Search results for "Category theory"

Analytic first and second derivatives for the CCSDT-n (n = 1–3) models: a first step towards the efficient calculation of CCSDT properties

2000

Analytic first and second derivatives of the energy are implemented for closed-shell systems described by the CCSDT-n (n=1, 1b, 2 and 3) and CC3 electron correlation models. A detailed discussion of the computational requirements of these calculations is given, along with diagrammatic formulas for all relevant quantities. The method is applied to calculate the nuclear magnetic shielding of H2O, CO and N2O and the structure and properties of propadienylidene.

Experimentally constrained density-functional calculations of the amorphous structure of the prototypical phase-change materialGe2Sb2Te5

2009

Phase change materials involve the rapid and reversible transition between nanoscale amorphous $(a\text{\ensuremath{-}})$ and crystalline $(c\text{\ensuremath{-}})$ spots in a polycrystalline film and play major roles in the multimedia world, including nonvolatile computer memory. The materials of choice are alloys of Ge, Sb, and Te, e.g., ${\text{Ge}}_{2}{\text{Sb}}_{2}{\text{Te}}_{5}$ (GST) in digital versatile disk--random access memory. There has been much speculation about the structure of $a\text{\ensuremath{-}}$ GST, but no model has yet received general acceptance. Here we optimize the structure by combining the results of density-functional calculations with high-energy x-ray diffr…

Mechanisms at structural phase transitions

2007

Abstract Structural phase transitions in crystalline solids are accompanied with the change of symmetry. After EHRENFEST [Ehrenfest, P., Phasenumwandlungen im ublichen und erweiterten Sinn, klassifiziert nach den entsprechenden Singularitaten des thermodynamischen Potentials. Proc. Kon., Amsterdam Acad., 1933, 36(Suppl 75b), 153–157] they can be distinguished between first and second order transitions. Two examples for first and second order transitions will be discussed in order two elaborate the characteristic features. The statements are verified by diffraction experiments; the second order transitions will be discussed on the basis of the LANDAU [Landau, L. and Lifshitz, E.M., Lehrbuch …

Categorical Modeling Method of Intelligent WorkFlow

2018

A category as well as a model is a mixture of graphical information and algebraic operations. Therefore, category language seems to be the most general to describe the models. It can provide us with the features that must characterize both the DSL language and the Modeling Method concept.

A new synthetic entry into the tricyclo[3.3.0.03,7] octane skeleton

1987

Abstract A short synthesis of dimethyl tricyclo[3.3.0.03,7] octane-1,5-dicarboxylate, 13 , and its 3,7-dimethyl-derivative, 14 , by iodine oxidation of the bis-enolate derived from the corresponding dimethyl cis -bicyclo[3.3.0] octane-3,7-dicarboxylate, 11 or 12 , is described.

Adjacent vertices can be hard to find by quantum walks

2018

Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element. We show that if the search space contains more than one marked element, their placement may drastically affect the performance of the search. More specifically, we study search by quantum walks on general graphs and show a wide class of configurations of marked vertices, for which search by quantum walk needs Ω(N) steps, that is, it has no speed-up over the classical exhaustive search. The demonstrated configurations occur for certain placements of two or more adjace…

On the subset sum problem for finite fields

2021

Abstract Let G be the additive group of a finite field. J. Li and D. Wan determined the exact number of solutions of the subset sum problem over G, by giving an explicit formula for the number of subsets of G of prescribed size whose elements sum up to a given element of G. They also determined a closed-form expression for the case where the subsets are required to contain only nonzero elements. In this paper we give an alternative proof of the two formulas. Our argument is purely combinatorial, as in the original proof by Li and Wan, but follows a different and somehow more “natural” approach. We also indicate some new connections with coding theory and combinatorial designs.

Epichristoffel Words and Minimization of Moore Automata

2014

This paper is focused on the connection between the combinatorics of words and minimization of automata. The three main ingredients are the epichristoffel words, Moore automata and a variant of Hopcroft's algorithm for their minimization. Epichristoffel words defined in [14] generalize some properties of circular sturmian words. Here we prove a factorization property and the existence of the reduction tree, that uniquely identifies the structure of the word. Furthermore, in the paper we investigate the problem of the minimization of Moore automata by defining a variant of Hopcroft's minimization algorithm. The use of this variant makes simpler the computation of the running time and consequ…

Basic Sequences in the Dual of a Fréchet Space

2001

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.