Mathematical Modeling and Computation of NM-Polynomial Indices for Physicochemical Properties Prediction

A drug's physicochemical properties fundamentally influence its metabolism. For instance, a drug's molecular size and shape critically determine its interaction with enzymes and transporters — larger drugs may face difficulty reaching enzyme active sites, altering their metabolic pathways. The pKa of a drug, which establishes its ionization state, can impact its solubility and absorption, thereby influencing metabolism.
The drug's acidity or basicity is essential in...

Certain organic substances change color in dilute solution when the hydronium ion concentration reaches a particular value. For example, phenolphthalein is a colorless substance in any aqueous solution with a hydronium ion concentration greater than 5.0 × 10−9 M (pH < 8.3). In more basic solutions where the hydronium ion concentration is less than 5.0 × 10−9 M (pH > 8.3), it is red or pink. Substances such as phenolphthalein, which can be used to determine the pH of a solution, are...

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...

Renal clearance of a drug is influenced by various factors, including its physicochemical properties and plasma levels. These factors play a significant role in determining how efficiently the kidneys eliminate a drug.
One important factor is the drug's molecular size. The kidneys readily excrete smaller molecules below 300 Daltons (Da). On the other hand, molecules weighing between 300 and 500 Da are excreted through both urine and bile. Larger molecules above 500 Da tend to be excreted...

Polynomial division is an essential algebraic process to simplify expressions and solve equations. Just as numerical division separates a number into quotient and remainder, polynomial long division partitions a polynomial into simpler components; in this context, the dividend is the polynomial being divided, the divisor is the expression dividing it, and the result is expressed in terms of a quotient and a remainder.The division begins by arranging the dividend and divisor in standard...

Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is...