Law and Order

Sanctions, Law and Public Order

Order Statistics and Benford's Law

Fix a base B > 1 and let ζ have the standard exponential distribution; the distribution of digits of ζ base B is known to be very close to Benford’s law. If there exists a C such that the distribution of digits of C times the elements of some set is the same as that of ζ, we say that set exhibits shifted exponential behavior base B. Let X1, . . . , XN be i.i.d.r.v. If the Xi’s are Unif, then as...

Law and order in algorithmics

LAW and ORDER in ALGORITHMICS An algorithm is the input-output effect of a computer program; mathematically, the notion of algorithm comes close to the notion of function. Just as arithmetic is the theory and practice of calculating with numbers, so is ALGORITHMICS the theory and practice of calculating with algorithms. Just as a law in arithmetic is an equation between numbers, like a(b + c) =...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Reverse order law in C∗-algebras

We study equivalent conditions for the reverse order law (a1a2 . . . an)† = an(a † 1a1a2 . . . ana † n) †a1 in C ∗-algebras. As corollaries, we obtain some recent and special results.