A closed form for the generalized Bernoulli polynomials via Fa\`a di Bruno's formula

We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.Comment: 4 pages; No figure

Construction of cusp forms using Rankin-Cohen brackets

For a fix modular form g and a non negative ineteger {\nu}, by using Rankin-Cohen bracket we first define a linear map $T_{g,{\nu}}$ on the space of modular forms. We explicitly compute the adjoint of this map and show that the n-th Fourier coefficients of the image of the cusp form f under this map is, upto a constant a special value of Rankin-Selberg convolution of f and g

Numerical Simulation guided Lazy Abstraction Refinement for Nonlinear Hybrid Automata

This draft suggests a new counterexample guided abstraction refinement (CEGAR) framework that uses the combination of numerical simulation for nonlinear differential equations with linear programming for linear hybrid automata (LHA) to perform reachability analysis on nonlinear hybrid automata. A notion of $\epsilon-$ structural robustness is also introduced which allows the algorithm to validate counterexamples using numerical simulations. Keywords: verification, model checking, hybrid systems, hybrid automata, robustness, robust hybrid systems, numerical simulation, cegar, abstraction refinement.Comment: 11 pages, 2 figure

Design of a Distributed Reachability Algorithm for Analysis of Linear Hybrid Automata

This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the computational problem among multiple computational nodes in a non-redundant manner by performing careful infeasibility analysis of linear programs corresponding to spurious counterexamples. The d-IRA algorithm is resistant to failure of multiple computational nodes. The experimental results provide promising evidence for the possible successful application of this technique.Comment: 8 page

Development of knowledge Base Expert System for Natural treatment of Diabetes disease

The development of expert system for treatment of Diabetes disease by using natural methods is new information technology derived from Artificial Intelligent research using ESTA (Expert System Text Animation) System. The proposed expert system contains knowledge about various methods of natural treatment methods (Massage, Herbal/Proper Nutrition, Acupuncture, Gems) for Diabetes diseases of Human Beings. The system is developed in the ESTA (Expert System shell for Text Animation) which is Visual Prolog 7.3 Application. The knowledge for the said system will be acquired from domain experts, texts and other related sources

Two new explicit formulas for the Bernoulli Numbers

In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more probably known formulas.Comment: Updated to give proofs of some necessary result

Achievable Rate Analysis of Relay Assisted Cooperative NOMA over Rician Fading Channels

Non-orthogonal multiple access (NOMA) is a key to multiple access techniques for the next generation 5G wireless communication networks. In this paper, to improve the performance gain of NOMA system, a cooperative fixed decode-and-forward (DF) relay system model based on NOMA (CRS-NOMA) is studied over Rician fading channels, considering the achievable rate of signals as the performance metric. In this technique, by exploiting the concept of NOMA, unlike the conventional method of cooperative relaying, the second time slot is also utilized for the realization of information sent from the transmitter end. Moreover, as the data symbols are transmitted by nodes with full power, the compulsion of complex power allocation coefficients is precluded. In conventional cooperative relaying systems, the receiver is only able to receive a single bit of information, while the receiver can reliably bring in two data symbols in two-time slots. In this regard, this scheme is able to acquire higher achievable rate performance than existing cooperative relaying schemes for larger channel powers over most of the transmit SNR regime. Furthermore, a mathematical expression is also derived for the total achievable rate of CRS-NOMA. The results are verified through Monte-Carlo simulations which validate accuracy and consistency of the derived analytical results.Comment: 5 pages, 4 figures, 4th IEEE International Conference on Recent Advances in Information Technology (RAIT 2018), Mar. 15-17, IIT(ISM) Dhanbad, INDI

Rare Top Decays in Minimal and Non-minimal Universal Extra Dimension

The flavour changing decays of the top quark are severely suppressed in the Standard Model by virtue of the Glashow-Iliopoulos-Maiani mechanism. Many beyond Standard Model extensions predict the decay rates at a level that is observable in the LHC. We perform a complete one-loop calculation of the flavour changing top quark decays $t\to c\gamma$ and $t\to ch$ in the universal extra dimensional model. Apart from considering the decay rates in the minimal version of the model, we also calculate the rates in the non-minimal scenario where the presence of boundary localised terms interestingly modify the set-up. We find that the decay rates in the minimal variant of the model do not change much from their Standard Model values. In the non-minimal version of this model, these decay rates can be higher for specific choices of the boundary localised parameters for a certain range of inverse compactification radius. But these model parameters lead to Kaluza-Klein particle masses that are in tension with various searches at the LHC.Comment: 31 pages, 11 figures; added more discussion, one section, a few clarifications and minor changes in the text and abstract; fixed typos; updated references; matches published versio

Performance analysis of dual-hop optical wireless communication systems over k-distribution turbulence channel with pointing error

In this paper, we investigate the performance of the dual-hop free space optical (FSO) communication systems under the effect of strong atmospheric turbulence together with misalignment effects (pointing error). We consider a relay assisted link using decode and forward (DF) relaying protocol between source and destination with the assumption that Channel State Information is available at both transmitting and receiving terminals. The atmospheric turbulence channels are modeled by k-distribution with pointing error impairment. The exact closed form expression is derived for outage probability and bit error rate and illustrated through numerical plots. Further BER results are compared for the different modulation schemes

Achievable Rate Analysis of Cooperative Relay Assisted Opportunistic-NOMA under Rician Fading Channels with Channel State Information

The average achievable rate of an Opportunistic Non-Orthogonal Multiple Access (O-NOMA) based Cooperative Relaying System (CRS) with Channel State Information (CSI) known at the transmitter end is analyzed under Rician fading channels. For opportunistic transmission of data signals, CSI is used for the source-to-relay and source-to-destination links, which helps the transmitter to select the best out of the cooperative NOMA transmission and the direct transmission of signals, instantaneously. The average achievable rate of the O-NOMA and conventional NOMA (C-NOMA) based CRSs is considered for the performance comparison and the exact and asymptotic analytical expressions of the achievable rates has been provided. Asymptotic results are verified through Monte Carlo simulations for various channel powers and power allocation coefficients. Numerical results verify that the derived analytical results are matched well with the Monte Carlo simulations and shows that O-NOMA-based CRS achieves better rate performance than C-NOMA-based CRS with the increasing power allocation coefficients, transmit Signal-to-Noise Ratios (SNRs) and channel powers.Comment: 13 pages, 9 figures, Wireless Personal Communications, Springe