This paper presents some results concerning the existence of solutions for a functional integral equation of Volterra type in two variables, via measure of noncompactness. Two examples are included to illustrate the main result.

This paper presents some results concerning the existence of solutions for a functional integral equation of Volterra type in two variables, via measure of noncompactness. Two examples are included to illustrate the main result.

The crossing number of a graph is the minimum number of edge crossings over all possible drawings of in a plane. The crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and VLSI circuit design. In this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

The AC electrical behaviour of nano porous silicon (PSi) with TiO2 thin films was examined over the range of frequency 102 to 105 Hz. Porous silicon (PSi) layers were obtained by electrochemical etching in HF solution and TiO2 thin films were deposited on PSi substrates by using electron beam evaporation technique at room temperature. The porosity of PSi layer was found by using the gravimetric method and the crystalline properties of the TiO2 thin films were obtained by an X-ray diffract meter. The surface morphology and AC electrical properties of samples were investigated by scanning electron microscopy (SEM) and electrometery respectively. For AC electrical properties we studied the dependence of capacitance and dissipation factor on frequency at different temperatures. The capacitance decreased with increasing frequency and increased with increasing temperature, and dissipation factor decreased with increasing frequency to a minimum value and after that increased. This behaviour is in good agreement with Goswami's theory. Also, the AC conductivity of sandwich structure films was studied over the range of frequency 102 to 105 Hz. Over the range of frequency<103Hz the band theory and over the range of frequency>103Hz hopping mechanism is applied in explaining the conductivity process.

In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. Some topological properties of these spaces are investigated. Further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence in a real 2-normed space, are defined. Also, some relations between these concepts are investigated.

It is essential to use statistical models and theoretical analysis of the data for preparing comprehensive geological and seismic hazard mapping. A cellular automaton consists of an array of cells, each one of which has a finite number of possible states, together with a rule for updating all cells simultaneously based only on the states of neighboring cells. In the present paper, Ising cellular automation modeling has been used for establishing temporal relations between the energy releases of the seismic events that occurred in neighboring parts of the crust. The catalogue is divided into time intervals, and the region is divided into cells which are declared active or inactive by means of a threshold energy release criterion. Thus, a pattern of active and inactive cells which evolves over time is determined. The best model is chosen by maximizing the mutual information between the past and the future states. Finally, a Probabilistic Seismic Hazard Map is given for the different energy releases considered. The method has been applied to the wide range of Iran's geological and geophysical data and Iran catalogue from ISC and USGS from 1960 to 2009, (ISC and USGS).

In this paper, we introduce a class of rings which is a generalization of reversible rings. Let R be a ring with identity. A ring R is called central reversible if for any a,b ∈ R, ab=0 implies ba belongs to the center of R. Since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. We prove that some results of reversible rings can be extended to central reversible rings for these general settings.

Thionyl chloride (or oxalyl chloride) has been used as an efficient and cheap acid activator for one-pot synthesis of β-lactams in good to excellent yields by reaction between imines and acids in the presence of triethylamine at room temperature.

In this study organotypic adult spinal cord slices were used to investigate whether caspases could participate in the apoptosis of motor neurons. The thoracic region of spinal cord was sliced using a tissue chopper and cultured in a medium for 6h. Morphological and biochemical features of apoptosis were assessed by fluorescent staining and terminal deoxynucleotidyl nick end labeling (TUNEL) method respectively. To investigate the role of caspases, general caspase inhibitor, Z-VAD.fmk, and immunohistochemistry for activated caspase-3 were used. After 6h in culture, many motor neurons displayed morphological features of apoptosis. In addition, the neurons appeared TUNEL positive. Z-VAD.fmk not only prevented apoptosis in the motor neurons but also increased motor neurons viability after 6h. At this time point, immunolocalization to activated caspase-3 was also detected in the cytoplasm and the nuclei of apoptotic motor neurons. Results of the present study suggest a caspase-dependent apoptosis in motor neurons of adult spinal cord slices.

Recently, Mohiuddine and Alghamdi introduced the notion of lacunary statistical convergence in a locally solid Riesz space and established some results related to this concept. In this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a Tauberian theorem to the locally solid Riesz space setting are proved. Further, we introduce the concepts of -summable and statistically lacunary convergence in locally solid Riesz space and establish a relationship between them.

A method for solving a class of weakly singular Volterra integral equations is given by using the fractional differential transform method. The approximate solution of these equations is calculated in the form of a finite series with easily computable terms. While in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy and the reliability of the fractional differential transform method.

Concentrations of elements (As, Co, Cu, Ni, Mo, Pb, V, Cd, Cr and Zn) are studied in the surface sediments of Bakhtegan Lake, northwest of Nyriz City, Iran, to assess metal contamination. The average abundance order of trace elements content in Bakhtegan Lake sediments is Cr>Ni> V> Zn> Cu> Co> As> Pb> Mo>Cd. The comparison of trace elements concentration in Bakhtegan Lake sediments with toxicological reference values, reveal that the average concentration of As, Cr and Ni in the present sediments is higher than threshold effective level (TEL). Ni shows higher concentration than toxic effect threshold (TET) and probable effective level (PEL) values. The results of contamination factor (CF) based on background value reveal that Cr, Cu, Zn, V, Co, Pb, Mo, As and Ni have moderate and Cd has considerable contamination factor. The application of modified degree of contamination values (mCd) based on background and mean shale values indicate low and very low degree of contamination in sediment samples, respectively. The calculated EF values indicate that Cd in Bakhtegan Lake sediments is enriched compared to the background value. The strong association of Cr, Ni, Zn, Co, Cu, Pb, and V in sediments and high loading of these trace elements with clay, Mn and Fe (PC1) agree with the measured correlation coefficients indicating that Mn and Fe hydroxides and clay content play a significant role in the distribution and sorption of trace elements in sediments. The results of PCA for As and Cd indicate that these elements are influenced by anthropogenic activities.

In this paper a new method is proposed for interpretation of 2D magnetic data, using multiples of the analytic signal method, in which the analytic signal of magnetic anomaly is used directly to compute the depth and the structural index of the source instead of using its higher order derivatives. This method only needs the computation of the first order derivatives of the magnetic anomaly, so the results are more stable than the results obtained by the other existing analytic signal methods. This method is applied on synthetic magnetic data with and without noise, and the proposed method can successfully obtain the depth and the structural index of the sources. We also applied this method to interpret a real magnetic data over a shallow source related to the SOURK Iron Ore mine in Iran, whose source parameters are known from closely core drilling data, and the estimated results are in agreement with the true values.