On the Ishikawa iteration process in Hilbert spaces

In this paper, we shall prove that a certain sequence of points which is iteratively defined converges always to a fixed point of some contractive mappings. The results generalize corresponding theorems of Singh and Qihou

Common fixed points of Greguš type multi-valued mappings

summary:This work is considered as a continuation of [19,20,24]. The concepts of $\delta$-compatibility and sub-compatibility of Li-Shan [19, 20] between a set-valued mapping and a single-valued mapping are used to establish some common fixed point theorems of Greguš type under a $\phi$-type contraction on convex metric spaces. Extensions of known results, especially theorems by Fisher and Sessa [11] (Theorem B below) and Jungck [16] are thereby obtained. An example is given to support our extension

Common Fixed Point Theorems for Weak Contraction Conditions of Integral Type

In this paper we shall establish two common fixed point theorems for a contractive condition and A-contraction mappings of integral type which improve and extend the results of P.B. Prajapati, R. Bhardwaj, M. O. Olatinwo and many others.Keywords: Common fixed point, general contractive mapps of integral type, weak contraction, metric spaces

Random Fixed Points For Occasionally Weakly Compatible Mappings

In this paper, we obtain common random fixed point theorems for two pairs of occasionally weakly compatible self random mappings under contractive conditions involving two generalized altering distance functions in a complete separable metric space. Keywords: Common random fixed point, Complete separable metric space, Generalized altering distance function, Occasionally weakly compatible mappings, Point of coincidence

HADAMARD GAPS IN WEIGHTED LOGARITHMIC BLOCH SPACE

We give a sufficient and a necessary condition for an analytic function "f" on the unit disk "D" with Hadamard gap to belong to a class of weighted logarithmic Bloch space as well as to the corresponding little weighted logarithmic Bloch space under some conditions posed on the defined weight function. Also, we study the relations between the class of weighted logarithmic Bloch functions and some other classes of analytic functions by the help of analytic functions in the Hadamard gap class

Stable oncogenic silencing in vivo by programmable and targeted de novo DNA methylation in breast cancer

With the recent comprehensive mapping of cancer genomes, there is now a need for functional approaches to edit the aberrant epigenetic state of key cancer drivers to reprogram the epi-pathology of the disease. In this study we utilized a programmable DNA-binding methyltransferase to induce targeted incorporation of DNA methylation (DNAme) in the SOX2 oncogene in breast cancer through a six zinc finger (ZF) protein linked to DNA methyltransferase 3A (ZF-DNMT3A). We demonstrated long-lasting oncogenic repression, which was maintained even after suppression of ZF-DNMT3A expression in tumor cells. The de novo DNAme was faithfully propagated and maintained through cell generations even after the suppression of the expression of the chimeric methyltransferase in the tumor cells. Xenograft studies in NUDE mice demonstrated stable SOX2 repression and long-term breast tumor growth inhibition, which lasted for >100 days post implantation of the tumor cells in mice. This was accompanied with a faithful maintenance of DNAme in the breast cancer implants. In contrast, downregulation of SOX2 by ZF domains engineered with the Krueppel-associated box repressor domain resulted in a transient and reversible suppression of oncogenic gene expression. Our results indicated that targeted de novo DNAme of the SOX2 oncogenic promoter was sufficient to induce long-lasting epigenetic silencing, which was not only maintained during cell division but also significantly delayed the tumorigenic phenotype of cancer cells in vivo, even in the absence of treatment. Here, we outline a genome-based targeting approach to long-lasting tumor growth inhibition with potential applicability to many other oncogenic drivers that are currently refractory to drug design

Waking up dormant tumor suppressor genes with zinc fingers, TALEs and the CRISPR/dCas9 system

The aberrant epigenetic silencing of tumor suppressor genes (TSGs) plays a major role during carcinogenesis and regaining these dormant functions by engineering of sequence-specific epigenome editing tools offers a unique opportunity for targeted therapies. However, effectively normalizing the expression and regaining tumor suppressive functions of silenced TSGs by artificial transcription factors (ATFs) still remains a major challenge. Herein we describe novel combinatorial strategies for the potent reactivation of two class II TSGs, MASPIN and REPRIMO, in cell lines with varying epigenetic states, using the CRISPR/dCas9 associated system linked to a panel of effector domains (VP64, p300, VPR and SAM complex), as well as with protein-based ATFs, Zinc Fingers and TALEs. We found that co-delivery of multiple effector domains using a combination of CRISPR/dCas9 and TALEs or SAM complex maximized activation in highly methylated promoters. In particular, CRISPR/dCas9 VPR with SAM upregulated MASPIN mRNA (22,145-fold change) in H157 lung cancer cells, with accompanying re-expression of MASPIN protein, which led to a concomitant inhibition of cell proliferation and induction of apoptotic cell death. Consistently, CRISPR/dCas9 VP64 with SAM upregulated REPRIMO (680-fold change), which led to phenotypic reprogramming in AGS gastric cancer cells. Altogether, our results outlined novel sequence-specific, combinatorial epigenome editing approaches to reactivate highly methylated TSGs as a promising therapy for cancer and other diseases

Radiological Hazard Evaluation of Some Egyptian Magmatic Rocks Used as Ornamental Stone: Petrography and Natural Radioactivity

Magmatic rocks represent one of the most significant rocks due to their abundance, durability and appearance; they can be used as ornamental stones in the construction of dwellings. The current study is concerned with the detailed petrography and natural radioactivity of seven magmatic rocks. All are commercial granitic rocks and are identified as black Aswan, Nero Aswan, white Halayeb, Karnak, Verdi, red Hurghada and red Aswan. Their respective mineralogical com-positions are classified as porpheritic granodiorite, granodiorite, tonalite, monzogranite, syenogran-ite, monzogranite and syenogranite. A total of nineteen samples were prepared from these seven rock types in order to assess their suitability as ornamental stones. Concentrations of 226Ra, 232Th and 40K radionuclides were measured using NaI (Tl) scintillation gamma-ray spectrometry. Among the studied magmatic rocks, white Halayeb had the lowest average values of226Ra (15.7 Bq/kg),232Th (4.71 Bq/kg) and40K (~292 Bq/kg), all below the UNSCEAR reported average world values or rec-ommended reference limits. In contrast, the other granitic rocks have higher values than the recom-mended limit. Except for the absorbed dose rate, other radiological hazard parameters including radium equivalent activity, annual effective dose equivalent, external, and internal hazard indices reflect that the White Halyeb rocks are favorable for use as ornamental stone in the construction of luxurious and high-demand residential buildings. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Funding: We deeply acknowledge Taif University for supporting the researchers through Taif University Researchers Supporting Project number (TURSP-2020/287), Taif University, Taif, Saudi Arabia

Global economic burden of unmet surgical need for appendicitis

Background: There is a substantial gap in provision of adequate surgical care in many low-and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods: Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results: Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion: For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially