Abstract: The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.
Abstract: The aim of the present paper is to study properties of
Quasi conformally flat LP-Sasakian manifolds with a coefficient α.
In this paper, we prove that a Quasi conformally flat LP-Sasakian
manifold M (n > 3) with a constant coefficient α is an η−Einstein
and in a quasi conformally flat LP-Sasakian manifold M (n > 3)
with a constant coefficient α if the scalar curvature tensor is constant
then M is of constant curvature.
Abstract: This paper aims at manipulating loop alignment in knitting a three-dimensional (3D) shape by its geometry. Two loop alignment methods are introduced to handle a surface with positive Gaussian curvature. As weft knitting is a two-dimensional (2D) knitting mechanism that the knitting cam carrying the feeders moves in two directions only, left and right, the knitted fabric generated grows in width and length but not in depth. Therefore, a 3D shape is required to be flattened to a 2D plane with surface area preserved for knitting. On this flattened plane, dimensional measurements are taken for loop alignment. The way these measurements being taken derived two different loop alignment methods. In this paper, only plain knitted structure was considered. Each knitted loop was taken as a basic unit for loop alignment in order to achieve the required geometric dimensions, without the inclusion of other stitches which give textural dimensions to the fabric. Two loop alignment methods were experimented and compared. Only one of these two can successfully preserve the dimensions of the shape.
Abstract: Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.
Abstract: To determine the potential of a low cost Irish
engineered timber product to replace high cost solid timber for use in
bending active structures such as gridshells a single Irish engineered
timber product in the form of orientated strand board (OSB) was
selected. A comparative study of OSB and solid timber was carried
out to determine the optimum properties that make a material suitable
for use in gridshells. Three parameters were identified to be relevant
in the selection of a material for gridshells. These three parameters
are the strength to stiffness ratio, the flexural stiffness of
commercially available sections, and the variability of material and
section properties. It is shown that when comparing OSB against
solid timber, OSB is a more suitable material for use in gridshells that
are at the smaller end of the scale and that have tight radii of
curvature. Typically, for solid timber materials, stiffness is used as an
indicator for strength and engineered timber is no different. Thus, low
flexural stiffness would mean low flexural strength. However, when
it comes to bending active gridshells, OSB offers a significant
advantage. By the addition of multiple layers, an increased section
size is created, thus endowing the structure with higher stiffness and
higher strength from initial low stiffness and low strength materials
while still maintaining tight radii of curvature. This allows OSB to
compete with solid timber on large scale gridshells. Additionally, a
preliminary sustainability study using a set of sustainability indicators
was carried out to determine the relative sustainability of building a
large-scale gridshell in Ireland with a primary focus on economic
viability but a mention is also given to social and environmental
aspects. For this, the Savill garden gridshell in the UK was used as
the functional unit with the sustainability of the structural roof
skeleton constructed from UK larch solid timber being compared
with the same structure using Irish OSB. Albeit that the advantages of
using commercially available OSB in a bending active gridshell are
marginal and limited to specific gridshell applications, further study
into an optimised engineered timber product is merited.
Abstract: It is known that residual welding deformations give
negative effect to processability and operational quality of welded
structures, complicating their assembly and reducing strength.
Therefore, selection of optimal technology, ensuring minimum
welding deformations, is one of the main goals in developing a
technology for manufacturing of welded structures.
Through years, JSC SSTC has been developing a theory for
estimation of welding deformations and practical activities for
reducing and compensating such deformations during welding
process. During long time a methodology was used, based on analytic
dependence. This methodology allowed defining volumetric changes
of metal due to welding heating and subsequent cooling. However,
dependences for definition of structures deformations, arising as a
result of volumetric changes of metal in the weld area, allowed
performing calculations only for simple structures, such as units, flat
sections and sections with small curvature. In case of complex 3D
structures, estimations on the base of analytic dependences gave
significant errors.
To eliminate this shortage, it was suggested to use finite elements
method for resolving of deformation problem. Here, one shall first
calculate volumes of longitudinal and transversal shortenings of
welding joints using method of analytic dependences and further,
with obtained shortenings, calculate forces, which action is
equivalent to the action of active welding stresses. Further, a finiteelements
model of the structure is developed and equivalent forces
are added to this model. Having results of calculations, an optimal
sequence of assembly and welding is selected and special measures to
reduce and compensate welding deformations are developed and
taken.
Abstract: A supersonic expansion cannot be achieved within a convergent-divergent nozzle if the flow velocity does not reach that of the sound at the throat. The computation of the flow field characteristics at the throat is thus essential to the nozzle developed thrust value and therefore to the aircraft or rocket it propels. Several approaches were developed in order to describe the transonic expansion, which takes place through the throat of a De-Laval convergent-divergent nozzle. They all allow reaching good results but showing a major shortcoming represented by their inability to describe the transonic flow field for nozzles having a small throat radius. The approach initially developed by Kliegel & Levine uses the velocity series development in terms of the normalized throat radius added to unity instead of solely the normalized throat radius or the traditional small disturbances theory approach. The present investigation carries out the application of these three approaches for different throat radiuses of curvature. The method using the normalized throat radius added to unity shows better results when applied to geometries integrating small throat radiuses.
Abstract: Contact stress is an important problem in industry.
This is a problem that in the first attention may be don-t appears, but
disregard of these stresses cause a lot of damages in machines. These
stresses occur at locations such as gear teeth, bearings, cams and
between a locomotive wheel and the railroad rail. These stresses
cause failure by excessive elastic deformation, yielding and fracture.
In this paper we intend show the effective parameters in contact
stress and ponder effect of curvature. In this paper we study contact
stresses on the surface of gear teeth and compare these stresses for
four popular profiles of gear teeth (involute, cycloid, epicycloids, and
hypocycloid). We study this problem with mathematical and finite
element methods and compare these two methods on different profile
surfaces.
Abstract: The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
Abstract: As the remedy used music becomes active and
meditation effect through the music is verified, people take a growing
interest about psychological balance or remedy given by music. From
traditional studies, it is verified that the music of which spectral
envelop varies approximately as 1/f (f is frequency) down to a
frequency of low frequency bandwidth gives psychological balance.
In this paper, we researched signal properties of music which gives
psychological balance. In order to find this, we derived the property
from voice. Music composed by voice shows large value in NCSD.
We confirmed the degree of deference between music by curvature of
normalized cumulative spectral distribution. In the music that gives
psychological balance, the curvature shows high value, otherwise, the
curvature shows low value.
Abstract: The paper describes a new approach for fingerprint
classification, based on the distribution of local features (minute
details or minutiae) of the fingerprints. The main advantage is that
fingerprint classification provides an indexing scheme to facilitate
efficient matching in a large fingerprint database. A set of rules based
on heuristic approach has been proposed. The area around the core
point is treated as the area of interest for extracting the minutiae
features as there are substantial variations around the core point as
compared to the areas away from the core point. The core point in a
fingerprint has been located at a point where there is maximum
curvature. The experimental results report an overall average
accuracy of 86.57 % in fingerprint classification.
Abstract: In this work some characterizations of semi Riemannian curvature tensor on almost split quaternion Kaehler manifolds and some characterizations of Ricci tensor on almost split quaternion Kaehler manifolds are given.