Evaluation of Continuous Power-Down Schemes

We consider a power-down system with two states—“on” and “off”—and a continuous set of power states. The system has to respond to requests for service in the “on” state and, after service, the system can power off or switch to any of the intermediate power-saving states. The choice of states determines the cost to power on for subsequent requests. The protocol for requests is “online”, which means that the decision as to which intermediate state (or the off-state) the system will switch has to be made without knowledge of future requests. We model a linear and a non-linear system, and we consider different online strategies, namely piece-wise linear, logarithmic and exponential. We provide results under online competitive analysis, which have relevance for the integration of renewable energy sources into the smart grid. Our analysis shows that while piece-wise linear systems are not specific for any type of system, logarithmic strategies work well for slack systems, whereas exponential systems are better suited for busy systems.

Mathematics Communication Skill Analysis in Means-End-Analysis Learning Assisted with Manipulative Property (APM) and Application Based on Self-Efficacy

This research analyzed mathematics communication skills with the Means-End Analysis model assisted with Manipulative Property (APM), MEA with Linear System Pro application, and PBL based on the eighth graders' self-efficacy. This quasi-experimental research used a nonequivalent pretest-posttest control group design. The subjects were eighth-graders of Public JHS 4 Adiwerna. The samples were VIII-C learners as the first experimental group, VIII-G learners as the second experimental group, and VIII-H learners as the control group. The data collecting techniques were mathematics communication skill test and self-efficacy inventory. The results were: (1) MEA with APM (82.75%), MEA with Linear System Pro (78.12%), and PBL (75%) of the learners reached the minimum mastery standard with a proportion percentage, 75%; (2) there were mean differences between MEA assisted by APM, MEA assisted by Linear System Pro, and PBL toward the learners’ mathematics communication skills, (3) there were significant differences of self-efficacy: high, moderate, and low toward the learners’ mathematics communication skills; and (4) there were interactions between learning models with the levels of self-efficacy toward learners’ mathematics communication skills. Keywords: Mathematics Communication Skill, Means-End-Analysis Learning Model (MEA), Manipulative Property (APM), Linear System Pro, Self-efficacy.

Dynamic logarithmic state and control quantization for continuous-time linear systems

This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

Comparative Study of SLAM Techniques for UAV

In the last few decades, the main problem which has attracted the attention of researchers in the field of aerial robotics is the position estimation or Simultaneously Localization and Mapping (SLAM) of aerial vehicles where the GPS system does not work. Aerial robotics are used to perform many tasks such as rescue, transportation, search, control, monitoring, and different military operations where the performance of humans is impossible because of their vast top view and reachability anywhere. There are many different techniques and algorithms which are used to overcome the localization and mapping problem. These techniques and algorithms use different sensors such as Red Green Blue and Depth (RGBD), Light Detecting and Range (LIDAR), Ultra-Wideband (UWB) techniques, and probability-based SLAM which uses two algorithms Linear Kalman Filter (LKF) and Extended Kalman filter (EKF). LKF consists of 5 phases and this algorithm is only used for linear system problems but on the other hand, EKF algorithm is also used for non-linear system. EKF is found better than LKF due to accuracy, practicality, and efficiency while dealing SLAM problem.

The generic isogeny decomposition of the Prym Variety of a cyclic branched covering

Let $$f:S'\longrightarrow S$$ f : S ′ ⟶ S be a cyclic branched covering of smooth projective surfaces over $${\mathbb {C}}$$ C whose branch locus $$\Delta \subset S$$ Δ ⊂ S is a smooth ample divisor. Pick a very ample complete linear system $$|{\mathcal {H}}|$$ | H | on S, such that the polarized surface $$(S, |{\mathcal {H}}|)$$ ( S , | H | ) is not a scroll nor has rational hyperplane sections. For the general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | consider the $$\mu _{n}$$ μ n -equivariant isogeny decomposition of the Prym variety $${{\,\mathrm{Prym}\,}}(C'/C)$$ Prym ( C ′ / C ) of the induced covering $$f:C'{:}{=}f^{-1}(C)\longrightarrow C$$ f : C ′ : = f - 1 ( C ) ⟶ C : $$\begin{aligned} {{\,\mathrm{Prym}\,}}(C'/C)\sim \prod _{d|n,\ d\ne 1}{\mathcal {P}}_{d}(C'/C). \end{aligned}$$ Prym ( C ′ / C ) ∼ ∏ d | n , d ≠ 1 P d ( C ′ / C ) . We show that for the very general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | the isogeny component $${\mathcal {P}}_{d}(C'/C)$$ P d ( C ′ / C ) is $$\mu _{d}$$ μ d -simple with $${{\,\mathrm{End}\,}}_{\mu _{d}}({\mathcal {P}}_{d}(C'/C))\cong {\mathbb {Z}}[\zeta _{d}]$$ End μ d ( P d ( C ′ / C ) ) ≅ Z [ ζ d ] . In addition, for the non-ample case we reformulate the result by considering the identity component of the kernel of the map $${\mathcal {P}}_{d}(C'/C)\subset {{\,\mathrm{Jac}\,}}(C')\longrightarrow {{\,\mathrm{Alb}\,}}(S')$$ P d ( C ′ / C ) ⊂ Jac ( C ′ ) ⟶ Alb ( S ′ ) .