We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in terms of the orbifold of a single free boson compactified on a circle of radius r=1; we adapt their results to include disorder operators. Using these boundary s...

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard, but can be solved in polynomial time in some restricted graph classes, such as P4-free graphs or 2K2-free graphs. For classes defined by finitely many forbidden induced subgraphs, the boundary separating diffi...

This paper introduces an isometric extension procedure for Riemannian manifolds with boundary, which preserves some lower curvature bound and produces a totally geodesic boundary. As immediate applications of this construction, one obtains in particular upper volume bounds, an upper intrinsic diameter bound for the boundary, precompactness, and a home-omorphism finiteness theorem for certain cl...

We consider the van der Waals’ free energy functional, with scaling parameter ε, in the plane domain R+ × R+, with inhomogeneous Dirichlet boundary conditions. We impose the two stable phases on the horizontal boundaries R+×{0} and R+×{∞}, and free boundary conditions on {∞}×R+. Finally, the datum on {0} ×R+ is chosen in such a way that the interface between the pure phases is pinned at some po...

For a Schr\"odinger operator on the plane $\mathbb{R}^2$ with electric potential $V$ and Aharonov--Bohm magnetic field we obtain an upper bound number of its negative eigenvalues in terms $L^1(\mathbb{R}^2)$-norm $V$. Similar to Calogero's one dimension, result is true under monotonicity assumptions Our proof method relies generalisation operator-valued potentials. We also establish similar for...

The definition of a Middle–Upper Pleistocene Subseries boundary is discussed. This boundary is at present not formally defined, but has up till now been placed at the beginning of the Last Interglacial (Eemian, Mikulino, Sangamonian, etc.) or Marine Isotope Stage 5. Although it may seem attractive to define the boundary in an ocean sediment sequence, the inherent imprecision of most of such seq...

There exist several papers about boundary value problems with impulŽ sive effects at fixed points, but the different techniques employed for w x w x instance, limit arguments in 1, 3 , topological degree 10 , fixed point w x w x. theorems 9 or set-valued maps 2 do not seem applicable to problems with impulses at variable times. Ž w x. Recently, some comparison principles have appeared see 4, 8 ...

in this paper, the direct extrusion process of bimetallic rods in conical dies is analyzed by an improved upper bound method. the deformation zone is subdivided into six smaller zones and by considering a non-spherical entrance boundary to the deformation zone, a velocity field is presented which is different from velocity fields employed in previous studies. the total power consumption of the ...

In this paper, an analytical method for noncircular shape extrusion is presented. Using this method, non-linear deformation field can be described with Hermit cubic spline which is prescribed by the boundary conditions of the die at its entryand exit. The upper bound method has been used to obtain optimum coefficient of the tangential boundary conditions. The results show that the optimum tange...

In this paper, an analytical method for noncircular shape extrusion is presented. Using this method, non-linear deformation field can be described with Hermit cubic spline which is prescribed by the boundary conditions of the die at its entryand exit. The upper bound method has been used to obtain optimum coefficient of the tangential boundary conditions. The results show that the optimum tange...