I discuss the status of the mass hierarchy problem and prospects for beyond the Standard Model physics in the light of the Higgs scalar discovery at the LHC and the experimental searches for new physics. In particular, I discuss in this context low energy supersymmetry and large extra dimensions with low string scale.

We summarize the foliation approach to $\cal N = 1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ (without boundary) down to AdS$_3$ spaces for the case when the internal part $\xi$ of the supersymmetry generator is chiral on some proper subset $\cal W$ of $M$. In this case, a topological no-go theorem implies that the complement $M \ \cal{W}$ must be a dense open subset, while $M$ admits a singular foliation $\bar{\cal F}$ (in the sense of Haefliger) which is defined by a closed one-form $\omega$ and is endowed with a longitudinal $G_2$ structure. The geometry of this foliation is determined by the supersymmetry conditions. We also describe the topology of $\bar{\cal F}$ in the case when $\omega$ is a
Morse form.

A second-order Lagrangian formulation with respect to a set of linear first-order field equations (either relativistic or not) is proposed. The general formalism is illustrated in the case of first-order field equations containing a single spatial derivative.

This paper aims to the determination of the number of degrees of freedom and also a generating set of gauge transformations for a theory whose dynamics is governed by a second-order Lagrangian that describes the evolution of an Abelian tensor gauge field of degree $(k + 1)$.

In this paper we consider a class of discrete dynamical systems obtained through mapping technique from 3/2 d.o.f. Hamiltonian systems and we present some results concerning the existence and the position of internal transport barriers and a method for creating transport barriers in a prescribed position. Then we apply the results for mappings that model the magnetic field configuration in tokamaks and we interpret them.

A generalized fractional transport equation for particles is proposed and studied. This model includes local effects (through Fokker-Planck equation) and non-local spatial effects (Levy flights modelled using fractional derivatives). External perturbations are introduced in the model as source term in the fractional equation. A specific code based on matrix approach is built in order so study numerically the model.

The generalized conditional symmetry (GCS) method is applied to a specific case of the Klein–Gordon–Fock (KGF) equation with central symmetry. We first investigate the conditions which yield the KGF equation that admits special class of second-order GCSs. The determining system for the unknown functions is solved in several special cases. New symmetry operators and related exact solutions, different in form and structure from the ones obtained using other methods, are pointed out. Several surface plots of solutions are displayed.

In this paper the noncommutative gravity is treated as a gauge theory of the non-commutative $SO(2, 3)_\star$ group on the noncommutative space with the constant non-commutativity. The enveloping algebra approach and the Seiberg-Witten map are used to relate noncommutative and the commutative gauge theory. By combining different actions a noncommutative gravity model is constructed in such a way that the cosmological constant term is not present in the commutative limit, but it is generated by the noncommutativity and it appears in the higher order expansion. We calculate the second order correction to this model and obtain terms that are zero-th, first, ... and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the low energy limit.

We examine a classical and quantum dynamics of systems described by the DBI-type Lagrangian with tachyon-like potentials and corresponding DBI Lagrangians on (non-)Archimedean spaces. The dynamic of tachyon fields in spatially homogeneous and in zero-dimensional limits is analysed. A formalism for connecting a wide class of potentials and DBI Lagrangians with the locally equivalent canonical Lagrangians is presented. The results for exponentially decaying and inverse cosine hyperbolic are reviewed and for the potentials of the form $V(x) = x^{-n}$ are discussed in more details. Classical actions and corresponding quantum propagators are calculated for these potentials in the Feynman path integral approach, on both Archimedean and non-Archemedean spaces.

We present a one-parameter families of mKdV-type equations related to ${\frak g} \simeq D_{4}^{(1)}$ and ${\frak g} \simeq D_{4}^{(2)}$. They are a set of partial differential equations, integrable via the inverse scattering method. They admit a Hamiltonian formulation and the corresponding Hamiltonians are also given. The Riemann-Hilbert problems for the two Lax operators are formulated on a set of $2h$ rays $l_nu$. We show that to each ray $l_\nu$ one can relate a subalgebra of $\frak g$ which is direct sum of $sl(2)$ subalgebras.

In this review the modulation instability of NLS type equations is investigated using the statistical approach developed by Alber (1978). Two representative equations are studied, namely the well known cubic NLS eq. and a derivative NLS one. Improving the existing results in the literature (for dNLS eq.) only the Gaussian approximation is used in the decoupling of higher order two point correlation functions that appear in writing the kinetic equation satisfied by the two-point correlation function $\rho(1, 2) = \langle \Psi(x_1)\Psi^*(x_2) \rangle$. Explicit results are obtained for a Lorentzian initial distribution function, the instability being restricted to the long wave lengths region of the perturbations and the long range correlations in the initial state. This seems to be an universal behavior in this class of equations.

We consider the standard model up to the second order of the perturbation theory (in the causal approach) and derive the most general form of the interaction Lagrangian for an arbitrary number of Higgs fields.

We study a family of cubic systems with degenerate infinity introduced in the paper [Chavarriga et al., Integrability of cubic systems with degenerate infinity, Differential Equations Dynam. Systems 6 (1998), 425-438]. For systems of the family having a monodromic singularity at the origin the sets in the space of parameters corresponding to the systems with a local analytic first integral are found.

We study the role of Chern–Simons couplings for the appearance of enhanced symmetries of Cremmer–Julia type in various theories. It is shown explicitly that for generic values of the Chern–Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer–Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras.

The paper investigates a specific type of nonlinear dynamical systems represented by electronic circuits with nonlinear elements, known as Chua circuits. Despite they are described by simple equations, with only one nonlinear function, they have a complex behavior, very rich in dynamical states and with interesting transitions from chaos to regular dynamics. The interest will be given to the problem of controlling the chaotic behavior using a technique specific for Hamiltonian systems. The main results which will be reported will concern the possibility of attaching a Lagrangian function and of transforming the Chua system into a variational one. The optimization of the dynamics will be achieved through a quadratic control term.

In this note we propose new flux configurations for M-theory compactifications which preserve supersymmetry and nevertheless give rise to potentials for space-filling M2 branes.

In the present paper the decorrelation trajectory method has been used in order to calculate some averaged quantities of interest for stochastic anisotropic magnetic field lines in a sheared slab magnetic configuration for several values of the magnetic Kubo number, of the shear parameter and of the stochastic anisotropy parameter. The study has shown that a rich variety of transport behaviors can be found by varying the previously parameters, mainly by varying the anisotropy parameter in the plane perpendicular to the average magnetic field.

In order to study the transport of charged particles (ions, electrons) or dust particles in tokamak plasma, we have used the numerical simulations method based on the TURBO code. The method can be applied for any value of the Kubo numbers $K$, $K_s$ specific for the analyzed problem. The particle’s transport depends on the level of turbulence and on the inhomogeneity of the magnetic field. The magnetic shear is shown to have a contribution in order to obtain the plasma stability. We present the specific autocorrelations for the electrostatic fluctuations implementing the TURBO code and we have calculated and interpreted the radial and poloidal mean squared displacements, the kurtosis and the skewness.

Hamiltonians related to foliations, analogous to Riemannian foliations, are studied in the paper. One prove that each of the following data: a bundle-like Hamiltonian, a transverse hyperregular Hamiltonian, a hyperregular Hamiltonian foliated cocycle or a geodesic orthogonal property are equivalent to the fact that a foliation have to be a Riemannian one. Relations with the analogous Lagrangian case, considered previously by the authors, are studied.

The analysis of the LHC data aims to minimize the vast amounts of data and the number of observables used. After slimming and skimming the data, the remaining terabytes of ROOT files hold a selection of the events and a flat structure for the variables needed that can be more easily inspected and traversed in the final stages of the analysis. PROOF has an efficient mechanism to distribute the analysis load by taking advantage of all the cores in modern CPUs through PROOF-Lite, PROOF Cluster or PROOF on Demand tools. In this paper we compared performance of different methods of file access (NFS, XROOTD, RFIO). The tests were done on Bucharest ATLAS Analysis Facility.

The massive Maxwell–Chern–Simons model and a higher order derivative extension of it are analyzed from the point of view of the Hamiltonian path integral quantization in the framework of the gauge-unfixing approach.

We investigate the complex structure of the conifold $C(T^{1,1})$ basically making use of the interplay between symplectic and complex approaches of the Kähler toric manifolds. The description of the Calabi-Yau manifold $C(T^{1,1})$ using toric data allows us to write explicitly the complex coordinates and apply standard methods for extracting special Killing forms on the base manifold. As an outcome, we obtain the complete set of special Killing forms on the five-dimensional Sasaki-Einstein space $T^{1,1}$.

We review the Coset Space Dimensional Reduction (CSDR) scheme and the best model constructed so far. Then we present some details of an alternative CSDR programme, in which the extra dimensions are considered to be fuzzy. Specifically, we present a four-dimensional ${\cal N} = 4$ SYM theory, orbifolded by $\mathbb{Z}_3$, which mimics the behaviour of a dimensionally reduced ${\cal N} = 1$, ten-dimensional gauge theory over a set of fuzzy spheres at intermediate high scales. This leads to the trinification GUT $SU(3)^3$ at slightly lower, which in turn can be spontaneously broken to the MSSM in low scales.