About Strong Dependence of the Complexity of Analysis of the Random 3-CNF Formulas on the Ratio of Number of Clauses to the Number of Variables

The results of a computational experiment on the assessment of the complexity of proving the unsatisfiability of random 3-CNF logical formulas are presented. The dependence of the complexity of this proving on the R-ratio of the number of clauses to the number of variables is demonstrated. The computational experiment was carried out for the range of the N-number of variables from 256 to 512. An exponential dependence of the median complexity of proving the unsatisfiability of formulas on the number of variables was revealed for each of R value: 4.3, 4.6, 5.0, 5.5, 6.0. A formula is constructed that approximates the results of the experiment. According to this formula the exponential component of the median complexity of the analysis of random 3-CNF is estimated as 2 to the power N / (8.4R-17.8).

The Mayr-Pentegov Model of Electric Arc Involving the Use of the Exponential Function and Enabling the Approximation of Static Characteristics

The article presents the justified use of functions containing the exponential component for the approximation of the static current-voltage characteristics of electric arc. The Author proposed a new function approximating the above-named characteristics which were next used in the mathematical Mayr-Pentegov model, expressed in two, i.e. differential and integral, forms. The two forms constituted the basis enabling the development of macromodels using controlled voltage and current sources. The article also presents families of dynamic current-voltage characteristics obtained through the simulation of processes in a circuit containing macromodels of arc powered by the source of current characterised by sinusoidal and trapezoidal waveforms and various frequency. The article demonstrates the usability of the proposed variants of the Mayr-Pentegov model.

Decomposing the composite face effect: Evidence for non-holistic processing based on the ex-Gaussian distribution

Composite faces fuse the top and bottom halves from two different faces to create a powerful illusion of a novel face. It has been argued that composite faces are processed holistically, namely that the constituent face parts are perceived as a template, rather than independent features. This study sought to uncover the locus of the composite face effect by relating its empirical reaction time distributions to theoretical ex-Gaussian parameters. The results showed that the composite face effect for unfamiliar (Experiment 1) and familiar (Experiment 2) faces is generated by pure changes in the exponential component of the ex-Gaussian distribution. This held true for both partial and complete design measures. The exponential component has been attributed to working memory and attentional processes. The results suggest the involvement of attentional and working memory processes in the composite face effect and in the perception of faces in general. They cast doubts on the holistic nature of face processing. The results also provide important constraints on future computational theories of the effect.

Digitized Multi-Exponential Deep-Level Transient Spectroscopy (DLTS) Using the Padé-Laplace Algorithm

We apply the Padé-Laplace algorithm to automatically extract from DLTS multi-exponential transient decay measurements, the amplitude and the time constant of each discrete exponential component as well as the number of components without a priori assumption. Then, after setting restriction on the resolution of the multi-exponential problem itself due to noise, we present the field of this method numerical validity. Finally, the performance obtained on real signals is shown.

On the Skewness of Order Statistics in Multiple-Outlier Models

Kochar and Xu (2009) proved that a parallel system with heterogeneous exponential component lifetimes is more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. In this paper we extend this study to the generalk-out-of-nsystems for the case when there are only two types of component in the system. An open problem proposed in Pǎltǎnea (2008) is partially solved.

On the Skewness of Order Statistics in Multiple-Outlier Models

Kochar and Xu (2009) proved that a parallel system with heterogeneous exponential component lifetimes is more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. In this paper we extend this study to the general k-out-of-n systems for the case when there are only two types of component in the system. An open problem proposed in Pǎltǎnea (2008) is partially solved.