This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

A remarkable correlation between chaotic systems and cryptography has been established with sensitivity to initial states, unpredictability, and complex behaviors. In one development, stages of a chaotic stream cipher are applied to a discrete chaotic dynamic system for the generation of pseudorandom bits. Some of these generators are based on 1D chaotic map and others on 2D ones. In the current study, a pseudorandom bit generator (PRBG) based on a new 2D chaotic logistic map is proposed that runs side-by-side and commences from random independent initial states. The structure of the proposed model consists of the three components of a mouse input device, the proposed 2D chaotic system, and an initial permutation (IP) table. Statist

Given the importance of ecology and its entry into various fields in general and the urban environment particularly; ecological cities take wide ranges of application at multiple regional and global levels. However, it repeatedly noted that there was a state of cognitive confusion and overlapping in the term ecology comes from the diversity of implementation within several disciplines. Architects, designers, and planners have instilled biological development directly into the formal principles as well as the social structures of the ecological cities. Therefore, the research presents a rapid review of the most relevant areas that dealt with the ecological cities by research and analysis at various levels, from the concept and definition of

Background: The transcriptional control of various cell types, especially in the development or functioning of immune system cells involved in either promoting or inhibiting the immune response against cancer, is significantly influenced by DNA or RNA methylation. Multifaceted interconnections exist between immunological or cancer cell populations in the tumor's microenvironment (TME). TME alters the fluctuating DNA (as well as RNA) methylation sequences in these immunological cells to change their development into pro- or anti-cancer cell categories (such as T cells, which are regulatory, for instance). Objective: This review highlights the impact of DNA and RNA methylation on myeloid and lymphoid cells, unraveling their intricate

Amygdalin (d-Mandelonitrile 6-O-β-d-glucosido-β-d-glucoside) and its semi synthetic product is Laetrile ( also called vitamin B17): a natural cyanogenic glycoside occurring in the seeds of some edible plants, such as bitter almonds and peaches. Early in the 19th century, Amygdalin was first isolated in 1830 by two French chemists, Robiquet and Boutron-Charlard, as active components in various fruit pits and raw nuts. However, the systematized study of vitamin B17 started when chemist Bohn (1802) discovered that a hydrocyanic acid is released during distillation of the water from bitter almonds. The various pharmacological effects of Laetrile include antiatherogenic, activity in renal fibrosis, pulmonary fibrosis, immune regulation, ant

Many patients with advanced type 2 diabetes mellitus (T2DM) and all patients with T1DM require insulin to keep blood glucose levels in the target range. The most common route of insulin administration is subcutaneous insulin injections. There are many ways to deliver insulin subcutaneously, such as vials and syringes, insulin pens, and insulin pumps. Though subcutaneous insulin delivery is the standard route of insulin administration, it is associated with injection pain, needle phobia, lipodystrophy, noncompliance, and peripheral hyperinsulinemia. Therefore, the need exists to deliver insulin in a minimally invasive or noninvasive way and in the most physiological way. Inhaled insulin was the first approved noninvasive and alternative way