One can prove X1 is not regular using the pumping lemma. One can prove X2 is not regular either by using the pumping lemma (a version with bounds on the prefix) or by contradiction: if X2 is regular than X2 ∩ a∗b∗ = X1 is regular. One cannot prove X3 non-regular with the pumping theorem directly; however one can prove its regular by contradiction: if X3 is regular than X3 = X2 is regular. We wi...

If the random variables X1, X2, · · · , Xn are independent, they are k-wise independent for any k. However, the converse is not true as shown by the following example. Also, if k1 > k2, k1-wise independence implies k2-wise independence. Example 2. Let X1, X2 be uniform independent random variables taking values in {0, 1}. Let X3 = X1 ⊕X2. It is easy to check that {X1, X2, X3} is pairwise indepe...

Introduction. A p-divisible group X can be seen as a tower of building blocks, each of which is isomorphic to the same finite group scheme X[p]. Clearly, if X1 and X2 are isomorphic then X1[p] ∼= X2[p]; however, conversely X1[p] ∼= X2[p] does in general not imply that X1 and X2 are isomorphic. Can we give, over an algebraically closed field in characteristic p, a condition on the p-kernels whic...

The articles [8], [1], [4], [2], [3], [5], [7], [12], [13], [6], [9], and [10] provide the notation and terminology for this paper. We follow the rules: h, r, r1, r2, x0, x1, x2, x3, x4, x5, x, a, b, c, k denote real numbers and f , f1, f2 denote functions from R into R. Next we state a number of propositions: (1)1 ∆[f ](x, x+ h) = ( ~ ∆h[f ])(1)(x) h . (2) If h 6= 0, then ∆[f ](x, x+ h, x+ 2 ·...

Some geometric facts concerning sets with positive reach in Ed are proved. For x1 and x2 in E d and R > 0 let us denote by H(x1, x2, R) the intersection of all closed balls of radius R containing x1 and x2. We prove that reach(K) ≥ R if and only if for every x1, x2 ∈ K such that ‖x1 − x2‖ < 2R, H(x1, x2, R) ∩ K is connected. A corollary is that if reach(K) ≥ R > 0 and D is a closed ball of radi...

A discrete memoryless multiple access channel (MAC) is a quadruple { X1,X2, PY |X1,X2 ,Y } where X1,X2 are the input alphabets, Y the output alphabet, and PY |X1,X2 a transition probability matrix from X1 × X2 to Y . For shorthand notation, we will refer to the MAC by PY |X1,X2 . A source pair is a triplet {U ,V, PU,V } where PU,V is a distribution on U × V . We use the following notation: rand...

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...