this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

In this paper, we consider the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem [Formula: see text]where [Formula: see text] is a bounded domain in [Formula: see text], [Formula: see text], with a smooth boundary [Formula: see text], [Formula: see text] and [Formula: see text]. By using variational approach and some subtle analytical skills, the existence ...

BACKGROUND This study aimed to evaluate the prediction accuracy of postoperative refractions using partial coherence interferometry (IOL-Master) and applanation ultrasound (AL-3000) assisted with corneal topography (TMS-4) in eyes that had undergone myopic laser-assisted in situ keratomileusis (LASIK). METHODS Haigis-L formula, Koch-Maloney method using Haigis formula, Shammas clinically deri...

although fluoridated toothpastes are among the most accessible fluoride sources for caries prevention, their remineralization potential remains questionable. this study sought to compare the effects of 5 different child formula dentifrices on remineralization of artificial primary enamel caries using a ph cycling model.twenty sound primary canine teeth were immersed in demineralizing solution f...

Abstract. We derive some Hodge integral identities by taking various limits of the Mariño-Vafa formula using the cut-and-join equation. These identities include the formula of general λg-integrals, the formula of λg−1-integrals on Mg,1, the formula of cubic λ integrals on Mg, and the ELSV formula relating Hurwitz numbers and Hodge integrals. In particular, our proof of the MV formula by the cut...

Shampoos are products which remove surface grease and dirt from the hair shaft and scalp. The cleansing or detergent action of a shampoo is a primary function. However, the foaming characteristic of a shampoo has an important role in its acceptability. Often alkanolamides are used for the formation of a stable foam; but because of producing nitrosamines, they are potentially carcinogenic compou...

A formula for deriving the price of SEW pigs using grain, soybean meal, and market hog prices was estimated based on return on investment being equal for all three phases of production – farrow, nursery, and finish. USDA reported SEW pig prices were compared with formula-derived prices. The level of correlation between these two series was sensitive to how grain, soybean meal, and market hog pr...