In this note we present the Green's functions and density of states for most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, Lieb lattice. Though results are well know, hope that their derivation performed in a uniform way is some pedagogical value.

We consider a set of voters who express preferences about two alternatives, indifferences included. characterize the class all strategy-proof and anonymous social choice functions by means geometric property related to an integer triangular grid representing number supporting each alternatives.

Adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from three-dimensional (3-D) perfectly conducting bodies. This algorithm employs the conventional moment method (MM) using the subsectional triangular patch basis functions and a special matrix transformation, which is derived from solving the Fredholm equation of the first kind by the multiscale technique. Thi...

In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences functions defined on a compactsubset real two-dimensional space. Based upon new convergencemethod, prove Korovkin-type approximation theorem. Finally, give some further developments.

We consider a classical linear conjugation problem for analytic vector-valued functions on piecewise smooth curve with triangular matrix coefficient in weighted H¨older spaces. In the twodimensional case, conditions existence of solution are found, this is given, and construction canonical function analyzed detail.

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These parti...

We apply Plechko’s Grassmann path-integral method to Ising cylinders of rectangular, triangular, and hexagonal lattices to obtain the analytic solutions of free energies for the periodic and antiperiodic boundary conditions in the joined circumferences of the cylinders. These analytic solutions are used to analyze the scaling functions of the interfacial tensions for isotropic and anisotropic c...

We investigate topological properties of Julia sets of iterated elliptic functions of the form g = 1/℘, where ℘ is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by C − {0}, and they all have a superattracting fixed point at zero and three other distinct critical values. We prove that the Julia set of g is either Cantor or connected, and we obtain...

Abstract A fuzzy EOQ model with backorders is considered in which the costs like setup, holding and penalty price are assumed as triangular FN (fuzzy numbers). Graded mean integration approach more simple accurate employed to defuzzify cost functions. The illustrated numerical examples compute optimal values.

Kim and Nelson[14] propose sequential procedures for selecting the simulated system with the largest steady-state mean from a set of alternatives that yield stationary output processes. Each procedure uses a triangular continuation region so that sampling stops when the relevant test statistic first reaches the region’s boundary. In applying the generalized continuous mapping theorem to prove t...