Abstract We present LT-PDR , a lattice-theoretic generalization of Bradley’s property directed reachability analysis (PDR) algorithm. identifies the essence PDR to be an ingenious combination verification and refutation attempts based on Knaster–Tarski Kleene theorems. introduce four concrete instances LT-PDR, derive their implementation from generic Haskell experimentally evaluate them. also c...

An exercise in Garrett Birkhoff’s renowned book on lattice theory asks for a lattice with 18 elements and of length 5 that has a dual automorphism, but no involutory dual automorphism. This note constructs a smaller lattice, 15 elements and length 4, with the same property.

In this work, we study some general property of a strongly correlated electron system defined on a lattice. Assuming that the lattice system exhibits off-diagonal long-range order, we show rigorously that this assumption would lead to Meissner effect. This generalizes previous results of continuous case to a lattice electron system.

Single phase Eu doped GdMnO3 ceramics were prepared using solid state reaction route. Several different characterization techniques were used to investigate the structural and magnetic properties of the samples, including X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDX) and Vibrating Sample Magnetometer (VSM). All samples indicated single p...

We argue that the “vortex-finding” property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. We explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of ga...

We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.

A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If there is an integer bilinear map s such that f(s(x,y)) = f(x)f(y) for all vectors x and y from the integer 2-dimensional lattice, then the form f has semigr...

A 1977 theorem of T. Harris states that an attractive spin system preserves the class of associated probability measures. We study analogues of this result for measures that satisfy various conditional positive correlations properties. In particular, we show that a spin system preserves measures satisfying the FKG lattice condition (essentially) if and only if distinct spins flip independently....

The most natural way of ordering portfolios is by comparing their payoffs. If a port­ folio has a payoff higher than the payoff of another portfolio, then it is greater than the other portfolio. This order is called the portfolio dominance order. An important property that a portfolio dominance order may have is the lattice property. It requires that the supremum and the infimum of any two port...