Duaa Abdullah
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View article: Bounds on the Albertson Index for Trees with Given Degree Sequences
Bounds on the Albertson Index for Trees with Given Degree Sequences Open
In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy \[ \operatorname{irr}(G)=\l…
View article: Generalized Natural Density DF(Fk) of Fibonacci Word
Generalized Natural Density DF(Fk) of Fibonacci Word Open
This paper explores profound generalizations of the Fibonacci sequence, delving into random Fibonacci sequences, k-Fibonacci words, and their combinatorial properties. We established that the nth root of the absolute value of terms in a ra…
View article: On the Asymptotic Palindrome Density of Fibonacci Infinite Words
On the Asymptotic Palindrome Density of Fibonacci Infinite Words Open
In this paper, we investigate the combinatorial and density properties of infinite words generated by Fibonacci-type morphisms, focusing on their subword structure, palindrome density, and extremal statistical behaviors. Using the morphism…
View article: The Effect of Using Popular Mathematical Puzzles on The Mathematical Thinking of Syrian Schoolchildren
The Effect of Using Popular Mathematical Puzzles on The Mathematical Thinking of Syrian Schoolchildren Open
In this paper we provide a good overview of the problems and the background of mathematics education in Syrian schools. We aimed to study the effect of using popular mathematical puzzles on the mathematical thinking of schoolchildren, by c…
View article: Behavior of The Extremal Bounds on the $σ$-Irregularity
Behavior of The Extremal Bounds on the $σ$-Irregularity Open
In this paper, we establishe the extremal bounds of the topological indices -- Sigma index -- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index, which is known $σ(G)=\sum_{uv\in E(G)}(d_G(u)-d_G(v))^2$. W…
View article: Extremal Bounds on the Properties of Sigma and Albertson Indices for Non-Decreasing Degree Sequences
Extremal Bounds on the Properties of Sigma and Albertson Indices for Non-Decreasing Degree Sequences Open
In this paper, we establish bounds on the topological index -- the Sigma index -- focusing on analyzing the upper bound of its maximum value, which is known as $σ_{\max}(\mathcal{S}) = \max \{σ(\mathscr{G}) \mid \mathscr{G} \in \mathcal{S}…
View article: Efficacy of Topical Corticosteroid Therapy in Chronic Rhinosinusitis Post-endoscopic Sinus Surgery: A Narrative Synthesis of Randomized Controlled Trials
Efficacy of Topical Corticosteroid Therapy in Chronic Rhinosinusitis Post-endoscopic Sinus Surgery: A Narrative Synthesis of Randomized Controlled Trials Open
Chronic rhinosinusitis (CRS) is a frequent inflammatory disorder that can markedly impair patients' quality of life. Endoscopic sinus surgery (ESS) remains the treatment of choice for refractory cases, but postoperative inflammation and ad…
View article: The Density of Zero and One in Fibonacci Word for Subwords and Their Palindromes
The Density of Zero and One in Fibonacci Word for Subwords and Their Palindromes Open
This paper studies the density of zero and one in subwords of the Fibonacci word with lengths less than thirty and compares them to the densities of their corresponding palindromes. We used computational methods to produce a sufficiently l…
View article: Applications of Combinatorics on Words with Symbolic Dynamics
Applications of Combinatorics on Words with Symbolic Dynamics Open
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical foundatio…
View article: On Topological Indices in Trees: Fibonacci Degree Sequences and Bounds
On Topological Indices in Trees: Fibonacci Degree Sequences and Bounds Open
In this paper, we have studied bounds based on topological indicators, from which we selected Albertson index $\mathrm{irr}$ and the Sigma index $σ$. The Sigma index was defined through the following relationship: \[ σ(G)=\sum_{uv\in E(G)}…
View article: A REVIEW ON Aerodramus SPP. IN TROPICAL ECOSYSTEMS: EMPHASIS ON FOOD SOURCES FOR EDIBLE BIRD NEST (EBN) PRODUCTION
A REVIEW ON Aerodramus SPP. IN TROPICAL ECOSYSTEMS: EMPHASIS ON FOOD SOURCES FOR EDIBLE BIRD NEST (EBN) PRODUCTION Open
Edible Bird Nests (EBNs) are highly coveted commercial products of saliva secretions from swiftlets, particularly Aerodramus spp. These nests are renowned for their nutritional value and medicinal properties, contributing significantly to …
View article: Bounds on Trees with Topological Indices Among Degree Sequence
Bounds on Trees with Topological Indices Among Degree Sequence Open
In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two topol…
View article: Comparison Between Early and Standard Oral Feeding After Emergency Bowel Surgery
Comparison Between Early and Standard Oral Feeding After Emergency Bowel Surgery Open
Background: Postoperative nutritional management plays a crucial role in patient recovery following emergency bowel surgery. Traditionally, oral feeding has been delayed to prevent complications like anastomotic leakage and ileus (standard…
View article: Comparative Analysis of the Modified Atlanta Classification and CT Severity Index in Assessing Acute Gallstone Pancreatitis: A Study at PIMS Hospital, Islamabad
Comparative Analysis of the Modified Atlanta Classification and CT Severity Index in Assessing Acute Gallstone Pancreatitis: A Study at PIMS Hospital, Islamabad Open
Background: Acute gallstone pancreatitis (AGP) is a significant gastrointestinal emergency with variable degrees of severity. Exact classification is important for guiding clinical management and predicting patient outcomes. The Modified A…
View article: Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis
Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis Open
This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical …
View article: Generalized Natural Density $\DF(\mathfrak{F}_n)$ of Fibonacci Word
Generalized Natural Density $\DF(\mathfrak{F}_n)$ of Fibonacci Word Open
This paper explores profound generalizations of the Fibonacci sequence, delving into random Fibonacci sequences, $k$-Fibonacci words, and their combinatorial properties. We established that the $n$-th root of the absolute value of terms in…
View article: Improvement Ergodic Theory For The Infinite Word $\mathfrak{F}=\mathfrak{F}_{b}:=\left({ }_{b} f_{n}\right)_{n \geqslant 0}$ on Fibonacci Density
Improvement Ergodic Theory For The Infinite Word $\mathfrak{F}=\mathfrak{F}_{b}:=\left({ }_{b} f_{n}\right)_{n \geqslant 0}$ on Fibonacci Density Open
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasin…
View article: Dynamic and Programmatic Analysis of Fibonacci Word Density
Dynamic and Programmatic Analysis of Fibonacci Word Density Open
Fibonacci word is the archetype of the Sturmian word, and it is one of the most studied of combinatorics on words. We studied the properties of the Fibonacci word and found its density for limited value then by calculating the limit associ…
View article: Regularities of Typical Sigma Index on Caterpillar Trees of Pendent Vertices
Regularities of Typical Sigma Index on Caterpillar Trees of Pendent Vertices Open
In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study on topological indices related to the Sigma index, which w…
View article: Assessing By Model Fitting Criteria and Comparing Between Stirling and Aitken Interpolation Formulas to Determine the Preferred Treatment of Choice, (Surgery) Or (Surgery with Chemotherapy), For Lung Cancer, In Kurdistan
Assessing By Model Fitting Criteria and Comparing Between Stirling and Aitken Interpolation Formulas to Determine the Preferred Treatment of Choice, (Surgery) Or (Surgery with Chemotherapy), For Lung Cancer, In Kurdistan Open
Numerical analysis is a branch of mathematical science; Interpolation is a method in Numerical analysis used for creating a model for group of discrete data points. This paper focused on two interpolations methods [Stirling's and Aitken] i…
View article: “Wound Healing and Hemostasis: An Experimental Study on Kadamba's Effect in Wistar Albino Rats”
“Wound Healing and Hemostasis: An Experimental Study on Kadamba's Effect in Wistar Albino Rats” Open
View article: Hadith Etiquette in the Holy Quran
Hadith Etiquette in the Holy Quran Open
Allah, Glory be to Him, has created man and bestowed upon him many great blessings and good and beautiful attributes. Among these great blessings that Allah bestowed on man is the blessing of eloquence and the ability to communicate and sp…