On a new two-parameter generalization of dual-hyperbolic Jacobsthal numbers

In this paper we introduce two-parameter generalization of dualhyperbolic Jacobsthal numbers: dual-hyperbolic (s,p)-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, d’Ocagne identities. Moreover, we give the generating function, matrix generator and summation formula for these numbers

Jets and threshold summation in Deductor

We explore jet physics in hadron collisions using the parton shower event generator Deductor. Of particular interest is the one jet inclusive cross section dsigma/dpT for jets of very high pT. Compared to the Born level, the cross section decreases substantially because of pT loss from the jet during showering. We compare to the same effect in Pythia and Dire. The cross section then increases substantially because of the summation of threshold logarithms included in Deductor. We also study the cross section to have a gap with no jets between two hard jets that are widely separated in rapidity. Here we compare Deductor with virtuality based ordering with Deductor with kT ordering and we check whether adding an underlying event and hadronization has a significant effect beyond that found with just a parton shower.Comment: 47 pages, 11 figures, published versio

Comparison analysis of stream cipher algorithms for digital communication

The broadcast nature of radio communication such as in the HF (High Frequency) spectrum exposes the transmitted information to unauthorized third parties. Confidentiality is ensured by employing cipher system. For bulk transmission of data, stream ciphers are ideal choices over block ciphers due to faster implementation speed and not introducing error propagation. The stream cipher algorithms evaluated are based on the linear feedback shift register (LFSR) with nonlinear combining function. By using a common key length and worst case conditions, the strength of several stream cipher algorithms are evaluated using statistical tests, correlation attack, linear complexity profile and nonstandard test. The best algorithm is the one that exceeds all of the tests

Generalized Stability Condition for Generalized and Doubly-Generalized LDPC Codes

In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (D-GLDPC) codes. It is proved that, in both cases, the stability condition only involves the component codes with minimum distance 2. The stability condition for GLDPC codes is always expressed as an upper bound to the decoding threshold. This is not possible for D-GLDPC codes, unless all the generalized variable nodes have minimum distance at least 3. Furthermore, a condition called derivative matching is defined in the paper. This condition is sufficient for a GLDPC or DGLDPC code to achieve the stability condition with equality. If this condition is satisfied, the threshold of D-GLDPC codes (whose generalized variable nodes have all minimum distance at least 3) and GLDPC codes can be expressed in closed form.Comment: 5 pages, 2 figures, to appear in Proc. of IEEE ISIT 200