[[EQUATION]]-optimal Designs for Hierarchical Linear Models: an Equivalence Theorem and a Nature-inspired Meta-heuristic Algorithm

Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses [[EQUATION]] -optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the [[EQUATION]] -optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study [[EQUATION]] -optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate [[EQUATION]] -optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally [[EQUATION]] -optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that [[EQUATION]] and [[EQUATION]] -optimal designs may be equivalent and we establish that [[EQUATION]] and [[EQUATION]] -optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question whether their equivalence applies more generally to other hierarchical models remains elusive.

THEORY OF OBJECTIVE FORMATION IN DESIGN PRODUCTS SEWING VIROBIV

Theory of objective shaping in the design of garments. Modern methods of designing garments are considered. It is determined that the current areas are: particular features of modeling, which take into account the dynamics of dimensional features; methods of two- and three-dimensional design with an attempt to take into account anthropometric features and features of sewing materials. The disadvantages of the subjective approach according to the methods of approximate design are pointed out The new scientific direction of objective shaping in clothing design with the corresponding theory with criterion complex dependences which allow to carry out objective controllability of process of shaping and the forecast of qualitative indicators is proved. An example of shells with pre-deformed and bent section and their criterion dependence is given.

Exploiting Energy–Quality (E–Q) Tradeoffs: A Case Study on Color-to-Grayscale Converters with Approximate Design on FPGA

Today, field programmable gate array (FPGA) is becoming widely used as computational accelerators in many application domains such as image/video processing, machine learning, and data mining. The inherent tolerance to the imprecise computation in such domains potentially provides an opportunity to trade quality of the results for higher energy efficiency. Therefore, this paper proposes a systematic methodology aiming to find the optimal energy saving corresponding to different quality bound, by approximating register-transfer level (RTL) designs on FPGA. As a case study, first, we investigate imprecise design on two submodules — adders and multipliers. By integrating the two combinational submodules with finite state machines (FSMs), several designs on a sequential circuit — color-to-grayscale converter — are further presented to offer a diverse range of energy consumption related to different quality constrains. Through this, we are able to set energy–quality (E–Q) parameters of our proposed methodology and configure the approximation knobs, capable of maximizing energy savings within different application-based quality margins. Experimental result demonstrates that leveraging E–Q leads to an average [Formula: see text]–[Formula: see text] savings in energy for modest loss in application output quality ([Formula: see text]), and [Formula: see text]–[Formula: see text] energy savings for impact on relaxed quality constraints (3–7.5%).

Development of Design Method for High Temperature Nuclear Reactor Cladded Components

High temperature nuclear reactors plan to use highly corrosive coolant such as molten salts, molten lead, and lead-bismuth eutectic mixtures. The existing Class A metallic materials qualified in the ASME Section III, Division 5 rules for high temperature nuclear reactors are not ideal for resisting corrosion when exposed to these coolants. One option to overcome this limitation would be to Code-qualify new corrosion-resistant materials for Class A service, however this process is long and expensive and requires long-term creep test data. A near-term alternative would be to allow designers to clad the existing Class A base materials with non-qualified corrosion-resistant materials. However, there are currently no ASME design rules for cladded components to guard against creepfatigue failure and ratcheting strain accumulation in elevated temperature nuclear service. This work addresses this deficiency by proposing a design strategy for cladded components that does not require long-term testing of clad materials. The proposed approach relies on approximate design analysis methods for two types of clad materials — soft clad that creeps faster than the base material and hard clad that creeps slower and has higher yield stress than the base material. The proposed approach treats a soft clad material as perfectly compliant and a hard clad material as linear elastic. Sample finite element analyses of representative high temperature reactor components are performed to verify the approach. At the end, a complete set of design rules is provided for each of the two types of cladded components.

Research of the Ionosphere Using Equipment, Placed on Nano-Satellites. Part 1. Modeling a Vacuum Transducer

The urgency of the task of studying the density and composition of the upper layers of the atmosphere with the help of tools placed in micro- and nano-satellites vehicles is substantiated. A brief description of the structure of the atmosphere is carried out, the relevance and problems of instrumental studies of the density and composition of the upper atmosphere (ionosphere) are shown. A solution to these problems is proposed by developing a combined density and ion composition sensor for the upper atmosphere layers placed on nanosatellites. An approximate design of a compact inverse-magnetron vacuum gauge transducer is proposed, on the basis of which a combined transducer of density and ion composition of the upper atmosphere is constructed by combining it with a charged particle trap. This trap not only ensures the accuracy of its readings, but also allows you to determine the concentration of negatively and positively charged particles. The simulation of ionization processes in the working area of a compact inverse magnetron vacuum gauge transducer is carried out.

High gain broadside mode operation of a cylindrical dielectric resonator antenna using simple slot excitation

In this work, the authors report the operation of a cylindrical dielectric resonator antenna (CDRA) in the high gain HEM13 δ mode, for the first time. This mode, excited with a standard microstrip slot, radiates in the broadside direction with gain in the range of 8−10 dBi. It is shown that through feed optimization, the HEM13 δ mode can be excited dominantly by suppressing the fundamental HEM11 δ mode of the CDRA. Detailed simulation studies show that the HEM13 δ mode is supported by cylindrical dielectric resonators with an aspect ratio (radius to height ratio or a/d) >1, and it resonates at a frequency approximately 2.2 times that of the fundamental HEM11 δ mode. The above features of the HEM13 δ mode CDRA can be used as approximate design rules. For a CDRA with dielectric constant ɛr = 24, diameter 2a = 19.43 mm, and height d = 7.3 mm (a/d = 1.3), the HEM13 δ mode is excited at 6.125 GHz with a peak gain of 10.14 dBi in simulation. Corresponding values from prototype measurement are 5.981 GHz and 9.62 dBi, respectively for the resonant frequency and the gain, verifying the simulation.