The Uttarakhand Board of School Education (UBSE) has structured the Class 11 Mathematics syllabus for the academic session ...

The original version of this story appeared in Quanta Magazine. In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was ...

Alzheimer’s disease is a devastating neurodegenerative disorder characterized by memory loss and cognitive decline. New AD treatments are essential, and drug repositioning is a promising approach. In ...

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures. Hofstadter was ...

Abstract: A new general Jacobi elliptic function rational expansion method, which is more general and powerful than the tanh method, the sine-cosine method, the Jacobi elliptic function method and the ...

While graphs for cosine and sine functions are similar, those for tangent functions differ significantly from them, sharing only in that they show periodicity and symmetry. Recall \(\tan(x)= ...

Linear functions are fundamental building blocks in mathematics and play a key role in solving real-world problems where the rate of change remains constant. Linear functions arise in a wide range of ...

Introduction: Age-related changes occurring in the kidney can lead to a reduction in Glomerular Filtration Rate (GFR); especially in older adults with multimorbidity and/or frailty, an accurate ...