New series representation for Madelung constant

A new series representation of the Madelung constant is given. We represent Madelung constant as a sum of an exact term plus an exponentially fast converging series. The remarkable result is that even if the series part is discarded, one obtains Madelung constant correct up to ten good decimal figures. This, to the best of our knowledge, may be the fastest converging series representation of the Madelung constant. A few other important identities are also obtained

Distributed Function Computation with Confidentiality

A set of terminals observe correlated data and seek to compute functions of the data using interactive public communication. At the same time, it is required that the value of a private function of the data remains concealed from an eavesdropper observing this communication. In general, the private function and the functions computed by the nodes can be all different. We show that a class of functions are securely computable if and only if the conditional entropy of data given the value of private function is greater than the least rate of interactive communication required for a related multiterminal source-coding task. A single-letter formula is provided for this rate in special cases.Comment: To Appear in IEEE JSAC: In-Network Computation: Exploring the Fundamental Limits, April 201

Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [M. A. Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation

On the Structure of ZnI2{\rm ZnI_2}

A new structure for ${\rm ZnI_2}$ is proposed which it exists in tetragonal state. In this structure the ${\rm ZnI_2}$ molecule exists in a nonlinear array and forms the basis of the tetragonal unit cell with one basis per unit cell. The structural analysis based on the reflections listed in ASTM 30-1479 shows that the proposed structure is correct.Comment: six pages and four figures. Manuscript prepared in RevTe

On Firms' Preferences for Product Differentiation

We examine firms' preferences for product differentiation when a firm has a demand-side and/or a cost-side advantage over its competitor. We show that if the magnitude of these advantages is small, then both firms prefer more differentiated products. However, if the magnitude of demand-side (cost-side) advantage is larger, then only the advantaged (disadvantaged) firm prefers more differentiated products.Competition