Shape-driven optofluidic rotational actuation

In the present work, we report light-induced rotation of millimeter-sized objects driven by their non-symmetric shape. The light-induced torque is originated by the thermal gradient on different sides of the teeth of star-shaped objects floating on liquid surfaces that leads to unbalanced surface tension due to the Marangoni effect. The dependence of the angular rotation on the number of teeth is demonstrated. The angular velocity is linearly dependent on the light intensity and follows a simple time behavior typical of objects moving under fluid friction. Graphic abstract

About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.

The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering

<abstract><p>In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.</p></abstract>

Simulation of the motion of a propellerless mobile robot controlled by rotation of the internal rotor

We consider a propellerless robot that moves on the surface of a fluid by rotating of the internal rotor. The robot shell has a symmetric shape of NACA 0040 airfoil. The equations of motion are written in the form of classical Kirchhoff equations with terms describing the viscous friction. The control action based on the derived model is proposed. The influences of various model parameters on the robot's trajectory have been studied.

On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length

For uninterrupted traffic flow, it is well-known that the fundamental diagram (FD) describes the relationship between traffic flow and density under steady state. To study the characteristics of interrupted traffic flow on a signalized link, a link fundamental diagram (LFD) for urban roads is proposed in this paper. First, a new variable, which synthesizes traffic flow with the speed of each vehicle, is defined. Then, the link fundamental diagram is obtained by drawing a scatter-plot of the velocity-weighted flow versus queue length, which takes on a unimodal curve with an approximately symmetric shape. Finally, simulation studies are conducted by modeling an urban link based on the traffic simulation software VISSIM. Compared with the traditional fundamental diagram, the proposed link fundamental diagram is more intuitive for showing the relationship between traffic condition and queue length. The impacts of the cycle time, green time, and split on the proposed link fundamental diagram are studied. Simulation results show that the shape of the link fundamental diagram fundamentally is determined by the split. The critical point is correlated to split values, and the green time exerts a great influence on both the velocity-weighted flow and the critical queue length. The cycle time has little effect on the critical queue length but has a great influence on the velocity-weighted flow.

Simultaneous Estimation of Aspirin, Atorvastatin Calcium and Clopidogrel Bisulphate in a Combined Dosage form by RP-HPLC

A rugged robust RP-HPLC method has been developed and validated for the simultaneous quantification of Aspirin (ASP), Atorvastatin calcium (ATO) and Clopidogrel bisulphate (CLO) in a combined dosage form. Optimized mobile phase composition of 25 mM KH2PO4: Methanol (20:80% v/v) pH 3.0 (adjusted with 20% o-phosphoric acid) isocratic mode with flow rate of 1 ml min-1, detection at 230 nm. Employed Princeton SPHER C18 (150 x 4.6 mm i.d. 5 µm) column for separation at ambient temperature with an isocratic flow. The linearity of each drug across the range of 0.5-32 µg/ml with correlation coefficient for ASP, ATO, and CLO in value of 0.979, 0.988 and 0.989 respectively. The retention time (min.) for ASP, ATO and CLO were found 1.85, 3.04 and 6.91 respectively. Limit of detection (LOD) of ASP, ATO and CLO - 0.04, 0.04, 0.08 (μg ml-1) respectively and Limit of Quantification (LOQ) of ASP, ATO and CLO- 0.14, 0.13, 0.28 (μg ml-1) in order. Performed analysis of marketed tablet formulation ASP (Ecosprin-75 mg), ATO (Aztor®40- 40 mg), CLO (Clopivas- 75 mg) found percentage recovery for ASP (99.93), ATO (100.00) and CLO (99.87). Performed stability studies found satisfactory results. Developed method has been validated, results of different parameter found in acceptable range. Chromatogram peaks are resolve, symmetric shape and without interference.

Symmetric Shape Transformations of Folded Shell Roofs Determining Creative and Rational Shaping of Building Free Forms

The paper presents an innovative approach to solving interdisciplinary problems emerging in the design process of building free forms roofed with elastically transformed corrugated shells. The effectiveness and rationality of shaping such free forms and the creativeness in searching for the parametric forms require the application of their regular and symmetric models which have to be derived from the geometric and mechanical properties of the rationally transformed subsequent folds of these shells. Simplified smooth models used for engineering developments and accurate folded models implemented for scientific research have to be created by means of unconventional methods different from those presented in classical courses. Owing to the variety of the forms of the proposed innovative reference tetrahedrons and their parametric description, the algorithms developed by the authors have to be implemented in computer programs. The rationality of the transformed roof shells, revealed in the limitation of the level of the fold’s initial stresses resulting from the shape transformation, and the attractiveness of these forms are achieved by the axial symmetry and contraction of each shell fold at its half-length. The symmetries adopted in the process of modeling such roof shells are also exploited by the discussed new method to obtain coherent unconventional general forms of entire buildings.