where T is a time scale such that 0, T ∈ T, δ,βi > 0, i = 1, . . . , m − 2, jp(s) = |s|s,p > 1,h Î Cld((0, T), (0, +∞)), and f Î C([0,+∞), (0,+∞)), 0 < ξ1 < ξ2 < · · · < ξm−2 < T ∈ T. By using several well-known fixed point theorems in a cone, the existence of at least one, two, or three positive solutions are obtained. Examples are also given in this article. AMS Subject Classification: 34B10;...

The principal aim of this paper is to establish the optimality (i.e., sharpness) constants A(m, α) and B(m, α), m ∈ ℕ, α ℝ, form

s s sg g gq q q: combinatorial algorithm, word algorithm, clustering, πpattern 1 t t tÁ Á Á YîY’‚t t¿ X ™ îY%0ù Ÿ X÷¿ t¿ ‘ !ú D† éüv !°. ¢ c¢ îY%0 ‘F ™ ³–—ù ‘‘ ‡ X Ÿ ’¦ î€bú ßꢰ. ” 5 ‘ • ’‚t¦ îY%¦ ¿t™ t¿ °õ ½ê !°. Œ, ¢ îY%0¦ ”Ýù °ô îY’ ‚t t¿ °ô aeX‚ 5Í@ ½ !°. 铂t ¢ šõ 0V snoRNA îY%¦ ÂÙÛù mýè ß3Á(polycistron)‚ ¦© ́üv mýèß3Á snoRNA Yu¿ Y€ý°. ¢, ó¡êi ½Ì (olfactory receptor, OR)™ jîê¦ îY‚t 6 ...

a general singular integral with parameter p > 0 and kernel k having the following property (P): k(u)^0 in 0 0 , and if k satisfies (P), then the following statements hold; (i) Jp(t) exists as a function of t almost everywhere, e~ Jp ELp(0, 00) for every c > 0 , and ...

Background and Objective: Multi-walled Carbon Nano Tubes (MWCNTs) as an important element of nanosciences have a remarkable absorption in the region of NIR window (650-900 nm) which can overcome the limitations of deep treatment in photothermal therapy. To disperse MWCNTs in water, it is proposed to attach carboxylated functional group (-COOH) to MWCNTs in order to increase dispersivity in wate...

Diabetes mellitus (DM) is a disease that can be identified by high levels of blood glucose. Garcinia plants have been widely used for many traditional medicines as antioxidant, anticancer, antidiabetics, and antiinflammation. The antioxidant antidiabetic activities ( picrorrhiza Miq.) or sesoot fruit extract were evaluated in this study compared with xanthone. ethanolic ripe G. (GpKar) was (ABT...

ã ä å ae å ae ç è é ê ë ì ä í î é ï ð í å ç ñ í ç å å ñ ò ó ô ç õ ç ñ ö ï ç ÷ ø é í å ae ù ú å ae ç ï ò ù å ae ò í è ì ä í î é ï ô é ø ø ê í ä ô ò å ä é í ü ò ô ý ç å ù ae ò ù ë ç ô é ø ç ò ø ò þ é ñ ä ù ù ê ç ÿ ae ç ñ é ê å ç ñ ê ù ç ù å ae ç è ç ù å ä í ò å ä é í ð ¢ ò è è ñ ç ù ù é ï å ae ç ä í ¤ ô é ø ä í î ü ò ô ý ç å å é ì é é ý ê ü å ae ç í ç ¦ å ae é ü ñ é ê å ç ñ å é ÷ ae ä ô ae å ae ç...

where Î denotes the Fourier transform, and ω denotes frequency. Proof 1 Taking the Fourier transform of the Heat Equation: { ∂tu(t, x) = ∆u(t, x) x ∈ R u(0, x) = I(x) t = 0 yields: ∂tû(t, ω) = (iω) · (iω)û(t, ω) = −|ω|û(t, ω), where û(t, ω) is the Fourier transform of u. Solving this differential equation yields û(t, ω) = e−|ω| 2tÎ(ω). We note that a = 0 when I ∈ L since Î(0) = ∫ R2 I(x) dx is ...