Arrays of optical vortices formed by "fork" holograms

Singular light beams with optical vortices (OV) are often generated by means of thin binary gratings with groove bifurcation ("fork holograms") that produce a set of diffracted beams with different OV charges. Usually, only single separate beams are used and investigated; here we consider the whole set of diffracted OV beams that, at certain conditions, are involved in efficient mutual interference to form a characteristic pattern where the ring-like structure of separate OV beams is replaced by series of bright and dark lines between adjacent diffraction orders. This pattern, well developed for high diffraction orders, reflects the main spatial properties of the diffracted beams as well as of the fork grating used for their generation. In particular, it confirms the theoretical model for the diffracted beams (Kummer beam model) and enables to determine the sign and the absolute value of the phase singularity embedded in the hologram.Comment: 9 pages, 8 figure

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-MIMO systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16x16 and 32x32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.Comment: v3: Performance/complexity comparison of the proposed scheme with other large-MIMO architectures/detectors has been added (Sec. IV-D). The paper has been accepted for publication in IEEE Journal of Selected Topics in Signal Processing (JSTSP): Spl. Iss. on Managing Complexity in Multiuser MIMO Systems. v2: Section V on Channel Estimation is update

The Stable Manifold Theorem for Stochastic Differential Equations

We formulate and prove a {\it Local Stable Manifold Theorem\/} for stochastic differential equations (sde's) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and It\^o-type equations are treated. Starting with the existence of a stochastic flow for a sde, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich sde's, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating sde. The proof of the stable manifold theorem is based on Ruelle-Oseledec multiplicative ergodic theory

NOVEL METHODS FOR SOLVING THE CONFORMABLE WAVE EQUATION

In this paper, a two-dimensional conformable fractional wave equation describing a circular membrane undergoing axisymmetric vibrations is formulated. It was found that the analytical solutions of the fractional wave equation using the conformable fractional formulation can be easily and efficiently obtained using separation of variables and double Laplace transform methods. These solutions are compared with the approximate solution obtained using the differential transform method for certain cases

Separation And Determination Of Benzoylated Polyamines (Spermidine Andspermine) Using Hplc Techniqe

A simple and sensitive reversed-phase high performance liquid chromatography (Rp -HPLC) was developed for separation and determination of polyamines (Spermidine and Spermine). Derivatization of polyamines was improved by dissolving benzoyl chloride in methanol to increase the detection of UV-Visible detector at ? max. 254  nm. The benzoylated polyamines eluted by Rp- HPLC using methanol : water (52 : 48) as mobile phase. The detection limited of this method is (50ng/ml) .The separation was performed on BDS-DB (250 x 4.6 mm I.D) column at flow rate 1 ml/ min. using standard solutions. The retention time of two compounds (Spermidine and Spermine) were (7.7 , 8.5 min.) respectively, this method suggested that monitoring the Spermidine and Spermine compounds could play an important role in diagnosis of different types of carcinoma and fallow up chemo and radiotherapy treatments

Separation and Determination of Benzoylated Polyamines (Spermidine Andspermine) using HPLC Techniqe

A simple and sensitive reversed-phase high performance liquid chromatography (Rp -HPLC) was developed for separation and determination of polyamines (Spermidine and Spermine). Derivatization of polyamines was improved by dissolving benzoyl chloride in methanol to increase the detection of UV-Visible detector at ? max. 254  nm. The benzoylated polyamines eluted by Rp- HPLC using methanol : water (52 : 48) as mobile phase. The detection limited of this method is (50ng/ml) .The separation was performed on BDS-DB (250 x 4.6 mm I.D) column at flow rate 1 ml/ min. using standard solutions. The retention time of two compounds (Spermidine and Spermine) were (7.7 , 8.5 min.) respectively, this method suggested that monitoring the Spermidine and Spermine compounds could play an important role in diagnosis of different types of carcinoma and fallow up chemo and radiotherapy treatments