On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules

Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and r=\depth_k(I,N) the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in S\mid\dim(R/\p){\ge}k}. We first prove in this paper that \Ass_R(H^j_I(N))_{\ge k} is a finite set for all $j{\le}r$}. Let \fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where \fR is a finitely generated standard graded algebra over $R_0=R$. Let $r$ be the eventual value of \depth_k(I,N_n). Then our second result says that for all $l{\le}r$ the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are stable for large $n$.Comment: To appear in Communication in Algebr

Sparse seismic imaging using variable projection

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simultaneously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with sparsity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demonstrate the algorithm on a seismic imaging example.Comment: 5 pages, 4 figure

On the cofiniteness of generalized local cohomology modules

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $M$, $N$ two finitely generated $R$-modules. The aim of this paper is to investigate the $I$-cofiniteness of generalized local cohomology modules \displaystyle H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N) of $M$ and $N$ with respect to $I$. We first prove that if $I$ is a principal ideal then $H^j_I(M,N)$ is $I$-cofinite for all $M, N$ and all $j$. Secondly, let $t$ be a non-negative integer such that \dim\Supp(H^j_I(M,N))\le 1 \text{for all} j Then $H^j_I(M,N)$ is $I$-cofinite for all $j<t$ and \Hom(R/I,H^t_I(M,N)) is finitely generated. Finally, we show that if $\dim(M)\le 2$ or $\dim(N)\le 2$ then $H^j_I(M,N)$ is $I$-cofinite for all $j$.Comment: 16 page

A Simplified Method For Securing Bluetooth Communication

Disclosed herein is a simplified Bluetooth communication mechanism that is secure and enables configuration of the security settings when paired with another Bluetooth device. Once paired, the system prompts the user to select either a normal or a secure access mode. The normal mode allows access to normal as well as sensitive or personal data available in the phone, while the secure access mode restricts access to sensitive data. Data access requests are handled by the system to permit access based on the security mode settings. This mechanism provides a single toggle that prevents personal data being synced to any publicly shared device. The system further allows the user to change mode of access as required. A typical use would be pairing a mobile phone with a rented car to leverage the car\u27s audio system for improved sound quality of a GPS app running on the phone

With exhaustible resources, can a developing country escape from the poverty trap ?

This paper studies the optimal growth of a developing non-renewable natural resource producer, which extracts the resource from its soil and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domestic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We study the optimal extraction and depletion of the exhaustible resource and the optimal paths of accumulation of capital and of domestic consumption. We show that the extent to which the country will optimally escape from the poverty trap and the exhaustible resource will be a blessing depends on the characteristics of its technology and of the revenues from the resource function, on its impatience, on the level of its initial stock of capital and on the abundance of the natural resource. If the marginal productivity of capital at the origin is greater than the sum of the social discount rate and the depreciation rate, the country will accumulate capital along the entire growth path and will escape from the poverty trap, whatever its initial stocks of capital and resource, and provided that the marginal revenue obtained from the exportation of the resource is finite at the origin. On the contrary, if the marginal productivity of capital is lower than the depreciation rate whatever the level of capital and if moreover the initial stock of capital is small, then the country will never accumulate ; it will consume the revenues obtained from selling abroad the extracted resource, until there is no resource left and the economy collapses. We also show that any optimal path may be decentralized in a competitive equilibrium by using a tax/subsidy scheme for firms.Optimal growth, exhaustible resource, convex-concave technology, poverty trap, competitive equilibrium with tax/subsidy.

With Exhaustible Resources, Can A Developing Country Escape From The Poverty Trap?

This paper studies the optimal growth of a developing non-renewable natural resource producer. It extracts the resource from its soil, and produces a single consumption good with man-made capital. More- over, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domes- tic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We show that the extent to which the country will escape from the poverty trap depends, besides the interactions between its technology and its impatience, on the characteristics of the resource revenue function, on the level of its initial stock of capital, and on the abundance of the natural resource.optimal growth;non-renewable resource;convex-concave technology;poverty trap;resource curse

General failure of logic programs

AbstractA classification of any logic program's failures into different levels of general finite failure is introduced. The general failure is then shown to be the limit of those general finite failures, and its interpretation coincides with the complement of the greatest model of the program. As a consequence of this, the negation-as-failure rule is proved