HPU2 Journal of Science: Natural Sciences and Technology

A probabilistic method to prove AM-QM inequality

2024-12-30T15:17:53+07:00

Inequality is one of the interesting topics in mathematics that attracts the attention of both students and researchers. Solving inequalities often requires creativity, making it a challenging topic for many students. The inequality of arithmetic and quadratic means, or AM-QM in short, states that the arithmetic mean of a list of non-negative real numbers is less than or equals to the square root of the quadratic mean of the same list. There are many methods of proving the AM-QM inequality. In this paper, we will present a probabilistic method to prove the weighted general AM-QM inequality and show that the classical AM-QM inequality is a special case of the generalized AM-QM inequality with equal weights.

An ab initio calculation on the structural, electronic and magnetic properties of Ni-doped \(\text{Bi}_{0.5}\text{Na}_{0.5}\text{TiO}_3\)

2024-12-30T15:17:51+07:00

The first principle calculation was employed to investigate the formation energies and structural, electronic, and magnetic properties of intrinsic and Ni-doped sodium bismuth titanate Bi_0.5Na_0.5TiO₃ (BNT). The obtained formation energies indicate that Ni atoms prefer to dope into Bi-sites in the lattice of BNT while the calculated band structure shows that the doping leads to the emergence of new mid-gap energy states in the bandgaps, reducing the bandgap value of doped materials. The PDOSs reveal that Bi-6p, O-2p and Ti-3d contribute major parts in BNT valence and conduction bands, while the Ni-3d and 4s play the main roles in the formation of new mid-gap states. The spin-resolved density of states, the integrated spin densities and the charge distributions suggest that all doped models exhibit magnetic behavior, mainly due to the interaction of Ni, O and Ti atoms. The study method of this research can be applied to predict new properties of BNT-based materials.

Stepwise grafting polyethyleneimine onto silica surface for Cu(II) removal

2024-12-30T15:17:46+07:00

Polyethyleneimine (PEI) is a novel polymer that contains multiple amine groups that are suitable for chelation with many heavy metal ions (HMI). Anchoring PEI onto the surface of a solid substrate has been widely adopted to develop adsorbent materials with the hope of combining the HMI chelating ability of PEI with the heterogeneity of the substrate. Herein, the preparation of PEI grafted SiO2 (PEI/SiO2) has been demonstrated by a stepwise method in which SiO2 nanoparticles were functionalized with 3-glycidoxypropyltrimethoxysilane (KH560) followed by refluxing with PEI. The method could provide PEI/SiO2 material with 23.4% of PEI by weight. Studying the adsorption properties of PEI/SiO2 with Cu(II) revealed that the adsorption of Cu(II) ions on PEI/SiO2 followed Langmuir and Dubinin-Radushkevich models and included both chemisorption and physisorption. The adsorption capacity was about 25.3-27.3 mg/g. The stepwise method demonstrated in this study may be adopted to fabricated PEI based materials for HMI removal.

Algebraic method for image reconstruction in ultrasonic tomography

2024-12-30T15:17:43+07:00

Ultrasound tomography is crucial due to its capability to deliver detailed, real-time, and non-invasive imaging. This is essential for early diagnosis, treatment planning, and guiding medical procedures. Its affordability, portability, and safety make it a versatile tool in medical and non-medical fields alike, driving ongoing advancements in technology and applications. The Distorted Born Iterative Method (DBIM) is an advanced technique used in ultrasound tomography to iteratively restore images, improving upon the standard Born approximation by addressing some of its limitations. However, the DBIM also has its own set of disadvantages when used for iterative image restoration, resulting in computational complexity, noise sensitivity, convergence issues, etc. In this paper, we introduce a new method for image reconstruction in ultrasound tomography by using the algebraic method. The numerical results indicate that this method has a shorter computational time and achieves high-resolution reconstructions and accurate solutions.

The one-pot fabrication of green-emitting composites based on PMMA

2024-12-30T15:17:48+07:00

Photoluminescent composites consisting of a photoluminescent material dispersed in a suitable matrix have been applied in many applications, such as light-emitting diodes, solar concentrators, and anti-counterfeiting inks. The traditional method for the fabrication of composites by blending an as-synthesized photoluminescent material and a matrix is very challenging as it is difficult to obtain homogeneous composites. In this study, we have demonstrated a one-step method to prepare homogeneous composites by inducing the formation of in-situ photoluminescent centers in a stable matrix. Poly(methyl methacrylate) (PMMA) coated with o-phenylenediamine (oPD) was thermally annealed at 165^oC for a duration of 5 minutes in an extruder to obtain green-emitting composites. The composites exhibited a broad absorption peak at 425 nm and an absorption shoulder at 495 nm. The emission spectrum of the composite was broad, ranging from 400 nm to 700 nm, and reached the maximum at 525 nm. The photoluminescent maximum position was independent of the excitation wavelength. The photoluminescent excitation spectrum of the composite resembled the absorption near 425 nm. Time-dependent density functional theory (TD-DFT) calculations suggested that 2,3-diaminophenazine and 3-amino-2-hydroxyphenazine are the main molecular fluorophores accounting for the optical properties of the composites. The synthetic method demonstrated in this study is transferable for preparing numerous photoluminescent thermoplastics.

An investigation into the morphological and anatomical characteristics of three cassava (\( Manihot \,\, esculenta\)) varieties collected from the Northern provinces of Vietnam

2024-12-30T15:17:40+07:00

Cassava (Manihot esculenta Crantz) is a crucial crop that sustains millions of people across tropical and subtropical regions, providing an essential source of carbohydrates and contributing significantly to food security. Morphologically, varieties KM94, 08SA06, and Ruột vàng exhibit distinct traits such as plant form, leaf structure, tuber shape, and starch content, which underline their adaptability and potential for high yield under diverse growing conditions. Anatomically, the stems of these varieties demonstrate unique structural features, including tightly packed epidermal cells with thick cuticle layers, varying layers of collenchyma and parenchyma, robust sclerenchyma rings, and well-organized vascular bundles. These features ensure efficient nutrient and water transport, structural integrity, and resilience against environmental stresses, essential for the growth and development of these cassava varieties. By highlighting these morphological and anatomical traits, this study emphasizes the importance of such detailed analyses for improving cassava cultivation practices.

Some data about endangered and rare plant species in Me Linh Station for Biodiversity, Vinh Phuc province

2024-12-30T15:17:38+07:00

Me Linh Station for Biodiversity has an area of 170.3 hectares, near Tam Dao National Park. Although the area is not large, it has with high biodiversity and rich flora, including many rare and threatened plant species. So, this place not only preserves biodiversity but also organizes research and educational activities to protect biodiversity and the environment. Some research projects have been done on species diversity, ecosystem diversity, and forest biomass... This study identifies 38 endangered and rare plant species. Among them, 20 species in Vietnam Red Data Book 2007; 20 species belong to Decree No. 84/2021/ND-CP; 16 species belong to Appendix II of CITES (2024), and 4 species belong to IUCN (2024). Simultaneously, this study added summary information about the conservation status, life forms, geographical factors, and uses of 38 plant endangered and rare species in Me Linh Station for Biodiversity, Vinh Phuc province.

On the second-order sufficient optimality condition in nonconvex multiobjective optimization problems

2024-12-30T15:17:36+07:00

The study of second-order optimality conditions is one of the most important topics in optimization theory and attracting the attention and interest of many authors. In this paper, we introduce a novel solution concept called “essential local efficient solutions of second-order” for nonconvex constrained multiobjective optimization problems. We then show that the new solution concept is stronger than the quadratic growth condition and under a mild constraint qualification, these solution concepts are equivalent. By using the second subderivative, we derive a sufficient optimality condition for a feasible solution to become an essential local efficient solution of second-order for the considered problem. Examples are provided to illustrate the obtained results.

On minimization of quadratic functions over closed convex sets in Hilbert spaces

2024-12-30T15:17:34+07:00

Quadratic programming problems are of primary importance in various applications and arise as subproblems in many optimization algorithms. In this paper, we investigate quadratic programming problems in Hilbert spaces. By utilizing the Legendre property of quadratic forms and an asymptotically linear set with respect to a cone, we establish a sufficient condition for the existence of solutions to the considered problems through a Frank-Wolfe type theorem. The proposed condition is based on the special structure of Hilbert spaces, extending the applicability of quadratic programming methods. Finally, we provide a numerical example to illustrate the results obtained and demonstrate that existing approaches cannot be applied in certain cases.

Hybrid affine cipher and eigenvector methods for cryptography

2024-12-30T15:17:32+07:00

This paper systematically presents a specific application of linear algebra in information security and cryptography, highlighting the crucial role of matrix operations and linear techniques in the design and analysis of encryption algorithms. Specifically, we focus on a method that utilizes linear algebra to enhance the security and efficiency of modern cryptographic systems. A detailed illustrative example is provided to help readers better understand how these mathematical tools are applied in practice. Furthermore, we review existing encryption techniques and propose a new matrix-based scheme that leverages linear algebra to improve data security, optimize the encryption-decryption process, and ensure the integrity and confidentiality of information throughout transmission and storage.