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 research explores the integration of multi-walled carbon nanotubes (MWCNTs) into polyvinyl alcohol (PVA) matrices to enhance their structural, electrical and thermal properties. Fourier-transform infrared spectroscopy analysis confirms the formation of a PVA-MWCNT complex. The incorporation of MWCNTs, even at low concentrations, leads to increased electrical conductivity, making the composite material suitable for applications in flexible electronics and sensors. Dielectric studies reveal frequency-dependent electrical behavior, attributed to interfacial polarization, suggesting potential uses in capacitors and energy storage devices. The introduction of MWCNTs into PVA leads to N-type semiconductor behavior, as indicated by the Hall c

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

This article deals with the impact of including transverse ribs within the absorber tube of the concentrated linear Fresnel collector (CLFRC) system with a secondary compound parabolic collector (CPC) on thermal and flow performance coefficients. The enhancement rates of heat transfer due to varying governing parameters were compared and analyzed parametrically at Reynolds numbers in the range 5,000–13,000, employing water as the heat transfer fluid. Simulations were performed to solve the governing equations using the finite volume method (FVM) under various boundary conditions. For all Reynolds numbers, the average Nusselt number in the circular tube in the CLFRC system with ribs was found to be larger than that of the plain abs

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

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

Background: Parenteral nutrition (PN) is a life‑saving intervention for neonates who are unable to meet their nutritional requirements through enteral feeding. Despite its essential role, PN is frequently associated with metabolic, electrolyte, and hepatobiliary complications. Objective: To evaluate the frequency and pattern of metabolic, electrolyte, and hepatobiliary complications associated with PN administration in neonates. Methods: A prospective case-series study was conducted in two tertiary neonatal intensive care units (NICUs) in Baghdad, Iraq. Term and preterm neonates who received PN for at least five days were included. PN‑related metabolic, electrolyte, hepatobiliary, and hematological complications were recorded an

      In this paper, thin films of undoped and nickel oxide (NiO) doped titanium dioxide (TiO2) were prepared using the chemical spray pyrolysis deposition (CSP) technique, with different concentrations of nickel oxide (NiO) in the range (3-9) wt%. The morphological, structural, electrical, and sensing properties of a gas of the prepared thin films were examined. XRD measurements showed that TiO2 films have a polycrystalline structure. AFM analysis showed that these films have a regular structure both before and after doping . The roughness of these films  decreased after adding  impurities but then the opposite of that took  place. The electrical and gas sensing properties of titanium dioxide  was also affected after dopin