Kolakoski sequence: links between recurrence, symmetry and limit density
ODAM-Vol. 4 (2021), Issue 1, pp. 29 – 44 Open Access Full-Text PDF
Alessandro Della Corte
Abstract: The Kolakoski sequence \(S\) is the unique element of \(\left\lbrace 1,2 \right\rbrace^{\omega}\) starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of \(S\) as a unifying tool to address the links between the main open questions – recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is \(\frac{1}{2}\).
Rate of convergence in total variation for the generalized inverse Gaussian and the Kummer distributions
OMS-Vol. 5 (2021), Issue 1, pp. 182 – 191 Open Access Full-Text PDF
Essomanda KONZOU
Abstract: The generalized inverse Gaussian distribution converges in law to the inverse gamma or the gamma distribution under certain conditions on the parameters. It is the same for the Kummer’s distribution to the gamma or beta distribution. We provide explicit upper bounds for the total variation distance between such generalized inverse Gaussian distribution and its gamma or inverse gamma limit laws, on the one hand, and between Kummer’s distribution and its gamma or beta limit laws on the other hand.
Prime and irreducible filters in strong quasi-ordered residuated systems
OMS-Vol. 5 (2021), Issue 1, pp. 172 – 181 Open Access Full-Text PDF
Daniel A. Romano
Abstract: In this article, we continue our research on quasi-ordered residuated systems introduced in 2018 by S. Bonzio and I. Chajda and various types of filters in them. Some fundamental properties of strong quasi-ordered residuated systems are given in this article. In addition, the concepts of prime and irreducible filters in such systems are introduced and analyzed.
Qualitative analysis of a mathematical model of divorce epidemic with anti-divorce therapy
EASL-Vol. 4 (2021), Issue 2, pp. 1 – 11 Open Access Full-Text PDF
Reuben Iortyer Gweryina, Francis Shienbee Kaduna, Muhammadu Yahaya Kura
Abstract: Marriage is the living together of two persons as husband and wife. Separation and Divorce are the frontier challenges facing the existence of stable family system. In this paper, we construct an epidemiological model of divorce epidemic using standard incidence function as force of marital disunity. The study examines qualitatively that the two equilibra (divorce-free and endemic equilibrium point) are globally stable by Lyapunov functions. Numerical results reveal that, anti-divorce protocols and reconciliation can jointly stabilize marriages, and Married cases that survive divorce epidemic in 30 years period of marriage (twice the survival period of separation) cannot break again.
Construction and classification of \(p\)-ring class fields modulo \(p\)-admissible conductors
OMS-Vol. 5 (2021), Issue 1, pp. 162 – 171 Open Access Full-Text PDF
Daniel C. Mayer
Abstract: Each \(p\)-ring class field \(K_f\) modulo a \(p\)-admissible conductor \(f\) over a quadratic base field \(K\) with \(p\)-ring class rank \(\varrho_f\) mod \(f\) is classified according to Galois cohomology and differential principal factorization type of all members of its associated heterogeneous multiplet \(\mathbf{M}(K_f)=\lbrack(N_{c,i})_{1\le i\le m(c)}\rbrack_{c\mid f}\) of dihedral fields \(N_{c,i}\) with various conductors \(c\mid f\) having \(p\)-multiplicities \(m(c)\) over \(K\) such that \(\sum_{c\mid f}\,m(c)=\frac{p^{\varrho_f}-1}{p-1}\). The advanced viewpoint of classifying the entire collection \(\mathbf{M}(K_f)\), instead of its individual members separately, admits considerably deeper insight into the class field theoretic structure of ring class fields. The actual construction of the multiplet \(\mathbf{M}(K_f)\) is enabled by exploiting the routines for abelian extensions in the computational algebra system Magma.
A prospective study for assessment of Serum Adenosine Deaminase, Erythrocyte Sedimentation Rate and C-Reactive Protein levels in patients with Psoriasis
TCMS-Vol. 1 (2021), Issue 1, pp. 21 – 25 Open Access Full-Text PDF
Leo Tauro, Nutsukpo Amankwa
Abstract:The aim of this paper is to assess Serum Adenosine Deaminase (ADA), Erythrocyte Sedimentation Rate (ESR) and C-Reactive Protein (CRP) levels in patients with Psoriasis. Sixty- four patients with psoriasis were divided into three groups (mild, moderate, and severe) based on PASI scores. PASI score <10 defined psoriasis as mild, between 10 and 20 as moderate, and >20 as severe. The hsCRP was assayed by an enzyme-linked immunosorbent assay BIOS kit. ADA was measured through kinetic method. ESR was calculated using Westergren method. Group I patients had 8 males (mild), 9 males (moderate) and 10 males (severe) and group II had 20 males. There were 12 females (mild), 14 females (moderate) and 11 females (severe) and group II had 30 females. A non- significant difference was observed (P> 0.05). The mean hSCRP level in group I patients was 54.2 ng/ml and in group II was 19.6 ng/ml. The mean ADA level in group I patients was 22.5 U/L and in group II was 8.1 U/L. The mean ESR was 28.4 mm/h in group I and 13.2 mm/h in group II. A significant difference was observed (P< 0.05). This study demonstrated higher hSCRP, ESR and ADA level among patients suffering from psoriasis compared to healthy control.
