The paper describes the use of topological indices in conjunction with high cholesterol drugs, specifically Fibrates, to predict their physicochemical properties and biological activities. Fibrates are known to lower high triglycerides, increase HDL cholesterol, and reduce the small dense fraction of LDL cholesterol. The study uses a quantitative structural-property relationships (QSPR) approach, which involves analyzing the relationships between physicochemical properties and topological indices using curvilinear regression. The QSPR model predicts the physicochemical properties of the drugs based on degrees and distances determined from topological indices. The study also conducted (DFT) calculations at the B3LYP/6-31G(d,p) level on the four investigated derivatives to gain insights into their optimized geometries, DOS plots, HOMO and LUMO orbital energies, and distribution. The theoretical results presented in the study suggest that the use of topological indices in QSPR models could provide a powerful tool for predicting the physicochemical properties and biological activities of molecules, including drugs. These findings could lead to the development of new cholesterol-lowering drugs with desirable properties.

Inertial microfluidics offers high throughput, label-free, easy to design, and cost-effective solutions and is a promising technique based on hydrodynamic forces (passive techniques) instead of external ones, which can be employed in lab-on-a-chip and micro-total-analysis-systems for focusing, manipulation, and separation of microparticles in chemical and biomedical applications. The current work, studies the focusing behavior of microparticles in an asymmetric curvilinear microchannel. For this purpose, focusing behavior, including position and band width, of microparticles of diameters of 10, 15 and 20 µm, which served as representatives of different cells, in an asymmetric curvilinear microchannel with curvature angle of 280° was experimentally studied at flow rates from 400 to 2700 µL/min (corresponding to Reynolds numbers between 30 and 205). The results revealed that the largest distance between focusing bands of 20 µm and 10 µm microparticles as well as between focusing bands of 15 µm and 10 µm was obtained at Reynolds number of 121. For the case of microparticles of diameters 20 µm and 15 µm, the largest distance was seen at Reynolds number of 144. The focusing band width became smaller in the asymmetric microchannel so that focusing could be more clearly observed in this configuration.

The extrusion-based additive manufacturing is a popular fabrication method, which has attracted the attention of various industries due to its simplicity, cheapness, ability to produce complex geometric shapes, and high production speed. One of the effective parameters in this process is the feed of filament that is presented in the production G-code. The feed of filament is calculated according to the layer height, the extrusion width and the length of printing path. All the required motion paths and filling patterns created by commercial software are a set of straight lines or circular arcs that are placed next to each other at a fixed distance. In special curved paths, the distance of adjacent ones is not equal at different points, and due to the weakness of common commercial software, it is not possible to create curved paths for proper printing. Therefore, making a special computer code that can be used to create various functions of curved paths is investigated in this research, and also the feed of filament parameter is studied in detail. Next, by introducing a correction technique, the feed of filament is changed during the curved path to distribute the polymer material uniformly. Finally, composite samples (which have variable stiffness) consisting of curved fibers are produced with the proposed method, and the high quality of printed samples confirm the suggested code and technique.

Abstract Unlike accelerated motion or curvalinear motion,a nonlinear motion state(non-inertial system) can be described by differential equations or the other algebric equations in axiom 2, the accelerated motion in axiom 3 can be considered to be described by using the equation of the linear and curvilinear process of the continuum extending to infinitely distance.Further, this linear and curvilinear process of the continuum is a quantitative continuum in essence as a unity of infinitely quantities and infinitely dimensions at infinite distance (infinity) relative to all orientations in which we exist. These indicates that an accelerated motion accumulates continuously started from a finite quantities, leaping to transit from finite to infinite quantities by an infinitely great accelerating force.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.