In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model (square lattice two lines). All these lead to representation N=2 algebra. We also extrapolate ideas for 3-leg triangular on cylinder.

We call grid n-ogon each n-vertex orthogonal simple polygon, with no collinear edges, that may be placed in a ) 2 / ( ) 2 / ( n n × unit square grid. In this paper we consider the Minimum Vertex Guard problem for this class of orthogonal polygons. As a step for the resolution of this general problem, we are going to study it for an interesting subclass of grid n-ogons: the SPIRAL grid nogons, w...

Let Gp be a random graph on 2 d vertices where edges are selected independently with a xed probability p > 1 4 , and let H be the d-dimensional hypercube Q d. We answer a question of Bollobb as by showing that, as d ! 1, Gp almost surely has a spanning subgraph isomorphic to H. In fact we prove a result which can be applied to many other graphs, improving also previous results for the lattice, ...

Mesoporous thin films based on neutral, porphyrin-bridged, tetrarhenium "square" compounds (metallacycles) display permeability to molecules smaller than the dimensions of an individual square cavity, but blocking behavior toward larger species (see schematic representation). The characteristic permeant size cutoff can be systematically and predictably manipulated by decorating the walls of the...

11.1 Prime fields of odd characteristic 201 Representations and reductions • Multiplication • Inversion and division • Exponentiation • Squares and square roots 11.2 Finite fields of characteristic 2 213 Representation • Multiplication • Squaring • Inversion and division • Exponentiation • Square roots and quadratic equations 11.3 Optimal extension fields 229 Introduction • Multiplication • Exp...

This paper first reviews some basic properties of cryptographic hash function, secret sharing scheme, and Latin square. Then we discuss why Latin square or its critical set is a good choice for secret representation and its relationship with secret sharing scheme. Further we enumerate the limitations of Latin square in a secret sharing scheme. Finally we propose how to apply cryptographic hash ...

where df{n) denotes the number of divisors of n, d = i (mod 4). In literature there are several proofs of (1) and (2). For instance, M. D. Hirschhorn [7; 8] proved (1) and (2) using Jacobi's triple product identity. S. Bhargava & Chandrashekar Adiga [4] have proved (1) and (2) as a consequence of Ramanujan's ^ summation formula [10]. Recently R. Askey [2] has proved (1) and also derived a formu...

Previous literature on the study of identity representation in political discourse has been mainly concerned with the spoken discourse and the representation of self. However, the way different groups of political agents represent others’ identities across languages has not attracted much attention. Using Wodak’s (2007) Discourse Historical approach to CDA, the present study investigates the wa...