Wasit Journal for Pure Sciences

This paper introduces and systematically investigates the notion of unitary quasi-square equivalence
for bounded linear operators on Hilbert spaces. This equivalence relation, defined through the unitary equivalence
of operator squares, provides a classification that preserves essential spectral and structural properties while
capturing higher-order similarities not detectable through classical unitary equivalence. We establish that this
relation defines a genuine equivalence relation and explore its connections with fundamental operator classes
including square normal operators, n-quasi-normal operators, hyponormal operators, and various isometric
structures. Our main contributions include complete characterization of spectral invariants preserved under this
equivalence, demonstration of preservation theorems for advanced operator classes and their C*-algebraic structure,
applications to concrete operator families, and development of decomposition theorems revealing the canonical
structure of equivalence classes. The theory developed provides a tool for operator classification with applications
to invariant subspace problems, similarity theory, and the structural analysis of non-normal operators.

The importance of nano-topology via graphs lies in its ability to represent data within a small yet
meaningful topological framework, which enhances the accuracy of classification and decision-making, and supports
comparison and categorization. This makes any model applicable in various fields such as healthcare and data
analysis. The main objective of this paper is to introduce a new concept of nano-connectivity, called nano-g
connectedness via graph. Which defined as the disjoint union of any pair of open sets. We also present a new
application to identify the main factors contributing to atherosclerosis.

This research presents an integrated approach that combines sensitivity analysis with fuzzy logic to
address uncertainty in operations research models. The study focuses on the right-hand side (RHS) of constraints as
a key parameter subject to variation. To capture this uncertainty, a symmetric heptagonal fuzzy membership function
is proposed, where the seven representative values are governed by a single weight parameter (r). A corresponding
fuzzy ranking function is developed to transform the fuzzy outcomes into comparable crisp values. The methodology
is applied to two illustrative linear programming examples drawn from textbooks, covering both maximization and
minimization problems. The results demonstrate that the fuzzy ranking approach, particularly under specific weight
programming under uncertainty.
configurations, provides more robust and realistic solutions than traditional sensitivity analysis. These findings
confirm the effectiveness of integ

To comprehend how epidemics develop and assess the efficacy of medical treatments, infectious
disease modeling is crucial. The SIR model, which separates the population into susceptible, infected, and recovered
groups, is one example of the mathematical and statistical models that scientists and policymakers use to describe the
dynamics of infection transmission among individuals within a society. These models may also be expanded to
incorporate other components, such vaccination, alterations in social behavior, and the results of medical treatments.
This work focuses on analyzing the spread of Oropouche fever using the SEIR model with a protective factor that
simulates the impact of interventions. The results demonstrate how interventions contribute to reducing the number
of infections and delaying the peak of the epidemic. The work also examines the use of the SIRD model in two
versions: the classic (without vaccination) and the modified (with vaccination). The numerical results clearly
demonstrate the role of vaccination in reducing morbidity and mortality rates, highlighting the importance of
mathematical modeling in designing effective strategies to combat epidemics.

The increasing deployment of 5G-based Internet of Things (IoT) infrastructure brings about
unparalleled opportunities and the exacerbated threat of malicious Distributed Denial-of-Service (DDoS) attacks.
Conventional signature-based or static rule-based intrusion detection systems are still inadequate for the dynamic and
high-volume traffic in such systems. In order to address these issues, in this paper, we propose a hybrid model with
CNN and LSTM. The network features spatial correlations, which are captured by the CNN layers, and the LSTM
units learn sequential dependencies for detecting attack behavior evolution. Experimental evaluations performed on
the CICDDoS2019 and BoT-IoT datasets show how each module helps, leading to an overall detection accuracy of
more than 99% and low false positive rates, and classification latency in real time, 19.5 ms for CICDDoS2019 and
13.6 ms for BoT-IoT), comparisons to relevant existing machine and deep learning baselines establish the trade-off
made between accuracy, scalability and practical deployment efficiency. The results show that the proposed model is
a suitable and practical choice for protecting 5G-enabled IoT systems against DDoS attacks.

This research examines the detection of fake Instagram accounts by comparing single machine learning
classifiers with a stacking ensemble model applied to integrated static and temporal features. A dataset of 7,594
accounts was collected over five months using multiple scraping tools, ensuring a balanced representation of real and
fake profiles. Key behavioral, engagement, and account-level features were extracted to capture users’ activity
patterns. Among the individual classifiers, Random Forest achieved the highest performance; however, the stacking
ensemble model outperformed all single models, reaching an accuracy of 0.9888 with superior precision, recall, and
F-measure values. The findings demonstrate that integrating temporal metrics with ensemble learning significantly
enhances detection

Ultrafiltration systems are considered clean and environmentally acceptable for removing bacteria and
contaminants from drinking water. This study used poly sulfone polymer (PSU), DMF, Kaolinite Nanoclay with
carbon nanoparticles synthesized from date seeds using reverse-phase technology. In this case, the performance of an
ultrafiltration (UF) membrane was improved. Carbon nanoparticles (0, 0.025, 0.050, and 0.075%) were examined,
and the polymer concentration was maintained at 17%. The membrane was tested for its ability to remove Escherichia
coli from contaminated drinking water. FTIR, AFM, SEM, and EDX tests were used to characterize the membrane
composition and structure. As the carbon nanoparticle concentrations varied, the membrane's morphology changed.
Various factors were also studied, such as the membrane's ability to remove bacteria from drinking water. The
synthesis of membrane (nanofilm) was confirmed using FTIR which conformed presence of active groups responsible
for the synthesis process. AFM show revealed an array of homogeneous particles with a regular surface, SEM show
a smooth spherical appearance with a diameter range of the particles between 27.69-63.74 nm, EDX spectra shown
the main components of the extract were carbon (C), and oxygen (O), , with percentages of 64.8%, and 24%,
respectively. The presence of minor components such as Al, Si, S, and Cl with percentages of 0.6%, 0.7%, 8.7%, and
0.3%, respectively. The results of removing contaminated bacteria from drinking water using membranes indicated
significant statistical differences (P≤0.05) between the membranes. The efficiency of the membranes was in the
following order: F4>F3>F2>F1 compared with sampled without treatments. The study demonstrated that the
fabricated nanoclay membrane reinforced with nanocarbon exhibited high efficiency in removing Escherichia coli
from contaminated drinking water.

Thyroid Cancer is a malignant tumor that develops from the cells of the thyroid gland. Biomarkers can assist to detect
thyroid cancer before evident clinical symptoms appear, improving early diagnosis. Thus, the object of this study was to
evaluate the role of Ki-67 and Galactin-3 (Gal-3) proteins as a biomarker for thyroid cancer diagnosis and to ascertain
how these proteins relate to the type and stage of the tumor. This study includes forty formalin-fixed, paraffin-embedded
thyroid carcinoma tissue samples were collected from the archives of Histopathology Department at Al-Karama Teaching
Hospital in Wasit Governorate, Iraq which diagnosed by a specialist physician. The streptavidin-peroxidase method was
used for immunohistochemical staining. “Gal-3 expression was evaluated based on staining intensity and the distribution
of positive cells, whereas K-67 expression was evaluated based on the proportion of positively stained nuclei”. The mean
age of the patients was 44.85 ± 10.3 years, with ages ranging from 24 to 72. Males made about 15% of cases, with women
making up the bulk (85%). The most prevalent histological pattern was papillary thyroid carcinoma (85%), which was
followed by multifocal papillary thyroid cancer (15%). Stage I diagnoses accounted for 80% of cases, whilst stage II
diagnoses made up 20%. 65% of cases had elevated Ki-67 protein levels, which were strongly correlated with the type
and stage of the tumor. In 70% of cases, especially papillary thyroid carcinoma, galectin-3 protein levels were substantially
positive. They also demonstrated a statistically significant link with the type and stage of the tumor. The findings suggest that Gal-3 and Ki-67 are useful markers for thyroid cancer diagnosis. While Gal-3 may be a crucial diagnostic marker for distinguishing malignant thyroid cancers, Ki-67 shows tumor growth activity and may suggest its aggressiveness.

This paper reports the development of luminescent zinc-based metal-organic frameworks (MOFs) as
optical sensors for monitoring pharmaceutical pollutants in water specifically diclofenac and ibuprofen. The MOFs
were synthesized under solvothermal conditions and exhibited crystalline, microporous structures with strong
fluorescent properties, enabling analyte-induced quenching for sensitively detection. Under optimized conditions a
rapid response was realized in 2 min with high selectivity towards common interferents. Stern -Volmer analysis
revealed that they behaved in a linear manner and their detection limits were 0.8 µg/L and 2.1 µg/L when using
diclofenac and ibuprofen respectively. Recovery tests in tap, river and wastewater sample produced 92-106% recovery
values which prove to be effective. The sensors have been found to be stable with a 90 % performance when they
were used repeatedly. These findings demonstrate luminescent MOFs as high-quality, reusable sensors in seconds of environmental surveillance of new pharmaceutical pollutants.