scholarly journals Twist-2 at seven loops in planar N $$ \mathcal{N} $$ = 4 SYM theory: full result and analytic properties

2016 ◽  
Vol 2016 (11) ◽  
Author(s):  
Christian Marboe ◽  
Vitaly Velizhanin
Keyword(s):  
Full Result

scholarly journals Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Robert Kantrowitz ◽  
Michael M. Neumann
Keyword(s):  
Present Article ◽  
Decisive Role ◽  
Valid Argument ◽  
Quadratic Polynomials ◽  
New Approach ◽  
Projectile Motion ◽  
Full Result ◽  
Air Resistance ◽  
Special Case ◽  
Natural Way

About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.

A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050070 ◽  
Author(s):  
CONG WU
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Comparison Principle ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Order Systems ◽  
Caputo Fractional Derivatives ◽  
Full Result

In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

scholarly journals Full result for the three-loop static quark potential

2010 ◽  
Author(s):  
Vladimir Smirnov ◽  
Alexander Smirnov ◽  
Matthias Steinhauser
Keyword(s):  
Full Result ◽  
Quark Potential ◽  
Static Quark

scholarly journals Proper holomorphic mappings between hyperbolic product manifolds

2014 ◽  
Vol 25 (04) ◽  
pp. 1450039 ◽  
Author(s):  
Jaikrishnan Janardhanan
Keyword(s):  
Riemann Surfaces ◽  
Holomorphic Mappings ◽  
Complex Manifolds ◽  
Finiteness Theorem ◽  
Important Special Case ◽  
Full Result ◽  
Hyperbolic Riemann Surfaces ◽  
Special Case ◽  
Proper Holomorphic Mappings

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

scholarly journals Full result for the QCD equation of state with 2+1 flavors

2014 ◽  
Vol 730 ◽  
pp. 99-104 ◽  
Author(s):  
Szabolcs Borsányi ◽  
Zoltán Fodor ◽  
Christian Hoelbling ◽  
Sándor D. Katz ◽  
Stefan Krieg ◽  
...  
Keyword(s):  
Equation Of State ◽  
Full Result

scholarly journals The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result

2000 ◽  
Vol 12 (5) ◽  
pp. 1045-1055 ◽  
Author(s):  
B. W. Knight ◽  
A. Omurtag ◽  
L. Sirovich
Keyword(s):  
Population Dynamics ◽  
Theoretical Prediction ◽  
Dynamical Equation ◽  
Step Change ◽  
Direct Simulation ◽  
Neuron Population ◽  
Integrate And Fire ◽  
Full Result ◽  
Series Convergence ◽  
Synaptic Event

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.

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