Search results for "algebra"
showing 10 items of 4129 documents
Synthesis and Reactivity of New β-Enamino Acid Derivatives: A Simple and General Approach to β-Enamino Esters and Thioesters
1998
A new strategy has been developed for the synthesis of several β-enamino acid derivatives. N,N‘-Carbonyldiimidazole has been used as C-acylating agent of methyl ketimines, providing a direct and simple route to new β-enamino carbonyl imidazole derivatives 2. These derivatives 2 were cleanly and efficiently transformed into β-enamino esters 4 (X = O) and thioesters 4 (X = S) by reaction with a great variety of alcohols and thiols, including tertiary ones. Alternative and complementary routes to compounds 4 were also investigated. In addition, β-keto esters 6 have been obtained by mild acid hydrolysis of β-enamino esters 4.
Dependence of the distortion of the square pyramids in N,N-dimethylethylenediammonium pentachloroantimonate(III) on the geometry of hydrogen bonds
2001
Abstract N ,N-Dimethylethylenediammonium pentachloroantimonate(III) crystallizes in the monoclinic system, in space group P21/c (a = 12.460(2), b = 10.252(2), c = 10.330(2) Å, β = 97.75(3)°, V = 1307.5(4) Å3, Z = 4, dc = 1.997, dm = 1.99(2) g/cm3). The crystal structure of [(CH3)2NH(CH2)2NH3][SbCl5] consists of isolated [SbCl5]2- anions and [(CH3)2NH(CH2)2NH3]2+ cations. The [SbCl5]2- anion has a distorted square pyramidal geometry, presenting one short axial and four long equatorial Sb-Cl bonds. The square pyramids are characteristically stacked one close to the other, parallel to the c axis. The voids between the anionic sublattice are filled by [(CH3)2NH(CH2)2NH3]2+ cations. The five non…
An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm
2022
Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, ar…
Implementation and evaluation of medical imaging techniques based on conformal geometric algebra
2020
Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of …
rac-12-Selena-13,14-diazatricyclo[9.3.0.02,4]tetradeca-11,13-diene
2020
The centrosymmetric crystal structure of the title compound, C11H16N2Se, is built up from alternating strands of (R,R)- and (S,S)-enantiomers. These strands, which propagate along the c-axis direction, are composed of homochiral molecules related to each other by twofold screw axes. The shape of the molecule is an almost planar unit around the selenadiazole ring with a hexamethylene chain as an arched handle.
Crystal structure and absolute configuration of (4S,5R,6S)-4,5,6-trihydroxy-3-methylcyclohex-2-enone (gabosine H)
2017
The absolute configuration of the title compound, determined as 4S,5R,6S on the basis of the synthetic pathway, was confirmed by single-crystal X-ray diffraction. The molecule is formed by a substituted six-membered cyclohexene ring adopting an envelope conformation and substituted by carbonyl, methyl and hydroxyl groups. The supramolecular structure is mainly built by a combination of O—H⋯O and weaker C—H⋯O hydrogen bonds.
Ģeogrāfiskās informācijas sistēmas izmantošana brīvas izvēles pārgājienu maršrutu plānošanā
2016
Bakalaura darbs ir veltīts zemāko izmaksu metodes izmantošanas iespējām tūrisma pārgājienu maršrutu izveidē. Došanās pārgājienos brīvā dabā kļūst arvien populārāka dažāda gadagājuma cilvēku vidū. Pārgājienu maršrutu izveide pamatā tiek balstīta uz jau eksistējošiem ceļiem un takām, kas palīdz radīt vieglas sarežģītības pakāpes maršrutus un atvieglo organizatoru darbu, taču tajā pašā laikā nesniedz iespēju nokļūt vietās, kas nav sasniedzamas ar ceļu tīklu. Pētījumā piedāvāts risinājums ar ģeogrāfiskās informācijas sistēmas palīdzību optimizēt un atvieglot pārgājienu maršrutu izveidi, pamatā neizmantojot jau esošos ceļus un kustoties brīvā telpā. Pētījuma mērķis ir izstrādāt metodiku izmaksu …
Teachers' procedures when introducing algebraic expression in two Norwegian grade 8 classrooms
2015
International audience; We investigate similarities and differences in two teachers’ way of introducing algebraic expressions by designed examples. One teacher moves from the specific to the general, and the other moves from the general to the specific. They both mediate the passage from the students’ real world and the school mathematics they know, to algebra.
Lipschitz Carnot-Carathéodory Structures and their Limits
2022
AbstractIn this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-fields structure, the distances associated to equi-Lipschitz vector-fields structures that converge uniformly on compact subsets, and to norms that converge uniformly on compact subsets, converge locally uniformly to the limit Carnot-Carathéodory distance. In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets. We show an example in which the limit distance is not…
Semigenerated Carnot algebras and applications to sub-Riemannian perimeter
2021
This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In add…