In lattice theory, lattice polynomials have been defined as well-formed expressions involving variables linked by the lattice operations ∧ and ∨ in an arbitrary combination of parentheses. In turn, such expressions naturally define lattice polynomial functions. For instance, p(x1, x2, x3) = (x1 ∧ x2) ∨ x3 is a 3-ary lattice polynomial function. The concept of lattice polynomial function can be ...

spear-like martensite thermally formed in the same alloy in several respects such as in shape, lattice invariant shear, habit plane and orientation relationship, even though both have the same crystal structure and lattice parameters. The lattice invariant strain of the martensite was found to be stacking faults on the basal plane, and a defectless region was observed at the middle of the marte...

‘Lattice parameters determined from the synchrotron X-ray diffraction scans of the cubic 200 and tetragonal 220/004 Bragg peaks. Fits to the cubic lattice parameter (black solid line) and the average tetragonal lattice parameter (= 2atet + ctet)/3 (blue solid line), were used to determine the linear coefficients of thermal expansion of 1.95 × 10−4 K−1 (cubic) and 2.66 × 10−4 K−1 (tetragonal). T...

We investigate generalizations of the Charlier polynomials on the lattice N, on the shifted lattice N + 1 − β, and on the bi-lattice N ∪ (N + 1 − β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to solutions of the fifth Painlevé equation PV (which can be transformed to the third Painlevé equation). Initial conditions for differe...

Due to their light weights and high load carrying capacities, composite structures are widely used in various industrial applications especially in aerospace industry. Stiffening ribs are the main features of lattice type composite structures. Strength to weight ratio is known to be as one of the most critical design parameter in these structures. In this study, the effect of some parameters su...

The problem of finding a lattice vector approximating a shortest nonzero lattice vector (approximate SVP) is a serious problem that concerns lattices. Finding a lattice vector of the secret key of some lattice-based cryptosystems is equivalent to solving some hard approximate SVP. We call such vectors very short vectors (VSVs). Lattice basis reduction is the main tool for finding VSVs. However,...

Lattice QCD simulations are routinely done nowadays using highly-improved actions, which are designed to remove the leading errors arising from the discretization of the continuum theory. Improved actions can be designed from both perturbative and nonperturbative considerations. In this review I describe techniques for doing the higher-order perturbation theory (PT) calculations that are necess...

The low energy eigenmodes of the continuum QCD Dirac operator are extended, but on the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes. These nonphysical modes can introduce strong lattice artifacts for observables that are sensitive to chiral symmetry, especially in mixed action simulations. We study how these lattice artifacts depend on the parameters ...

The NTRU Signature Scheme (NSS) is a digital signature scheme based on a hard lattice problem. This lattice problem also underlies the NTRU Public Key Cryptosystem described in [1]. In this section we remind the reader of the standard description of the NTRU lattice problem in terms of products of polynomials in convolution rings. For further details, see [1]. Fix three positive integer paramet...

We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i) a better statistical behavior as estimators of the topological charge density on the lattice, i.e. less noisy; (ii) a multiplicative renormalization much cl...