Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application

Numerical study on the correlation between CP violation in neutrino oscillations and baryogenesis

We numerically study the correlation between CP violation in the neutrino oscillations and baryogenesis in the seesaw model. In this study we get the heavy Majorana neutrino masses and lepton number asymmetries from their decays by fitting the data of neutrino oscillations and by working on some hypothesis of the Dirac-Yukawa term for neutrinos.Comment: 3 pages, 2 figures, Latex, presented at KEKTC5(Nov. 2001), to be published in Nucl. Phys. Proc. Supp

Statistics Of The Burst Model At Super-critical Phase

We investigate the statistics of a model of type-I X-ray burst [Phys. Rev. E, {\bf 51}, 3045 (1995)] in its super-critical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time evolution of the percentage of space covered by burnable clusters. A relation between the time-average and the peak percentage of space covered by burnable clusters is also derived.Comment: 11 Pages in Revtex 3.0. Two figures available by sending request to [email protected]

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

Optimising poly(lactic-co-glycolic acid) microparticle fabrication using a Taguchi orthogonal array design-of-experiment approach

© 2019 Mensah et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.The objective of this study was to identify, understand and generate a Taguchi orthogonal array model for the formation of 10–50 μm microparticles with applications in topical/ocular controlled drug delivery. Poly(lactic-co-glycolic acid) (PLGA) microparticles were fabricated by the single emulsion oil-in-water method and the particle size was characterized using laser diffraction and scanning electronic microscopy (SEM). Sequential Taguchi L 12 and L 18 orthogonal array (OA) designs were employed to study the influence of ten and eight parameters, respectively, on microparticle size (response). The first optimization step using the L 12 design showed that all parameters significantly influenced the particle size of the prepared PLGA microparticles with exception of the concentration of poly(vinyl alcohol) (PVA) in the hardening bath. The smallest mean particle size obtained from the L 12 design was 54.39 μm. A subsequent L 18 design showed that the molecular weight of PLGA does not significantly affect the particle size. An experimental run comprising of defined parameters including molecular weight of PLGA (89 kDa), concentration of PLGA (20% w/v), concentration of PVA in the emulsion (0.8% w/v), solvent type (ethyl acetate), organic/aqeuous phase ratio (1:1 v/v), vortexing speed (9), vortexing duration (60 seconds), concentration of PVA in hardening bath (0.8% w/v), stirring speed of hardening bath (1200 rpm) and solvent evaporation duration (24 hours) resulted in the lowest mean particle size of 23.51 μm which was predicted and confirmed by the L 18 array. A comparable size was demonstrated during the fabrication of BSA-incorporated microparticles. Taguchi OA design proved to be a valuable tool in determining the combination of process parameters that can provide the optimal condition for microparticle formulation. Taguchi OA design can be used to correctly predict the size of microparticles fabricated by the single emulsion process and can therefore, ultimately, save time and costs during the manufacturing process of drug delivery formulations by minimising experimental runs.Peer reviewedFinal Published versio