Search results for "model theory"

Guaranteed Error Bounds I

2014

In Chap. 3, we discussed the main ideas of fully reliable error control methods and the corresponding numerical algorithms with the paradigm of simple elliptic type problems. This chapter is intended to show a deep connection between a posteriori estimates of the functional type and physical relations generating the problem. Also, the goal of this chapter is to consider a wider set of problems arising in various applications and explain things in terms of computational mechanics. For this purpose, we begin with a simple class of mechanical problems (straight beams) and after that consider curvilinear beams and more complicated models of continuum mechanics (linear elasticity, viscous fluids…

On a projective representation of chain geometries

1984

We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.

Sequent Depth Ratio of a B-Jump

2011

A B-jump is defined as the jump having the toe section located on a positively sloping upstream channel and the roller end on a downstream horizontal channel. This jump often occurs in the stilling basins with a horizontal bottom and located downstream of a steep channel. For a B-jump, a completely theoretical approach is not sufficient to solve the momentum equation and to establish the sequent depth ratio. In this paper, by using the laboratory measurements carried out in this investigation, some available empirical relationships useful for estimating the sequent depth ratio are tested. Then, by using the Π theorem of the dimensional analysis and the incomplete self-similarity theory, a g…

Other definitions of Sobolev-type spaces

2015

Sobolev-Poincaré implies John

1995

We establish necessary conditions for the validity of Sobolev-Poincaré type inequalities. We give a geometric characterisation for the validity of this inequality for simply connected plane domains.

How to Comprehend Large and Complicated Systems

2002

The basic problem at early analysis stage of the development life cycle is how to quickly comprehend a large and complicated system. One of the ways to comprehend such a system is to build an object model, as it was suggested by the pioneers of object modelling approach such as J.Rumbaugh1 and J.Martin2. In up-to-date terminology it means building a UML class diagram. The authors have got convinced in their everyday practice on extreme efficiency of this type of modelling, though at the same time a significant experience for this job is also required. To make this job easier, a modelling methodology must be developed. The goal of this paper is, on the one hand, to give some methodological r…

A topology-constrained distance network algorithm for protein structure determination from NOESY data.

2005

This article formulates the multidi- mensional nuclear Overhauser effect spectroscopy (NOESY) interpretation problem using graph theory and presents a novel, bottom-up, topology-con- strained distance network analysis algorithm for NOESY cross peak interpretation using assigned resonances. AutoStructure is a software suite that implements this topology-constrained distance net- work analysis algorithm and iteratively generates structures using the three-dimensional (3D) protein structure calculation programs XPLOR/CNS or DY- ANA. The minimum input for AutoStructure in- cludes the amino acid sequence, a list of resonance assignments, and lists of 2D, 3D, and/or 4D-NOESY cross peaks. AutoStru…

A microscopic monomeric mechanism for interpreting intrinsic optical bistability observed in Yb3+-doped bromide materials

2004

We present a mechanism able to show intrinsic bistable behaviour involving single Yb3+ ions embedded into bromide lattices, in which intrinsic optical bistability (IOB) has been observed. The mechanism is based on the experimentally found coupling between the Yb3+ ion and the totally symmetric local mode of vibration of the [YbBr6]3- coordination unit. The model reproduces the IOB observed in CsCdBr3:1% Yb3+ and allows to understand the experimentally found presence of the phenomenon in the other bromides, but its absence in Cs3Lu2Cl9:Yb3+.

Computerized Interpretation of H P L C Chromatogramms by Means of Absorbance Ratio Method and Derivative Spectroscopy

1985

As in other chromatographic processes it is the aim of high pressure liquid chromatography (HPLC) to identify the components of a mixture, whereby there may be some information on the class of substances in question. The analytical procedure can shortly be desribed as follows. The mixture is injected in a mobile phase (solvent) and passes a column where the separation takes place. The separated components leave the column at different retention times. A following detection device generates a signal as a function of concentration (chromatographic peak). Usually the components are identified by relating retention times of external standards to the times of occurence of chromatographic peaks. …

Importance of the Window Function Choice for the Predictive Modelling of Memristors

2021

Window functions are widely employed in memristor models to restrict the changes of the internal state variables to specified intervals. Here, we show that the actual choice of window function is of significant importance for the predictive modelling of memristors. Using a recently formulated theory of memristor attractors, we demonstrate that whether stable fixed points exist depends on the type of window function used in the model. Our main findings are formulated in terms of two memristor attractor theorems, which apply to broad classes of memristor models. As an example of our findings, we predict the existence of stable fixed points in Biolek window function memristors and their absenc…