scholarly journals On the Hidden Beauty of Trigonometric Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 57
Author(s):  
Jiri Stavek
Keyword(s):  
Transverse Momentum ◽  
Trigonometric Function ◽  
Moving Object ◽  
Longitudinal Momentum ◽  
Trigonometric Functions ◽  
Beta Particles ◽  
Latent Energy ◽  
Old Babylonian ◽  
School Of Athens ◽  
Clay Tablet

In the unit circle with radius R = E0 = mc2 = 1 we have defined the trigonometric function cos(Theta) = v/c. The known trigonometric functions revealed the hidden relationships between sensible energy, latent energy, sensible momentum and latent momentum of the moving object, and the absorbed momentum from outside and the available momentum in the outside of the moving object. We present the trigonometric concept inspired by the old Babylonian clay tablet IM 55357 and based on the knowledge of the School of Athens (the fresco of Raphael) and the work of many generations of the Masters of trigonometry. The concept of the Divided Line of Plato can be now quantitatively tested. For the experimental analysis of this concept we propose to study in details the very well known beta decay of RaE to determine the sensible and latent energy (heat) of those beta particles and the sensible and latent energy of the remaining nucleus. The longitudinal momentum and the transverse (latent) momentum can be studied on the effects of the slow neutrons. The longitudinal momentum and the transverse momentum of photons can be manipulated in a convenient medium in order to prepare slow photons. The photoormi effect might improve the efficiency of the light-to-electricity conversion and the efficiency of the light-to-heat conversion.

scholarly journals An Old Babylonian manuscript of the Weidner god-list from Tell Taban

Iraq ◽  
2009 ◽  
Vol 71 ◽  
pp. 33-42 ◽  
Author(s):  
Daisuke Shibata
Keyword(s):  
Old Babylonian ◽  
History Of ◽  
Clay Tablet

AbstractThis article presents a fragment of an Old Babylonian clay tablet excavated in 2007 at Tell Taban, ancient Ṭābatum, near Hassake in Syria. The text is a common Babylonian scholarly composition known as the Weidner god-list. It is the oldest exemplar of this list so far recovered from north Mesopotamia and important for the history of the diffusion of Babylonian scholarship.

scholarly journals An Axiom of True Courses Calculation in Great Circle Navigation

2021 ◽  
Vol 9 (6) ◽  
pp. 603
Author(s):  
Mate Baric ◽  
David Brčić ◽  
Mate Kosor ◽  
Roko Jelic
Keyword(s):  
Trigonometric Function ◽  
Great Circle ◽  
Trigonometric Functions ◽  
Spherical Trigonometry ◽  
Software Packages ◽  
Vector Algebra ◽  
Computer Aided ◽  
Essential Knowledge

Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.

Mass and energy dependence of the transverse momentum densities in covariant parton model

2015 ◽  
Vol 30 (27) ◽  
pp. 1550133 ◽  
Author(s):  
M. M. Yazdanpanah ◽  
A. Mirjalili ◽  
A. Behjat Ramezani
Keyword(s):  
Binding Energy ◽  
Transverse Momentum ◽  
Quark Model ◽  
Energy Dependence ◽  
Parton Model ◽  
Longitudinal Momentum ◽  
Transverse Momentum Dependent ◽  
Unpolarized Case ◽  
Covariant Quark Model ◽  
Good Agreement

The parton densities which are dependent on transverse momentum, open a way to understand better the structure of quarks and gluons in a more complete way. We are investigating a method based on the covariant quark model which enables us to extract the transverse momentum dependent (TMD) densities from the usual parton densities which are just dependent on the longitudinal momentum. In continuation, we obtain the dependence of the TMDs on binding energy and the mass of quarks. We do some calculations to obtain the TMDs in the unpolarized case while the mass and binding energy of partons are varying. Considering these effects, the results for TMDs are in good agreement with the results of the recent related models.

The production of π±, K±, p and p̄ in p–Pb collisions at sNN = 5.02 TeV

2018 ◽  
Vol 33 (17) ◽  
pp. 1850094 ◽  
Author(s):  
U. Tabassam ◽  
Y. Ali ◽  
M. Suleymanov ◽  
A. S. Bhatti ◽  
M. Ajaz
Keyword(s):  
Transverse Momentum ◽  
Longitudinal Momentum ◽  
Momentum Range ◽  
Text Production ◽  
Cronin Effect ◽  
Protons And Neutrons ◽  
Baryon Resonances ◽  
Rhic Data

In this study, we are reporting comprehensive results on [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] production in the transverse momentum range of [Formula: see text] 4 GeV/c at midrapidity of [Formula: see text] 0.5 GeV/c, in p–Pb collisions at [Formula: see text] = 5.02 TeV. HIJING 1.0 and UrQMD 3.4 event generators are used to perform simulations and the results are compared with the ALICE and RHIC data. It is observed from the comparison that the yields for the baryons are more complex compared to the mesons and the complexity in baryons is due to the striping dynamics (spectators, leading particles of projectiles) of inner nucleus protons and neutrons. Though all the mesons could be produced during the interaction, they have maximum longitudinal momentum [Formula: see text]; baryons and mesons could be produced as a result of decay of massive baryon-resonances. Yields for the [Formula: see text] mesons are greater than the yield for the [Formula: see text] mesons. These are the well-known results from the RHIC data, which stated that the Cronin Effect is mainly due to [Formula: see text] mesons that can be produced as a result of multi-particle inner nucleus cascade. There exists the regions where yields for the [Formula: see text] mesons and baryons are same that may be due to the appearance of parton nature. The code used in simulation includes the parton dynamics earlier than it is included in the experiment.

scholarly journals Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1039
Author(s):  
Sixiao Kong ◽  
Chunbiao Li ◽  
Haibo Jiang ◽  
Yibo Zhao ◽  
Yanling Wang
Keyword(s):  
Numerical Simulation ◽  
Hardware Implementation ◽  
Trigonometric Function ◽  
Initial Condition ◽  
Trigonometric Functions ◽  
Negative Coefficient ◽  
Offset Boosting

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.

scholarly journals TRANSVERSE MOMENTUM DISTRIBUTION IN THE B MESONS IN THE HEAVY-QUARK LIMIT: THE WANDZURA–WILCZEK PART

2003 ◽  
Vol 18 (11) ◽  
pp. 799-805 ◽  
Author(s):  
HIROYUKI KAWAMURA ◽  
JIRO KODAIRA ◽  
CONG-FENG QIAO ◽  
KAZUHIRO TANAKA
Keyword(s):  
Transverse Momentum ◽  
Heavy Quark ◽  
Momentum Distribution ◽  
B Mesons ◽  
Equations Of Motion ◽  
Transverse Momentum Distribution ◽  
Wave Functions ◽  
Effective Theory ◽  
Longitudinal Momentum ◽  
Heavy Quark Limit

In the heavy-quark limit, the valence Fock-state components in the B mesons are described by a set of two light-cone wave functions. We show that these two wave functions obey simple coupled differential equations, which are based on the equations of motion in the Heavy Quark Effective Theory (HQET), and the analytic solutions for them are obtained. The results generalize the recently obtained longitudinal-momentum distribution in the Wandzura–Wilczek approximation by including the transverse momenta. We find that the transverse momentum distribution depends on the longitudinal momentum of the constituents, and that the wave functions damp very slowly for large transverse separation between quark and antiquark.

scholarly journals THE TRANSVERSE MOMENTUM DEPENDENT STATISTICAL PARTON DISTRIBUTIONS REVISITED

2013 ◽  
Vol 28 (09) ◽  
pp. 1350026 ◽  
Author(s):  
CLAUDE BOURRELY ◽  
FRANCO BUCCELLA ◽  
JACQUES SOFFER
Keyword(s):  
Transverse Momentum ◽  
Transverse Energy ◽  
Inelastic Collisions ◽  
Longitudinal Momentum ◽  
Momentum Dependence ◽  
Proton Target ◽  
Wigner Rotation ◽  
Parton Distributions ◽  
Sum Rule ◽  
Transverse Momentum Dependent

The extension of the statistical parton distributions to include their transverse momentum dependence (TMD) is revisited by considering that the proton target has a finite longitudinal momentum. The TMD will be generated by means of a transverse energy sum rule. The new results are mainly relevant for electron–proton inelastic collisions in the low Q2 region. We take into account the effects of the Melosh–Wigner rotation for the helicity distributions.

scholarly journals Relationship between Trigonometry Functions with Hyperbolic Function

2019 ◽  
Vol 1 (4) ◽  
pp. 82
Author(s):  
Sri Rejeki Dwi Putranti
Keyword(s):  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Complex Numbers ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Complex Functions ◽  
Engineering Problems ◽  
The Relationship

Many engineering problems can be solved by methods involving complex numbers and complex functions. In the definitions below we will prove the relationship between trigonometric functions and hyperbolic functions, where the hyperbolic function is an extension of the trigonometric function. Keywords: trigonometric functions; hyperbolic functions

scholarly journals T-odd generalized and quasi transverse momentum dependent parton distribution in a scalar spectator model

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Xuan Luo ◽  
Hao Sun
Keyword(s):  
Transverse Momentum ◽  
Total Momentum ◽  
Longitudinal Momentum ◽  
Momentum Fraction ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Longitudinal Momentum Fraction ◽  
Generalized Parton Distributions ◽  
Active Quark ◽  
Spectator Model

AbstractGeneralized transverse momentum dependent parton distributions (GTMDs), as mother funtions of transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs), encode the most general parton structure of hadrons. We calculate four twist-two time reversal odd GTMDs of pion in a scalar spectator model. We study the dependence of GTMDs on the longitudinal momentum fraction x carried by the active quark and the transverse momentum $$|\vec k_T|$$ | k → T | for different values of skewness $$\xi $$ ξ defined as the longitudinal momentum transferred to the pion as well as the total momentum $$|\vec \Delta _T|$$ | Δ → T | transferred to the pion. In addition, the quasi-TMDs and quasi-GPDs of pion have also been investigated in this paper.

Ein Altbabylonischer Text Betreffend Die Lieferung Von Schilfrohr

2001 ◽  
Vol 5 (1) ◽  
pp. 37-40
Author(s):  
Horst Klengel ◽  
Evelyn Klengel
Keyword(s):  
The Other ◽  
The Third ◽  
Old Babylonian ◽  
Battle Scenes ◽  
The Given ◽  
Seal Impressions ◽  
Clay Tablet ◽  
Inventory Number

AbstractThe article which had been originally dedicated to the late Armenian Academician Gagik Sarkisian describes a Babylonian clay tablet document from the collection of the Vorderasiatisches Museum Berlin (inventory number VAT 952). The text of the document is a contract dealing with the terms of delivery of 960 bundles of reed. It is dated with the third full year of reign of king Samsuiluna, the successor of 'Ammurapi. On the cover of the tablet some not very well preserved seal impressions can be found . The authors attempt to (partly) reconstruct these seal impressions, which are connected with people involved in the contract. One of the better preserved impressions shows two formally interconnected battle scenes, one between a man and a lion, the other between a men and a lion-dragon. Although these kind of scenes are rarely to be met with on Old Babylonian seals, the given impression can be compared to a well preserved representation of a similar scene on a clay tablet from Sippar.

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