On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

Usability of augmented reality technology in tele-mentorship for managing clinical scenarios - A study protocol

BackgroundTele-mentorship is considered to offer a solution to training and providing professional assistance at a distance. Tele-mentoring is a method in which a mentor interactively guides a mentee at a different geographic location in real time using a technological communication device. During a healthcare procedure, tele-mentoring can support a medical expert, remote from the treatment site, to guide a less-experienced practitioner at a different geographic location. Augmented Reality (AR) technology has been incorporated in tele-mentoring systems in healthcare environments globally. However, evidence is absent about the usability of AR technology in tele-mentoring clinical healthcare professionals in managing clinical scenarios.AimThis study aims to evaluate the usability of Augmented Reality (AR) technology in tele-mentorship for managing clinical scenarios.MethodsThis study uses a quasi-experimental design. Four experienced health professionals and a minimum of twelve novice health practitioners will be recruited for the roles of mentors and mentees, respectively. In the experiment, each mentee wearing the AR headset performs a maximum of four different clinical scenarios in a simulated learning environment. A mentor who stays in a separate room and uses a laptop will provide the mentee remote instruction and guidance following the standard protocols for the treatment proposed for each scenario. The scenarios of Acute Coronary Syndrome, Acute Myocardial Infarction, Pneumonia Severe Reaction to Antibiotics, and Hypoglycaemic Emergency are selected, and the corresponding clinical management protocols developed. Outcome measures include the mentors and mentees’ perception of the AR’s usability, mentorship effectiveness, and the mentees’ self-confidence and skill performance.EthicsThe protocol was approved by the Tasmania Health and Medical Human Research Ethics Committee (Project ID: 23343). The complete pre-registration of our study can be found at https://osf.io/q8c3u/

Development of a Prediction System for 3D Printed Part Deformation

The Additive Manufacturing (AM) process is applied in industrial applications. However, quality issues of the printed parts, including part distortion and cracks caused by high temperature and fast cooling, result in high residual stress. The theoretical calculation equation shows elastic behavior which is the linear behavior between strain and stress. However, in practice with the additive manufacturing process, strain and stress have nonlinear behavior. So, the prediction of the deformation of a printed part is inaccurate. The contribution of this research is the creation of an Inherent Strain (IS)-based part deformation prediction method during the Selective Laser Melting (SLM) process. To have the deformation in the design stage, we developed software for calculating the IS value and predicting the deformation. The difference between the calculated results and the experimental results is still there, so, we proposed an algorithm and developed an optimization module for the system to minimize this difference. In the final optimal printing process, the parameters are derived in order for the real printing process to have the required quality of the SLM printed part

Effect of fly ash on mechanical properties and morphology of plasterboard based on recycled poly(ethylene terephthalate)

The purpose of this study was to synthesize plasterboard based on recycled poly(ethylene terephthalate) (PET) and fly ash. The molecular weight determination of unsaturated polyester (UP) from recycled PET was performed by functional titration method. The effect of initiator, benzoyl peroxide (BPO) on the curing kinetic of UP from recycled PET was studied by differential scanning calorimetry (DSC) and at 2 phr BPO led to good curing process. The content of fly ash (50, 100, 150, 200 phr) at 2007 nm in diameter was used and the effect of fly ash content on some properties such as flexural strength, vickers hardness, and impact strength of plasterboard was researched. Test results showed an increase in mechanical properties, especially at 150 and 175 phr filler amount. In addition, the morphology of plasterboard at different fly ash contents was characterized by scanning electron microscopy (SEM). Also, chemical resistance of plasterboard was evaluated from the weight change in different chemical environment. Keywords. Unsaturated polyester, Recycled PET, Fly ash, Plasterboard

Preparation and Foliar Application of Oligochitosan - Nanosilica on the Enhancement of Soybean Seed Yield

Oligochitosan with weight average molecu-lar weight (Mw) of 5000 g/mol was prepared by gamma Co-60 radiation degradation of 4% chitosan solution containing 0.5% H2O2 at 21 kGy. Nanosilica with size of 10 – 30 nm was synthesized by calcination of acid treated rice husk at 700o C for 2 h. The mixture of 2% oligo-chitosan-2% nanosilica was prepared by dispersion of nanosilica in oligochitosan solution. Oligochitosan, nanosilica and their mixture were characterized by gel permeation chromatography (GPC), transmission electr-on microscopy (TEM), X-ray diffraction (XRD), energy dispersive x-ray spectroscopy (EDX), Ultraviolet-visible spectroscopy (UV-Vis), and Furrier transform infrared spectroscopy (FT-IR). Effect of foliar application of oli-gochitosan and oligochitosan-nanosilica on soybean seed yield was conducted in experimental field. Results indi-cated that soybean seed yield increased 10.5 and 17.0% for oligochitosan and oligochitosan-nanosilica, respect-tively for the control. Radiation degraded oligo-chitosan and its mixture with nanosilica can be potentially used for cultivation of soybean with enhanced seed yield

Multi-response optimization of process parameters for powder mixed electro-discharge machining according to the surface roughness and surface micro-hardness using Taguchi-TOPSIS

In this study, the efficiency of integration between Taguchi and TOPSIS in multi-response optimi-zation of powder mixed electrical discharge machining (PMEDM) process was evaluated. The in-put parameters, such as workpiece and tool electrode material, polarity, pulse on time (ton), pulse off time (toff), Current (I) and powder concentration have been selected to optimize two responses; namely surface roughness (Ra) and surface hardness (HV). The results show that titanium powder mixed dielectric fluid improves multi-response optimization efficiency in PMEDM. In addition, machining conditions, such as tool electrode material, powder concentration, pulse on time, polarity, current density, A×G and B×G interactions play a very important role on S/N ratio of C* whereby powder concentration has the strongest influence. TOPSIS -Taguchi is a potential method for multi-response optimization in PMEDM. However, the optimal results using ANOVA analysis show that there is a necessity to have more studies in TOPSIS-Taguchi to improve the in-tegration efficiency between two methods for optimizing multiple responses in PMEDM