Proof of Observation 1. Before the proof, we remind that what we want to prove is the following statement: (∀ε ∈ R) ε > 0⇒ ((∃N ∈ N)(∀n ∈ N) n ≥ N ⇒ |an − x | < ε). To this end, choose arbitrary positive real ε > 0 and pick a positive rational ε′ with 0 < ε′ < ε by utilizing the Archimedean property. Then there exists N (depending on ε′ and hence on ε) such that j, k ≥ N ⇒ |a j − ak | < ε′. Now...

Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...

In this paper, we study ε-generalized weak s...

هدف: هدف از این پژوهش بررسی واسطه‌­ای راهبردهای سازش نایافته تنظیم شناختی هیجان در رابطه باورهای فراشناختی با اضطراب امتحان بود. روش: روش حاضر توصیفی و نوع همبستگی جامعه آماری را کلیه دانش‌­آموزان پسر دوره دوم متوسطه شهر تهران سال تحصیلی 1401-1400 تشکیل دادند که تعداد 456 نفر به نمونه‏‌گیری دسترس انتخاب شرکت کردند. ابزارها شامل سیاهه ابوالقاسمی همکاران (1375)، پرسشنامه باکو دیگران (2009)، فرم ک...

We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in [0, 1]. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximations of these range spaces through ε-nets and εsamples (aka ε-approximations). We characterize when size ...

There are many chemical molecules whose names are Cannabigerol (CBG), cannabidol (CBD), cannabichromene (CBC), tetrahydrocannabivarin (THCV), cannabigerovarinic acid (CBGV) and cannabidiolic acid (CBDA) derived from Marijuana. Theoretical methods were used to compare the chemical and biological activities of the six major molecules. Molecules were compared with their chemical activities using m...

Let ε > 0 and consider ε2u′′(t; ε) + u′(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε)ds+ f(t; ε), t ≥ 0, u(0; ε) = u0(ε), u ′(0; ε) = u1(ε), and w′(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t), t ≥ 0, w(0) = w0, in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear operator for t ≥ 0. With some conv...