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Journal articles on the topic 'Primitives Element'

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Published: 4 June 2021

Last updated: 9 February 2022

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1

Brunner, A. M., R. G. Burns, and Sheila Oates-Williams. "On Almost Primitive Elements of Free Groups With an Application to Fuchsian Groups." Canadian Journal of Mathematics 45, no. 2 (April 1, 1993): 225–54. http://dx.doi.org/10.4153/cjm-1993-011-9.

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AbstractAn element of a free group F is called almost primitive in F, if it is primitive in every proper subgroup containing it, though not in F itself. Several examples of almost primitive elements (APEs) are exhibited. The main results concern the behaviour of proper powers wℓ of certain APEs w in a free group F (and, more generally, in free products of cycles) with respect to any subgroup H containing such a power “minimally“: these assert, in essence, that either such powers of w behave in H as do powers of primitives of F, or, if not, then they “almost” do so and furthermore H must then have finite index in F precisely determined by the smallest positive powers of conjugates of w lying in H. Finally, these results are applied to show that the groups of a certain class (potentially larger than that of finitely generated Fuchsian groups) have the property that all their subgroups of infinité index are free products of cyclic groups.

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2

Manzini, Maria Rita, and Leonardo M. Savoia. "Reducing ‘case’ to denotational primitives." Linguistic Variation 11, no. 1 (December 5, 2011): 76–120. http://dx.doi.org/10.1075/lv.11.1.03man.

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The nominal inflection system of Albanian includes specifications of case, definiteness, number and nominal class (gender). Our analysis recognizes three types of properties as theoretically relevant, namely N(ominal class), Q(quantification), D(efiniteness). Q inflections are responsible for the so-called oblique case - effectively a dyadic operator yielding a ‘zonal inclusion’ (possession) relation between the element to which it attaches and the internal argument of the verb (dative) or the head of a noun phrase (genitive). Q inflections are further responsible for plurality, while N inflections satisfy argument-of contexts (accusative)and D characterizes EPP contexts(nominative). Syncretisms (e.g. of dative and genitive, nominative and accusative) are not the result of morphological rules requiring Late Insertion of exponents (Distributed Morphology). Rather they are instances of ambiguity, resolved in the syntax (different embeddings) or at the interpretive interface. As such they are compatible with projection of the morphosyntax from lexical entries. Keywords: Case, nominative, accusative, oblique, syncretism, nominal class, plural, definiteness, possessor, locative.

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3

Mathur, K. K., and S. L. Johnsson. "Communication primitives for unstructured finite element simulations on data parallel architectures." Computing Systems in Engineering 3, no. 1-4 (January 1992): 63–71. http://dx.doi.org/10.1016/0956-0521(92)90095-z.

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4

Yang, H., and D. A. Hoeltzel. "Automatic Finite Element Mesh Generation Over Intersecting Rigid Body-Movable Subdomains for the Automation of Parametric Conceptual Design." Journal of Mechanical Design 116, no. 4 (December 1, 1994): 1049–57. http://dx.doi.org/10.1115/1.2919486.

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An approach for the automatic generation and refinement of three-dimensional finite element meshes subdivided by multiply connected, rigid body movable subdomains has been developed. A combination of computational geometry and geometric modeling techniques have been employed to implement parametric computer-aided design based on the finite element method. Nonconvexity of an overall three-dimensional domain has been handled by combining convex geometric primitives as subdomains for the construction of a three-dimensional domain. A clipping technique is employed for determining intersection points between subdomains bounded by traingulated surface, following their rigid body movements. To demonstrate the utility of this approach to parametric redesign, a series of meshes that model a hip joint prosthesis and a reciprocating internal combustion engine, as assemblies of parametrically-defined geometric primitives, has been developed.

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5

Jessa, Mieczysław, and Łukasz Matuszewski. "Producing Random Bits with Delay-Line-Based Ring Oscillators." International Journal of Electronics and Telecommunications 59, no. 1 (March 1, 2013): 41–50. http://dx.doi.org/10.2478/eletel-2013-0005.

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Abstract One of the sources of randomness for a random bit generator (RBG) is jitter present in rectangular signals produced by ring oscillators (ROs). This paper presents a novel approach for the design of delays used in these oscillators. We suggest using delay elements made on carry4 primitives instead of series of inverters or latches considered in the literature. It enables the construction of many high frequency ring oscillators with different nominal frequencies in the same field programmable gate array (FPGA). To assess the unpredictability of bits produced by RO-based RBG, the restarts mechanism, proposed in earlier papers, was used. The output sequences pass all NIST 800-22 statistical tests for smaller number of ring oscillators than the constructions described in the literature. Due to the number of ROs with different nominal frequencies and the method of construction of carry4 primitives, it is expected that the proposed RBG is more robust to cryptographic attacks than RBGs using inverters or latches as delay element.

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6

Sosnik, Ronen, Eliyahu Chaim, and Tamar Flash. "Stopping is not an option: the evolution of unstoppable motion elements (primitives)." Journal of Neurophysiology 114, no. 2 (August 2015): 846–56. http://dx.doi.org/10.1152/jn.00341.2015.

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Stopping performance is known to depend on low-level motion features, such as movement velocity. It is not known, however, whether it is also subject to high-level motion constraints. Here, we report results of 15 subjects instructed to connect four target points depicted on a digitizing tablet and stop “as rapidly as possible” upon hearing a “stop” cue (tone). Four subjects connected target points with straight paths, whereas 11 subjects generated movements corresponding to coarticulation between adjacent movement components. For the noncoarticulating and coarticulating subjects, stopping performance was not correlated or only weakly correlated with motion velocity, respectively. The generation of a straight, point-to-point movement or a smooth, curved trajectory was not disturbed by the occurrence of a stop cue. Overall, the results indicate that stopping performance is subject to high-level motion constraints, such as the completion of a geometrical plan, and that globally planned movements, once started, must run to completion, providing evidence for the definition of a motion primitive as an unstoppable motion element.

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7

Weissman, Jon B., Andrew S. Grimshaw, and R. D. Ferraro. "Parallel Object-Oriented Computation Applied to a Finite Element Problem." Scientific Programming 2, no. 4 (1993): 133–44. http://dx.doi.org/10.1155/1993/859092.

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The conventional wisdom in the scientific computing community is that the best way to solve large-scale numerically intensive scientific problems on today's parallel MIMD computers is to use Fortran or C programmed in a data-parallel style using low-level message-passing primitives. This approach inevitably leads to nonportable codes and extensive development time, and restricts parallel programming to the domain of the expert programmer. We believe that these problems are not inherent to parallel computing but are the result of the programming tools used. We will show that comparable performance can be achieved with little effort if better tools that present higher level abstractions are used. The vehicle for our demonstration is a 2D electromagnetic finite element scattering code we have implemented in Mentat, an object-oriented parallel processing system. We briefly describe the application. Mentat, the implementation, and present performance results for both a Mentat and a hand-coded parallel Fortran version.

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8

BENTIVEGNA, DARRIN C., CHRISTOPHER G. ATKESON, ALEŠ UDE, and GORDON CHENG. "LEARNING TO ACT FROM OBSERVATION AND PRACTICE." International Journal of Humanoid Robotics 01, no. 04 (December 2004): 585–611. http://dx.doi.org/10.1142/s0219843604000307.

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We present a method for humanoid robots to quickly learn new dynamic tasks from observing others and from practice. Ways in which the robot can adapt to initial and also changing conditions are described. Agents are given domain knowledge in the form of task primitives. A key element of our approach is to break learning problems up into as many simple learning problems as possible. We present a case study of a humanoid robot learning to play air hockey.

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9

HASEGAWA, KYOKO, SAORI OJIMA, YOSHIYUKI SHIMOKUBO, SUSUMU NAKATA, KOZABURO HACHIMURA, and SATOSHI TANAKA. "PARTICLE-BASED TRANSPARENT FUSED VISUALIZATION APPLIED TO MEDICAL VOLUME DATA." International Journal of Modeling, Simulation, and Scientific Computing 04, supp01 (August 2013): 1341003. http://dx.doi.org/10.1142/s1793962313410031.

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This paper proposes a method to create 3D fusion images, such as volume–volume, volume–surface, and surface–surface fusion. Our method is based on the particle-based rendering, which uses tiny particles as rendering primitives. The method can create natural and comprehensible 3D fusion images simply by merging particles prepared for each element to be fused. Moreover, the method does not require particle sorting along the line of sight to realize right depth feel. We apply our method to realize comprehensible visualization of medical volume data.

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10

Iordache, Mihai, Lucia Dumitriu, Mircea Perpelea, Ioana-Gabriela SÃ®rbu, and Lucian Mandache. "SPICE-like Models for Nonlinear Capacitors and Inductors." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 12, no. 2 (December 28, 2013): 3228–40. http://dx.doi.org/10.24297/ijct.v12i2.3287.

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Some new models for nonlinear capacitors and nonlinear inductors built with SPICE-like element primitives are presentedhere. They have the advantage that they can be used for simulation in SPICE of those circuits which contain nonlinearcapacitors controlled either in voltage or in charge, and nonlinear inductors controlled either in current or in flux. TheseSPICE-like models contain current sources whose controlling variables are charge time-derivative and sources whosecontrolling variables are flux time-derivative. For validation, the models are included in nonlinear circuits; their behavior isstudied by simulation using two different simulators and the results are compared.

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11

Thoeni, K., A. Effeindzourou, Bruno Chareyre, and A. Giacomini. "Discrete Modelling of Soil-Inclusion Problems." Applied Mechanics and Materials 846 (July 2016): 397–402. http://dx.doi.org/10.4028/www.scientific.net/amm.846.397.

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A generalised approach for the modelling of arbitrary shaped deformable structures in the framework of the discrete element method is presented. Minkowski sums of polytopes and spheres are used to describe the geometry of rounded cylinders and particle facets. In the current formulation, these new elements can be deformable. Their deformation is defined by the set of positions and orientations of their nodes. The elements can be connected to form arbitrary structures, such as grids and membranes. The constitutive behaviour of such connections is defined via an elastic perfectly plastic beam model. Contacts between other not connected structures or particles are detected based on three simple primitives: spheres, cylinders and thick rounded facets. The introduction of a virtual sphere at the contact point not only allows for straightforward contact handling but as well for the use of standard contact models based on sphere–sphere interactions. Hence, there is no need for developing new contact models. The approach is implemented into the open-source framework YADE. The capability of the newly developed approach for the modelling of soil–inclusion problems is presented.

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12

Tseng, Yi-Fan, Zi-Yuan Liu, and Raylin Tso. "Practical Inner Product Encryption with Constant Private Key." Applied Sciences 10, no. 23 (December 3, 2020): 8669. http://dx.doi.org/10.3390/app10238669.

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Inner product encryption, first introduced by Katz et al., is a type of predicate encryption in which a ciphertext and a private key correspond to an attribute vector and a predicate vector, respectively. Only if the attribute and predicate vectors satisfy the inner product predicate will the decryption in this scheme be correct. In addition, the ability to use inner product encryption as an underlying building block to construct other useful cryptographic primitives has been demonstrated in the context of anonymous identity-based encryption and hidden vector encryption. However, the computing cost and communication cost of performing inner product encryption are very high at present. To resolve this problem, we introduce an efficient inner product encryption approach in this work. Specifically, the size of the private key is only one G element and one Zp element, and decryption requires only one pairing computation. The formal security proof and implementation result are also demonstrated. Compared with other state-of-the-art schemes, our scheme is the most efficient in terms of the number of pairing computations for decryption and the private key length.

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13

Yang, X., M. Koehl, and P. Grussenmeyer. "MESH-TO-BIM: FROM SEGMENTED MESH ELEMENTS TO BIM MODEL WITH LIMITED PARAMETERS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2 (May 30, 2018): 1213–18. http://dx.doi.org/10.5194/isprs-archives-xlii-2-1213-2018.

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Building Information Modelling (BIM) technique has been widely utilized in heritage documentation and comes to a general term Historical/Heritage BIM (HBIM). The current HBIM project mostly employs the scan-to-BIM process to manually create the geometric model from the point cloud. This paper explains how it is possible to shape from the mesh geometry with reduced human involvement during the modelling process. Aiming at unbuilt heritage, two case studies are handled in this study, including a ruined Roman stone architectural and a severely damaged abbey. The pipeline consists of solid element modelling based on documentation data using <i>Autodesk Revit</i>, a common BIM platform, and the successive modelling from these geometric primitives using <i>Autodesk Dynamo</i>, a visual programming built-in plugin tool in <i>Revit</i>. The BIM-based reconstruction enriches the classic visual model from computer graphics approaches with measurement, semantic and additional information. <i>Dynamo</i> is used to develop a semi-automated function to reduce the manual process, which builds the final BIM model from segmented parametric elements directly. The level of detail (LoD) of the final models is dramatically relevant with the manual involvement in the element creation. The proposed outline also presents two potential issues in the ongoing work: combining the ontology semantics with the parametric BIM model, and introducing the proposed pipeline into the as-built HBIM process.

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14

Bodaghi, Mahdi, Reza Noroozi, Ali Zolfagharian, Mohamad Fotouhi, and Saeed Norouzi. "4D Printing Self-Morphing Structures." Materials 12, no. 8 (April 25, 2019): 1353. http://dx.doi.org/10.3390/ma12081353.

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The main objective of this paper is to introduce complex structures with self-bending/morphing/rolling features fabricated by 4D printing technology, and replicate their thermo-mechanical behaviors using a simple computational tool. Fused deposition modeling (FDM) is implemented to fabricate adaptive composite structures with performance-driven functionality built directly into materials. Structural primitives with self-bending 1D-to-2D features are first developed by functionally graded 4D printing. They are then employed as actuation elements to design complex structures that show 2D-to-3D shape-shifting by self-bending/morphing. The effects of printing speed on the self-bending/morphing characteristics are investigated in detail. Thermo-mechanical behaviors of the 4D-printed structures are simulated by introducing a straightforward method into the commercial finite element (FE) software package of Abaqus that is much simpler than writing a user-defined material subroutine or an in-house FE code. The high accuracy of the proposed method is verified by a comparison study with experiments and numerical results obtained from an in-house FE solution. Finally, the developed digital tool is implemented to engineer several practical self-morphing/rolling structures.

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15

Polzer, Thomas, Robert Najvirt, Florian Beck, and Andreas Steininger. "On the Appropriate Handling of Metastable Voltages in FPGAs." Journal of Circuits, Systems and Computers 25, no. 03 (December 28, 2015): 1640020. http://dx.doi.org/10.1142/s021812661640020x.

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The significant process, voltage and temperature (PVT) variations seen with modern technologies make strictly synchronous design inefficient. Asynchronous design with its flexible timing is a promising alternative, but prototyping is difficult on the available FPGA platforms which are clock centric and do not provide the required functional primitives like mutual exclusion or Muller C-elements. The solutions proposed in the literature so far work nicely in principle but cannot safely handle metastability issues that are inevitable even at some interfaces in asynchronous designs. In this paper, we propose reliable implementations of the fundamental function blocks required to safely convert potential intermediate voltage levels that result from metastability into late transitions that can be reliably handled in the asynchronous domain. These are high- and low-threshold buffers as well as a Schmitt-trigger. We give elaborate background analysis for the proposed circuits and also present the associated routing constraints to make the Schmitt-trigger circuit work properly in spite of the uncertain routing within FPGAs. Furthermore, we propose a procedure for an “in situ reliability assessment” of the specific Schmitt-trigger element under consideration, which also applies to metastability containment with high- or low-threshold buffers only. Our proof of concept is based on experimental results for both Xilinx and Altera FPGA platforms.

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16

Tarigan, Karisma Erikson, and Mulyadi Mulyadi. "An Analysis of Polysemy of “anding-andingen” Proverb in Karo Language: Problems of Natural Semantic MetaLanguage." Budapest International Research and Critics in Linguistics and Education (BirLE) Journal 3, no. 4 (December 24, 2020): 2208–20. http://dx.doi.org/10.33258/birle.v3i4.1497.

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This article aims at proposing a way to identify polysemy ‘anding-andingen’ or proverb in bahasa karo. The writer has an interest to use proverb or anding-aningen in this study because in proverb contains a lot of semantic meaning. This study was conducted using the descriptive qualitative approach in nature; therefore it only describes the semantic knowledge theory. The results of this study indicate that the element DO may occur either with a subject (Actor) alone with a second (Patient) argument as well (in English, as DO TO). It opened the way for a new semantically-inspired approach to grammar constructions. An analysis of ‘X does this’ as ‘X can say this’ and of ‘A because B’ as if not B, the not A’, the writers admitted that both DO and BECAUSE into the stable of semantic primitives. A similar entailment-like relationship obtains between PEOPLE and SOMEONE, but there is at least one significant syntactic difference, namely, that PEOPLE cannot occur with quantifier ONE.

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17

Rallis, I., N. Bakalos, N. Doulamis, and A. Doulamis. "ADAPTABLE AUTOREGRESSIVE MOVING AVERAGE FILTER TRIGGERING CONVOLUTIONAL NEURAL NETWORKS FOR CHOREOGRAPHIC MODELING." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2020 (August 3, 2020): 467–74. http://dx.doi.org/10.5194/isprs-annals-v-2-2020-467-2020.

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Abstract. Choreographic modeling, that is identification of key choreographic primitives, is a significant element for Intangible Cultural Heritage (ICH) performing art modeling. Recently, deep learning architectures, such as LSTM and CNN, have been utilized for choreographic identification and modeling. However, such approaches present sensitivity to capturing errors and fail to model the dynamic characteristics of a dance, since they assume a stationarity between the input-output data. To address these limitations, in this paper, we introduce an AutoRegressive Moving Average (ARMA) filter into a conventional CNN model; this means that the classification output feeds back to the input layer, improving overall classification accuracy. In addition, an adaptive implementation algorithm is introduced, exploiting a first-order Taylor series expansion, to update network response in order to fit dance dynamic characteristics. This way, the network parameters (e.g., weights) are dynamically modified improving overall classification accuracy. Experimental results on real-life dance sequences indicate the out-performance of the proposed approach with respect to conventional deep learning mechanisms.

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18

Harris, Randy Allen. "The origin and developmemt of generative semantics." Historiographia Linguistica 20, no. 2-3 (January 1, 1993): 399–440. http://dx.doi.org/10.1075/hl.20.2-3.07har.

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Summary Against the background of the controversial and polarized work of Frederick Newmeyer and Robin Tolmach Lakoff, this paper chronicles the early development of generative semantics, an internal movement within the transformational model of Chomsky’s Aspects of the Theory of Syntax. The first suggestions toward the movement, whose cornerstone was the obliteration of the syntax-semantics boundary, were by George Lakoff in 1963. But it was the work conducted under the informal banner of “Abstract Syntax” by Paul Postal that began the serious investigations leading to such an obliteration. Lakoff was an active participant in that research, as were Robin Tolmach Lakoff, John Robert (“Háj”) Ross and James D. McCawley. Through their combined efforts, particularly those of McCawley on semantic primitives and lexical insertion, generative semantics took shape in 1967: positing a universal base, importing notions from predicate calculus, decomposing lexical structure, and, most contentiously, rejecting the central element of the Aspects model, deep structure.

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19

Tarigan, Karisma E., and Mulyadi Mulyadi. "An Analysis of Polysemy of “anding-andingen” Proverb in Karo Language: Problems of Natural Semantic MetaLanguage." Budapest International Research and Critics in Linguistics and Education (BirLE) Journal 4, no. 1 (January 14, 2021): 89–101. http://dx.doi.org/10.33258/birle.v4i1.1559.

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This article aims at proposing a way to identify polysemy ‘anding-andingen’ or proverb in bahasa karo. The writer has an interest to use proverb or anding-aningen in this study because in proverb contains a lot of semantic meaning. This study was conducted using the descriptive qualitative approach in nature; therefore it only describes the semantic knowledge theory. The results of this study indicate that the element DO may occur either with a subject (Actor) alone with a second (Patient) argument as well (in English, as DO TO). It opened the way for a new semantically-inspired approach to grammar constructions. An analysis of ‘X does this’ as ‘X can say this’ and of ‘A because B’ as if not B, the not A’, the writers admitted that both DO and BECAUSE into the stable of semantic primitives. A similar entailment-like relationship obtains between PEOPLE and SOMEONE, but there is at least one significant syntactic difference, namely, that PEOPLE cannot occur with quantifier ONE.

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20

Wülker, Christian, Sipu Ruan, and Gregory S. Chirikjian. "Quantizing Euclidean Motions via Double-Coset Decomposition." Research 2019 (September 15, 2019): 1–16. http://dx.doi.org/10.34133/2019/1608396.

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Concepts from mathematical crystallography and group theory are used here to quantize the group of rigid-body motions, resulting in a “motion alphabet” with which robot motion primitives are expressed. From these primitives it is possible to develop a dictionary of physical actions. Equipped with an alphabet of the sort developed here, intelligent actions of robots in the world can be approximated with finite sequences of characters, thereby forming the foundation of a language in which robot motion is articulated. In particular, we use the discrete handedness-preserving symmetries of macromolecular crystals (known in mathematical crystallography as Sohncke space groups) to form a coarse discretization of the space SE(3) of rigid-body motions. This discretization is made finer by subdividing using the concept of double-coset decomposition. More specifically, a very efficient, equivolumetric quantization of spatial motion can be defined using the group-theoretic concept of a double-coset decomposition of the form Γ\SE(3)/Δ, where Γ is a Sohncke space group and Δ is a finite group of rotational symmetries such as those of the icosahedron. The resulting discrete alphabet is based on a very uniform sampling of SE(3) and is a tool for describing the continuous trajectories of robots and humans. An efficient coarse-to-fine search algorithm is presented to round off any motion sampled from the continuous group of motions to the nearest element of our alphabet. It is shown that our alphabet and this efficient rounding algorithm can be used as a geometric data structure to accelerate the performance of other sampling schemes designed for desirable dispersion or discrepancy properties. Moreover, the general “signals to symbols” problem in artificial intelligence is cast in this framework for robots moving continuously in the world.

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21

Kotukh, E. V., O. V. Severinov, A. V. Vlasov, L. S. Kozina, A. O. Tenytska, and E. O. Zarudna. "Methods of construction and properties of logariphmic signatures." Radiotekhnika, no. 205 (July 2, 2021): 94–99. http://dx.doi.org/10.30837/rt.2021.2.205.09.

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Development and promising areas of research in the construction of practical models of quantum computers contributes to the search and development of effective cryptographic primitives. Along with the growth of the practical possibilities of using quantum computing, the threat to classical encryption and electronic signature schemes using classical mathematical problems as a basis, being overcome by the computational capabilities of quantum computers. This fact motivates the study of fundamental theorems concerning the mathematical and computational aspects of candidate post-quantum cryptosystems. Development of a new quantum-resistant asymmetric cryptosystem is one of the urgent problems. The use of logarithmic signatures and coverings of finite groups a promising direction in the development of asymmetric cryptosystems. The current state of this area and the work of recent years suggest that the problem of factorizing an element of a finite group in the theory of constructing cryptosystems based on non-Abelian groups using logarithmic signatures is computationally complex; it potentially provides the necessary level of cryptographic protection against attacks using the capabilities of quantum calculations. The paper presents logarithmic signatures as a special type of factorization in finite groups; it also considers their properties and construction methods.

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22

Drensky, Vesselin. "Additive primitive length in relatively free algebras." International Journal of Algebra and Computation 29, no. 05 (July 8, 2019): 849–59. http://dx.doi.org/10.1142/s0218196719500310.

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The additive primitive length of an element [Formula: see text] of a relatively free algebra [Formula: see text] in a variety of algebras [Formula: see text] is equal to the minimal number [Formula: see text] such that [Formula: see text] can be presented as a sum of [Formula: see text] primitive elements. We give an upper bound for the additive primitive length of the elements in the [Formula: see text]-generated polynomial algebra over a field of characteristic 0, [Formula: see text]. The bound depends on [Formula: see text] and on the degree of the element. We show that if the field has more than two elements, then the additive primitive length in free [Formula: see text]-generated nilpotent-by-abelian Lie algebras is bounded by 5 for [Formula: see text] and by 6 for [Formula: see text]. If the field has two elements only, then our bounds are 6 for [Formula: see text] and 7 for [Formula: see text]. This generalizes a recent result of Ela Aydın for two-generated free metabelian Lie algebras. In all cases considered in the paper, the presentation of the elements as sums of primitive elements can be found effectively in polynomial time.

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23

Stupak, Eugeniuš, and Romualdas Baušys. "GENERATION OF THE UNSTRUCTURED FE-GRIDS FOR COMPLEX 2D OBJECTS/NESTRUKTŪRINIŲ BE TINKLŲ GENERAVIMAS SUDĖTINGIEMS DVIMAČIAMS OBJEKTAMS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 6, no. 1 (February 28, 2000): 17–24. http://dx.doi.org/10.3846/13921525.2000.10531559.

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For the numerical simulation of engineering problems, the finite element method (FEM) is among the most popular approaches. One of the main concerns in a finite element analysis is the adequacy of the finite element grid. The accuracy of the FEM depends on the size, shape and placement of the elements. On the other hand, the total computational cost is determined by the total number of elements in FE model. An increased accuracy can be obtained by the global reduction of the element size, but this can be characterised by drastically increased computational cost. Thus, in many engineering applications it is desirable to generate not regular FE mesh with finer grid in the regions where accuracy of numerical simulation is of most importance and with more coarse grid in the other regions. In this paper we present a new approach to the grid generation of the multimaterial or multidomain engineering systems by the advancing front technique. This technique has proved successful in generating unstructured meshes in two and three dimensions [1–9]. The algorithm of the technique is summarised in section 2. Common for all approaches of advancing front mesh generation is that the generation problem is divided into three parts. First, the specification of the mesh size attributes, second, the discretisation of the boundaries, and, third, the discretisation of the interior of the domain. In the advancing front technique the front is defined as the boundary between the gridded and ungridded region. The key algorithmic step that must be addressed to advancing front methods is the proper introduction of new elements into the ungridded region. For triangular and tetrahedral grids the elements are introduced sequentially one at a time. The most obvious advantage of the advancing front method is that it directly incorporates free form geometry. Direct implementation of the advancing front technique for multimaterial or multidomain engineering applications is still challenging. Grid generation in the place of few materials or domain contact must ensure the compatibility of nodes on common boundary segments (nodes on common boundary segments must be in the same positions). The advancing front technique does not include non-convex domain, so at the first step non-convex domain of discretisation is decomposed into few convex subdomains. The subdomain of interest must be defined by describing a course background mesh of triangle elements, covering the entire multidomain region, which forms the input for finite element analysis. In this work, a black box architecture expert system has been developed which incorporates the information about the object geometry as well as the boundary and loading conditions, distribution of materials characteristics to generate an a priori (before the finite element analysis is carried out) mesh which is more refined around the critical regions (singularities, re-entrant corners, regions with high-stress concentration, etc) of the problem domain. This system uses a new concept of subtracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal meshes, will be more accurate and efficient. Several numerical examples are presented and discussed. Examples demonstrate that our approach enables to generate the compatible meshes for multimaterial or multidomain problems. The quality of meshes is good, there are no ill-shaped elements. By the proposed expert system we can generate the mesh for any complex structure. The generation of 2D meshes is only the first step using the proposed expert system; in future we shall extend it for 3D meshes. During the last decade a lot of research has been devoted to extension of the advancing front technique to the parallel computers [8, 10, 11]. But the application of the technique to parallel processors is still challenging. In fact, we have to solve how to minimise inter-processor communication during mesh generation of subdomains. The proposed expert system for complex structures grid generation enables to use it with parallel computers. At the first step the domain of discretisation is decomposed into subdomains and all the surfaces defining the boundaries of subdomains to be gridded are triangulated. Later all subdomains can be meshed concurrently and no more inter-processor communication is required. The master task sends to workers tasks information about dividing common boundaries and information of each subdomain. The workers tasks receive their subdomain data and mesh their subdomain. Later the master receives the information from the workers tasks and joins gridded subdomains to one structure, ensuring the compatibility of nodes on common boundaries. So this suggested expert system enables to minimise the communications and costs of computations. The implementation of the expert system to parallel processors is to be done in the future.

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24

Nikolopoulos, Christos, and Panagiotis Nikolopoulos. "Generalizations of the primitive element theorem." International Journal of Mathematics and Mathematical Sciences 14, no. 3 (1991): 463–70. http://dx.doi.org/10.1155/s0161171291000637.

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In this paper we generalize the primitive element theorem to the generation of separable algebras over fields and rings. We prove that any finitely generated separable algebra over an infinite field is generated by two elements and if the algebra is commutative it can be generated by one element. We then derive similar results for finitely generated separable algebras over semilocal rings.

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25

Isupov, Konstantin. "High-Performance Computation in Residue Number System Using Floating-Point Arithmetic." Computation 9, no. 2 (January 21, 2021): 9. http://dx.doi.org/10.3390/computation9020009.

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Residue number system (RNS) is known for its parallel arithmetic and has been used in recent decades in various important applications, from digital signal processing and deep neural networks to cryptography and high-precision computation. However, comparison, sign identification, overflow detection, and division are still hard to implement in RNS. For such operations, most of the methods proposed in the literature only support small dynamic ranges (up to several tens of bits), so they are only suitable for low-precision applications. We recently proposed a method that supports arbitrary moduli sets with cryptographically sized dynamic ranges, up to several thousands of bits. The practical interest of our method compared to existing methods is that it relies only on very fast standard floating-point operations, so it is suitable for multiple-precision applications and can be efficiently implemented on many general-purpose platforms that support IEEE 754 arithmetic. In this paper, we make further improvements to this method and demonstrate that it can successfully be applied to implement efficient data-parallel primitives operating in the RNS domain, namely finding the maximum element of an array of RNS numbers on graphics processing units. Our experimental results on an NVIDIA RTX 2080 GPU show that for random residues and a 128-moduli set with 2048-bit dynamic range, the proposed implementation reduces the running time by a factor of 39 and the memory consumption by a factor of 13 compared to an implementation based on mixed-radix conversion.

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26

Evans, Martin J. "Presentations of the Free Metabelian Group of Rank 2." Canadian Mathematical Bulletin 37, no. 4 (December 1, 1994): 468–72. http://dx.doi.org/10.4153/cmb-1994-068-9.

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AbstractLet F3 denote the free group of rank 3 and M2 denote the free metabelian group of rank 2. We say that x * F3 is a primitive element of F3 if it can be included a in some basis of F3. We establish the existence of presentations such that N does not contain any primitive elements of F3.

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27

MIKHALEV, ALEXANDER A., and ANDREJ A. ZOLOTYKH. "RANK AND PRIMITIVITY OF ELEMENTS OF FREE COLOUR LIE (p-)SUPERALGEBRAS." International Journal of Algebra and Computation 04, no. 04 (December 1994): 617–55. http://dx.doi.org/10.1142/s021819679400018x.

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Using Fox differential calculus we study characteristics of orbits of elements of free colour Lie (p-)superalgebras under action of the automorphism groups of these algebras. In particular, an effective criterion for an element to be primitive and an algorithm for finding the rank of an element are obtained.

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28

Konieczny, Jochen, Gerhard Rosenberger, and Julia Wolny. "Tame Almost Primitive Elements." Results in Mathematics 38, no. 1-2 (August 2000): 116–29. http://dx.doi.org/10.1007/bf03322435.

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29

Artamonov, V. A., A. V. Klimakov, A. A. Mikhalev, and A. V. Mikhalev. "Primitive and Almost Primitive Elements of Schreier Varieties." Journal of Mathematical Sciences 237, no. 2 (January 18, 2019): 157–79. http://dx.doi.org/10.1007/s10958-019-4148-2.

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30

Weintraub, Steven H. "The Theorem of the Primitive Element." American Mathematical Monthly 128, no. 8 (September 14, 2021): 753–54. http://dx.doi.org/10.1080/00029890.2021.1944757.

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31

Szaniawski, Hubert, and Stefan Bengtson. "Origin of euconodont elements." Journal of Paleontology 67, no. 4 (July 1993): 640–54. http://dx.doi.org/10.1017/s0022336000024963.

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Primitive euconodont elements from the Upper Cambrian of Sweden are investigated histologically and compared with co-occurring elements of paraconodonts. The proposed close relationship between the two groups is confirmed. Typical euconodont and paraconodont elements are bridged by intermediate forms. The ontogenetic development of the early euconodont elements shows striking similarities to the evolutionary development from paraconodonts to euconodonts, suggesting that evolution generally followed a peramorphic pattern (“recapitulation”). The conodont crown originated through extension of the growth lamellae around the whole element, accompanied by stronger mineralization. The first denticulation in Proconodontus arose when a jagged posterior edge in juvenile specimens was enhanced by the subsequent deposition of growth lamellae, a process comparable to the regeneration of broken tips. The most primitive euconodont elements probably erupted from the epithelium earlier in ontogeny than in more advanced forms. After the appearance of the phosphatic crown, conodont elements underwent a very rapid morphological differentiation. Cordylodus may have arisen from Proconodontus serratus.

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32

de Smit, Bart. "Primitive elements in integral bases." Acta Arithmetica 71, no. 2 (1995): 159–70. http://dx.doi.org/10.4064/aa-71-2-159-170.

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33

Umirbaev, U. U. "Primitive elements of free groups." Russian Mathematical Surveys 49, no. 2 (April 30, 1994): 184–85. http://dx.doi.org/10.1070/rm1994v049n02abeh002233.

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34

Chou, Wun-Seng, and Stephen D. Cohen. "Primitive Elements with Zero Traces." Finite Fields and Their Applications 7, no. 1 (January 2001): 125–41. http://dx.doi.org/10.1006/ffta.2000.0284.

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35

Evans, Martin J. "Primitive elements in free groups." Proceedings of the American Mathematical Society 106, no. 2 (February 1, 1989): 313. http://dx.doi.org/10.1090/s0002-9939-1989-0952315-1.

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36

Cao, Xiwang, and Peipei Wang. "Primitive elements with prescribed trace." Applicable Algebra in Engineering, Communication and Computing 25, no. 5 (July 8, 2014): 339–45. http://dx.doi.org/10.1007/s00200-014-0228-1.

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37

Onoda, Nobuharu, Takasi Sugatani, and Ken-ichi Yoshida. "Accurate Elements and Super-Primitive Elements over Rings." Journal of Algebra 245, no. 1 (November 2001): 370–94. http://dx.doi.org/10.1006/jabr.2001.8930.

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38

Schutte, H. J. "Primitiewe elemente vir kommutatiewe ringuitbreidings." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 10, no. 2 (July 8, 1991): 67–71. http://dx.doi.org/10.4102/satnt.v10i2.489.

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The existence of primitive elements for integral domain extensions is considered with reference to the well known theorem about primitive elements for field extensions. Primitive elements for extensions of a commutative ring R with identity are considered, where R has only a finite number of minimal prime ideals with zero intersection. This case is reduced to the case for ring extensions of integral domains.

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39

Martínez-Guerra, Rafael, and Juan L. Mata-Machuca. "Generalized synchronization via the differential primitive element." Applied Mathematics and Computation 232 (April 2014): 848–57. http://dx.doi.org/10.1016/j.amc.2014.01.142.

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40

Tareeq, Saifuddin Md, and Tetsunari Inamura. "2A1-D20 Rapid Behavior Adaptation for Human-centered Robots based on Integration of Primitive Confidence on Multi-sensor Element." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2010 (2010): _2A1—D20_1—_2A1—D20_4. http://dx.doi.org/10.1299/jsmermd.2010._2a1-d20_1.

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41

Morris, George A., and Robert A. Creaser. "Crustal recycling during subduction at the Eocene Cordilleran margin of North America: a petrogenetic study from the southwestern Yukon." Canadian Journal of Earth Sciences 40, no. 12 (December 1, 2003): 1805–21. http://dx.doi.org/10.1139/e03-063.

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The early Eocene (57.355.4 Ma) Bennett Lake and Mount Skukum Volcanic Complexes lie on the Coast Plutonic Complex and Intermontane Belt boundary of the Canadian Cordillera at the British Columbia Yukon border, some 200 km east of the current and Eocene continental margin. Both complexes contain rock types from basaltic andesite to rhyolite in a series of lava and pyroclastic flows. The location relative to the continental margin, the rock types, and the presence of an enhanced LILE/HFSE (large-ion lithophile / high field strength element) signatures in all samples imply that contemporaneous subduction was the controlling factor in the formation of these complexes. The majority of samples, however, return unusually low compatible element concentrations for given rock types. We interpret this data to show that partial melting of the crust was the major source of erupted magmas. One formation of andesites at Mount Skukum and one late dyke at Bennett Lake do show higher concentrations of compatible trace elements, suggesting the presence of primitive magmas in the crust at the time of eruption, which contaminated and were erupted with the crustal melts. SrNd isotopic data at both complexes are consistently primitive regardless of rock type and compatible element content, requiring a primitive crustal source for these magmas. We propose that the complexes were formed as a result of early Eocene subduction of the Kula Plate beneath the Canadian Cordillera. Intrusion of hot primitive melts caused partial melting of young crust to produce the majority of lavas observed. Contamination of these melts by primitive magmas is observed at both Mount Skukum and Bennett Lake.

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42

Johnson, Kirby D., Xin Gao, Rajendran Sanalkumar, Amy P. Hsu, Myung-Jeom Ryu, Jinyong Wang, Meghan E. Boyer, et al. "Genetic Determinants of the Definitive Hematopoietic Stem/Progenitor Cell Compartment." Blood 120, no. 21 (November 16, 2012): 1226. http://dx.doi.org/10.1182/blood.v120.21.1226.1226.

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Abstract Abstract 1226 How transcriptional and post-transcriptional mechanisms control the levels/activities of master developmental regulators has fundamental importance for understanding complex developmental processes such as hematopoiesis and associated pathological disorders. GATA-2 is an essential regulator of hematopoiesis, and GATA-2 mutations characterize heritable disease associated with myelodysplastic syndrome and acute myeloid leukemia, including MonoMAC (syndrome of monocytopendia, B and NK cell lymphopenia, and mycobacterial, fungal and viral infection). However, many questions remain unanswered regarding mechanisms underlying GATA-2 regulation and function. We demonstrated that a MonoMAC patient harbors a 28 bp deletion within GATA2 intron 5 that eliminates a conserved E-box and 5 base pairs of an 8 base pair spacer between the E-box and a conserved GATA motif, which constitutes an E-box-GATA composite element. This composite element resides within the +9.5 kb “GATA switch site” that binds GATA-2 and GATA-1 in the transcriptionally active and repressed states, respectively, and confers hematopoietic and vascular endothelial enhancer activities in transgenic mouse embryos. Importantly, this patient lacked mutations in the GATA2 coding sequence characteristic of other MonoMAC patients, but exhibited prototypical MonoMAC. To elucidate the mechanism underlying the function of the +9.5 composite element, we generated a targeted deletion of the murine element, which yielded embryonic lethality at E13 to E14. Prior to death, +9.5−/− mice exhibit reduced liver size, hemorrhaging, and edema. Nucleated primitive red cells are abundant in the +9.5−/− embryos, in contrast to Gata2 knockout mice, which die at approximately E10.5 from anemia due to failure of primitive and definitive hematopoiesis. Furthermore, primitive erythroid (EryP) colony assays conducted with yolk sacs revealed that the mutation does not affect primitive erythroid precursor functionality. However, the +9.5 deletion strongly reduced Gata2 expression at sites of definitive hematopoiesis, including the fetal liver (8.1 fold, P < 0.004) and cultured explants of the hematopoietic stem cell-generating Aortic Gonadal Mesonephric (AGM) region (4.0 fold, P < 0.001). The homozygous mutant animals exhibited a nearly complete loss of hematopoietic stem cells as determined by flow cytometry (20-fold reduction of Lin-Mac1+CD41-CD48-CD150+Sca+Kit+ cells, P < 0.005) and competitive repopulation (complete loss, P < 0.02) assays, as well as progenitors as determined by colony assays (BFU-E, 60-fold reduction, P < 0.002; CFU-GM, 8.8-fold reduction, P < 0.0001; CFU-GEMM, 19-fold reduction, P < 0.001). To investigate the underlying mechanisms, we developed an allele-specific Formaldehyde-Assisted Isolation of Regulatory Elements (FAIRE) assay with heterozygous fetal liver cells to test whether the deletion influences Gata2 chromatin accessibility at the +9.5 region. The deletion significantly reduced (8.4 fold reduction, P < 0.001) chromatin accessibility at this region within the mutant allele, while the wild type allele was unaffected. Thus, any potential remaining cis-elements are insufficient to confer chromatin accessibility, supporting a model in which the transcription factors that normally occupy this GATA switch site lose the capacity to access their respective cis-elements in the context of the mutant allele. Our human and murine studies have therefore revealed a cis-element indispensable for the regulation of Gata2 expression in multiple developmental contexts and necessary for the generation of the definitive hematopoietic stem/progenitor cell compartment. As additional elements are likely to confer Gata2 expression in distinct contexts, including primitive erythropoiesis, we have implemented a multi-faceted effort to identify such elements and to compare their mechanisms with that of the +9.5 site, which will provide fundamental insights into genetic mechanisms controlling normal and malignant hematopoiesis. Disclosures: No relevant conflicts of interest to declare.

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43

Justiz, O. C., E. M. CapÃ³, P. F. Arrozarena, and G. S. GÃ³mez. "A REDUCED TABLEOF THE ZECHÂ´S LOGARITHM." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 7 (July 18, 2016): 6422–28. http://dx.doi.org/10.24297/jam.v12i7.5483.

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In this work we will solve the problem of expression of the sum of two given elements of a finite field, as power of the primitive element of the field. We obtain a reduced table of the Zech's logarithm from our proposal that relate the Zech'slogarithm with the partition of the exponents of the powers of elements over finite field ð‘®ð‘(ð’‘ð’) in p-cyclotomic cosets modulo (ð’‘ð’âˆ’ðŸ). This reduces, in a significant way, the quantity of information to store and it facilitates its use in several cryptographic algorithms, specifically in asimetric cryptography. It is illustrated the computationof the Zech'slogarithm of any element thatdoesn't appear in the obtained reduced table.

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44

Anju and R. K. Sharma. "On primitive normal elements over finite fields." Asian-European Journal of Mathematics 11, no. 02 (March 19, 2018): 1850031. http://dx.doi.org/10.1142/s1793557118500316.

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Let [Formula: see text] be an extension of the field [Formula: see text] of degree [Formula: see text] where [Formula: see text] for some positive integer [Formula: see text] and prime [Formula: see text] In this paper, we establish a sufficient condition for the existence of a primitive element [Formula: see text] such that [Formula: see text] is also primitive as well as a primitive normal element [Formula: see text] of [Formula: see text] over [Formula: see text] such that [Formula: see text] is primitive.

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45

Burillo, J., and E. Ventura. "COUNTING PRIMITIVE ELEMENTS IN FREE GROUPS." Electronic Notes in Discrete Mathematics 10 (November 2001): 50–53. http://dx.doi.org/10.1016/s1571-0653(04)00357-9.

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46

GREITHER, CORNELIUS, and TOUFIK ZAÏMI. "CM FIELDS WITHOUT UNIT-PRIMITIVE ELEMENTS." Bulletin of the Australian Mathematical Society 96, no. 3 (September 20, 2017): 398–99. http://dx.doi.org/10.1017/s0004972717000661.

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This is an addendum to a recent paper by Zaïmi, Bertin and Aljouiee [‘On number fields without a unit primitive element’, Bull. Aust. Math. Soc.93 (2016), 420–432], giving the answer to a question asked in that paper, together with some historical connections.

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47

Yokoyama, Kazuhiro, Masayuki Noro, and Taku Takeshima. "Computing primitive elements of extension fields." Journal of Symbolic Computation 8, no. 6 (December 1989): 553–80. http://dx.doi.org/10.1016/s0747-7171(89)80061-6.

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48

Kharchenko, V. K. "An algebra of skew primitive elements." Algebra and Logic 37, no. 2 (March 1998): 101–26. http://dx.doi.org/10.1007/bf02671596.

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49

Gow, Rod, and John Sheekey. "On primitive elements in finite semifields." Finite Fields and Their Applications 17, no. 2 (March 2011): 194–204. http://dx.doi.org/10.1016/j.ffa.2010.11.003.

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50

Mikhalev, A. A., A. V. Mikhalev, A. A. Chepovskiy, and K. Champagnier. "Primitive elements of free nonassociative algebras." Journal of Mathematical Sciences 156, no. 2 (January 2009): 320–35. http://dx.doi.org/10.1007/s10958-008-9269-y.

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