GEOMETRIC MODELS OF THE CHASE METHOD ON THE PLANE AND ON THE SURFACE DELIVERY

In this article models of the pursuit method in the pursuit problem. The considered models are based on the correction of the vector of the direction of motion. Suppose, on a plane, the intended direction is the line of sight of the pursuer and the target. Correction of the direction of movement consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. Have been developed models for calculating the trajectories of the pursuer and the target in the problem of studying the plane and on the surface. Modifications of the mathematical models of the methods of parallel dropping and chasing were made in relation to the plane and the surface. In our models and algorithms, the speed of the pursuer can be directed arbitrarily. With the modification of the parallel displacement method, the straight line of this movement was replaced by a predicted trajectory of movement at a point in time, which moves to itself. When modifying the chase method, the line of sight was also replaced with a compound curve, taking into account the restrictions on the curvature of the pursuer trajectory. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.

Gauge field theories and propagators in curved space-time

In this paper, DeWitt’s formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite-dimensional invariance groups may be carried out in a manifestly covariant (non-Hamiltonian) fashion, even in curved space-time. Another important virtue of DeWitt’s approach is that it emphasizes the common features of apparently very different theories such as Yang–Mills theories and General Relativity; moreover, it makes it possible to classify all gauge theories in three categories characterized in a purely geometrical way, i.e. by the algebra which the generators of the gauge group obey; the geometry of such theories is the fundamental reason underlying the emergence of ghost fields in the corresponding quantum theories, too. These “tricky extra particles”, as Feynman called them in 1964, contribute to a physical observable such as the stress-energy tensor, which can be expressed in terms of Feynman’s Green function itself. Therefore, an entire section is devoted to the study of the Green functions of the neutron scalar meson: in flat space-time, the choice of a particular Green’s function is the choice of an integration contour in the “momentum” space; in curved space-time the momentum space is no longer available, and the definition of the different Green functions requires a careful discussion itself. After the necessary introduction of bitensors, world function and parallel displacement tensor, an expansion for the Feynman propagator in curved space-time is obtained. Most calculations are explicitly shown.

Modeling of ventilation in living premises with air intake through adjustable window sashes

The article presents the results of investigating the systems of natural supply and exhaust ventilation of residential premises with air supply through window structures. In particular, the analysis focuses on cases of air intake through a gap in tilting window sash and parallel opening window sash (room’s ventilation). There are provided the study results concerning the air velocity and temperature fields in the room`s volume, as well as the internal air temperature changes during the room’s ventilation in cases of active and inactive heating appliance. There is studied the air intake by the parallel displacement of the sash from the frame with formation of a gap in the living premises where heating convectors are used. The distribution of air flows is explored using STAR-CCM+ hydrodynamic analysis software package. The installation of window blocks in residential buildings with the function of parallel displacement of the sash allows for the standards-compliant air exchange in the premises without the use of special supply devices. When closed, the window block complies with regulatory requirements to heat transfer resistance and soundproofing.

Surfaces of congruent sections on cylinders

Introduction. The definition of surfaces of congruent sections was first formulated in the work written by I.I. Kotov. These and several other types of surfaces, generated by the motion of a curve, belonged to the class of kinematic surfaces. Such kinematic surfaces as those of plane parallel displacement, surfaces of rotation, Monge surfaces, cyclic surfaces with ge-nerating circles having constant radius, rotative and spiroidal surfaces, helical some helix-shaped surfaces can be included into the class of surfaces that have congruent sections. Materials and methods. Using I.I. Kotov’s methodology, the authors first derived parametrical and vector equations for eight surfaces of congruent pendulum type cross sections of circular, elliptic, and parabolic cylinders and several helix-shaped surfaces. Circles, ellipses, and parabolas, located in the plane of the generating curve of a guiding cylinder or in the planes of a bundle that passes through the longitudinal axis of a cylinder, generate plane curves. Ellipses, analyzed in the article, can be easily converted into circles and this procedure can increase the number of shapes analyzed here. Results. Formulas are provided in the generalized form, so the shape of a plane generating curve can be arbitrary. Some surfaces of congruent sections are determined by two varieties of parametric equations. In one case, the central angle of the guiding cylindrical surface was used as an independent parameter, but in the other case, one of rectangular coordinates of the cylinder’s guiding curve served as an independent parameter. Two types of surfaces are analyzed: 1) when local axes of generating curves remain parallel in motion; 2) when these axes rotate. Conclusions. The analysis of the sources and the results, recommendations and proposals for application of surfaces, having congruent sections, is made with a view to their use in architecture and technology. The list of references has 27 positions, and it shows that the surfaces considered in this paper are being analyzed by architects, engineers, and geometricians both in Russia and abroad.

Investigation of ventriculoperitoneal shunt disconnection for hydrocephalus treatment

OBJECTIVEThis investigation is aimed at gaining a better understanding of the factors that lead to mechanical failure of shunts used for the treatment of hydrocephalus, including shunt catheter-valve disconnection and shunt catheter fracture.METHODSTo determine the root cause of mechanical failure, the authors created a benchtop mechanical model to mimic mechanical stressors on a shunt system. To test shunt fracture, cyclical loading on the catheter-valve connection site was tested with the shunt catheter held perpendicular to the valve. Standard methods were used to secure the catheter and valves with Nurolon. These commercial systems were compared to integrated catheters and valves (manufactured as one unit). To test complete separation/disconnection of the shunt catheter and valve, a parallel displacement test was conducted using both Nurolon and silk sutures. Finally, the stiffness of the catheters was assessed. All mechanical investigations were conducted on shunts from two major shunt companies, assigned as either company A or company B.RESULTSCyclical loading experiments found that shunts from company B fractured after a mean of 4936 ± 1725 cycles (95% CI 2990–6890 cycles), while those of company A had not failed after 8000 cycles. The study of parallel displacement indicated complete disconnection of company B’s shunt catheter-valve combination using Nurolon sutures after being stretched an average 32 ± 5.68 mm (95% CI 25.6–38.4 mm), whereas company A’s did not separate using either silk or Nurolon sutures. During the stiffness experiments, the catheters of company B had statistically significantly higher stiffness of 13.23 ± 0.15 N compared to those of company A, with 6.16 ± 0.29 N (p < 0.001).CONCLUSIONSMechanical shunt failure from shunt catheter-valve disconnection or fracture is a significant cause of shunt failure. This study demonstrates, for the first time, a correlation between shunt catheters that are less mechanically stiff and those that are less likely to disconnect from the valve when outstretched and are also less likely to tear when held at an angle from the valve outlet. The authors propose an intervention to the standard of care wherein less stiff catheters are trialed to reduce disconnection.

Examination of the Abstraction Process of Complex Number Knowledge

The aim of this study was to examine the abstraction process of tenth grade students' complex number knowledge. A semi-structured interview was held with two students who were successful at mathematics and who voluntarily participated in the study. In this interview, the students faced three different research problems prepared by the researcher in order to reveal the students' knowledge formation processes. The students studied these research problems together. In the meantime, their cognitive processes related to recognizing, building-with, and constructing of discourses was analysed. The analyses indicated that both of the students recognized and built-with the preliminary knowledge necessary for them to construct the knowledge of complex numbers. Moreover, it was understood that one of these students recognized and build-with their previous knowledge of linear functions, coordinate systems, and parallel displacement. In conclusion, it could be said that this student constructed the knowledge of complex plane.

Generating finite element method in constructing complex-shaped multigrid finite elements

The calculations of three-dimensional composite bodies based on the finite element method with allowance for their structure and complex shape come down to constructing high-dimension discrete models. The dimension of discrete models can be effectively reduced by means of multigrid finite elements (MgFE). This paper proposes a generating finite element method for constructing two types of three-dimensional complex-shaped composite MgFE, which can be briefly described as follows. An MgFE domain of the first type is obtained by rotating a specified complex-shaped plane generating single-grid finite element (FE) around a specified axis at a given angle, and an MgFE domain of the second type is obtained by the parallel displacement of a generating FE in a specified direction at a given distance. This method allows designing MgFE with one characteristic dimension significantly larger (smaller) than the other two. The MgFE of the first type are applied to calculate composite shells of revolution and complex-shaped rings, and the MgFE of the second type are used to calculate composite cylindrical shells, complex-shaped plates and beams. The proposed MgFE are advantageous because they account for the inhomogeneous structure and complex shape of bodies and generate low-dimension discrete models and solutions with a small error.

The quantum Higgs field and the resolution of the cosmological constant paradox in the Weyl-geometrical Universe

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the [Formula: see text] as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar–tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: [Formula: see text] is expressed in terms of the dark energy potential: [Formula: see text] via the “mass reduction parameter”: [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a [Formula: see text]-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of [Formula: see text] offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “[Formula: see text]-paradox”). Indeed, our “universal” theory offers a resolution of the “[Formula: see text]-paradox” for all exponential inflationary potentials: [Formula: see text], and for all linear superpositions of these potentials, where [Formula: see text] belongs to the mathematical set of the “real numbers”. An explicit solution of the [Formula: see text]-Paradox is reported for [Formula: see text]. The results of the theory are analyzed in the framework of the recent experimental data of the PLANCK Mission. The average vacuum-energy density in the Universe is found: [Formula: see text], the mass-reduction parameter: [Formula: see text] and the value of the “cosmological constant”: [Formula: see text](eV/c[Formula: see text]. A quite remarkable result of the theory consists of the complete formulation of the Einstein equation including in its structure the “cosmological constant”, [Formula: see text]. This was the term that Einstein added “by hand” to his famous equation. The critical stability of the Universe is also discussed.

Open Wedge Osteotomy with Ulnar Shortening for Madelung Deformity Using a Computer-Generated Template

A variety of osteotomies have been reported to correct Madelung deformity using plain radiographs. However, evaluation of the deformity using 2-dimensional plain radiography is difficult because of its complex 3-dimensional nature. Therefore, we performed corrective osteotomy using recently developed 3D simulation technology on an adult woman with Madelung deformity, and achieved an excellent outcome. In this study, we calculated the amount of parallel displacement as well as the rotational angle for more precise correction, and performed open wedge osteotomy. Furthermore, we performed concurrent ulnar shortening. An exaggerated radial inclination was observed in the posteroanterior radiograph. A palmar shift of the carpus and dorsal dislocation of the ulnar head were observed in the lateral radiograph. In the preoperative findings, radial inclination (RI), volar tilt (VT), and ulnar variance (UV) were 35°, 40°, and 12 mm, respectively. The wrist showed improvement, with an RI of 25°, VT of 14°, and UV of 0 mm. At present, 14 months after surgery, there has been no loss of correction, instability of the ulnar head, or pain on the ulnar side. The procedure resulted in improvements in the protrusion and pain in the ulnar portion of the patient’s wrist. Based on this result, we believe that accurate corrective osteotomy with ulnar shortening should be performed for Madelung deformity.