The Keralese origin of these series is independent of the discovery in a later century of the inverse-tangent expansion [ A ] by JAMES GREGORY (1671) and GOTTFRIED WILHELM LEIBNIZ (1673), of the sine and cosine series by ISAAC NEWTON (1670) and LEIBNIZ (1676). The Malay~]am work Yukti-bhCtsa, where these series are found, belongs unquestionably to the sixteenth century, and there is not the sli...

The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are know...

Two versions of approximation formulae for periodic Ateb-sine and Ateb-cosine in the first quarter their common period are proposed. The version is a Pade type derived when constructing analytical solution corresponding integral equation by iteration method with transforming power series into closed sum Shanks’ formula. approximations considered. one more concise but worse accuracy which deteri...

Presence or absence of a minimal zone of keratinized tissue around dental implants has been a matter of controversy. However, a consensus exists that a thick zone of keratinized zone around implants provides a prosthetic friendly environment, facilitates precise prosthetic procedures, allows oral hygiene maintenance, resists recession, and enhances esthetic blending. The aim of the present case...

Cellulose nanofibril (CNF) suspensions are not easily coatable because of their excessively high viscosity and yield stress, even at low solids concentrations. In addition, CNF suspensions vary widely in their properties depending on the production process used, which can affect their processability. This work reports roll-to-roll coating of three different types of CNF suspensions with a slot-...

The subsequence matching in a large time-series database has been an interesting problem. Many methods have been proposed that cope with this problem in an adequate extent. One of the good ideas is reducing properly the dimensionality of time-series data. In this paper, we propose a new method to reduce the dimensionality of high-dimensional time-series data. The method is simpler than existing...

Aluminium and its alloys belong to the most widely used metallic materials for industrial applications. One of the possible casting methods is twin-roll casting which produces sheets with high solid solution supersaturation. Decomposition of this supersaturated material during heat treatment was studied in aluminium alloys from the AW-3003 series – one standard grade and the other modified by a...