It is pointed out that one-component φ theory in four dimensions has a non-perturbative sector that can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a consequence, the φ-theory turns out to have, in the broken symmetry phase, a remarkably rich spectrum of physical states corresponding to membrane excitations. A numerical...

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description ...

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect t...

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m + 3m+ 9 and non-isomorphic simplest cubic fields. By applying R. Okazaki’s result for non-isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m+ 9.

It is usually said that two-dimensional (1+1) gauge theories are trivial. In the continuum there are no transverse degrees of freedom to sustain any dynamics. Likewise, in the lattice formulation, the system factorizes (after gauge fixing) and a partition function reduces to a simple one-plaquette integral [1–3]. This picture neglects boundary conditions. It is well known [4] that, e.g., Quantu...

We obtain multiple non-trivial solutions of the Neumann problem for p-Laplacian systems using Morse theory.

We address the feasibility (existence of non-trivial solutions) of the pair of alternative conic systems of constraints

In this paper we are dealing with entire solutions of a general class of anisotropic equations. Under some appropriate conditions on the data, we show that the corresponding equations cannot have non-trivial positive solutions bounded from above.