Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at Ys : −1 < y1 < · · · < ys < 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys. We show that provided n is sufficiently large, depending on the location of the points Ys, the rate of approximation is estimated by the third Ditzian–To...

Given a singular modulus $j_0$ and set of rational primes $S$, we study the problem effectively determining moduli $j$ such that $j-j_0$ is an $S$-unit. For every $j_0 \neq 0$, provide effective way finding this for infinitely many choices $S$. The same true if $j_0=0$ assume Generalized Riemann Hypothesis. Certain numerical experiments will also lead to formulation "uniformity conjecture" $S$-...

Let χ be a real odd Dirichlet character of modulus d, and let L(s, χ) be the associated Dirichlet L-function. As a consequence of the work of Low and Purdy, it is known that if d ≤ 800 000 and d 6= 115 147, 357 819, 636 184, then L(s, χ) has no positive real zeros. By a simple extension of their ideas and the advantage of thirty years of advances in computational power, we are able to prove tha...

We show that the low frequency, long wavelength dynamics of the phase of the pair field for a BCS-type s-wave superconductor at T=0 is equivalent to that of a time-dependent non-linear Schrödinger Lagrangian (TDNLSL), when terms required by Galilean invariance are included. If the modulus of the pair field is also allowed to vary, the system is equivalent to two coupled TDNLSL’s. PACS#s:74.20.-...

This paper studies divisibility properties of sequences defined inductively by n,=l, a n+1 =Sa,+tLea,], where s, t are integers, and 0 is a quadratic irrationality. Under appropriate hypotheses (especially that s + t0 be a PV-number) it is proved that the highest power of A that divides a,, where A is the discriminant of 19, tends to infinity. This is noteworthy in that truncation would normall...

In this research, the influence of adding micro- and nano- sized calcium carbonate powders to nylon-66 was investigated. Mechanical properties of micro and nano- composites, including tensile strength, elongation, and Young’s modulus, before and after ageing, were determined and analyzed. For this purpose, micro- and nano-sized CaCO3 particles were used as fillers to prepare micro-composites (c...

background substrates in medical science are hydrophilic polymers undergoing volume expansion when exposed to culture medium that influenced on cell attachment. although crosslinking by chemical agents could reduce water uptake and promote mechanical properties, these networks would release crosslinking agents. in order to overcome this weakness, silicone rubber is used and reinforced by nanocl...

in this work we simulated the representative volume element (rve) of carbon nanotube (cnt) which is surrounded by high temperature superconductor (ybco) by using ansys finite element software. first we considered perfect model (for ybco and cnt) and investigated the effect of radius, length, and the number of nanotube in young’s modulus of the ybco by applying force on rve. then, a third region...