scholarly journals Resolutions of the Jerk and Snap Vectors for a Quasi Curve in Euclidean 3-Space

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3128
Author(s):  
Ebrahem Hamouda ◽  
Clemente Cesarano ◽  
Sameh Askar ◽  
Ayman Elsharkawy
Keyword(s):  
Plane Curve ◽  
Tangential Direction ◽  
Point Particle

This work aims at studying resolutions of the jerk and snap vectors of a point particle moving along a quasi curve in Euclidean 3-space E3. In particular, we obtain the resolution of the jerk and snap vectors along the quasi vectors and offer an alternative resolution of the jerk and snap vectors along the tangential direction and two special radial directions that lie in the osculating and rectifying planes. This alternative resolution for a quasi plane curve in Euclidean 3-space E3 is given as corollary. Moreover, our results are illustrated via some examples.

Best Matching: Technical Details

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Point Particle ◽  
Euclidean Group ◽  
Scale Invariant ◽  
Similarity Group ◽  
N Body Problem ◽  
Technical Details ◽  
Matching Procedure ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Gauge Connection

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

scholarly journals The Little-Bang and the femto-nova in nucleus-nucleus collisions

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Nu Xu ◽  
Kenji Fukushima ◽  
Bedangadas Mohanty
Keyword(s):  
Collision Energy ◽  
Particle Production ◽  
Gluon Plasma ◽  
Baryon Density ◽  
Point Particle ◽  
Current Status ◽  
Density Region ◽  
Qcd Critical Point ◽  
Qcd Phase Diagram ◽  
Lower Collision Energy

AbstractWe make a theoretical and experimental summary of the state-of-the-art status of hot and dense QCD matter studies on selected topics. We review the Beam Energy Scan program for the QCD phase diagram and present the current status of the search for the QCD critical point, particle production in high baryon density region, hypernuclei production, and global polarization effects in nucleus-nucleus collisions. The available experimental data in the strangeness sector suggests that a grand canonical approach in the thermal model at high collision energy makes a transition to the canonical ensemble behavior at low energy. We further discuss future prospects of nuclear collisions to probe properties of baryon-rich matter. Creation of a quark-gluon plasma at high temperature and low baryon density has been called the “Little-Bang” and, analogously, a femtometer-scale explosion of baryon-rich matter at lower collision energy could be called the “femto-nova”, which could possibly sustain substantial vorticity and a magnetic field for non-head-on collisions.

High-speed electrical sliding wear behaviors of Cu-WS2-graphite-WS2 nanotubes composite

2018 ◽  
Vol 25 (2) ◽  
pp. 343-351
Author(s):  
Gang Qian ◽  
Yi Feng ◽  
Jing-Cheng Zhang ◽  
Yang Wang ◽  
Tian-Ci Zhang ◽  
...  
Keyword(s):  
Wear Rate ◽  
Contact Resistance ◽  
Photoelectron Spectroscopy ◽  
High Speed ◽  
Electrical Current ◽  
Tangential Direction ◽  
Sliding Velocity ◽  
Graphite Composite ◽  
Slip Ring ◽  
Electrical Wear

AbstractCu-WS2-graphite-WS2nanotubes composite was fabricated by the powder metallurgy hot-pressed method. The effects of electrical current (5–15 A/cm2) and sliding velocity (5–15 m/s) on the electrical wear behaviors of the composite were investigated using a block-on-slip ring wear tester rubbing against Cu-5 wt% Ag alloy ring under 2.5 N/cm2of applied load. The lubricating effect of WS2nanotubes and composition of tribo-film were analyzed. The results demonstrated that the contact resistance decreases but the wear rate increases as electrical current increases, because the adverse effects of electrical current soften the materials at “a-spots” and damage the tribo-film. Due to the adsorption of gaseous molecule film on the tangential direction of slip ring surface, with the rise of sliding velocity, the contact resistance increases while the wear rate reaches the minimum at a sliding velocity of 10 m/s. The reasonable addition of WS2nanotubes into the Cu-WS2-graphite composite to replace WS2powder can result in a reduction of both contact resistance and wear rate. X-ray photoelectron spectroscopy (XPS) analyses revealed that copper oxides, graphite, WS2and WS2nanotubes in the tribo-film play the main lubrication action at the tribo-interface.

Cell grouping and primary wall generations in the cambial zone, xylem, and phloem in Pinus

1968 ◽  
Vol 16 (2) ◽  
pp. 177 ◽  
Author(s):  
A Mahmood
Keyword(s):  
Cell Division ◽  
Mother Cell ◽  
Secondary Wall ◽  
Radial Direction ◽  
Cell Plate ◽  
Tangential Direction ◽  
Primary Wall ◽  
Photographic Evidence ◽  
Secondary Wall Deposition ◽  
Cambial Zone

The use of the term cambium, or equivalent terms, in modern literature is discussed. The term cambial zone adopted in this paper includes the cambial initial and the dividing and enlarging cells. The tissue mother cell produced at each division of the initial produces a group of four cells in xylem or two cells in phloem. Theoretical constructs have been made for xylem and phloem production by associating the concepts that xylem and phloem are produced in alternate series of initial divisions and that a new primary wall is deposited around each daughter protoplast at each cell division. Correlations are derived from the theoretical constructs for the thickness of primary wall layers lying in the tangential direction and of those lying in the radial direction at progressive histological levels. Deductions from theoretical constructs are made when the initial is producing xylem, when it changes its polarity from xylem to phloem production, and when the reverse change occurs. Most of the theoretical deductions are supported by photographic evidence. The chief point of this study is the demonstration of generations (multiplicity) of primary parental walls. The term intercellular material proposed in this paper includes the cell plate plus any remnants of ancestral primary walls between the current primary walls surrounding the adjacent protoplasts. This term is still applicable to cells where secondary wall deposition is taking place or has been completed.

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

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