Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point

summary:Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map $T$ with a fixed point $p$ and prove that these iterates converge to a fixed point $q$ of $T$ under certain conditions. This fixed point $q$ may be different from $p$. To illustrate this phenomenon, an example is given

Common fixed point theorems of different compatible type mappings using Ciric\u27s contraction type condition

The purpose of this paper is to establish necessary and sufficient conditions for the existence of common fixed points for a compatible pair of selfmaps under Ciric\u27s contraction type condition. These theorems improve and generalize the results of Mukherjee and Verma [11] and Jungck [9] to a pair of selfmaps. Also established the existence of common fixed points for a pair of compatible mappings of type (B), and obtain a result on the existence of common fixed points for a pair of compatible mappings of type (A) as corollary. Greguš fixed point theorem follows as a special case to our results

SCAVENGING OF FREE RADICALS AND TOTAL PHENOLS OF METHANOL EXTRACT OF AZIMA TETRACANTHA LAM

Objective: To report the antioxidant activity, phenolic acid profile of the Azima tetracantha methanolic extract and find the correlation between the total phenolic content and their relative antioxidant activity Methods: The total antioxidant activity, hydroxyl radical and hydrogen peroxide scavenging of A. tetracantha methanol extract was evaluated by adopting various standard methods. Total phenolic content was estimated from dried methanolic extract and the phenolic acids in the extract were identified by HPLC. Results: The methanolic extract of A. tetracantha showed free radical scavenging in a concentration dependant manner. The studies showed that the extract possess high free radical scavenging property, especially against hydroxyl radicals (67.61±0.42%). The correlation analysis results showed linear relation between phenolics content of methanolic extract and antioxidant assays (R2=0.97, 0.94, 0.99 and 0.98, significance at P<.0.001). The phenolic acid profile showed the presence of both benzoic acid and cinnamic acid derivatives, well known for their antioxidant potential. Conclusion: The current observations suggested that the methanol extract of A. tetracantha exhibited multiple antioxidant activities, by scavenging free radicals. So, it can be concluded that the extract is a source of natural antioxidant, suggesting its traditional use as a rejuvenating agent

Removal of heavy metals Pb(II), Cd(II) and Cu(II) from waste waters using synthesized chromium doped nickel oxide nano particles

Adsorption of metal ions Pb(II), Cd(II) and Cu(II) are observed on chromium doped nickel nano metal oxide. Chromium doped nickel oxide was synthesized by combustion technique using glycine as a fuel. In this work, transmission electronic microscopy (TEM), scanning electronic microscopy (SEM), X-ray diffraction (XRD) and  Brunauer–Emmett–Teller (BET) are applied to study the composition and structure of chromium doped nickel oxide. Batch equilibrium experiments were performed to study the removal efficiency of heavy metal ions. The effects of different parameters such as contact time, pH and adsorbent dose on the adsorption process were investigated. The adsorption kinetics and adsorption isotherms studies were also performed. The formation of hydroxide on the surface of chromium doped nickel oxide could be the main factor of cations removal due to its high adsorption affinity for aqueous solutes. Chromium doped nickel oxide may offer a potential remediation method for the removal of metals from water and environment.               KEY WORDS: Adsorption isotherms, BET, Adsorption efficiency, Batch equilibrium, Adsorption kinetics Bull. Chem. Soc. Ethiop. 2018, 32(2), 225-238.DOI: https://dx.doi.org/10.4314/bcse.v32i2.

Fast Local Binary Patterns for Efficient Face Recognition

LBP, Local Binary Patterns, is an accepted technique for efficient face recognition. The local features improve the recognition process. However, high memory and computational resources are needed for LBP required approaches to improve the performance. Many people used LBP for extracting features and Support Vector Machine (SVM), histogram matching, neural networks as recognition tools. These approaches consume considerable computational resources. We have proposed a fast LBP which uses Two-level Correlation for the classification & recognition. The exhaustive experiments on FERET database 8750 images substantiate the performance compared to others. [Keywords— Face Recognition, LBP, Histogram Matching, Two-level Correlation, FERET data set

Intermediate scale as a source of lepton flavor violation in SUSY SO(10)

In supersymmetric SO(10) grand unified models, we examine the lepton flavor violation process $\mu \rightarrow e\gamma$ from having the SU(2)$_R\times$U(1)$_{B-L}$ gauge symmetry broken at an intermediate scale $M_I$ below the SO(10) grand unification scale $M_G$. Even in the case that supersymmetry is broken by universal soft terms introduced at the scale $M_G$, we find significant rates for $\mu\rightarrow e\gamma$ with $M_I \sim 10^{12}$ GeV or less. These rates are further enhanced if the universal soft terms appear at a scale greater than $M_G$.Comment: 12 pages (Latex), 3 PS Figures (uuencoded, epsf.tex), small addition to discussion in the text, as to appear in Phys. Rev. D Rapid Communication

Efficacy of Preserving Sea Foods Using Marine Lactobacillus

Scombroid food poisoning is a food borne illness that results from eating spoiled (decayed) fish. Histamine is the causative agent of scombroid poisoning, a food borne chemical intoxication. Histamine is one of the main biogenic amines and it is heterocyclic and biologically active primary amine, formed post-mortem in the muscles of scombroid and   non-scombroid fish. The present study was carried out to isolate histamine-producing bacteria from a local fish and to test antibacterial activity of mangrove isolates of Lactobacillus species against the histamine producing bacteria. Fresh tuna fish (Euthinus affinis) obtained from   Parangipettai coast and they were divided in to three groups. One group of the fish samples were stored directly and another two group of the fish  samples were dipped in cold distilled water containing bacteriocin of   Lactobacillus sp. and partially purified bacteriocin (10 ml, 1% v/v) respectively. The fish samples, after treatment were stored at 5, 15, 20 and 25 0C for the period of 24, 48, 72 and 96 h, respectively. Histamine quantification was performed at an interval of 24 h for four days. According to the results obtained it was proved that mangrove isolates of  Lactobacillus species having high antimicrobial activity against histamine-producing bacteria which is responsible for spoilage of sea foods