In this article we investigate the metric signature as a non-differentiable degree of freedom. The specific model is a vacuum 7D Universe on the principal bundle with an SU(2) structural group. An analytical solution is found which to a 4D observer appears as a flat Universe with a fluctuating metric signature, and frozen extra dimensions with an SU(2) instanton gauge field. A piece of this sol...

We study the dynamics of a particle in space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity motion body lives their realm. use mathematical concept fiber bundle to characterize multivalued geodesic trajectories going through point Then, we generalize our concepts everywhere non-smooth structures. The ...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.

Given non-degenerate intervals X of R and an increasing ordered mapping Φ : X × · · · ×X → R , games in strategic form between N players with the X as action sets with the following three properties are studied: the set of Nash equilibria E is convex, Φ is constant on E and in each Nash equilibrium at least one payoff function is not partially differentiable w.r.t. its own action. The results a...

1 Morse, Marston, "The existence of polar non-degenerate functions on differentiable manifolds," Annals of Math., 71 (1960). 2 Morse, Marston, "Differentiable mappings in the Schoenflies Theorem," Compositio Mathematica, 14, (1959). 3Seifert, H., and W. Threlfall, Variationsrechung im Grossen, ed. B. G. Teubner (Leipzig and Berlin: Teubner, 1938), pp. 97-100. 4Morse, Marston, "Functional topolo...

Open-system quantum dynamics described by non-Hermitian effective Hamiltonians have become a subject of considerable interest. Studies physics revealed general principles, including relationships between the topology complex eigenvalue space and breakdown adiabatic control strategies. We study here single qubit, similar to recently realized experimental systems in which non-Hermiticity arises f...

Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of simple base distribution. However, there are often applications that require more than invertibility. For instance, the computation energies and forces in physics requires second derivatives to be well-defined continuous. Smooth normalizing employ infinitely differentiable tra...

Generative adversarial learning is a popular new approach to training generative models which has been proven successful for other related problems as well. The general idea is to maintain an oracle D that discriminates between the expert’s data distribution and that of the generative model G. The generative model is trained to capture the expert’s distribution by maximizing the probability of ...

in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz‎. ‎necessary optimality conditions and regularity conditions are given‎. ‎our approach are based on the michel-penot subdifferential.

BACKGROUND In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research...