Arithmetic properties of 5-regular bipartitions

Let Bt(n) denote the number of t-regular bipartitions of n. In this work, we establish several infinite families of congruences modulo powers of 2 and 5 for B5(n). For example, we find that for all nonnegative integers n, i and j and r ϵ 23, 47, B5 (22i+4.52j+1n + r.22i+1.52j-1/3) 0(mod24). © 2017 World Scientific Publishing Company

Color Partition Identities Arising from Ramanujan's Theta-Functions

We establish several partition identities with distinct colors that arise from Ramanujan’s theta-function identities and formulas for multipliers in the theory of modular equations. Also, we deduce few partition congruences as a corollary of some partition identities

On some new modular relations for Ramanujan's remarkable product of theta functions

In this paper, we establish several new P-Q mixed modular equations involving thetafunctions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new general formulas for explicit evaluations of Ramanujan's remarkable product of theta-functions and a remarkable product of theta-functions

Comparative evaluation of shear bond strength of universal dental adhesives : an in vitro study

Patient demand for tooth colored restorations and desire for minimally invasive restorations have made composites an indispensable part of the restorative process. An important factor affecting the intra-oral performance of composite restorations is bonding. Ninty six freshly extracted molar teeth were collected and occlusal 3mm is removed using a diamond disc to expose dentine. Following with samples were divided in to two main groups (self-etch and total etch). Each main group is again sub divided in to three groups each according to bonding agent used (Tetric N- Bond Universal, Single Bond Universal, Tetric N Bond Total etch in total etch group and Clear Fill SE in self etch group). Following which bonding protocol is followed according to manufacture instructions, a composite buildup of 2x3 mm is done on each specimen and then specimen were subjected to shear bond test under universal testing machine. All the readings were noted and subjected to statistical analysis using One way ANOVA and Tukey?s posthoc test. It showed that there is no significant difference among the groups in both self-etch and total etch modes. It can be concluded that application of an etching step prior to Universal Adhesives significantly improves their dentine penetration pattern, although this does not affect their mean SBS. The bond strength values of the TBU regardless of application mode were comparable to SBU making them reliable for working under different clinical conditions

New P�Q mixed modular equations and their applications

In his second notebook, Ramanujan recorded total of seven P�Q modular equations involving theta-function (Formula presented.) with moduli of orders 1, 3, 5 and 15. In this paper, modular equations analogous to those recorded by Ramanujan are obtained for higher orders. As a consequence, several values of quotients of theta-function are evaluated. The cubic singular modulus is evaluated at (Formula presented.) for (Formula presented.), where (Formula presented.). © 2017 Università degli Studi di Ferrar