Related papers: Variational representations for N-cyclically monot…

We discuss chirality-preserving nilpotent deformations of four-dimensional N=(1,1) Euclidean harmonic superspace and their implications in N=(1,1) supersymmetric gauge and hypermultiplet theories, basically following [hep-th/0308012] and…

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two…

Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The model in this regime is solvable and the corresponding exact beta function is…

We identify a cubic holomorphic constraint that subtends the total breaking of N=2 supersymmetry in a vector multiplet and exhibit its microscopic origin. The new constraint leaves behind, at low energies, a vector and the two goldstini, in…

We carry out the N=1 supersymmetrization of a physical non-Abelian tensor with non-trivial consistent couplings in four dimensions. Our system has three multiplets: (i) The usual non-Abelian vector multiplet (VM) (A_\mu{}^I, \lambda^I),…

A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…

Let $\mathcal{H}$ be a complex Hilbert space and $T:\mathcal{H}\to \mathcal{H}$ be a contraction. Let $$A_nf=\frac{1}{n}\sum_{j=1}^nT^jf$$ for $f\in \mathcal{H}$. Let $(n_k)$ be a lacunary sequence, then there exists a constant $C_1>0$ such…

Let $n$ and $r$ be integers with $n-2\ge r\ge 3$. We prove that any $r$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with spectral radius $\lambda(\mathcal{H}) > \binom{n-2}{r-1}$ must contain a Hamiltonian Berge cycle unless…

We consider problems about packing and counting Hamilton $\ell$-cycles in hypergraphs of large minimum degree. Given a hypergraph $\mathcal H$, for a $d$-subset $A\subseteq V(\mathcal H)$, we denote by $d_{\mathcal H}(A)$ the number of…

We provide a short proof of the theorem that every real multivariate polynomial has a symmetric determinantal representation, which was first proved in J. W. Helton, S. A. McCullough, and V. Vinnikov, Noncommutative convexity arises from…

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…

We consider D=6, N=1, Z_M orbifold compactifications of heterotic strings in which the usual modular invariance constraints are violated. It is argued that in the presence of non-perturbative effects many of these vacua are nevertheless…

In this paper, we characterize arbitrary polynomial vector fields on $S^n$. We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional sphere $S^{2n-1}$ to be Hamiltonian. Additionally, we…

Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the…

We study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions $D=d+1$. Starting in a `Coulomb' phase, topological defects of dimension $d-h-1$ ($(d-h-1)$-branes) may…

The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields in one variable over a henselian valued field with…

We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally…

The family of Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit a ${\cal N} = 2$ supersymmetric extension of the same kind as that introduced by Freedman and Mende…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $X_\varepsilon$ $$ X_\varepsilon : \left\{ \begin{array}{llr} \dot{x}=\;\; H_y+\varepsilon f(x,y)\\…