2 D-module fundamentals 4 2.1 DX and DX -modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Inverse images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Direct images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Tensor products . . . . . . . . . . . . . . . . . . . . . . . . ....

3. (a) Let M be an infinite σ-algebra of subsets of some set X. There exists a countably infinite subcollection C ⊆M, and we may choose C to be closed under taking complements (adding in missing complements if necessary). For each x ∈ X, define Dx := ∩{C ∈ C | x ∈ C}, so that Dx ∈ M. Let x, y ∈ X and suppose y ∈ Dx. Then y ∈ C for all C ∈ C with x ∈ C. Moreover, if y ∈ C for some C ∈ C, then y ...

Following electronic or collisional excitation of a solid by a fast ion, an energized cylindrical region is produced which can lead to sputtering. Here ejection from such a region is studied via molecular-dynamics simulations using Lennard-Jones and Morse potentials. Over the full range of excitations studied the yield vs the energy release per unit path length in the solid, which we call dE/dx...

In this paper we state the following weighted Hardy type inequality for any functions $ \varphi in a Sobolev space and weight \mu of quite general \begin{document}$ \begin{align*} c_{N, \mu} \int_{ \mathbb{R}^N}V\, \varphi^2\mu(x)dx\le \mathbb{R}^N}|\nabla \varphi|^2\mu(x)dx +C_\mu \mathbb{R}^N}W \varphi^2\mu(x)dx, \end{align*} $\end{document} where V is multipolar potential W bounded function ...

This paper presents a very fast and low-power address bus encoder, whose critical path delay and area are only weakly dependent on the address bus width. Although the encoding algorithm of the proposed structure is the same as the INC-XOR encoding, its encoder and decoder architectures, called DX, are much faster. The DX architecture implements the INC-XOR encoding partially (partial DX archite...

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation q0 = i q2, q2 = i q0, α ⇀↽ γ. It is shown that the magnetic solution obtained with the help of the procedure used in Ref. [6], can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnet...

DX-9065a, a newly synthesized anticoagulant that selectively inhibits factor Xa, is a zwitterion and has characteristics of high water solubility and low lipophilicity. We predicted the fraction absorbed (Fa) of DX-9065a to be approximately 15-35% in humans, based on the boundary layer theory using the intestinal perfusion method in rats. However, human oral bioavailability was 2-3% in clinical...

PURPOSE To determine whether multiple primary breast cancers have similar genetic profiles, specifically Oncotype Dx Recurrence Scores, and whether obtaining Oncotype Dx on each primary breast cancer affects chemotherapy recommendations. METHODS A database of patients with hormone receptor-positive, lymph node-negative, breast cancer was created for those tumors that were sent for Oncotype Dx...

The research object focuses on the digital transformation (DX) process of enterprises and corresponding management policies from State. In context a transition economy, deeply integrated into world facing competition pressure many times higher than one in domestic market, businesses have themselves prepared such things like understanding how DX is, DX-ready they are, much to invest where are pa...

For a Brownian directed polymer in Gaussian random environment, with $q(t,\cdot)$ denoting the quenched endpoint density and \[ Q_n(t,x_1,\ldots,x_n)=\mathbf{E}[q(t,x_1)\ldots q(t,x_n)], \] we derive hierarchical PDE system satisfied by $\{Q_n\}_{n\geq1}$. We present two applications of system: (i) compute generator $\{\mu_t(dx)=q(t,x)dx\}_{t\geq0}$ for some special functionals, where $\{\mu_t(...