On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces

The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegative orders of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa(RN) converge uniformly on every compact set, and if a + s > (N – 1)/2 and ap = N, then for any x0∈ RN there exists a continuous finite function from the Sobolev space such, that the corresponding Riesz means of the N-fold Fourier integrals diverge to infinity at x0. AMS 2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C1

Polipropilen va qatlamli silikatlar asosida nanokompozitlar olish va ularning strukturaviy va mexanik xossalari

Polipropilen (PP), fizik-mexanik va harorat xususiyatlari tufayli mashinasozlik va elektrotexnika sanoatida keng qo'llaniladi. PP makromolekulalarining degradatsiyasi tufayli termal ta'sir qilish jarayonida elastiklik kuchini yo'qotishi kuzatiladi. Olingan ma'lumotlar polipropilenni qayta ishlash shartlarini tanlash uchun qiziqish uyg'otadi

Structural and Functional Analyses of the Interaction Between the USP7-NTD and the E2-Conjugating Enzymes, UbE2E2 and UbE2E3

Ubiquitin-specific protease 7 (USP7) is a deubiquitinating enzyme that regulates the turnover of proteins in a cell. To date several interacting partners that are involved in various cellular processes have been identified for USP7. Many of the interacting partners of USP7 contain a P/AxxS motif. We have identified two E2 ubiquitin-conjugating enzymes, UbE2E2 and UbE2E3, which contain the P/AxxS motif. Using a co-immunoprecipitation assay we have shown that these E2 proteins interact with USP7 through their P/AxxS motif. Co-crystal structures of the N-terminal domain of USP7 (USP7-NTD) and the E2 peptides reveal that the interactions are formed between USP7-NTD residues 164DWGF167 and the E2 P/AxxS motifs. It has also been established that USP7 may be involved in regulating the cellular levels of UbE2E2. Overall, our findings suggest USP7, a de-ubiquitinating enzyme, is a regulator of ubiquitin-conjugating enzymes, which are involved in the ubiquitination cascade

The diffusion equation with piecewise smooth initial conditions

In this paper we consider an initial-value problem for diffusion equation in three dimensional Euclidean space. The initial value is a piecewise smooth function. To solve this problem we apply Fourier transform method and since Fourier integrals of a piecewise smooth function do not converge everywhere, we make use of Riesz summation method