Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity

Since the introduction of complex fractals by Mandelbrot they gained much attention by the researchers. One of the most studied complex fractals are Mandelbrot and Julia sets. In the literature one can find many generalizations of those sets. One of such generalizations is the use of the results from fixed point theory. In this paper we introduce in the generation process of Mandelbrot and Julia sets a combination of the S-iteration, known from the fixed point theory, and the s-convex combination. We derive the escape criteria needed in the generation process of those fractals and present some graphical examples

Higher Order Methods of the Basic Family of Iterations via S-Iteration Scheme with s-Convexity

There are many methods for solving a polynomial equation and many different modifications of those methods have been proposed in the literature. One of such modifications is the use of various iteration processes taken from the fixed point theory. In this paper, we propose a modification of the iteration processes used in the Basic Family of iterations by replacing the convex combination with an s-convex one. In our study, we concentrate only on the S-iteration with s-convexity. We present some graphical examples, the so-called polynomiographs, and numerical experiments showing the dependency of polynomiograph’s generation time on the value of the s parameter in the s-convex combination

The Role of Five Major Shari’ah Legal Maxims ( Al-Qawaid Al-Kubra ) in the Establishment of Maqasid Al-Shari’ah in Islamic Financial Products: A Discussion on Some Cases

Maqasid al-shari’ah is the science in Islamic jurisprudence that combines the elements of usul al-fiqh and qawa’id al-fiqhiyah. This article limits the discussion of maqasid al-shari’ah only on the role of qawa’id al-fiqhiyah. It aims to analyze some of the shari’ah legal maxims that are founded based on the understanding of maqasid al-shari’ah, and simultaneously contribute in building the science in the Islamic finance sector. The methodology used is content analysis from the ideas of traditional as well as contemporary scholars by focusing on the five major shari’ah legal maxims (al-qawaid al-kubra) with reference to the some cases applied in Islamic finance practices today. The study finds that the science of qawaid al-fiqhiyah plays significant role in establishing the objectives of shari’ah in general view and contributes ideas and opinions in designing the methodologies, parameters and characteristics for the comprehensive formation of maqasid al-shari’ah in modern Islamic finance products. Keywords:Qawaid al-Fiqhiyah, Maqasid al-Shari’ah, Islamic Financ

Antimicrobial and phytochemical screening of Oligochaeta ramose against different pathogenic microbes- An In vitro study

Biologically active compounds obtained from the medicinal plants are the effective chemotherapeutic agents and offering a broad spectrum of activity with greater emphasis on preventive action. The present study was aimed at evaluating the antimicrobial activities of crude methanolic extract of Oligochaeta ramose (Asteraceae) against pathogenic bacteria species of both G +ve strains (Staphylococcus aureus, Bacillus pumilus, Streptococcus pneumoniae), G -ve strains, (Escherichia coli, Citrobacter freundii, Klebsiella pneumoniae) and fungal species (Candida albicans, Aspergillus niger). In-vitro antimicrobial test was performed by disc diffusion method on nutrient agar and sabouraud dextrose agar for bacteria and fungi respectively, in order to analyze the percentage zone of inhibition and phytochemical screening was also performed. Methanolic extract showed significantly high inhibitory effect against G +ve strains, as compared to G -ve strains, whereas, no effect against C. albicans and A. niger. Modified agar well diffusion method was used to measure the minimum inhibitory concentration (MIC) and MIC values lies within the range of 75 to 150 ?g /ml for the G +ve while 300 to 600 ?g /ml for G-ve. Or.Cr was found to contain alkaloids, tannins, saponins, flavonoids and antraquinones and these agents may be responsible for antibacterial activity of this plant. Keywords: Oligochaeta ramose, Methanolic extract, Antimicrobial assay, Nutrient aga

The Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets

In recent years, researchers have studied the use of different iteration processes from fixed point theory in the generation of complex fractals. For instance, the Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations have been used. In this paper, we study the use of the Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets. We prove the escape criterion for the (k + 1)st degree complex polynomial. Moreover, we present some graphical and numerical examples regarding Mandelbrot and Julia sets generated using the proposed iteration

Immunophenotypic analysis of Non-Hodgkin\u27s Lymphoma

One hundred and three cases of Non-Hodgkin’s lymphoma were evaluated immunohistochemically using a panel of monoclonal antibodies which includes leucocyte common antigen (LCA), CD45R (Pan-B marker), L-26 (CD 20-Pan-B marker) and UCHL-1 (Pan-T marker). Of the total 63 cases (61.17%) showed a B-cell phenotype while 40(38.83%) were of T-cell origin. Most B-cell neoplasms belonged to intermediate (79.36%) or high grade (15.87%) according to the international Working Formulation (WF). Most T- cell lymphomas were of either intermediate (52.5%) or high grade (32.5%) neoplasms. Some T-cell neoplasms presented as specific clinicopathological entities like lymphomatoid granulomatosis (2 cases), mycosis fungoides (1 case) and AILD type NHL (1 case). in 27 cases the immunostaining pattern of two .Pan-B markers i.e., L26 and CD45R was compared. L26 staining was expressed in all 27 cases (100% sensitivity) while CD45R showed positive reaction in 22 cases (82% sensitivity). UCHL-1 is proved to be a sensitive and lineage specfic T-cell markerand in 67% cases the staining pattern was moderate (++) to intense (+++). The mean age for the B-cell lymphomas was 49 years and 36 years in T-cell neoplasm. Male to female ratio in both types of lymphomas was 2:1. The study indicates a high prevalence of T-cell lymphomas when comparing the data from western countries and lower to those from Japan and Caribbean countries

Assessment of antibacterial potential of Saccharum spontaneum Linn. (family: Poaceae), against different pathogenic microbes- an in vitro study.

In this study, Saccharum spontaneum (Family: Poaceae), was evaluated for its antibacterial potential against human pathogenic bacterial strains. In-vitro antibacterial tests were performed by disc diffusion method on nutrient agar, in order to analyze the percentage zone of inhibition. Whole plant’s extract showed the significant zone of inhibition (mm), against Staphylococcus aureus (17.00), Streptococcus pneumoniae (16.50), Bacillus cereus (15.90), Bacillus pumilus (15.45), Escherichia coli (18.00), Klebsiella pneumoniae (17.10), Pseudomonas aeruginosa (15.20) and Citrobacter freundii (14.00), with relative percentages of inhibition of 76.90, 71.60, 57.40, 56.85, 70.40, 69.90, 61.05 and 54.30 respectively. Modified agar well diffusion method was used to measure the minimum inhibitory concentration (MIC) and MIC values lies within the range of 75 to 300?g /ml for the G+ve strains while 75 to 600?g /ml for G-ve.  Due to presence of tannins and flavonoids, it inhibits the growth of bacteria on most regulatory levels such as peptidoglycan, DNA, RNA and protein synthesis

Evaluation of excessive lifetime cancer risk due to natural radioactivity in the rivers sediments of Northern Pakistan

Naturally occurring radionuclides 226Ra, 232Th and 40K present in the rivers sediments of Northern Pakistan were measured using HPGe γ-ray spectrometer to evaluate the radiation health hazard indices and excess lifetime cancer risk (ELCR). Average concentrations of 226Ra, 232Th and 40K in the sediments were found to be 50.66 ± 1.29, 70.15 ± 1.45 and 531.70 ± 5.45 Bq kg−1 respectively. Radium equivalent activity (190.89 Bq kg−1), outdoor external dose (87.47 nGy h−1), indoor external dose (165.39 nGy h−1), and total average annual effective dose (0.92 mSv) were calculated. The hazard indices are higher than the world's average values. Total excess lifetime cancer risk (ELCR) was found to be 3.21 × 10−3 which is relatively higher. Numerous cancer deaths are annually reported from the Northern areas of Pakistan, which may be related to high radioactivity in the area. Keywords: Activity concentration, 226Ra, 232Th and 40K, Hunza, Gilgit and Indus Rivers, Radiation indices, Annual effective dose, Excess lifetime cancer risk (ELCR

Fractal generation via CR iteration scheme with s-convexity

The visual beauty, self-similarity, and complexity of Mandelbrot sets and Julia sets have made an attractive eld of research. One can nd many generalizations of these sets in the literature. One such generalization is the use of results from xed-point theory. The aim of this paper is to provide escape criterion and generate fractals (Julia sets and Mandelbrot sets) via CR iteration scheme with s-convexity. Many graphics of Mandelbrot sets and Julia sets of the proposed three-step iterative process with s-convexity are presented. We think that the results of this paper can inspire those who are interested in generating automatically aesthetic patterns.Dong-A University Funds, Busan, South Koreahttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639am2020Mathematics and Applied Mathematic