Galois Actions on the Eigenproblem of the Heisenberg Heptagon

2012 ◽  
Vol 19 (02) ◽  
pp. 1250012 ◽  
Author(s):  
Jan Milewski ◽  
Grzegorz Banaszak ◽  
Tadeusz Lulek ◽  
Mirosław Łabuz ◽  
Ryszard Stagraczyński
Keyword(s):  
Fourier Transforms ◽  
Cyclotomic Field ◽  
Galois Groups ◽  
Point Of View ◽  
Kummer Theory ◽  
Computer Based ◽  
Heisenberg Field ◽  
Galois Actions ◽  
Xxx Model

We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field ℚ of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant. These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices.

scholarly journals Evaluation of the Ability to Accurately Produce Angular Details by 3D Printing of Plastic Parts

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 150
Author(s):  
Andrei Marius Mihalache ◽  
Gheorghe Nagîț ◽  
Laurențiu Slătineanu ◽  
Adelina Hrițuc ◽  
Angelos Markopoulos ◽  
...  
Keyword(s):  
3D Printing ◽  
Point Of View ◽  
Vertex Angle ◽  
Function Type ◽  
Constant Height ◽  
3D Printers ◽  
3D Printed ◽  
Mathematical Processing ◽  
Plastic Parts

3D printing is a process that has become widely used in recent years, allowing the production of parts with relatively complicated shapes from metallic and non-metallic materials. In some cases, it is challenging to evaluate the ability of 3D printers to make fine details of parts. For such an assessment, the printing of samples showing intersections of surfaces with low angle values was considered. An experimental plan was designed and materialized to highlight the influence of different factors, such as the thickness of the deposited material layer, the printing speed, the cooling and filling conditions of the 3D-printed part, and the thickness of the sample. Samples using areas in the form of isosceles triangles with constant height or bases with the same length, respectively, were used. The mathematical processing of the experimental results allowed the determination of empirical mathematical models of the power-function type. It allowed the detection of both the direction of actions and the intensity of the influence exerted by the input factors. It is concluded that the strongest influence on the printer’s ability to produce fine detail, from the point of view addressed in the paper, is exerted by the vertex angle, whose reduction leads to a decrease in printing accuracy.

Determination of a Rubber-Like Material Model as an Inverse Problem

2011 ◽  
Vol 70 ◽  
pp. 225-230 ◽  
Author(s):  
Agnieszka Derewonko ◽  
Andrzej Kiczko
Keyword(s):  
Selection Process ◽  
Axial Stress ◽  
Constitutive Models ◽  
Material Model ◽  
Polyester Fabric ◽  
Point Of View ◽  
Air Cushion ◽  
Ill Conditioning ◽  
Stress States

The purpose of this paper is to describe the selection process of a rubber-like material model useful for simulation behaviour of an inflatable air cushion under multi-axial stress states. The air cushion is a part of a single segment of a pontoon bridge. The air cushion is constructed of a polyester fabric reinforced membrane such as Hypalon®. From a numerical point of view such a composite type poses a challenge since numerical ill-conditioning can occur due to stiffness differences between rubber and fabric. Due to the analysis of the large deformation dynamic response of the structure, the LS-Dyna code is used. Since LS-Dyna contains more than two-hundred constitutive models the inverse method is used to determine parameters characterizing the material on the base of results of the experimental test.

Resistance to Outflow of Cerebrospinal Fluid Determined by Bolus Injection Technique and Constant Rate Steady State Infusion in Humans

Neurosurgery ◽  
1985 ◽  
Vol 16 (3) ◽  
pp. 336-340 ◽  
Author(s):  
Michael Kosteljanetz
Keyword(s):  
Cerebrospinal Fluid ◽  
Steady State ◽  
Bolus Injection ◽  
Point Of View ◽  
Injection Technique ◽  
Communicating Hydrocephalus ◽  
Constant Rate ◽  
High Degree ◽  
Infusion Technique

Abstract Two methods for the determination of resistance to the outflow of cerebrospinal fluid, the bolus injection technique and the constant rate steady state infusion technique, were compared. Thirty-two patients with a variety of intracranial diseases (usually communicating hydrocephalus) were studied. There was a high degree of correlation between the resistance values obtained with the two methods, but values based on the bolus injection technique were systematically and statistically significantly lower than those obtained with the constant rate infusion test. From a practical point of view. both methods were found to be applicable in a clinical setting.

Determination of In-plane Shear Strength of Unidirectional Composite Materials Using the Off-axis Three-point Flexure and Off-axis Tensile Tests

2010 ◽  
Vol 44 (21) ◽  
pp. 2487-2507 ◽  
Author(s):  
G. Vargas ◽  
F. Mujika
Keyword(s):  
Shear Strength ◽  
Composite Materials ◽  
Tensile Tests ◽  
Unidirectional Composite ◽  
Point Of View ◽  
Experimental Point ◽  
Plane Shear ◽  
Lift Off ◽  
Flexure Test

The aim of this work is to compare from an experimental point of view the determination of in-plane shear strength of unidirectional composite materials by means of two off-axis tests: three-point flexure and tensile. In the case of the off-axis three-point flexure test, the condition of small displacements and the condition of lift-off between the specimen and the fixture supports have been taken into account. Some considerations regarding stress and displacement fields are presented. The in-plane shear characterization has been performed on a carbon fiber reinforced unidirectional laminate with several fiber orientation angles: 10°, 20°, 30°, and 45°. Test conditions for both off-axis experimental methods, in order to ensure their applicability, are presented. Off-axis flexure test is considered more suitable than off-axis tensile test for the determination of in-plane shear strength.

Natural Locomotion Based on Foot-Mounted Inertial Sensors in a Wireless Virtual Reality System

2015 ◽  
Vol 24 (4) ◽  
pp. 298-321 ◽  
Author(s):  
Ernesto de la Rubia ◽  
Antonio Diaz-Estrella
Keyword(s):  
Virtual Reality ◽  
Gait Cycle ◽  
Inertial Sensors ◽  
Low Cost ◽  
Point Of View ◽  
Handheld Devices ◽  
Preliminary Evaluation ◽  
Virtual Reality System ◽  
Object Searching

Virtual reality has become a promising field in recent decades, and its potential now seems clearer than ever. With the development of handheld devices and wireless technologies, interest in virtual reality is also increasing. Therefore, there is an accompanying interest in inertial sensors, which can provide such advantages as small size and low cost. Such sensors can also operate wirelessly and be used in an increasing number of interactive applications. An example related to virtual reality is the ability to move naturally through virtual environments. This is the objective of the real-walking navigation technique, for which a number of advantages have previously been reported in terms of presence, object searching, and collision, among other concerns. In this article, we address the use of foot-mounted inertial sensors to achieve real-walking navigation in a wireless virtual reality system. First, an overall description of the problem is presented. Then, specific difficulties are identified, and a corresponding technique is proposed to overcome each: tracking of foot movements; determination of the user’s position; percentage estimation of the gait cycle, including oscillating movements of the head; stabilization of the velocity of the point of view; and synchronization of head and body yaw angles. Finally, a preliminary evaluation of the system is conducted in which data and comments from participants were collected.

Inversion of the Dorso-ventral Axis in Amphibian Embryos by Unilateral Restriction of Oxygen Supply

Development ◽  
1958 ◽  
Vol 6 (3) ◽  
pp. 486-490
Author(s):  
S. Løvtrup ◽  
A. Pigon
Keyword(s):  
Oxygen Supply ◽  
Nile Blue ◽  
Bilateral Symmetry ◽  
Radial Symmetry ◽  
Point Of View ◽  
Low Permeability ◽  
Grey Crescent ◽  
Protein Coat ◽  
Amphibian Embryos

According to the hypothesis advanced by Løvtrup (1958) the supply of oxygen is one of the factors responsible for the determination of bilateral symmetry in amphibian embryos. The protein coat covering the outside of the egg is known to have a very low permeability (Holtfreter, 1943), and it was suggested in the hypothesis that the formation of the grey crescent consists in a stretching of this coat by which the permeability is increased (cf. the work of Dalcq & Dollander (1948) and of Dollander & Melnotte (1952) on permeability of Nile blue), in this way the radial symmetry of the egg is changed to a bilateral symmetry from a metabolic point of view. As a consequence of the increase in permeability those oxidative, energy-supplying processes which are associated with gastrulation are enabled to proceed at a higher rate at one side of the egg.

USING MALIC ACID SOLUTIONS FOR THE HYDRATION OF VEGETABLE OILS AND LECITHIN PRODUCTION

2020 ◽  
Author(s):  
Л.А. МАРЧЕНКО ◽  
Т.Н. БОКОВИКОВА ◽  
Е.В. ЛИСОВАЯ ◽  
С.А. ИЛЬИНОВА ◽  
Е.П. ВИКТОРОВА
Keyword(s):  
Malic Acid ◽  
Complex Compounds ◽  
Point Of View ◽  
Magnesium Ions ◽  
Ph Values ◽  
Calcium And Magnesium ◽  
The Stability ◽  
The Cost ◽  
Calcium And Magnesium Ions

Исследована возможность применения яблочной кислоты (ЯК) в качестве гидратирующего агента для перевода негидратируемых форм фосфолипидов в гидратируемые. Выбор ЯК обусловлен ее стоимостью, которая в 1,5 раза меньше стоимости янтарной кислоты, широко применяемой в качестве гидратирующего агента, а также большей доступностью с точки зрения промышленного производства. Исследование процесса комплексообразования и определение состава комплексных соединений ЯК с ионами кальция и магния осуществляли методом потенциометрического титрования. Установлено, что внесение в раствор ЯК ионов кальция и магния приводит к снижению значений рН, что свидетельствует о наличии комплексообразования в указанных системах. Наиболее устойчивыми являются комплексы ионов кальция и магния с непротонированным лигандом при соотношении Ме2 : лиганд 1 : 1. В процессе комплексообразования ионы Ca2 и Mg2 вытесняют протоны только карбоксильных групп ЯК, которая с ионами кальция образует более устойчивые комплексы, чем с ионами магния. Показано, что устойчивость комплексов ЯК с ионами кальция и магния значительно выше, чем устойчивость комплексов фосфатидилсеринов и фосфатидных кислот с указанными ионами. Использование водных растворов ЯК в качестве гидратирующего агента позволит повысить эффективность процесса гидратации и увеличить выход фосфолипидов и, следовательно, готового продукта лецитина. The possibility of using malic acid (MA) as a hydrating agent for converting non-hydrated forms of phospholipids into hydrated ones has been investigated. The choice of MA is due to its cost, which is 1,5 times less than the cost of succinic acid, as well as greater availability from the point of view of industrial production. The study of the complexation process and determination of the composition of complex compounds of MA with calcium and magnesium ions was carried out by the method of potentiometric titration. It was found that the introduction of calcium and magnesium ions into the MA solution leads to a decrease in pH values, which indicates the presence of complexation in these systems. Complexes of calcium and magnesium ions with an unprotected ligand at a ratio of ME2 : ligand 1 : 1 are the most stable. In the process of complexing, Ca2 and Mg2 ions displace protons only of the carboxyl groups of MA, which forms more stable complexes with calcium ions than with magnesium ions. It is shown that the stability of MA complexes with calcium and magnesium ions is significantly higher than the stability of phosphatidylserine and phosphatidic acid complexes with these ions. Using water solutions of MA as a hydrating agent will increase the efficiency of the hydration process and increase the yield of phospholipids and, consequently, the finished product lecithin.

Grapho-Analytical Determination of the Profile Disc Tool for Manufacturing of Complex Helicoidal Surfaces

2013 ◽  
Vol 837 ◽  
pp. 164-169 ◽  
Author(s):  
Gheorghe Pleşu
Keyword(s):  
Point Of View ◽  
Disc Cutter ◽  
Analytical Determination ◽  
Great Effort ◽  
Numerical Determination ◽  
Projection System ◽  
Tool Profile ◽  
Helicoidal Surfaces ◽  
Helicoidal Surface

Helicoidal surfaces correspond to a cathegory of widely spread surfacesin the technical field. From the point of view of the manufacturing of helicoidal surfaces through the moving of a profile around the helix, the two elements defining such a surface can be distinguished: the profile and the helix. The numerical determination of the profile of the disc type tool drawn on an analytical method with a large number of points [1- (the number reaches even 1500 in some cases) implies a great effort so that the technician can verify the correctness of results, even in the present case when there is the possibility of the numerical determination through the resolution of the inverse problem of the frontal profile of the complex helicoidal surface. In order to facilitate this work and to give the possibility of introducing some new profiles in the projection system, some methods of grapho-analytical determination have been conceived to process the profiles of the complex helicoidal surfaces, as well as the profiles of the helicoidal surfaces for a given tool profile. This paper presents the graphic-analytical determination of the disc tool profile designed to dress the complex helicoidal surfaces. The methods referred to by using the possibilities provided by the programming environment AutoCAD and its development languages allow to determin numerically the profile of the disc-cutter with a high precision, above the precision level required in practice.

scholarly journals SUBSTANTIATION OF THE FORM AND DETERMINATION OF THE CONSTRUCTIVE PARAMETERS OF THE ROTATION ROLLER OF SOIL

2018 ◽  
Vol 13 (3) ◽  
pp. 72-76
Author(s):  
Гумар Булгариев ◽  
Gumar Bulgariev ◽  
Геннадий Пикмуллин ◽  
Gennadiy Pikmullin ◽  
Ильгиз Галиев ◽  
...  
Keyword(s):  
Analytical Study ◽  
Point Of View ◽  
Design Parameters ◽  
Industrial Complex ◽  
Stage Of Development ◽  
Pass Through ◽  
Spiral Plate ◽  
Working Device ◽  
Important Design

At the present stage of development of the country’s agro-industrial complex, the technological process of surface tillage by combined soil-cultivating machines, simultaneously combining a number of operations in one pass through the field, causes the presence in their designs of the necessary set of various promising working organs. In view of the foregoing, a rotary soil ripper with a spiral-plate working member equipped with radially directed teeth and connected by means of rods with end flanges has been developed. Also, the researched ripper has the limits of penetration of the working element in the form of flat discs equipped with flanges and the radial stop have the ability to rotate around their axes independently of the ripper shaft. An analytical study of the working units of this ripper was carried out from the point of view of the influence of their size and teeth on the process of interaction with the soil, on the basis of which some of their parameters were determined. In conclusion, it was concluded that the analytical equations obtained allow us to justify the choice of the most important design parameters of the proposed new design and design a toothed rotary working device that reduces to constructive implementation after calculating their basic dimensions.

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