Comparing Entire Prototypes at Semigroup Homomorphisms and Specifically at Regular Languages Substitutions

The following statements are proven: A correspondence of a semigroup in another one is a homomorphism if and only if when the entire prototype of the product of images contains (always) the product of their entire prototypes. The Kleene closure of the maximal rewriting of a regular language at a regular language substitution contains in the maximal rewriting of the Kleene closure of the initial regular language at the same substitution. Let the image of the maximal rewriting of a regular language at a regular language substitution covers the entire given regular language. Then the image of any word from the maximal rewriting of the Kleene closure of the initial regular language covers by the image of a set of some words from the Kleene closure of the maximal rewriting of this given regular language everything at the same given regular language substitution. The purposefulness of the ¯rst statement is substantiated philosophically and epistemologically connected with the spirit of previous mathematical results of the author. A corollary of its is indicated about the membership problem at a regular substitution.

An Improvement to the Achievement of the Griesmer Bound

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper is to determine nq(k, d) for d = dk as nq(k, d) = gq(k, d) + 1 for q ≥ k with 3 ≤ k ≤ 8 except for (k, q) = (7, 7), (8, 8), (8, 9).

Characterisation of baseline oscillation in congenital nystagmus eye movement recordings

Congenital nystagmus is an ocular-motor disorder that develops in the first few months of life; its pathogenesis is still unknown. Patients affected by congenital nystagmus show continuous, involuntary, rhythmical oscillations of the eyes. Monitoring eye movements, nystagmus main features such as shape, amplitude and frequency, can be extracted and analysed. Previous studies highlighted, in some cases, a much slower and smaller oscillation, which appears added up to the ordinary nystagmus waveform. This sort of baseline oscillation, or slow nystagmus, hinder precise cycle-to-cycle image placement onto the fovea. Such variability of the position may reduce patient visual acuity. This study aims to analyse more extensively eye movements recording including the baseline oscillation and investigate possible relationships between these slow oscillations and nystagmus. Almost 100 eye movement recordings (either infrared-oculographic or electrooculographic), relative to different gaze positions, belonging to 32 congenital nystagmus patients were analysed. The baseline oscillation was assumed sinusoidal; its amplitude and frequency were computed and compared with those of the nystagmus by means of a linear regression analysis. The results showed that baseline oscillations were characterised by an average frequency of 0.36 Hz (SD 0.11 Hz) and an average amplitude of 2.1° (SD 1.6°). It also resulted in a considerable correlation (R2 scored 0.78) between nystagmus amplitude and baseline oscillation amplitude; the latter, on average, resulted to be about one-half of the correspondent nystagmus amplitude. © 2009 Elsevier Ltd. All rights reserved.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

Linear Fresnel mirror solar concentrator with tracking

Solar energy is the most abundant, widely distributed and clean renewable energy resource. Since the insolation intensity is only in the range of 0.5 - 1.0 kW/m2, solar concentrators are required for attaining temperatures appropriate for medium and high temperature applications. The concentrated energy is transferred through an absorber to a thermal fluid such as air, water or other fluids for various uses. This paper describes design and development of a 'Linear Fresnel Mirror Solar Concentrator' (LFMSC) using long thin strips of mirrors to focus sunlight on to a fixed receiver located at a common focal line. Our LFMSC system comprises a reflector (concentrator), receiver (target) and an innovative solar tracking mechanism. Reflectors are mirror strips, mounted on tubes which are fixed to a base frame. The tubes can be rotated to align the strips to focus solar radiation on the receiver (target). The latter comprises a coated tube carrying water and covered by a glass plate. This is mounted at an elevation of few meters above the horizontal, parallel to the plane of the mirrors. The reflector is oriented along north-south axis. The most difficult task is tracking. This is achieved by single axis tracking using a four bar link mechanism. Thus tracking has been made simple and easy to operate. The LFMSC setup is used for generating steam for a variety of applications. © 2013 The Authors. Published by Elsevier Ltd.

Method of Averaging for Impulsive Differential Inclusions

AMS subject classification: Primary 49N25, Secondary 49J24, 49J25.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

SG Pseudo-Differential Operators and Weak Hyperbolicity

2002 Mathematics Subject Classification: 35S05, 47G30, 58J42.

Domaine Numérique du produit AB avec A normal

2000 Mathematics Subject Classification: 18B30, 47A12.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Design of nonlinear regenerative transmission systems with high capacity

We present the design of nonlinear regenerative communication channels that have capacity above the classical Shannon capacity of the linear additive white Gaussian noise channel. The upper bound for regeneration efficiency is found and the asymptotic behavior of the capacity in the saturation regime is derived. © 2013 IEEE.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Analysis of Wiener-Hammerstein equalizer for downlink LTE system

We propose a Wiener-Hammerstein (W-H) channel estimation algorithm for Long-Term Evolution (LTE) systems. The LTE standard provides known data as pilot symbols and exploits them through coherent detection to improve system performance. These drivers are placed in a hybrid way to cover up both time and frequency domain. Our aim is to adapt the W-H equalizer (W-H/E) to LTE standard for compensation of both linear and nonlinear effects induced by power amplifiers and multipath channels. We evaluate the performance of the W-H/E for a Downlink LTE system in terms of BLER, EVM and Throughput versus SNR. Afterwards, we compare the results with a traditional Least-Mean Square (LMS) equalizer. It is shown that W-H/E can significantly reduce both linear and nonlinear distortions compared to LMS and improve LTE Downlink system performance.