Let Lm,p(Rn) be the homogeneous Sobolev space for p?(n,?), ? a Borel regular measure on Rn, and Lm,p(Rn)+Lp(d?) of measurable functions with finite seminorm ?f?Lm,p(Rn)+Lp(d?):=inff1+f2=f?{?f1?Lm,p(Rn)p+?Rn|f2|pd?}1/p. We construct linear operator T:Lm,p(Rn)+Lp(d?)?Lm,p(Rn), that nearly optimally decomposes every function in sum space: ?Tf?Lm,p(Rn)p+?Rn|Tf?f|pd??C?f?Lm,p(Rn)+Lp(d?)p C dependent...

In this paper, it is shown that the linearized Boltzmann-Enskog collision operator cannot be dissipative in the L2-space setting contrarily to the linearized Boltzmann operator. Some estimates useful for the spectral theory are given. The Enskog equation is a modification of the Boltzmann kinetic equation, in which each particle is considered as a hard sphere with nonzero diameter a > 0 (and th...

We study the structure of length three polynomial automorphisms of R[X, Y ] when R is a UFD. These results are used to prove that if SLm(R[X1, X2, . . . , Xn]) = Em(R[X1, X2, . . . , Xn]) for all n,≥ 0 and for all m ≥ 3 then all length three polynomial automorphisms of R[X, Y ] are stably tame. 1. Introducton Unless otherwise specified R will be a commutative ring with 1 and R = R[X ] = R[X1, ....

Let A be a class of the analytic functions { f : f(z) = z + a2z + ... } , z ∈ U , where U is the unit disk, U = {z : |z| < 1} . By S we denote the subclass of A consisting of function univalent in the unit disk. Let p be a real number with the property 0 < p ≤ 2. We define the class S (p) as the class of the functions f ∈ A that satisfy the conditions f (z) 6= 0 and ∣(z/f (z))′′ ∣∣ ≤ p, z ∈ U. ...

هدف: هدف این پژوهش، تبیین و شناسایی قوت‌ها، ضعف‌ها، فرصت‌ها تهدیدهای نظام آموزش عالی ایران در مواجهه فعال با جهانی شدن است.مواد روش‌ها: رویکرد پژوهش حاضر کیفی روش مبتنی بر پدیدارشناسی بود. جامعه تمامی متخصصان حوزه حیطه موضوعی ‌شدن بودند. ملاک‌های انتخاب نمونه عبارت‌اند از عضو هیئت علمی بودن، اشتهار سطوح ملی بین‌المللی یا دارا بودن اثر مکتوب زمینه نظر گرفته شد. نمونه‌گیری هدفمند به صاحب‌نظران کل...

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1} → {0, 1} a randomized F2-sketch is a distributionM over d×n matrices with elements over F2 such thatMx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show tha...

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1} → {0, 1} a randomized F2-sketch is a distributionM over d×n matrices with elements over F2 such thatMx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show tha...