The order of growth of solutions to linear differential equations in complex plane have been investigated since 1980's and many results have been obtained by defining the order as \(\rho(f)=\limsup\limits_{r\to\infty}\frac{\log T(r,f)}{\log r}\). In this paper, by defining the order as \(\sigma_{T, z_{0}}=\limsup\limits_{r\to 0}\frac{\log^{+}T_{z_{0 ...
Samir Cherief, Saada Hamouda
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Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness
We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ - u= h(u){f} \ \ \text{in}\,\ , $$ where $f$ is an irregular datum, possibly a measure, and $h$ is a continuous function that may blow up at zero.
OLIVA, FRANCESCANTONIO +1 more
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Orientifolds and duality cascades: confinement before the wall
We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities.
Riccardo Argurio, Matteo Bertolini
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Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime [PDF]
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that
Saini, Sahil, Singh, Parampreet
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Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality [PDF]
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network,
Koji Nemoto +4 more
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Dynamical Cobordism and Swampland Distance Conjectures
We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite ...
Ginevra Buratti +3 more
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Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities [PDF]
Agraïments: The third author is supported by NSERC. The fourth author is also supported by the grant 12.839.08.05F from SCSTD of ASM and partially by NSERC.In this work we classify, with respect to the geometric equivalence relation, the global ...
Artés, Joan Carles +3 more
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On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof [PDF]
We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the permeability ...
Granero-Belinchón, Rafael +1 more
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Global Wilson–Fisher fixed points
The Wilson–Fisher fixed point with O(N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative ...
Andreas Jüttner +2 more
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Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
We further exploit the relation between tropical Grassmannians and Gr(4, n) cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory at higher ...
Niklas Henke, Georgios Papathanasiou
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