Generalized Induced Norms

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.Comment: 8 page

Surgical clipping compared to endovascular coiling of ruptured coil able middle cerebral aneurysms: A single-center experience

Objective: The middle cerebral artery (MCA) is the third most common site for ruptured intracranial aneurysms. Aneurysms in this location are known to be challenging to treat endovascularly and are commonly treated with microsurgery. Although advances in endovascular treatment options for cerebral aneurysms have markedly reduced the need for surgery in recent years and decades, there is no compelling scientific evidence that endovascular treatments are superior to surgical treatment. The present study aimed to determine the appropriate treatment modality in ruptured MCA aneurysms. Methods: We retrospectively evaluated and compared the treatment outcomes of 80 patients with ruptured MCA aneurysms who underwent either endovascular or microsurgical treatment in our center between 2011 and 2016. Post-treatment clinical and radiological outcomes were assessed in all patients. Furthermore, we compared intraoperative complications and the need for re-treatments between the two groups. Results: According to our findings, complete aneurysm occlusion was achieved in 90.5 and 89.2 of the patients in the clipping and coil group, respectively (p = 0.850). Moreover, 14.3 of the patients in the clipping group and 15.8 of the subjects in the coil group developed intraoperative complications (p = 0.851), including 3 cases of intraoperative hemorrhage and 3 cases of ischemia in the clipping group as well as 2 cases of thromboembolism and 4 cases of vasospasm during endovascular treatment in the coil group. There was an improvement in the modified Rankin score (mRS) at six months, with no significant difference between the two groups (p = 0.916). Conclusion: The results of coiling only with coil able MCA aneurysms were comparable to the results of clipping with difficult cases. Sufficient follow-up study of recurrence and retreatment are needed to determine the indication for coiling for ruptured MCA aneurysm. © 202

Recent advances and future perspectives on microfluidic liquid handling

© 2017 by the authors. The interdisciplinary research field of microfluidics has the potential to revolutionize current technologies that require the handling of a small amount of fluid, a fast response, low costs and automation. Microfluidic platforms that handle small amounts of liquid have been categorised as continuous-flow microfluidics and digital microfluidics. The first part of this paper discusses the recent advances of the two main and opposing applications of liquid handling in continuous-flow microfluidics: mixing and separation. Mixing and separation are essential steps in most lab-on-a-chip platforms, as sample preparation and detection are required for a variety of biological and chemical assays. The second part discusses the various digital microfluidic strategies, based on droplets and liquid marbles, for the manipulation of discrete microdroplets. More advanced digital microfluidic devices combining electrowetting with other techniques are also introduced. The applications of the emerging field of liquid-marble-based digital microfluidics are also highlighted. Finally, future perspectives on microfluidic liquid handling are discussed

Modeling of mass transfer enhancement in a magnetofluidic micromixer

© 2019 Author(s). The use of magnetism for various microfluidic functions such as separation, mixing, and pumping has been attracting great interest from the research community as this concept is simple, effective, and of low cost. Magnetic control avoids common problems of active microfluidic manipulation such as heat, surface charge, and high ionic concentration. The majority of past works on micromagnetofluidic devices were experimental, and a comprehensive numerical model to simulate the fundamental transport phenomena in these devices is still lacking. The present study aims to develop a numerical model to simulate transport phenomena in microfluidic devices with ferrofluid and fluorescent dye induced by a nonuniform magnetic field. The numerical results were validated by experimental data from our previous work, indicating a significant increase in mass transfer. The model shows a reasonable agreement with experimental data for the concentration distribution of both magnetic and nonmagnetic species. Magnetoconvective secondary flow enhances the transport of nonmagnetic fluorescent dye. A subsequent parametric analysis investigated the effect of the magnetic field strength and nanoparticle size on the mass transfer process. Mass transport of the fluorescent dye is enhanced with increasing field strength and size of magnetic particles

Electronic Journal of Theoretical Physics Bi-parameter Semigroups of linear operators

Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s�0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X, whose first and second generators are d and σ, respectively, and if d is also a σ-derivation then d n (ab) =(d + σ) n (a) ⋆ (d + σ) n (b) andαt,0(ab) =αt,1(a) ⋆αt,1(b) for all a, b ∈X

Evaluation of the effect of NT-3 and biodegradable poly-l-lactic acid nanofiber scaffolds on differentiation of rat hair follicle stem cells into neural cells in vitro

Recent improvement in neuroscience has led to new strategies in neural repair. Hair follicle stem cells are high promising source of accessible, active, and pluripotent adult stem cells. They have high affinity to differentiate to neurons. Aside from using cell-scaffold combinations for implantation, scaffolds can provide a suitable microenvironment for cell proliferation, migration, and differentiation. NT-3 is the most interesting neurotrophic factors being an important regulator of neural survival and differentiation. Since treatment duration in neural repair is very important, this study aims to evaluate the effect of NT-3 and poly-l-lactic acid (PLLA) on differentiation time of bulge stem cells of rat hair follicle to neural-like cells. HFSCs of rat whisker was isolated and cultured on PLLA and differentiated with 10 ng/mL NT-3. Biological features of cultured cells were evaluated with immunocytochemistry and flowcytometry methods by using CD34, nestin, and β III-tubulin markers. For cell viability and morphological assessment, MTT assay and SEM were performed. Our results showed that bulge stem cells of hair follicle can express CD34 and Nestin before differentiation. By using NT-3 during differentiation process, the cells showed positive reaction to β III-tubulin antibody. MTT results demonstrated that PLLA significantly increased cell viability. Finally, HFSCs adhesion was confirmed by SEM results. The results indicate that 10 ng/mL NT-3 and PLLA have significant effect on differentiation time of rat HFSCs to neural cells even in 10 days. © 2013 Springer Science+Business Media New York