Fixed Point Theory for Three φ–Weak Contraction Functions

Alber and Guerre-Delabriere demonstrated the “concept of weak contraction” in 1997. Actually in concept of weak contraction, the authors defined such mappings for single-valued maps on Hilbert spaces and proved the existence of fixed points. Rhoades showed that most results of concept of weak contraction are still true for any Banach space along with that he has proved the following very interesting fixed point theorem which is one of generalizations of the Banach contraction principle because it contains contractions as special cases (φ(t)=(1–k)t).

Bayesian Regression Analysis of Correlates of Modern Contraceptive Method Usage: A Case Study in Hawassa City, Ethiopia

Despite widespread adoption of family planning in the developing world contraceptive use is still very low in sub-Saharan Africa including Ethiopia and in other regions. The general objective of this study was identifying the socioeconomic factors of modern contraceptive methods usage among married women of reproductive ages (15-49years old) in Hawassa city. From a total 990 sampled married women about 57.9% (573) were modern contraception methods users. 

Bayesian logistic regression procedure was adopted to make inference about the parameters of a logistic regression model. The purpose of this method is generating the posterior distribution of the unknown parameters given both the data and some prior density for the unknown parameters. Bayesian inference for logistic regression models is derived applying a Markov Chain Monte Carlo algorithm to simulate from the joint posterior distribution of the regression and the link parameters.

Statistical Models to Assess the Trends and Wav Regularities of Mass Glaciers

Different types of natural objects like oceanic waves; glaciers etc. are studied scientifically to assess the constant changes in the climate and its effect on the living organism on the planet. Applicability of statistical model to certain parameters of points that are subjected to fluctuations of balance such as the mass of glaciers of Earth is proved. This method of identification allows allocation of significant parameters of glaciers and the binary relations between them in which it will be necessary to increase the accuracy of future measurements. 

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Classification of Canonical Bases for (n−1)−dimensional Subspaces of n− Dimensional Vector Space

Canonical bases for (n-1)-dimensional sub spaces of n-dimensional vector space are introduced and classified in the article. This result is very prospective to utilize canonical bases at all applications. For example, maximal sub algebras of Lie algebras can be found using them.

The canonical bases for (n-1)-dimensional sub spaces of n− dimensional vector space are introduced in the article, and all non equivalent of them are classified (Theorem 2). This result generalizes a particular result for 5-dimensional sub spaces of 6-dimensional vector space obtained in the previous article of the same author.To analyze the general case, reduced row echelon forms of matrices are utilized; about reduced row echelon forms. In addition to the principal result, all non-equivalent reduced row echelon forms for (n−1)×n matrices of the rank (n−1) are found.

Advances in Logic, Operations and Computational Mathematics

Journal of Applied & Computational Mathematics Volume 5, Issue 2 comprised of 7 research articles and 4 opinion articles and are focused on the innovation of polygon, Euler, linear and non-linear equations.

EL-Kholy et al., in their research article discussed about balanced folding over a polygon and Euler numbers. The study proved that for a balanced folding of a simply connected surface M, there is a subgroup of the group which is called all homeomorphisms of M that will acts 1- transitively on the 2-cells of M.

Gil et al., in their research have reported about the exponentially stabile non-linear, non-autonomous multi variable discrete systems. Based on the recent estimates on matrix equations, the findings suggest that a class of non-autonomous discrete-time systems is governed by semi-linear vector difference equations along with slowly varying linear parts.

Methods for the Analysis of Missing Data in FMRI Studies

Functional neuroimaging has provided fundamental advances in our understanding of human brain function and is increasingly used clinically for defining atypical function and surgical planning. For example, functional imaging with blood oxygenation level dependent (BOLD) contrast as a response measure is used as a clinical tool for defining atypical development, pathology, surgical planning, and evaluating treatment outcomes. 

Despite years of statistical advances in the analysis of complete whole brain data, there has been a limited statistical advance toaddress the pronounced missingness in many functional imaging studies that uselarge discovery or small clinical case data. For example, functional magnetic resonance imaging (fMRI) analyses do not always include the entire brain due to image acquisition space limitations and susceptibility artifacts (a loss and spatial distortion of signal that results from a disruption in the magnetic field). 

Identification of Wave Regularities According to Statistical Data of Parameters of 24 Pulsars

The method of identification is shown on the example of tabular these measurements of six parameters at 24 pulsars. The equations of a trend and oscillatory indignations on the basis of steady laws on the generalized wave function in the form of an asymmetric wavelet signal with variables of amplitude and the period of fluctuation are received. 

On the remains it is possible to receive a set of micro fluctuations and to bring identification to an error of measurements. Schedules of components of the generalized model of a wavelet signal allow to see visually a picture of mutual influence of all six parameters of pulsars. On the revealed equations it is possible to carry out the amplitude-frequency analysis. Quality of basic data is estimated by rank distributions of values of parameters of pulsars. Thus ranging of values of parameters on a preference pre order vector "better worse" is carried out in the beginning, the rating of pulsars is formed further.

How to Prove the Riemann Hypothesis

The aim of this paper is to prove the celebrated Riemann Hypothesis. I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5. I assume that any such zero is s=a+bi. I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent, and verify that a=0.5. From equation (60) onward I view (a) as a parameter (a <0.5) and arrive at a contradiction. At the end of the proof (from equation (73)) and through the assumption that (a) is a parameter, I verify again that a=0.5.

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Theoretical Investigation of New Organic Electroluminescent Materials Based on 4-Azaindole Groups and Oligopyrrole

The electronic properties of four new organic compounds (I-IV) were studied theoretically for application as hole-transporting materials in electroluminescent (EL) devices. We investigated theoretically, the effect of increasing number of pyrrole rings between 4-azainole end moieties. The time dependent density functional theory (TD-DFT/ B3LYP/6-31G(d)) calculated energy gap (E-gap) of the studied compounds decreases in the order of I>II>III>IV; 

the significant reduction of E-gap of compound IV with 2.7 eV compared to 4.27 eV of compound II is due to the bridging effect of C=C(CO2H)2 which remove the steric effect, caused by high dihedral angle between two central pyrrole rings in the non-bridged II. Compound IV posses slow-lying lowest occupied molecular orbital(LUMO) energy levels and low lying highest occupied molecular orbital (HOMO) energy levels, may be promising candidate for hole transporting and bright blue to red emitting layer in organic light emitting device (OLED) fabrication.

Fast Computation of Significance Threshold in QTL Mapping of Dynamic Quantitative Traits

Functional Mapping is a popular statistical method in QTL mapping studies for longitudinal data. The threshold for declaring statistical significance of a QTL is commonly obtained through permutation tests, which can be time consuming. 

To improve the computational efficiency of a permutation test of mixture models used in Functional Mapping, we first quantified the correlation between QTL and longitudinal data, using a curve clustering method. Then, the QTL s which are highly correlated with the outcome were computed in the improved permutation tests. As a result, it reduces the amount of computation in permutation tests and speeds up the computation for Functional Mapping analysis. Simulation studies and real data analysis were conducted to demonstrate that the proposed approach can greatly improve the computational efficiency of QTL mapping without loss of accuracy.

Biplot Simulation to Determine the Growth Rate of Body Dimension in Local Bali Ducks

Biplot simulation using factor analysis rotation promax kapa 90 was conducted to determine the growth rate of body dimension in female Bali duck of 0-16 week-old. The result of the biplot simulation showed that the body dimension of female Bali ducks that belongs to slow growth rate was in quadran II including the length of radius ulna, femur, tarsal and humerus. 

The body dimensions of female Bali ducks with the moderate growth rates were in quadrant I such as the length of carpal, chest circumference, body weight, the length necks, the length of digital 1 and the length of head. The body dimension with fast growth rate such as head circumference, neck circumference, abdominal circumference, and the length of digital 2, 3 and 4, and the length of tibia-fibula. Based on the ages, the coordinates distances in two dimension Eigen vector space were as follows. At the most distance position was at the age of 0-2 weeks, followed by the age of 2-4 weeks, and finally with closest distance was at the age of maturity.

Exploring the Multiple applications of Topology

Topological formulas are applied in many fields in our daily life including mathematics, biochemistry, information systems. Topology itself consist of several different branches such as point set topology, algebraic topology and differential topology which have relatively little in common this richness of applications and difference between branches of topology. The study introduced new class of near open sets namely, b*-open set. And studs same of their properties, also we study the relation between this class among this classes. Also, we introduce some topological properties and we shall study same of their properties.

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