We introduce the \textit{modular intersection kernel}, and we use it to study how geodesics intersect on full modular surface $\mathbb{X}=PSL_2\left(\mathbb{Z}\right) \backslash \mathbb{H}$. Let $C_d$ be union of closed with discriminant $d$ let $\beta\subset \mathbb{X}$ a compact geodesic segment. As an application Duke's theorem kernel, prove that $ \{\left(p,\theta_p\right)~:~p\in \beta \cap...

MOTIVATION Most secondary structure prediction programs target only alpha helix and beta sheet structures and summarize all other structures in the random coil pseudo class. However, such an assignment often ignores existing local ordering in so-called random coil regions. Signatures for such ordering are distinct dihedral angle pattern. For this reason, we propose as an alternative approach to...

Miscut surfaces of layered crystals can exhibit a stair-like sequence terraces having periodic variation in their atomic structure. For hexagonal close-packed and related crystal structures with an {\alpha}{\beta}{\alpha}{\beta} stacking sequence, there have been long-standing questions regarding how the differences adatom attachment kinetics at steps separating affect fractional coverage {\alp...

AIM Prospectively analyze the long term structural and functional changes in patients of primary open angle glaucoma (POAG) receiving medical therapy (beta blockers and non beta blockers). In this study an attempt has been made to evaluate whether medical reduction of IOP prevents or delays the progression of glaucomatous visual field loss and/or optic nerve damage in patients with open angle g...

The structure of 14-protofilament microtubules reassembled from dogfish shark brain tubulin was analyzed by high resolution electron microscopy and optical diffraction. The simultaneous imaging of the protofilaments from near and far sides of these tubules produces a moiré pattern with a period of approximately 96 nm. Optical diffraction patterns show that the 5-nm spots that arise from the pro...

In orthodontic diagnosis and treatment planning, an accurate antero-posterior measurement of jaw relationships is critically important. Previously described angular and linear measurements can be inaccurate because of their dependency on various factors. The purpose of this study was to introduce a new cephalometric measurement, named the W angle, to assess the sagittal relationship between max...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.