The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

This current study aimed to explore the mediation effects of mother's mental health symptoms between marital adjustment and child development aspects. (666) participants of mothers and their children were the sample of the study. The researchers used the marital adjustment scale prepared by Manson, Morse, Lerner, Arthur, as well as, a package of tests for some aspects of growth Kindergarten children prepared by Kenawi and Mohamed (1999). In addition, theyemployed a list of modified symptoms (Symptom Checklist-90- Revised (SCL) -90-, prepared by Derogatis, Lipman and Lipogun & Cov (1976), The results of the current study showed there is a statistically significant relationship between marital adjustment and the symptoms of mental diso

Laser is a powerful device that has a wide range of applications in fields ranging from materials science and manufacturing to medicine and fibre optic communications. One remarkable

The determiner phrase is a syntactic category that appears inside the noun phrase and makes it definite or indefinite or quantifies it. The present study has found wide parametric differences between the English and Arabic determiner phrases in terms of the inflectional features, the syntactic distribution of determiners and the word order of the determiner phrase itself. In English, the determiner phrase generally precedes the head noun or its premodifying adjectival phrase, with very few exceptions where some determiners may appear after the head noun. In Arabic, parts of the determiner phrase precede the head noun and parts of it must appear after the head noun or after its postmodifying adjectival phrase creating a discontinu

Purpose: This study aimed to evaluate the influence of vitamin D3 levels on bone density, primary dental implant stability, and successful osseointegration.

Materials and Methods: Clinical and radiological examination with a standardized cone‐beam computed tomography (CBCT) machine and laboratory investigation for serum levels of vitamin D3 were performed for all patients. Only patients in need of single or multiple straightforward dental implant surgery in either jaw with no history of systemic disease or condition that may interfere with bone healing were included in this study to receive the dental implant by the same oral and maxillofacial surgeon, which re‐opened

Essential approaches involving photons are among the most common uses of parallel optical computation due to their recent invention, ease of production, and low cost. As a result, most researchers have concentrated their efforts on it. The Basic Arithmetic Unit BAU is built using a three-step approach that uses optical gates with three states to configure the circuitry for addition, subtraction, and multiplication. This is a new optical computing method based on the usage of a radix of (2): a binary number with a signed-digit (BSD) system that includes the numbers -1, 0, and 1. Light with horizontal polarization (LHP) (↔), light with no intensity (LNI) (⥀), and light with vertical polarization (LVP) (↨) is represen

A cumulative review with a systematic approach aimed to provide a comparison of studies’ investigating the possible impact of the active form of vitamin D3, calcitriol (CTL), on the tooth movement caused by orthodontic forces (OTM) by evaluating the quality of evidence, based on collating current data from animal model studies, in vivo cell culture studies, and human clinical trials. Methods: A strict systematic review protocol was applied following the application of the International Prospective Register of Systematic Reviews (PROSPERO). A structured search strategy, including main keywords, was defined during detailed search with the application of electronic database systems: Medline/Pubmed, EMBASE, Scopus, Web of Science, and

Purpose: This study aimed to evaluate the influence of vitamin D3 levels on bone density, primary dental implant stability, and successful osseointegration.

Materials and Methods: Clinical and radiological examination with a standardized cone‐beam computed tomography (CBCT) machine and laboratory investigation for serum levels of vitamin D3 were performed for all patients. Only patients in need of single or multiple straightforward dental implant surgery in either jaw with no history of systemic disease or condition that may interfere with bone healing were included in this study to receive the dental implant by the same oral and maxillofacial surgeon, which re‐opened