. V. "On the product of two primitive elements of maximal subfields of a finite field." Journal of Pure and Applied Algebra 178, no. 3 (March 2003): 297–306. http://dx.doi.org/10.1016/s0022-4049(02)00196-2.

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24

Atencia, Jesús, Isabel Arias, Manuel Quintanilla, Ana García, and Ana M. López. "Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements." Applied Optics 38, no. 19 (July 1, 1999): 4011. http://dx.doi.org/10.1364/ao.38.004011.

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25

Volta, Francesca Dalla. "Regular sets for the affine and projective groups over the field of two elements." Journal of Geometry 33, no. 1-2 (October 1988): 17–26. http://dx.doi.org/10.1007/bf01230600.

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26

FEDOROVA, T. A., A. V. KOROL, and I. A. SOLOVJEV. "RELATIVISTIC CALCULATION OF THE TWO-PHOTON BREMSSTRAHLUNG PROCESS." Surface Review and Letters 09, no. 02 (April 2002): 1185–90. http://dx.doi.org/10.1142/s0218625x02003494.

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We present analytical and numerical results on the relativistic calculation of the two-photon bremsstrahlung process. For the approximate calculation of relativistic free–free two-photon matrix elements in the central field, we applied the method based on the accurate treatment of the diagonal singularities in the relativistic free–free single-photon matrix elements. Numerical calculations are carried out with the Furry–Sommerfeld–Maue wave functions. The obtained results are compared with the results of the relativistic Born approximation.

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27

Weill, Anne, Avraham Shitzer, and Pinhas Bar-Yoseph. "Finite Element Analysis of the Temperature Field Around Two Adjacent Cryo-Probes." Journal of Biomechanical Engineering 115, no. 4A (November 1, 1993): 374–79. http://dx.doi.org/10.1115/1.2895500.

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A finite element code was developed for the analysis of the temperature field around two adjacent cylindrical cryo-probes. The two-phase, two-dimensional Stefan problem is solved using a moving boundary approach and space-time finite elements. Solution of one-cryo-probe problem compared well with an existing analytic solution. The two-cryo-probes problem yielded reasonable results. The program simulated the nonsymmetric activation of two probes and the merging of the two freezing fronts in the case of symmetric activation.

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28

Rahmawati, Dian, Imam Jauhari Maknun, and Irwan Katili. "An evaluation on the performance of two simple triangular bending plate elements." MATEC Web of Conferences 192 (2018): 02046. http://dx.doi.org/10.1051/matecconf/201819202046.

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This paper will study and compare two different three-node triangular bending plate elements with three degree of freedom per node, i.e. MITC3 and DKMT. Both elements, which were developed based on Reissner-Mindlin plate theory and independent shear strain field, have simple formulation and have already been used widely. In this paper, numerical tests for circular plate case are conducted to verify the performance and show the convergence of these two triangular elements.

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29

Tuszyński, J. A., R. Chatterjee, and J. M. Dixon. "Racah algebra of two-body double-tensor operators." Canadian Journal of Physics 63, no. 9 (September 1, 1985): 1220–27. http://dx.doi.org/10.1139/p85-200.

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Two-body double-tensor (TBDT) operators are introduced in the LS- and jj-coupling schemes following Racah's definition of irreducible tensor operators. These operators are shown to contain well-known one-body double tensors as a subset. The result of applying parity, charge conjugation, and time reversal to the TBDT operators is investigated so as to obtain selection rules for their matrix elements. On the basis of their rotation properties, these Hermitian tensor operators are shown to satisfy an SU(2) algebra, and consequently the Wigner–Eckart theorem is applied to calculate their matrix elements. The derivation of the reduced matrix elements is provided. We show some examples of interactions investigated in the literature that can be represented as TBDT operators. For one such operator, the spin-correlated crystal field, a detailed numerical evaluation of its matrix elements is given.

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30

Xu, Yu, Bing Cheng Yuan, and Hong Gang Zhang. "A Study on Transition from Near Field to Far Field of Echoes from Underwater Simulated Targets." Advanced Materials Research 187 (February 2011): 826–30. http://dx.doi.org/10.4028/www.scientific.net/amr.187.826.

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With the distance between sonar system and target enlarging, the underwater target transits from near field to far field. Based on planar element scattering similarity, a novel algorithm is presented in this paper. In this thesis, an underwater target model is set up and meshed with triangular planar element by using the software of Ansys. Due to the sonar system is in far field to every planar element, the matrixes whose elements are the planar elements target strength can be calculated. In the course of an underwater target transits from near field to far field, the matrix whose elements are the planar elements target strength is becoming more and more similar to that in far field. Thus the correlation coefficient between the above two matrixes can be used to analyze the transition of an underwater target. Numerical calculation are presented, and the results show that the underwater target scattering characteristics in critical distance approximate the characteristics in far field, but the target strength which is calculated in critical distance is also should be modified little.

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31

LI, YUEYUE, and JIE-TAI YU. "FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES." Bulletin of the Australian Mathematical Society 95, no. 2 (October 20, 2016): 209–13. http://dx.doi.org/10.1017/s0004972716000630.

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Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

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32

Schrempf, Konrad. "A standard form in (some) free fields: How to construct minimal linear representations." Open Mathematics 18, no. 1 (November 23, 2020): 1365–86. http://dx.doi.org/10.1515/math-2020-0076.

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Abstract We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra techniques for the construction of minimal linear representations (in standard form) for the sum and the product of two elements (given in a standard form). This completes “minimal” arithmetic in free fields since “minimal” constructions for the inverse are already known. The applications are wide: linear algebra (over the free field), rational identities, computing the left gcd of two non-commutative polynomials, etc.

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33

Abdara, Amirulmukminin. "Analisis Kemampuan Calon Guru Matematika Dalam Pengajuan Masalah Ditinjau dari Gaya Kognitif Field Independent dan Field Dependent." Kreano, Jurnal Matematika Kreatif-Inovatif 8, no. 1 (June 14, 2017): 69–75. http://dx.doi.org/10.15294/kreano.v8i1.7120.

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Penelitian ini bertujuan untuk mendeskripsikan kemampuan calon guru matematika dalam pengajuan masalah ditinjau dari gaya kognitif field independent (FI) dan field dependent (FD). Terdapat dua subjek dalam penelitian ini, yaitu mahasiswa calon guru Pendidikan Matematika semester VI, IKIP Mataram. Gaya kognitif subjek ditentukan berdasarkan skor pemberian instrument GEFT dan kemampuan pengajuan masalah diperoleh melalui TPM dan wawancara. SFI dan SFD masing-masing mengajukan 10 masalah dari informasi berbentuk grafik dan kalimat verbal. Secara umum, kemampuan SFI lebih bagus dibandingkan SFD yaitu: (1) SFI mengajukan 7 masalah sementara SFD hanya mengajukan 5 masalah yang berkaitan dengan aritmetika sosial, (2) SFI mampu mengajukan masalah yang memenuhi semua unsur sintaksis dan semantik, sementara masalah yang diajukan SFD dari informasi grafik hanya memuat 2 unsur sintaksis dan 2 unsur semantik dan dan masalah yang diajukan dari informasi kalimat verbal masing-masing memuat 2 unsur sintaksis dan 3 unsur semantik, (3) SFI mengajukan 5 masalah, sementara SFD hanya mengajukan 1 masalah yang memuat data baru, (4) SFI mengajukan 2 masalah yang tidak bisa diselesaikan karena rasa penasaran, sementara SFD mengajukan 5 masalah yang tidak dapat diselesaikan karena kesalahan pemilihan kata, dan (5) SFI mengajukan masalah yang termasuk kategori mudah, sedang, dan sulit, sementara masalah yang diajukan SFD hanya masuk kategori masalah mudah.This is descriptive research with qualitative approach which has purpose to describe the skill of preserve teacher in problem posing observed from cognitive style of field independent (FI) and field dependent (FD). The subjects are two the mathematic students in the sixth semester, IKIP Mataram. Cognitive style of each subject was determined by giving GEFT instrument and to know the skill of preserve mathematics teacher in posing problem was obtained through TPM and interview. SFI and SFD each posed ten problems from graph information and verbal sentence. SFI has better skill in problem posing than SFD: (1) SFI posed seven problems, while SFD only posed five problems related to arithmetic, (2) on SFI, all problems which were posed fulfilled all syntaxes and semantic elements which had been decided. While, the graph information of SFD could only posed the information which showed two syntaxes elements and two semantic elements, and each posed problems of verbal sentence information has two syntaxes elements and three semantic elements, (3) SFI pose five new data, while SFD could only show one problem which contained new data, (4) SFI posed two unsolved problems because of wondering, while SFD posed five unsolved problems because of choosing words error, and (5) SFI posed problems were included in each easy, middle and difficult category, while SFD only posed problem in easy category.

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34

Makarchuk, O., D. Calus, and V. Moroz. "MATHEMATICAL MODEL TO CALCULATE THE TRAJECTORIES OF ELECTROMAGNETIC MILL OPERATING ELEMENTS." Tekhnichna Elektrodynamika 2021, no. 2 (February 23, 2021): 26–34. http://dx.doi.org/10.15407/techned2021.02.026.

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The purpose of the research under consideration is to develop a mathematical model to calculate the trajectories of the ferromagnetic operating elements (millstones) of an electromagnetic mill, moving in a rotating magnetic field under electrodynamic and hydrodynamic resistance forces being limited by the space of the mill’s working chamber. The millstone motion is described through the equations of plane motion of arbitrary-shaped two-dimensional body. The driving forces of this motion are determined on the basis of the approximation of the tabulated functions connecting the module and the orientation of the equivalent force applied to the millstone, with its position in the working chamber and composite MMF phase of mill inductor winding. These tabulated functions are derived from the estimation of the magnetic field inside a working chamber with millstones, in two-dimensional quasi-stationary approximation, using FEM analysis. The publication contains the approximation algorithm for these tabulated vector functions of a vector argument, mathematical statement of millstones trajectories calculating, and analysis of mathematical experiments results that make it possible to evaluate the adequacy of the model. The developed tool enables conducting quantitative analysis of grinding/mixing process and will help to establish relationships between the electromagnetic mill design parameters and its performance. References 21, figures 6.

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35

Caley, A. J., A. J. Waddie, and M. R. Taghizadeh. "A novel algorithm for designing diffractive optical elements for two colour far-field pattern formation." Journal of Optics A: Pure and Applied Optics 7, no. 6 (May 9, 2005): S276—S279. http://dx.doi.org/10.1088/1464-4258/7/6/004.

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POLLACK, PAUL, and LEE TROUPE. "TWO PROBLEMS CONCERNING IRREDUCIBLE ELEMENTS IN RINGS OF INTEGERS OF NUMBER FIELDS." Bulletin of the Australian Mathematical Society 96, no. 1 (March 2, 2017): 44–58. http://dx.doi.org/10.1017/s0004972716001325.

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Let $K$ be a number field with ring of integers $\mathbb{Z}_{K}$. We prove two asymptotic formulas connected with the distribution of irreducible elements in $\mathbb{Z}_{K}$. First, we estimate the maximum number of nonassociated irreducibles dividing a nonzero element of $\mathbb{Z}_{K}$ of norm not exceeding $x$ (in absolute value), as $x\rightarrow \infty$. Second, we count the number of irreducible elements of $\mathbb{Z}_{K}$ of norm not exceeding $x$ lying in a given arithmetic progression (again, as $x\rightarrow \infty$). When $K=\mathbb{Q}$, both results are classical; a new feature in the general case is the influence of combinatorial properties of the class group of $K$.

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Aisbett, Janet, and Victor Snaith. "K3 of truncated polynomial rings over fields of characteristic two." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (May 1987): 509–21. http://dx.doi.org/10.1017/s0305004100066871.

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Write F for the finite field, , having 2m elements. Let W2(F) denote the Witt vectors of length two over F (for a definition, see [4] or [10], §10). Write F(q) for the truncated polynomial ring, F[t]/(tq).

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38

Dong, Yuhao, Xuejun Zhao, Xiujiu Yuan, Jialin Li, Jiang Li, and Haoxiang Sun. "Construction of Optimal Codes in Two Element Field." Journal of Physics: Conference Series 1087 (September 2018): 052033. http://dx.doi.org/10.1088/1742-6596/1087/5/052033.

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LEVENE, MARK, and GEORGE ROUSSOS. "A TWO-PLAYER GAME OF LIFE." International Journal of Modern Physics C 14, no. 02 (February 2003): 195–201. http://dx.doi.org/10.1142/s0129183103004346.

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We present a new extension of Conway's game of life for two players, which we call "p2life". P2life allows one of two types of token, black or white, to inhabit a cell and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine, using simulation, that the asymptotic density of p2life approaches 0.0362.

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Chama, A., and B. D. Reddy. "Stability and Convergence of Two Three-Field Finite Element Formulations for Elasticity." Computational Methods in Applied Mathematics 14, no. 3 (July 1, 2014): 305–16. http://dx.doi.org/10.1515/cmam-2014-0014.

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Abstract.In this work analyses are carried out to verify the well-posedness of two three-field formulations for linear elasticity that have been shown to work well in practice, but for which analyses are absent. Both are formulated in three dimensions on tetrahedral elements. The first has as primary unknowns the displacement, pressure, and dilatation, and the second is a formulation with primary unknowns the displacement, pressure and enhanced strain, with the space of enhanced strains spanned by functions that are bubble functions on a surface of the element. It is shown that the first-mentioned formulation is a special case of a general three-field formulation, for which well-posedness conditions have been established. These conditions are used here to show that the pressure-dilatation-displacement formulation is uniformly convergent in the incompressible limit. The pressure-enhanced strain-displacement formulation is not amenable to such an approach; instead, it is reformulated in the form of a standard discrete saddle point problem, and the uniform convergence of the formulation established directly by verifying the ellipticity and inf-sup conditions.

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Casco, Clara, and Donatella Spinelli. "Left—Right Visual Field Asymmetry in Bistable Motion Perception." Perception 17, no. 6 (December 1988): 721–27. http://dx.doi.org/10.1068/p170721.

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Twelve observers viewed two alternating frames, each consisting of three rectangular bars which were displaced laterally by one cycle in one frame with respect to the other. At long interframe intervals (IFIs) observers perceived a group of three elements moving as a whole (group movement), whereas with IFIs shorter than 40–60 ms the overlapping elements in each frame appeared stationary while the third element appeared to move from one end of the display to the other (end-to-end movement). The percentage of group movement responses in central viewing was compared to those obtained for stimulus presentation in the left and right visual fields (4 deg eccentricity), for opposite horizontal directions of motion. All ten right-handed subjects showed a left-field advantage in sensitivity to group movement. The two left-handed subjects showed a similar advantage in sensitivity with right-field presentation. The effects of monocular vision, hand used in the task, spatial frequency, and contrast on visual field asymmetry were all investigated in two right-handed subjects. None of these factors affected the left—right asymmetry.

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Álvarez Esteban, Ramón, and Pedro Aguado Rodríguez. "Datos textuales como elementos activos en sensometría = Textual data as active elements in sensometry." Pecvnia : Revista de la Facultad de Ciencias Económicas y Empresariales, Universidad de León, no. 2012 (March 3, 2012): 31. http://dx.doi.org/10.18002/pec.v0i2012.1106.

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<p>La utilización de datos textuales en estudios estadísticos sobre sensometría generalmente se ha realizado tratando de explicar e interpretar los resultados alcanzados a partir de datos cuantitativos. Este trabajo muestra una metodología que permite utilizar datos textuales como elementos activos. Dos catas de vinos ilustran el procedimiento.</p><p>The use of textual data in statistical studies into sensometric field has been conducted generally seeking to explain and interpret results obtained from quantitative data. This work shows a methodology that allows use textual data as active elements. Two wine tastings illustrate the procedure.</p>

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Álvarez Esteban, Ramón, and Pedro Aguado Rodríguez. "Datos textuales como elementos activos en sensometría = Textual data as active elements in sensometry." Pecvnia : Revista de la Facultad de Ciencias Económicas y Empresariales, Universidad de León, Monog (March 3, 2012): 31. http://dx.doi.org/10.18002/pec.v0imonog.1106.

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<p>La utilización de datos textuales en estudios estadísticos sobre sensometría generalmente se ha realizado tratando de explicar e interpretar los resultados alcanzados a partir de datos cuantitativos. Este trabajo muestra una metodología que permite utilizar datos textuales como elementos activos. Dos catas de vinos ilustran el procedimiento.</p><p>The use of textual data in statistical studies into sensometric field has been conducted generally seeking to explain and interpret results obtained from quantitative data. This work shows a methodology that allows use textual data as active elements. Two wine tastings illustrate the procedure.</p>

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44

Mordkovich, V. N., K. K. Abgaryan, D. L. Reviznikov, and A. V. Leonov. "Simulation of Hall field elements based on nanoscale silicon-on-insulator heterostructures." Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering 23, no. 2 (September 15, 2020): 109–15. http://dx.doi.org/10.17073/1609-3577-2020-2-109-115.

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The article is devoted to the issues of numerical simulation of field Hall sensors based on the "silicon on insulator" structure with two control gates. To solve the problem, a two-level local-one-dimensional computational model is used. At the first level, a series of one-dimensional Schrödinger—Poisson equations are solved, which describe the distribution of the electron density across the heterostructure in different sections. The obtained information is transmitted to the second level, where the current characteristics of the element are calculated. The numerical simulation results are compared with the experimental data obtained for field Hall sensors. Comparative analysis shows good agreement between calculated and experimental data. The developed computer model makes it possible to carry out a multivariate analysis of various heterostructures, which creates the basis for optimizing devices of the class under consideration.

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Lee, R. S., and C. T. Kwan. "A Three-Dimensional Upper Bound Elemental Technique for Forging Analysis." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 210, no. 4 (August 1996): 353–59. http://dx.doi.org/10.1243/pime_proc_1996_210_128_02.

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In this paper, two kinematically admissible velocity fields are derived for the proposed three-dimensional arbitrarily triangular and trapezoidal prismatic upper bound elemental technique (UBET) elements. These elements are applied to the portions between the circular shaped part and the straight rod part with three-dimensional metal flow in connecting rod forging, and then the capability of the proposed elements are shown. From the derived velocity fields, the upper bound loads on the upper die and the velocity field are determined by minimizing the total energy consumption with respect to some chosen parameters. Experiments with connecting rod forging were carried out with commercial pure lead billets at ambient temperature. The theoretical predictions of the forming load is in good agreement with the experimental results. It is shown that the proposed UBET elements in this work can effectively be used for the prediction of the forming load and velocity field in connecting rod forging.

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Masuda, Ariane M., Lucia Moura, Daniel Panario, and David Thomson. "Low Complexity Normal Elements over Finite Fields of Characteristic Two." IEEE Transactions on Computers 57, no. 7 (July 2008): 990–1001. http://dx.doi.org/10.1109/tc.2007.70845.

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Khan, Reem, Antonio Radoi, Sidra Rashid, Akhtar Hayat, Alina Vasilescu, and Silvana Andreescu. "Two-Dimensional Nanostructures for Electrochemical Biosensor." Sensors 21, no. 10 (May 12, 2021): 3369. http://dx.doi.org/10.3390/s21103369.

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Current advancements in the development of functional nanomaterials and precisely designed nanostructures have created new opportunities for the fabrication of practical biosensors for field analysis. Two-dimensional (2D) and three-dimensional (3D) nanomaterials provide unique hierarchical structures, high surface area, and layered configurations with multiple length scales and porosity, and the possibility to create functionalities for targeted recognition at their surface. Such hierarchical structures offer prospects to tune the characteristics of materials—e.g., the electronic properties, performance, and mechanical flexibility—and they provide additional functions such as structural color, organized morphological features, and the ability to recognize and respond to external stimuli. Combining these unique features of the different types of nanostructures and using them as support for bimolecular assemblies can provide biosensing platforms with targeted recognition and transduction properties, and increased robustness, sensitivity, and selectivity for detection of a variety of analytes that can positively impact many fields. Herein, we first provide an overview of the recently developed 2D nanostructures focusing on the characteristics that are most relevant for the design of practical biosensors. Then, we discuss the integration of these materials with bio-elements such as bacteriophages, antibodies, nucleic acids, enzymes, and proteins, and we provide examples of applications in the environmental, food, and clinical fields. We conclude with a discussion of the manufacturing challenges of these devices and opportunities for the future development and exploration of these nanomaterials to design field-deployable biosensors.

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KOCAREV, LJ, LJ KARADZINOV, and L. O. CHUA. "N-DIMENSIONAL CANONICAL CHUA'S CIRCUIT." Journal of Circuits, Systems and Computers 03, no. 01 (March 1993): 239–58. http://dx.doi.org/10.1142/s0218126693000186.

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In this paper we present an n-dimensional canonical piecewise-linear electrical circuit. It contains 2n two-terminal elements: n linear dynamic elements (capacitors and inductors), n - 1 linear resistors and one nonlinear (piecewise-linear) resistor. This circuit can realize any prescribed eigenvalue pattern, except for a set of measure zero, associated with (i) any n-dimensional two-region continuous piecewise-linear vector fields and (ii) any n-dimensional three-region symmetric (with respect to the origin) piecewise-linear continuous vector fields. We also proved a theorem that specifies the conditions for a vector field, realized with our canonical circuit, to have two or three equilibrium points.

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Babu, C. Ramesh, and G. Prathap. "A field-consistent two-noded curved axisymmetric shell element." International Journal for Numerical Methods in Engineering 23, no. 7 (July 1986): 1245–61. http://dx.doi.org/10.1002/nme.1620230705.

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Elliott, Charles M., and Björn Stinner. "Computation of Two-Phase Biomembranes with Phase DependentMaterial Parameters Using Surface Finite Elements." Communications in Computational Physics 13, no. 2 (February 2013): 325–60. http://dx.doi.org/10.4208/cicp.170611.130112a.

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AbstractThe shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.

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