‎the annihilator graph $ag(r)$ of a commutative ring $r$ is a simple undirected graph with the vertex set $z(r)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$‎. ‎in this paper we give the sufficient condition for a graph $ag(r)$ to be complete‎. ‎we characterize rings for which $ag(r)$ is a regular graph‎, ‎we show that $gamma (ag(r))in {1,2}$ and...

 In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix  over a UFD is nil-clean.

A number of theories have been developed to characterize ALogTime (or uniform NC, or just NC), the class of languages accepted by alternating logtime Turing machines, in the same way that Buss’s theory S12 characterizes polytime functions. Among these, ALV ′ (by Clote) is particularly interesting because it is developed based on Barrington’s theorem that the word problem for the permutation gro...

In hematological malignancies, homozygous deletion of @/6â@NK4A is primarily limited to ALL3 and non-Hodgkin's lymphoma (10—13). Although ALL has among the highest reported rates of homozygous deletion at 9p2l in primary neoplasia (6, 9—1, 14), assigning a tumor suppressor role to p16@―@4― alone in these malignancies is difficult, because most cases include both p15@―4'@and p16@―4â...

We present a new technique for the analysis of spatiotemporal data. In our approach the concept of intermediate-scale determinism is combined with a test on unstable periodic orbits. A comparison of original data with appropriate surrogate data provides a statistical assessment of the results. The method is applied to both numerically generated data and data from a natural system.

Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five consi...

Auditory noise is a sound, a random variation in air pressure. More generally, random " noise " can be introduced into any stimulus, including a visual display. Noise added to the stimulus can probe the computations underlying perception of the stimulus. With power and precision, the noise, by restricting the information available, places fundamental constraints on attainable performance and pr...

We investigate the question of which graphs have planar emulators (a locally-surjective homomorphism from some finite planar graph)—a problem raised already in Fellows’ thesis (1985) and conceptually related to the better known planar cover conjecture by Negami (1986). For over two decades, the planar emulator problem lived poorly in a shadow of Negami’s conjecture—which is still open—as the tw...

In this article, the effect of potassium on structure and anticorrosion properties of zinc phosphate pigments has been investigated. The co-precipitation method was selected as synthesis method of potassium zinc phosphate pigment. Then the synthesized pigment was characterized by x-ray diffraction XRD, Fourier transform infrared FTIR and Raman spectroscopy. Morphology of the powders was investi...