LEONARD PAIRS OF RACAH AND KRAWTCHOUK TYPE IN LB-TD FORM

Alnajjar, Hasan Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.2

Let ${\mathcal{F}}$ denote an algebraically closed field with characteristic not two. Fix an integer $d{\geq}3$, let $Mat_{d+1}({\mathcal{F}})$ denote the ${\mathcal{F}}$-algebra of $(d+1){\times}(d+1)$ matrices with entries in ${\mathcal{F}}$. An ordered pair of matrices A, $A^*$ in $Mat_{d+1}({\mathcal{F}})$ is said to be LB-TD form whenever A is lower bidiagonal with subdiagonal entries all 1 and $A^*$ is irreducible tridiagonal. Let A, $A^*$ be a Leonard pair in $Mat_{d+1}({\mathcal{F}})$ with fundamental parameter ${\beta}=2$, with this assumption there are four families of Leonard pairs, Racah, Hahn, dual Hahn, Krawtchouk type. In this paper we show from these four families only Racah and Krawtchouk have LB-TD form.

LEONARD PAIRS GENERATED FROM U_q(sl₂)

ALQDERAT, AMANI,ALNAJJAR, HASAN The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6

Consider the quantum algebra U_q(sl₂) over field 𝓕 (char(𝓕) = 0) with equitable generators x^±1, y and z, where q is fixed nonzero, not root of unity scalar in 𝓕. Let V denote a finite dimensional irreducible module for this algebra. Let Λ ∈ End(V), and let {A₁, A₂, A₃} = {x, y, z}. First we show that if Λ, A₁ is a Leonard pair, then this Leonard pair have four types, and we show that for each type there exists a Leonard pair Λ, A₁ in which Λ is a linear combination of 1, A₂, A₃, A₂A₃. Moreover, we use Λ to construct 𝚼 ∈ U_q(sl₂) such that 𝚼, A^-1₁ is a Leonard pair, and show that 𝚼 = I + A₁Φ + A₁ΨA₁ where Φ and Ψ are linear combination of 1, A₂, A₃.

Study of the Ribavirin drug adsorption on the surfaces of carbon nanotube and graphene nanosheet using density functional theory calculations

Sheikhi Masoome,Shahab Siyamak,Balali Ebrahim,Alnajjar Radwan,Kaviani Sadegh,Khancheuski Maksim,Al Saud Sultan 대한화학회 2021 Bulletin of the Korean Chemical Society Vol.42 No.11

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations were performed in the solvent water for the study of the adsorption of the Ribavirin (RIB) on surfaces of the carbon nanotube (CNT) and graphene nanosheet (GNS). After the adsorption, the electronic properties of the CNT and GNS change. The adsorption energies are shown the strong adsorption in GNS/RIB (0.816 eV) rather than CNT/RIB (0.544 eV). The dipole moment of CNT and GNS changes with the adsorption of the RIB from 0.00 to 4.57 and 7.05 Debye in CNT/RIB and GNS/RIB, respectively. The adsorption of the RIB molecule on CNT and GNS increases the value of λmax. The localized orbital locator and electron location function values for the C C bond confirm the stronger interaction between carbon atoms of GNS and RIB. Based on the results, it is suggested that GNS with a lower energy gap (3.03 eV) is a more suitable structure for adsorption of the RIB in comparison with the CNT (3.021).

Intranasal Insulin for Alzheimer's Disease and Amnestic Mild Cognitive Impairment: Systematic Review and Meta-analysis

사라 알라자르,진혜경,강지은,박소현,이정연,Alnajjar, Sarah,Jin, Hye Kyung,Kang, Ji Eun,Park, So Hyun,Rhie, Sandy Jeong Korean College Of Clinical Pharmacy 2017 한국임상약학회지 Vol.27 No.3

Background: There is recent evidence that insulin resistance is responsible for increasing the risk of developing cognitive dysfunction. To systematically review the influence of intranasal insulin treatment on the cognitive function in Alzheimer's disease patients. Methods: Randomized controlled trials comparing the cognitive effects of intranasal insulin therapy in Alzheimer's disease patients with controlled interventions were retrieved from Pubmed, Medline, Embase and Cochrane library. Meta-analysis was conducted on the cognitive measurements with a subgroup analysis by dose, gender and apolipoprotein E allele 4 (ApoE ${\varepsilon}4$) status. Results: Seven randomized controlled trials were eligible for inclusion. Intranasal insulin had a positive influence on the cognitive function as compared to placebo without a statistical significance (standardized mean difference; SMD = 0.109; 95% confidence interval; CI -0.04 to 0.26; P=0.14). In subgroup analysis, a 20 IU dose of intranasal insulin induced a significant improvement in cognitive function (SMD = 0.14; 95% CI 0.05 to 0.24; P=0.004), but 40 IU did not show this effect (SMD = -0.01; 95% CI -0.11 to 0.09; P=0.82). ApoE ${\varepsilon}4$ positive patients showed a significant decline in cognitive function as compared to ApoE ${\varepsilon}4$ positive patients in the control group (SMD = -0.213; 95% CI -0.38 to -0.04; P=0.015). Such an effect was not apparent in ApoE ${\varepsilon}4$ negative patients. Gender had no influence on the cognitive outcomes. Conclusion: The results indicate that intranasal insulin may have beneficial effect in improving the cognitive function in Alzheimer's disease patients.

Microorganism penetration in dentinal tubules of instrumented and retreated root canal walls. In vitro SEM study

Al-Nazhan, Saad,Al-Sulaiman, Alaa,Al-Rasheed, Fellwa,Alnajjar, Fatimah,Al-Abdulwahab, Bander,Al-Badah, Abdulhakeem The Korean Academy of Conservative Dentistry 2014 Restorative Dentistry & Endodontics Vol.39 No.4

Objectives: This in vitro study aimed to investigate the ability of Candida albicans (C. albicans) and Enterococcus faecalis (E. faecalis) to penetrate dentinal tubules of instrumented and retreated root canal surface of split human teeth. Materials and Methods: Sixty intact extracted human single-rooted teeth were divided into 4 groups, negative control, positive control without canal instrumentation, instrumented, and retreated. Root canals in the instrumented group were enlarged with endodontic instruments, while root canals in the retreated group were enlarged, filled, and then removed the canal filling materials. The teeth were split longitudinally after canal preparation in 3 groups except the negative control group. The teeth were inoculated with both microorganisms separately and in combination. Teeth specimens were examined by scanning electron microscopy (SEM), and the depth of penetration into the dentinal tubules was assessed using the SMILE view software (JEOL Ltd). Results: Penetration of C. albicans and E. faecalis into the dentinal tubules was observed in all 3 groups, although penetration was partially restricted by dentin debris of tubules in the instrumented group and remnants of canal filling materials in the retreated group. In all 3 groups, E. faecalis penetrated deeper into the dentinal tubules by way of cell division than C. albicans which built colonies and penetrated by means of hyphae. Conclusions: Microorganisms can easily penetrate dentinal tubules of root canals with different appearance based on the microorganism size and status of dentinal tubules.

Microorganism penetration in dentinal tubules of instrumented and retreated root canal walls. In vitro SEM study

Saad Al-Nazhan,Alaa Al-Sulaiman,Fellwa Al-Rasheed,Fatimah Alnajjar,Bander Al-Abdulwahab,Abdulhakeem Al-Badah 대한치과보존학회 2014 Restorative Dentistry & Endodontics Vol.39 No.4

Objectives: This in vitro study aimed to investigate the ability of Candida albicans (C. albicans) and Enterococcus faecalis (E. faecalis) to penetrate dentinal tubules of instrumented and retreated root canal surface of split human teeth. Materials and Methods: Sixty intact extracted human single-rooted teeth were divided into 4 groups, negative control, positive control without canal instrumentation, instrumented, and retreated. Root canals in the instrumented group were enlarged with endodontic instruments, while root canals in the retreated group were enlarged, filled, and then removed the canal filling materials. The teeth were split longitudinally after canal preparation in 3 groups except the negative control group. The teeth were inoculated with both microorganisms separately and in combination. Teeth specimens were examined by scanning electron microscopy (SEM), and the depth of penetration into the dentinal tubules was assessed using the SMILE view software (JEOL Ltd). Results: Penetration of C. albicans and E. faecalis into the dentinal tubules was observed in all 3 groups, although penetration was partially restricted by dentin debris of tubules in the instrumented group and remnants of canal filling materials in the retreated group. In all 3 groups, E. faecalis penetrated deeper into the dentinal tubules by way of cell division than C. albicans which built colonies and penetrated by means of hyphae. Conclusions: Microorganisms can easily penetrate dentinal tubules of root canals with different appearance based on the microorganism size and status of dentinal tubules.