A sufficient condition for the energy of a point such that a local minimum of the energy exists at every triangular lattice point is obtained. The condition is expressed as a certain type of strong convexity condition of the function which defines the energy. New results related to Riemann sum of a function with such the convexity and new inequalities related to sums on triangular lattice point...

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quantities q, |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symmetry...

In the digital era we live in, efficient representation of data generated by a discrete source and its reliable transmission are unquestionable need. In this work we have focused on source coding taking image as source. Lattice Vector Quantization (LVQ) can be used for source coding as well as for channel coding. (LVQ) with Generator Matrix (GM) and codebook is implemented. When implementation ...

Measurements of the longitudinal nuclear spin relaxation time, Ti, in molecular gases are analogous to non-resonant absorption measurements; Ti is determined primarily by that part of the spin-lattice interaction which couples free molecular states of the same energy. The contribution to Ti of matrix elements of the spin-lattice interaction between rotational states of different energy is quenc...

Using lattice simulations of a one-component (λΦ 4) 4 theory, we have measured the energy spectrum ω(k) in the broken phase at various lattice sizes. Our data show that the energy-gap ω(0) is not the 'Higgs mass' M h but an infrared-sensitive quantity that, conceivably, vanishes in the infinite-volume limit.

and Energy Functions in Solvable Lattice Models Atsushi Nakayashiki and Yasuhiko Yamada Graduate School of Mathematics, Kyushu University Abstract The relation between the charge of Lascoux-Schuzenberger and the energy function in solvable lattice models is clari ed. As an application, A.N.Kirillov's conjecture on the expression of the branching coe cient of c sln=sln as a limit of Kostka polyn...

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quan­ tities q , |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symme...

In this paper we propose 2D constellation design based on geometric lattice for circularly symmetric sources as it allows easier performance evaluation. Geometric Z lattice quantization of Gaussian source is analyzed. Constellation design provides lower energy for the same error probability. It enables more efficient data transmission and energy saving for wireless systems. The exact error prob...

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Where...

Title of dissertation: TOPICS IN LATTICE QCD AND EFFECTIVE FIELD THEORY Michael I. Buchoff, Doctor of Philosophy, 2010 Dissertation directed by: Associate Professor Paulo Bedaque Department of Physics Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The ...