Suitable Matrices Research Articles

Hadamard matrices of order 28 m, 36 m and 44 m

We show that if four suitable matrices of order m exist then there are Hadamard matrices of order 28 m, 36 m, and 44 m. In particular we show that Hadamard matrices of orders 14( q + 1), 18( q + 1), and 22( q + 1) exist when q is a prime power and q ≡ 1 (mod 4). Also we show that if n is the order of a conference matrix there is an Hadamard matrix of order 4 mn. As a consequence there are Hadamard matrices of the following orders less than 4000: 476, 532, 836, 1036, 1012, 1100, 1148, 1276, 1364, 1372, 1476, 1672, 1836, 2024, 2052, 2156, 2212, 2380, 2484, 2508, 2548, 2716, 3036, 3476, 3892. All these orders seem to be new.

On a theorem of M. Artin

(S,, is the symmetric group on 2n elements and 1 CJ 1 is the signature of u) and 2, does not satisfy any identity of degree less than 2n [4]. We also recall that, if p(x, ,..., x3 is a polynomial with coefficients in 2 and if p(x, ,..., xk) does not vanish identically on every ring A, of n x n matrices over a ring A of characteristic p, then, if F is an infinite field of characteristic p, det p(a, ,..., ak) is nonzero for suitable matrices ai EF, [5].

Four-pole transducer analogues of electro-optic modulators

It is generally accepted that, at the present time, crystals which exhibit the linear electro-optic (Pockels) effect produce the most useful range of electro-optic modulators. Modulators employing such crystals and all optical components used in light modulation can be conceived as four-pole optical transducers and represented by suitable matrices. Such matrices are given. Using these matrices separate expressions are derived for the demodulation spectrum of amplitude modulated vibrations with suppressed carrier and demodulation spectrum of amplitude modulated vibrations with unsuppressed carrier.

Matrix -Related Stability and Viability of Microencapsulated Probiotics

We aimed to obtain and characterize (morphology, spectroscopy, viability) different types of microcapsules built with alginate or chitosan matrices which entrap Streptococcus thermophilus and Lactobacillus delbrueckii subsp. bulgaricus as probiotics. We used as matrices chitosan (CH) (1%, 1.5%, 2% w/v) and alginate (AG) (1%, 1.5%, 2% w/v) and the same percentage of probiotics (1mg/10ml matrix solution) to obtain microcapsules by coacervation. The concentration of AG and CH influenced the diameter, aspect, compactness of beads. Capsules of AG 1.5%, had the biggest area (4,1mm2) and diameter (2mm) while CH 2% had the smallest area (1.5 mm2) and diameter (2,1mm). As a complementary characterization the FTIR–HATR spectroscopy was able to fingerprint the free matrix, and encapsulated probiotics, identifying the specific markers located at 900-1100 cm-1(carbohydrates), 1560-1620 cm-1 (for sugar ring stretching) and a large band (for water) at 3100-3700 cm-1.The fingerprint of encapsulated probiotic is recognised by 2 signals identified at 2880 and 2920 cm-1. The most suitable matrices for probiotic encapsulation were established to be AG 2%, AG 1.5%.The viability of probiotic powder in culture was 109 ml-1 while in capsules the viability was 10 6 ml-1 . We can notice that capsules with AG 1.5% and CH 1.5% released more bacteria and the viability was higher then in AG 2% and CH 2%, respectively.

The Effect of Viscous and Pressure Gradient Torques on a Free-Rotor Gyroscope

The equations are derived for the torques on a spherical rotor. Using suitable transformation matrices, these error torques are related to the bearing compliances and the so-called g2 coefficients. The method of determining these coefficients is indicated, using the experimental technique of tumble testing the gyroscope.