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.

Concentrations 25, 50 and 100 mg of nano-capsules linolenic acid and non-capsulated fatty acid for 1kg of Milk was used for yogurt manufacture. The results showed no significant differences in the ratio of titration acidity and pH values between all processed treatments at the beginning and during of period storage. The treatments was added to it coated omega-3 by nano method were the least exposed to the oxidation process from the non-capsules omega-3, And for shield of The poly lactic acid had a significant role in the protection of alpha-linolenic acid against lipolysis by the formation of a protective layer to protect the acid from the activity of lipases enzymes, and the addition of fatty acid linolenic to milk was determined the gr

Nanoparticles generation by laser ablation of a solid target in a liquid environment is an easy method. Cadmium Telluride (CdTe) colloidal nanoparticles have been synthesized by laser ablation Nd:YAG with wavelengths of 1064nm and double frequency at 532 nm, number of pulses 50 pulses, with pulse energy= 620mJ, 700mJ of a solid target CdTe is immersed in double distilled deionized water (DDIW) and in methanol liquid. Influences of the laser energy and different solutions on the formation and optical characterization of the CdTe nanoparticles have been studied using atomic force microscope (AFM) and the UV-Vis absorption. As a results, it leads to the absorbance in UV-Vis spectra of samples prepared in water at laser wavelength of 532nm i

Pulsed laser ablation in liquid (PLAL) has become an increasingly important technique for metals production and metal oxides nanoparticles (NPs) and others. This technique has its many advantages compared with other conventional techniques (physical and chemical). This work was devoted for production of zirconia (ZrO2) nanoparticles via PLAL technique from a solid zirconium target immersed in a wet environment in order to study the effect of this environment on the optical properties and structure of ZrO2 nanoparticles. The solutions which used for this purpose is distilled water (D.W). The produces NPs were characterized by mean of many tests such as UV-visible (UV-Vis.), transmission electron microscope (TEM) and Z-Potential. The UV-Vis.

Background: Wound healing is a complicated, interactive, integrative process involving cellular and chemotactic activity, the release of chemical mediators and associated vascular response which includes number of phases: inflammatory phase, proliferative phase and remodeling phase. Low level laser therapy can be more effective in the three overlapping phases of wound healing. Biostimulation appears to have an effect on the cellular level, by increasing cellular function and stimulating various cells. The aim of present study was to evaluate histologically the effect of 780-805 diode laser the intensity of inflammation and pattern of epithelization in mice model. Material and methods: The experimental study was performed on ninety six white

A new scheme of plasma-mediated thermal coupling has been implemented which yields the temporal distributions of the thermal flux which reaches the metal surface, from which the spatial and temporal temperature profiles can be calculated. The model has shown that the temperature of evaporating surface is determined by the balance between the absorbed power and the rate of energy loss due to evaporation. When the laser power intensity range is 107 to108 W/cm2 the temperature of vapor could increase beyond the critical temperature of plasma ignition, i.e. plasma will be ignited above the metal surface. The plasma density has been analyzed at different values of vapor temperature and pressure using Boltzmann’s code for calculation of elec

In the last years, new non-invasively laser methods were used to detect breast tumors for pre- and postmenopausal females. The methods based on using laser radiation are safer than the other daily used methods for breast tumor detection like X-ray mammography, CT-scanner, and nuclear medicine.  

      One of these new methods is called FDPM (Frequency Domain Photon Migration). It is based on the modulation of laser beam by variable frequency sinusoidal waves. The modulated laser radiations illuminate the breast tissue and received from opposite side.

      In this paper the amplitude and the phase shift of the received signal were calculated according to the orig

A theoretical model is developed to determine time evolution of temperature at the surface of an opaque target placed in air for cases characterized by the formation of laser supported absorption waves (LSAW) plasmas. The model takes into account both plasma dynamics and time variation of incident laser pulse (i.e. pulse shape or profile).Shock tube relations were employed in formulating plasma dynamics over target surface. Gaussian function was chosen in formulating the pulse profile in the present modeling

Four photosensitizers were used to test inhibitory effect of Helicobacter pylori bacteria using
low power helium: neon red laser radiation. Biopsies were collected from 176 patients and H. pylori were
isolated, identified and bacterial suspension was prepared. Samples of this suspension were mixed with
various low concentrations of the test sensitizer. The mixture samples were exposed to different laser
radiation doses. The samples were then inoculated and the inhibition zones were studied and compared
with their analogues of control samples. The most effective sensitizer with optimum concentration and
irradiation dose was determined. Statistical analysis of results was performed. The sensitizers' toluidine
blue and

The main goal of this in vivo study was to evaluate the effect of 532nm Q-switched Nd: YAG Laser in combination with Human Serum Albumin 20% concentration (as a welding aid) on the liver tissue repair clinically, and histologically. The animals used in this study were 21 male rabbits divided into three main groups: control group (3 rabbits), conventionally treated group (9 rabbits) and Laser treated group (9 rabbits). Each two main groups (conventional and laser treated) consist of three sub-groups depending on the response evaluation at three different periods. The Laser group was treated using 532nm Q-switched Nd: YAG laser after adding human serum albumin immediately on the incised liver’s tissue. The energy of was 460mJ, and 4Hz fr