N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

Approximation Properties of Schurer-Stancu Type Polynomials

MSC 2010: 41A25, 41A35

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Letter to the Editor. Remarks on Some Inequalities for Polynomials

MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

2000 Mathematics Subject Classification: 12D10.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

WDM orthogonal subcarrier multiplexing

Electro-optical transceivers can be implemented employing all-analog signal processing in order to achieve low values of power consumption and latency. This paper shows that the spectral efficiency of such solutions can be increased by combining orthogonal multicarrier techniques and off-the-shelf microwave components. A real-time 108-Gbit/s experiment was performed emulating a wavelength division multiplexing (WDM) system composed of five optical channels. The optical carriers were provided by an externally injected gain switched optical frequency comb. Each optical channel transmitted a 21.6-Gbit/s orthogonal subcarrier multiplexing (SCM) signal that was modulated and demodulated in the electrical domain without the requirement for digital signal processing. The net data rate remained higher than 100 Gbit/s after taking into account forward error correction overheads. The use of orthogonally overlapping subchannels achieves an unprecedented spectral efficiency in all-analog real-time broadband WDM/SCM links.

Orthogonal frequency division multiplexing based air interfaces and multiple input multiple output techniques in cooperative satellite communications for 4th generation mobile systems

Recently, wireless network technology has grown at such a pace that scientific research has become a practical reality in a very short time span. Mobile wireless communications have witnessed the adoption of several generations, each of them complementing and improving the former. One mobile system that features high data rates and open network architecture is 4G. Currently, the research community and industry, in the field of wireless networks, are working on possible choices for solutions in the 4G system. 4G is a collection of technologies and standards that will allow a range of ubiquitous computing and wireless communication architectures. The researcher considers one of the most important characteristics of future 4G mobile systems the ability to guarantee reliable communications from 100 Mbps, in high mobility links, to as high as 1 Gbps for low mobility users, in addition to high efficiency in the spectrum usage. On mobile wireless communications networks, one important factor is the coverage of large geographical areas. In 4G systems, a hybrid satellite/terrestrial network is crucial to providing users with coverage wherever needed. Subscribers thus require a reliable satellite link to access their services when they are in remote locations, where a terrestrial infrastructure is unavailable. Thus, they must rely upon satellite coverage. Good modulation and access technique are also required in order to transmit high data rates over satellite links to mobile users. This technique must adapt to the characteristics of the satellite channel and also be efficient in the use of allocated bandwidth. Satellite links are fading channels, when used by mobile users. Some measures designed to approach these fading environments make use of: (1) spatial diversity (two receive antenna configuration); (2) time diversity (channel interleaver/spreading techniques); and (3) upper layer FEC. The author proposes the use of OFDM (Orthogonal Frequency Multiple Access) for the satellite link by increasing the time diversity. This technique will allow for an increase of the data rate, as primarily required by multimedia applications, and will also optimally use the available bandwidth. In addition, this dissertation approaches the use of Cooperative Satellite Communications for hybrid satellite/terrestrial networks. By using this technique, the satellite coverage can be extended to areas where there is no direct link to the satellite. For this purpose, a good channel model is necessary.