The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

The paper discusses the structural and optical properties of In 2 O 3 and In 2 O 3-SnO 2 gas sensor thin films were deposited on glass and silicon substrates and grown by irradiation of assistant microwave on seeded layer nucleated using spin coating technique. The X-ray diffraction revealed a polycrystalline nature of the cubic structure. Atomic Force Microscopy (AFM) used for morphology analysis that shown the grain size of the prepared thin film is less than 100 nm, surface roughness and root mean square for In 2 O 3 where increased after loading SnO 2 , this addition is a challenge in gas sensing application. Sensitivity of In 2 O 3 thin film against NO 2 toxic gas is 35% at 300 o C. Sensing properties were improved after adding Tin Oxi

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

The research was carried out in lathhouse on one-year-old apple seedlings of the Ibrahimi variety in the Karma-Fallujah region for the 2021 growing season to study the effect of methods of adding nano-fertilizer and humic acid on seedling growth. A two-factor experiment was designed according to a randomized complete block design, with three replicates and two seedlings per experimental unit, so the number of seedlings was 54. The first factor includes NPK nanofertilizer at three levels (0- and 2-ml L-1 foliar spray and 5 ml L-1 soil application). The second factor is humic acid at three levels (0 and 5 g of seedlings - 1 foliar spray and 10 g of seedlings - 1 soil application). The results of the study show that the NPK nano-fertil

A study of characteristics of the lubricant oils and the physical properties is essential to know the quality of lubricant oils. The parameters that lead to classify oils have been studied in this research. Three types of multi-grades lubricant oils were applied under changing temperatures from 25 ^oC to 78^oC to estimate the physical properties and mixture compositions. Kinematic viscosity, viscosity gravity constant and paraffin (P), naphthenes (N) and aromatics (A) (PNA) analysis are used to predict the composition of lubricants oil. Kinematic viscosity gives good behaviors and the oxidation stability for each lubricant oils. PNA analysis predicted fractions of paraffin (X_P), naphthenes (X_N),

Orphenadrine is an anticholinergic ,antimuscarinic , centrally acting skeletal muscle relaxant .It presents in the form of citrate and HCl salts which are used in treatment of the symptoms of mild Parkinson's disease and also it is used as adjuvant with other drugs in the therapy .

      Many trials were made to formulate Orphenadrine citrate as a plain tablet using wet granulation or direct compression technique in order to get a satisfactory formula through studying the effect of various factors such as binders , diluents and disintegrants types .

    The best formula was obtained by using Poly Vinyl Pyrolidine (PVP) as a binder also the results indicated that starch and mannitol

A transdermal drug delivery system (TDDS) is characterized by the application of medications onto the skin's surface to deliver drugs at a controlled and predefined rate through the skin. Spanlastics, an elastic nanovesicle capable of transporting various pharmacological substances, shows promise as a drug delivery carrier. It offers numerous advantages over traditional vesicular systems applied topically, including enhanced stability, flexibility in penetration, and improved targeting capabilities. This study aims to develop meloxicam (MX)-loaded spanlastics gel as skin delivery carriers and to look into the effects of formulation factors like Tween80, Brij 35, and carbopol concentration on the properties of spanlastics gel, like pH, drug

Meloxicam is a non-steroidal anti-inflammatory drug. It is practically insoluble in water. It is associated with gastrointestinal side effects at high doses on long  term treatment. The aim of this investigation to formulate and evaluate gellified nanoemulsion of meloxicam as a topical dosage form to enhance meloxicam therapeutic activity and reduce systemic side effect.

The pseudo ternary phase diagrams were made, including  the oil mixture which is composed of almond oil and peppermint oil at a ratio (1:2), variable surfactant mixture (S mix) which are tween 80 and ethanol at ratios of (1:1, 2:1, 3:1, and 4:1) and double distilled water. Slow dripping of double distilled water to the combination  of the oil mixtu

Background: Sliding mechanics is widely used during orthodontic treatment. One of the disadvantages of this mechanics is the friction generated at the bracket/archwire interface, which may reduce the amount of desired orthodontic movement obtained. The aim of the present in vitro study was to evaluate and compare the static frictional forces produced by two passive self-ligating brackets stainless-steel and hybrid and two conventional brackets stainless-steel and monocrystal ligated with stainless-steel ligature wire at two degrees of torque(zero and twenty) under dry condition. Materials and method: One hundred and sixty brackets were used in this study divided into four groups each group consisted of forty brackets these are: Two self-li

“Orodispersible Tablet” a tablet that is to be placed in oral cavity where it disperses rapidly by saliva with no need for water before swallowing. Zaltoprofen (ZLP) is one of NSAIDs which is used in the treatment of rheumatoid arthritis and osteoarthritis as well as to relieve inflammation and pain after surgery, injury and tooth extraction. The present study was aimed to prepare rapidly dissolved lyophilized Zaltoprofen tablet with different pharmaceutical excipients and studying the factors affecting pharmaceutical properties like (solubility, disintegration time DT, dissolution, etc.) of tablets. The lyophilized disintegrating tablets (LDTs) were prepared using Zydis technique by lyophilization an aqueous