Thyroid fibrous band and levator glandulae thyroideae muscle: Two different structures associated with the pyramidal lobe of the thyroid gland

We investigated two structures that are in close association with the pyramidal lobe of the thyroid gland. Our investigation was performed using microdissection and histological examination in 106 human postmortem specimens. The first investigated structure was identified as the thyroid fibrous band that was present in 28.3% of cases. This band was always associated with the pyramidal lobe (which was significantly longer and thicker when associated with this band) and it had a constant hyo-pyramidal extension; it was located close to the midsagittal plane and predominantly composed of dense irregular connective tissue. The second investigated structure was the levator glandulae thyroideae muscle, which was associated with the pyramidal lobe in only 13.6% of cases. This muscle had a double extension, hyo-pyramidal and laryngo-pyramidal, located farther from the midsagittal plane, it was longer and thinner than the thyroid fibrous band and predominantly composed of striated muscle fibers. We confirmed our hypothesis that the thyroid fibrous band, which may be considered as the partial fibrous remnant of the thyroglossal duct and levator glandulae thyroideae, and which may be considered as infrahyoid or laryngeal muscle, are two different structures of the thyroid gland.

Odd-quadratic Leibniz superalgebras

An odd-quadratic Leibniz superalgebra is a (left or right) Leibniz superalgebra with an odd, supersymmetric, non-degenerate and invariant bilinear form. In this paper, we prove that a left (resp. right) Leibniz superalgebra that carries this structure is symmetric (meaning that it is simultaneously a left and a right Leibniz superalgebra). Moreover, we show that any non-abelian (left or right) Leibniz superalgebra does not possess simultaneously a quadratic and an odd-quadratic structure. Further, we obtain an inductive description of odd-quadratic Leibniz superalgebras using the procedure of generalized odd double extension and we reduce the study of this class of Leibniz superalgebras to that of odd-quadratic Lie superalgebras. Finally, several non-trivial examples of odd-quadratic Leibniz superalgebras are included.

Formation of Quinary Gordon-Mills-Welch Sequences for Discrete Information Transmission Systems

An algorithm for the formation of the quinary Gordon-Mills-Welch sequences (GMWS) with a period of N=54-1=624 over a finite field with a double extension GF[(52)2] is proposed. The algorithm is based on a matrix representation of a basic M-sequence (MS) with a primitive verification polynomial hмs(x) and a similar period. The transition to non-binary sequences is determined by the increased requirements for the information content of the information transfer processes, the speed of transmission through communication channels and the structural secrecy of the transmitted messages. It is demonstrated that the verification polynomial hG(x) of the GMWS can be represented as a product of fourth-degree polynomials-factors that are indivisible over a simple field GF(5). The relations between roots of the polynomial hмs(x) of the basic MS and roots of the polynomials hсi(x) are obtained. The entire list of GMWS with a period N=624 can be formed on the basis of the obtained ratios. It is demonstrated that for each of the 48 primitive fourth-degree polynomials that are test polynomials for basis MS, three GMWS with equivalent linear complexity (ELC) of ls=12, 24, 40 can be formed. The total number of quinary GMWS with period of N=624 is equal to 144. A device for the formation of a GMWS as a set of shift registers with linear feedbacks is presented. The mod5 multipliers and summators in registers are arranged in accordance with the coefficients of indivisible polynomials hсi(x). The symbols from the registers come to the adder mod5, on the output of which the GMWS is formed. Depending on the required ELC, the GMWS forming device consists of three, six or ten registers. The initial state of cells of the shift registers is determined by the decimation of the symbols of the basic MS at the indexes of decimation, equal to the minimum of the exponents of the roots of polynomials hсi(x). A feature of determining the initial States of the devices for the formation of quinary GMWS with respect to binary sequences is the presence of cyclic shifts of the summed sequences by a multiple of N/(p–1). The obtained results allow to synthesize the devices for the formation of a complete list of 144 quinary GMWS with a period of N=624 and different ELC. The results can also be used to construct other classes of pseudo-random sequences that allow analytical representation in finite fields.

Un grammairien “oublié” : Ibn Muʿṭī

Ibn Muʿṭī est un grammairien originaire du Maghreb, mais qui a émigré au Machrek, où il est mort en 628/1231. Auteur de la premièreʾAlfiyya, il est aussi l’auteur d’un ouvrage en prose intituléal-Fuṣūl al-ḫamsūn. Celui-ci tire son nom de ce qu’il est divisé en « cinquante sections », mais rassemblées en cinq chapitres. Il est donc comparable auMufaṣṣaldu Persan al-Zamaḫšarī (m. 538/1144), divisé en sections, rassemblées en quatre parties. Chez al-Zamaḫšarī l’exposé grammatical se fait selon les parties du discours d’une part, la flexibilité/inflexibilité désinentielles (ʾiʿrāb/bināʾ) de ces parties d’autre part. Chez Ibn Muʿṭī, il se fait selon leʿamal(litt. « action »), qui est avec leʾiʿrābdans la relation de cause à effet. C’est ce qui explique la priorité donnée au verbe (ch. 2), considéré comme le régissant principal, les autres régissants étant regroupés dans le chapitre 3. C’est là l’influence duǦumald’al-Zaǧǧāǧī (m. 337/949 ou 339-340/950-952), une des références majeures de la grammaire arabe dans l’Occident musulman. Elle est particulièrement sensible dans la double extension dutaʿaddīet la classification des compléments du verbe.