In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Letters in Biomathematics · Jul 7, 2025Letters in Biomathematics · Jul 7, 2025 Show publication This paper, presents the application of the B-spline transform as an effective and precise technique for estimating key parameters i.e., drift, volatility, and jump intensity for Lévy processes. Lévy processes are powerful tools for representing phenomena with continuous trends with abrupt changes. The proposed approach is validated through a simulated biological case study on animal migration in which movements are mo

Applying a well-performing heat exchanger is an efficient way to fortify the relatively low thermal response of phase-change materials (PCMs), which have broad application prospects in the fields of thermal management and energy storage. In this study, an improved PCM melting and solidification in corrugated (zigzag) plate heat exchanger are numerically examined compared with smooth (flat) plate heat exchanger in both horizontal and vertical positions. The effects of the channel width (0.5 W, W, and 2 W) and the airflow temperature (318 K, 323 K, and 328 K) are exclusively studied and reported. The results reveal the much better performance of the horizontal corrugated configuration compared with the smooth channel during both melti

Background: Chronic kidney disease is a gradual loss of kidney function with diabetes and hypertension as the leading cause. Chronic kidney disease is one of these systemic diseases that can affect salivary contents. Aims: This study aimed to assess salivary immunoglobulin A, interleukin-6 and C- reactive protein in chronic kidney disease patients on hemodialysis and those on conservative treatment in comparison with control subjects. Materials and methods: Ninety subjects were included in this study divided into three groups: 30 patients with chronic kidney disease on hemodialysis for at least 6 months ago; 30 patients with chronic kidney disease on conservative treatment and 30 healthy control subjects. Secretory immunoglobulin A, inte

Nano-crystalline iron oxide nanoparticles (magnetite) was synthesized by open vessel ageing process. The iron chloride solution was prepared by mixing deionized water and iron chloride tetrahydrate. The product was characterized by X-Ray, Surface area and pore volume by Brunauer-Emmet-Teller, Atomic Force Microscope (AFM) and Fourier Transform Infrared Spectroscopy(FTIR)  .  The results showed that the XRD in compatibility of the prepared iron oxide (magnetite) with the general  structure of standard iron oxide, and in Fourier Transform Infrared Spectroscopy, it is strong crests in 586 bands, because of  the expansion vibration manner related to the metal oxygen absorption band (Fe–O bonds in the crystals of iron ox

This study showed that the lens in baloot muluki fish Chondrostoma regium is transparent, spherical shape, and solid in textures, while in the tree frog Hyla arborea savignyi, freshwater turtles Clemmys caspia caspia, white–eared bulbul Pycnonotus leucotis and brown rat Rattus norvegicus are transparent, soft and biconvex, it is very soft in white–eared bulbul. There are many significant differences have been recorded between the average weight lens and the total concentration of the protein in the lens all studied animals. Electrical migration process for lens proteins showed that there is one bundle of crystalline –? and one bundle also crystalline–? in all studied species, either crystalline–? may represent one bundle character

Objective: Rheumatoid arthritis (RA) patients have increased morbidity and mortality from premature cardiovascular (CV) disease (CVD). Framingham risk score (FRS) is a simplified coronary prediction tool developed to enable clinicians to assess the risk of a cardiovascular event and to identify candidate patients for risk factors modifications worldwide. The predictive ability of the FRS varies between populations, ethnic groups, and socio-economic status. The aim of this study is to find if there is any correlation between the Framingham risk score and the inflammatory and biochemical parameters used to measure disease activity and functional ability in Iraqi patients with active RA.

This study focused on the expression and regulation of BRCA1 in breast cancer cell lines compared to normal breast. BRCA1 transcript levels were assessed by real time quantitative polymerase chain reaction (RT-qPCR) in the cancer cell lines. Our data show overexpression of BRCA1 mRNA level in all the studied breast cancer cell lines: MCF-7, T47D, MDA-MB-231 and MDA-MB-468 along with Jurkat, leukemia T-lymphocyte, the positive control, relative to normal breast tissue. To investigate whether a positive or negative correlation exists between BRCA1 and the transcription factor E2F6, three different si-RNA specific for E2F6 were used to transfect the normal and cancerous breast cell lines. Interestingly, strong negative relationship was found b

Abstract:

     Due to the importance of technology and the accompanying changes of the environment affecting companies that use the technology mainly in their work, especially as most companies live in an unstable dynamic environment, which motivated the researchers to choose the International Company for smart card (Keycard) as a field of research and find ways to them to face Those changes.

     The problem of the study was "limited attention to the components of technological change", which included research and development, innovation and information technology, which had an impact on the design decisions of the process (process selection, cust