A memorial tribute to Helena Vrbova

A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse axis is...

Histone variants are the histone proteins with structural and sequence variations. These variants may be regarded as “mutant” forms that replace their canonical histone counterparts in the nucleosomes. Specific post-translational modifications on the histone variants enable further chromatin complexity and regulate tissue-specific gene expression. The most common histone variants are from histone H2A, H2B, and linker histone H1 families. However, several variants of histone H3 variants are also...

In eukaryotic DNA replication, a single-stranded DNA fragment remains at the end of a chromosome after the removal of the final primer. This section of DNA cannot be replicated in the same manner as the rest of the strand because there is no 3’ end to which the newly synthesized DNA can attach. This non-replicated fragment results in gradual loss of the chromosomal DNA during each cell duplication. Additionally, it can induce a DNA damage response by enzymes that recognize single-stranded DNA.

In eukaryotic DNA replication, a single-stranded DNA fragment remains at the end of a chromosome after the removal of the final primer. This section of DNA cannot be replicated in the same manner as the rest of the strand because there is no 3’ end to which the newly synthesized DNA can attach. This non-replicated fragment results in gradual loss of the chromosomal DNA during each cell duplication. Additionally, it can induce a DNA damage response by enzymes that recognize single-stranded DNA.

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...