Let $(A,\Delta)$ be a {\it weak multiplier Hopf algebra} as introduced in [VD-W3] (see also [VD-W2]). It is a pair of a non-degenerate algebra $A$, with or without identity, and a coproduct $\Delta$ on $A$, satisfying certain properties. If the algebra has an identity and the coproduct is unital, then we have a Hopf algebra. If the algebra has no identity, but if the coproduct is non-degenerate (which is the equivalent of being unital if the algebra has an identity), then the pair would be a multiplier Hopf algebra. If the algebra has an identity, but the coproduct is not unital, we have a weak Hopf algebra. In the general case, we neither assume $A$ to have an identity nor do we assume $\Delta$ to be non-degenerate and so we work with a {\it genuine} weak multiplier Hopf algebra. It is called {\it regular} if its antipode is a bijective map from $A$ to itself. \snl In this paper, we {\it continue the study of weak multiplier Hopf algebras}. We recall the notions of the source and target maps $\varepsilon_s$ and $\varepsilon_t$, as well as of the source and target algebras. Then we investigate these objects further. Among other things, we show that the canonical idempotent $E$ (which is eventually $\Delta(1)$) belongs to the multiplier algebra $M(B\ot C)$ where $B=\varepsilon_s(A)$ and $C=\varepsilon_t(A)$ and that it is a {\it separability idempotent} (as studied in [VD4.v2]). If the weak multiplier Hopf algebra is regular, then also $E$ is a {\it regular} separability idempotent. \snl We also consider {\it special cases and examples} in this paper. In particular, we see how for any weak multiplier Hopf algebra $(A,\Delta)$, it is possible to make $C\ot B$ (with $B$ and $C$ as above) into a new weak multiplier Hopf algebra. In a sense, it forgets the 'Hopf algebra part' of the original weak multiplier Hopf algebra and only remembers the source and target algebras. It is in turn generalized to the case of any pair of non-degenerate algebras $B$ and $C$ with a separability idempotent $E\in M(B\ot C)$. We get another example using this theory associated to any discrete quantum group (a multiplier Hopf algebra of discrete type with a normalized cointegral). Finally we also consider the well-known 'quantization' of the groupoid that comes from an action of a group on a set. All these constructions provide interesting new examples of weak multiplier Hopf algebras (that are not weak Hopf algebras).

This paper presents a study on optimization of Overcurrent relay (OCR) coordination protection scheme for Sustainable Standalone Hydrokinetic Renewable Energy (SHRE) distribution network at Batang Rajang river, located at Kapit Sarawak, Malaysia by turning river stream into power generation source. The purpose of the project is to develop rural electrification system for native long houses along the river. The research study is tested on a DigSILENT develop model of the SHRE distribution network and in accordance with all respectively unique parameters and relevant standards. Since this is a new standalone distribution system, an efficient and properly coordinated overcurrent protection system must be provided. Improper and miscoordination among OCRs result in maloperation of the protection system that can lead to false tripping and an unnecessary outage and power system instability. Thus, the objective of this work is to employ Genetic Algorithm (GA) technique in Matlab/Simulink for optimal overcurrent coordination and settings among all OCRs in the proposed distribution network in order to improve the speed of OCR tripping operation. The GA is used because the project is fast track and requiring the simplest method available. In this strategy, time dial setting (TDS) is optimized by using plug setting multiplier (PSM) as the constraint. The obtained results show a significant improvement of the relay operating time of 36.01% faster than that of conventional numerical technique during fault occurrence. Thus, an efficient and reliable overcurrent protection scheme has been achieved for the SHRE distribution network.

Convolution forms one of the most essential operations for the FPGA-based hardware accelerator. However, the existing designs often neglect the inherent architecture of FPGA, which puts forward an austere challenge on hardware resource requirements. Even though some previous works have proposed approximate multipliers or convolution acceleration algorithms to deal with this issue, the inevitable accuracy loss and resource occupation easily lead to performance degradation. Toward this, we first propose two kinds of resource-efficient optimized accurate multipliers based on LUTs or carry chains. Then targeting FPGA-based platforms, a generic multiply-accumulate structure is constructed by directly accumulating the partial products produced by our proposed optimized radix-4 Booth multipliers without intermediate multiplication and addition results. Experimental results demonstrate that our proposed multiplier achieves a maximum 51% look-up-table (LUT) reduction compared to the Vivado area optimized multiplier IP. Furthermore, the convolutional process unit using the proposed structure achieves a 36% LUT reduction compared to existing methods. As case studies, the proposed method is applied to DCT transformer and LeNet to achieves hardware resource saving without loss of accuracy.

The increasing amount of data transmitted through digital broadcasting and communication channels requires efficient transmission methods that make the most of limited resources such as frequency, time, and power. The layered division multiplexing (LDM) system, which is adopted by the Advanced Television Systems Committee (ATSC) 3.0 standard, is considered one of a solution for achieving efficient transmission. Additionally, the layered time-division multiplexing (LTDM) and time layered division multiplexing (TLDM) systems have been developed as well. These layered transmission systems, utilizing multiple physical layer pipes (PLPs), offer a wide range of services including mobile and rooftop TV. To compare the efficiencies of different layered transmission systems, the article introduces the concept of normalized channel capacity. This measure allows for a fair comparison among the systems by taking into account the specific channel capacity requirements of each service. By summing the normalized channel capacities, a method is proposed to select the most efficient transmission system among the four systems: LDM, LTDM, TLDM, and time division multiplexing (TDM). The Lagrange multiplier method is employed to find the parameters that maximize the sum of the normalized channel capacities in these systems. Through simulations conducted with the determined parameters, it is demonstrated that the LDM system exhibits the highest efficiency among the four systems.

This paper presents a 612–1152 MHz Injection Locked Frequency Multiplier (ILFM). The proposed ILFM is only used for sending an input signal to the receiver in the I/Q mismatch calibration mode. Using the Phase-Locked Loop (PLL) to calibrate the receiver places a burden on this system due to the extra area required and power consumption. Instead of the PLL, to satisfy high frequency, low jitter, and low area, a Ring Oscillator is proposed. The free-running frequency of the ILFM is automatically digitally calibrated to reflect the frequency of the injected signal from the harmonics of the reference clock. To control the frequency of the ILFM, the load current is digitally tuned with 6-bit digital control signal. The proposed ILFM locks to the target frequency using a digitally controlled Frequency Locked Loop (FLL). This chip is fabricated using 1-poly 6-metal 0.18 µm CMOS and achieve the wide tuning range of 612–1152 MHz. The power consumption is 0.95 mW from a supply voltage of 1.8 V. The measured phase noise of the ILFM is −108 dBc/Hz at a 1 MHz offset.

In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equations 193: 1-45, 2012) and the second-order energy.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

Employing low tensor rank decompositions in image inpainting has attracted increasing attention. This paper exploits a novel tensor-augmentation schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed augmentation schemes enhance the low-rankness of an image under three tensor decompositions: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solve the image inpainting problem with three low-rank con-strained models which use the matrix rank, TT rank, and tubal rank as constrained priors re-spectively. The tensor tubal rank and tensor train multi-rank are developed from t-SVD and TT decomposition respectively. We exploit efficient ADMM algorithms for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and supe-rior to numerous close methods.

Given any sequence a = (an)n1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n1 such that y=a = (yn=an)n1 2 E. In this paper, we use the spaces w1, w0 and w of strongly bounded, summable to zero and summable sequences, that are the sets of all sequences y such that ? n?1Pn k=1 jykj
n is bounded, tends to zero and such that y ? le 2 w0, for some scalar l, respectively, (cf. [24, 22]). These sets where used in the statistical convergence, (cf. [17, Chapter 4]). Then we deal with the solvability of each of the (SSIE) F
 E + F0x where E is a linear space of sequences, F = c0, c, `1, w0, w, or w1 and F0 = c0, c, or `1. For instance, the solvability of the (SSIE) w
 w0+s(c) x consists in determining the set of all sequences x = (xn)n1 2 U+ that satisfy the following statement. For every sequence y that satisfy the condition limn!1 n?1Pn k=1 jyk ? yk?1 ? lj = 0, there are two sequences u and v, with y = u+v such that limn!1 n?1Pn k=1 jukj = 0 and limn!1 (vn=xn) = L for some scalars l and L. These results extend those stated in [11, 12, 10].

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

For Convolutional Neural Network (CNN), Depthwise Separable CNN (DSCNN) is a preferred architecture for Application Specific Integrated Circuit (ASIC) implementation on edge devices. It can benefit from a multi-mode approximate multiplier proposed in this work. The proposed approximate multiplier uses two 4-bit multiplication operations to implement a 12-bit multiplication operation by reusing the same multiplier array. With this approximate multiplier, sequential multiplication operations are pipelined in a modified DSCNN to fully utilize the PE array in the convolutional layer. This Approximate (A-DSCNN) was implemented on TSMC 40-nm CMOS process with a supply voltage of 0.9 V. At the clock frequency of 200 MHz, the design achieves 4.78 GOPs/mW while occupying 1.24 mm x 1.24 mm silicon area. Compared to conventional DSCNN implemented in a similar process node, the chip area and power consumption were reduced by 53% and 25%, while the throughput was improved by 17%.

In this paper, we prove that the sub convexlikeness introduced by V. Jeyakumar [1], and the subconvexlikeness defined in V. Jeyakumar [2] are equivalent in loccallly convex topological spaces. And then, we work with set-valued vector optimization problems and obtain some vector saddle-point theorems and vector Lagrangian theorems.

The VisionCube is a 2-unit CubeSat developed in-house, of which the primary mission is aimed at detecting the occurrence of transient luminous events in the upper atmosphere and obtaining corresponding images from the low Earth orbit. An on-board TLE observation system of the VisionCube cubesat is designed and developed by incorporating a photon-sensitive MaPMT and a CMOS image sensor. Also, a distinctive TLE observation software which enables detecting the TLEs and capturing images in a timely manner is devised. By taking into account the limited resources of a small CubeSat in size and power, the on-board observation system is developed employing a system-on-chip design architecture by which both hardware and software can be integrated seamlessly. The purpose of this study is to investigate the functionality of the hardware and the validity of the software algorithm to show the on-board system will operate properly with no human intervention during the space operation. To this end, a ground simulation facility is constructed to emulate the space environment of the TLE occurrence using a set of UV LEDs inside a darkbox. Based on the analysis of the spectral and temporal properties of the TLEs, the randomly generated UV LED pulses are opted for verification scenarios for the TLE observation system. The validation results show that the hardware and the software algorithm of the on-board observation system can effectively detect the TLEs and obtain the images during the on-orbit operation.