VLSI modules are proposed for fast, efficient generation of high-throughput Blum-Blum-Shub (BBS) and BBS-like sequences using Montgomery Multiplication, where post-processing associated with Montgomery’s algorithm can be eliminated.

We give conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions are known, i.e., for modules of codimension two, for Gorenstein algebras of codimension t...

where the map R/(x1 , . . . , x m n ) −→ R/(x m+1 1 , . . . , x m+1 n ) is multiplication by the image of the element x1 · · ·xn. As these descriptions suggest, H a(R) is usually not finitely generated as an R-module. However local cohomology modules have useful finiteness properties in certain cases, e.g., for a local ring (R,m), the modules H m(R) satisfy the descending chain condition. This ...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

In this paper, a double precision IEEE 754 floating-point multiplier with high speed and low power is presented. The bottleneck of any double precision floatingpoint multiplier design is the 53x53 multiplication of the mantissas (52 bit mantissa+1 hidden bit). This paper proposes a approach to improve this performance bottleneck by adding a redundant 54 bit initialized to ‘0’ in the mantissas o...

The Fast Fourier Transform (FFT) is most widely used in DSP such as imaging, signal processing, frequency communication, applied wireless system. In this paper, a reconfigurable DIT8 point FFT design using Vedic multiplier with small area and low power is presented. Urdhava Triyakbhyam algorithm, an ancient Vedic Indian Mathematics sutra, is utilized to achieve high throughput. In the proposed ...

The thermal safety of lithium-ion traction batteries is a highly concerning issue in the field electric transportation. large amount gas emissions during runaway process has high hazards, such as fire and explosion. quantitative analysis one important challenges testing evaluating battery safety. Focusing on quantifying using large-scale propagation modules packs, based idea cell result multipl...

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

Colmez [Col93] conjectured a product formula for periods of abelian varieties over number fields with complex multiplication and proved it in some cases. His conjecture is equivalent to a formula for the Faltings height of CM abelian varieties in terms of the logarithmic derivatives at s = 0 of certain Artin L-functions. In a series of articles we investigate the analog of Colmez’s theory in th...