On Quasi-Periodicity in Proth-Gilbreath Triangles

Let PG be the Proth-Gilbreath operator that transforms a sequence of integers into the sequence of the absolute values of the differences between all pairs of neighbor terms. Consider the infinite tables obtained by successive iterations of PG applied to different initial sequences of integers. We study these tables of higher order differences and characterize those that have near-periodic features. As a biproduct, we also obtain two results on a class of formal power series over the field with two elements F2 that can be expressed as rational functions in several ways

An Algebraic Structure for Square-Prime Numbers

In the paper "An Abelian Loop for Non-Composites" (arXiv:110.14716), we introduced a group-like structure consisting of odd prime numbers and 1, with properties that allowed us to prove analogous results to well known theorems in Number Theory. In this paper, we explore some theorems and conjectures in the SP space

Inhibition of Al corrosion in 0.5 M HCl solution by Areca flower extract

The corrosion inhibition property of Areca flower extract species on the Al surface in acid (0.5 M HCl) medium was tested by weight loss, Tafel plot, impedance, scanning electron microscopy and atomic force microscopy techniques. The influence of different concentrations of Areca flower extract, 0.5 M HCl solution temperature and aluminum immersion (contact) time was also evaluated. Parameters such as Ea, ΔH∗, ΔS∗, Kads and ΔG°ads were calculated by the gravimetric (weight loss) technique. Results of mass loss technique indicated that, the Areca flower extract molecules are strongly adsorbed at Al- 0.5 M HCl solution interface and follows the law of the Langmuir adsorption model. Tafel curves show that, the Areca flower extract molecules effectively adsorbed on the active Al sites by replacing the H2O molecules and strongly interact with cathodic and anodic sites impeding the dissolution reaction by mixed mode. Hence, Al metal is protected. Electrochemical impedance results indicate that, area of a semicircle (Nyquist plots) in the presence of the Areca flower extract is high compared to the bare system. The variation in the surface topography of aluminum was analyzed through scanning electron microscopy and atomic force microscopy techniques. Further, AFM results show that, surface roughness values in the protected Al system are low compared to the unprotected Al system. Keywords: Aluminum, Areca flower, Hydrochloric acid, Langmuir adsorption model, Surface morpholog

Glucometer as a chairside device to assess blood glucose in periodontal patients

Background: Diabetes mellitus is a common finding in the medical history of patients receiving treatment for periodontal disease. The incidence of diabetes is on the rise worldwide. Virtually, every dentist and especially the periodontist are likely to encounter an increasing number of undiagnosed diabetic patients. The conventional laboratory methods employed to detect blood glucose are time consuming and require elaborative equipment. The advent of blood glucose monitors allows the clinician to assess blood glucose at the chair side. Materials and Methods: The use of gingival capillary blood as a marker for blood glucose estimation using glucometer against the conventional laboratory method has been assessed in 60 diabetics and 70 controls. Results: The correlation between gingival and finger-stick blood was r = 0.996, P<0.001 in diabetics and controls. Correlation between gingival and laboratory method was r = 0.994, P<0.001 in cases and controls. Conclusion: The results suggest that capillary blood from the outer surface of gingiva provide an acceptable source for measuring blood glucose

Lithium d‑Isoascorbate Monohydrate, a New Nonlinear Optical Material

Single crystals of lithium d-isoascorbate monohydrate (LDAM), (C₆H₇O₆Li·H₂O), are grown by a solution growth method. The crystal structure of LDAM is solved using single crystal X-ray diffraction. The space group is orthorhombic <i>P</i>2₁2₁2₁ with four formula units per unit cell and lattice parameters <i>a</i> = 7.7836(3) Å, <i>b</i> = 8.7456(3) Å, and <i>c</i> = 11.0368(4) Å. Solubility of the material in water is determined thermogravimetrically and found to have a positive temperature coefficient of solubility. Large optical quality single crystals are subsequently grown from aqueous solution by a slow cooling method. The crystal has a bulky prismatic habit and among the prominent faces the <i>c</i> face appears as the only principal morphological face. The crystal exhibits a (010) cleavage. Dielectric spectroscopy reveals a nearly Debye type Cole–Cole behavior with anisotropy in relaxation. Optical transmission range is found to be from 300 to 1400 nm. The principal refractive indices of this biaxial crystal, measured using Brewster’s angle method, at wavelengths 405, 543, and 632.8 nm, show high dispersion. The crystal is negative biaxial with 2<i>V</i>_<i>z</i> = 107.8° (405 nm) and belongs to the Hobden class 3. Theoretically generated type 1 and type 2 second order phase matching curves match very well with the experimental results. The second-order nonlinear coefficient <i>d</i>₁₄ was determined to be 7 × 10^–13 m/V. For the optimum phase matching direction (type 2), the second-order effective nonlinear coefficient and the walk off angle are determined to be 0.84 times <i>d</i>₁₄ and 3.5° respectively. The crystal possesses high multiple surface damage thresholds of 18 GW/cm² and 8 GW/cm² at laser wavelengths 1064 and 532 nm, respectively

Lithium d‑Isoascorbate Monohydrate, a New Nonlinear Optical Material

Single crystals of lithium d-isoascorbate monohydrate (LDAM), (C₆H₇O₆Li·H₂O), are grown by a solution growth method. The crystal structure of LDAM is solved using single crystal X-ray diffraction. The space group is orthorhombic <i>P</i>2₁2₁2₁ with four formula units per unit cell and lattice parameters <i>a</i> = 7.7836(3) Å, <i>b</i> = 8.7456(3) Å, and <i>c</i> = 11.0368(4) Å. Solubility of the material in water is determined thermogravimetrically and found to have a positive temperature coefficient of solubility. Large optical quality single crystals are subsequently grown from aqueous solution by a slow cooling method. The crystal has a bulky prismatic habit and among the prominent faces the <i>c</i> face appears as the only principal morphological face. The crystal exhibits a (010) cleavage. Dielectric spectroscopy reveals a nearly Debye type Cole–Cole behavior with anisotropy in relaxation. Optical transmission range is found to be from 300 to 1400 nm. The principal refractive indices of this biaxial crystal, measured using Brewster’s angle method, at wavelengths 405, 543, and 632.8 nm, show high dispersion. The crystal is negative biaxial with 2<i>V</i>_<i>z</i> = 107.8° (405 nm) and belongs to the Hobden class 3. Theoretically generated type 1 and type 2 second order phase matching curves match very well with the experimental results. The second-order nonlinear coefficient <i>d</i>₁₄ was determined to be 7 × 10^–13 m/V. For the optimum phase matching direction (type 2), the second-order effective nonlinear coefficient and the walk off angle are determined to be 0.84 times <i>d</i>₁₄ and 3.5° respectively. The crystal possesses high multiple surface damage thresholds of 18 GW/cm² and 8 GW/cm² at laser wavelengths 1064 and 532 nm, respectively