PDF for mathematics from the official Punjab Board website. Access chapter-wise details for mathematics with the link to ...

This article covers the Punjab Board's 2025–2026 Class 11 Physics Syllabus. Class 11 students can download the syllabus in PDF format to become acquainted with the subjects that will be studied during ...

This study introduces a valuable spring-bead model for epithelial cell layers, designed to improve previous cell-resolved approaches and to understand the connection between the biophysics of ...

This important study demonstrates the significance of incorporating biological constraints in training neural networks to develop models that make accurate predictions under novel conditions. By ...

Financial Independence, Retire Early (FIRE) is a movement dedicated to living frugally to retire at a young age. FIRE devotees aim to save at least 25 times their annual expenses.

This paper recommends a set of standards for notation and nomenclature that would assist prospective authors interested in submitting papers in the area of nonsinusoidal, complete, orthogonal sets of ...

is finally obtained. In equation (1), u0(x) and v0(x) represent the axial and transverse displacement, respectively, of the section centroidal axis, θ(x) indicates the rotation of the cross section, ...

That would be more flexible than just removing the definition, though might need consideration w.r.t. indentation. That would probably be good enough for us, though it's not quite as maintainable in ...

The find_zeros function can be used to search for all zeros in a specified interval. The basic algorithm essentially splits the interval into many subintervals. For each, if there is a bracket, a ...