In this paper, dual bicomplex Balancing and Lucas-Balancing numbers are defined, and some identities analogous to the classic properties of the Fibonacci and Lucas sequences are produced. We give the ...relationship between these numbers and Pell and Pell-Lucas numbers. From these, the basic bicomplex properties for the norm and its conjugate of these numbers are also developed. These in turn lead to the Binet formula, the generating functions and exponential generating functions, which are important concepts for number sequences. The Cassini identity, which is important for number sequences, actually emerged to solve the famous Curry paradox. We calculated the Cassini, Catalan, Vajda and d’Ocagne identities for these numbers.
Air-balancing is a key technique in HVACs to achieve accurate air supply for better IAQ and energy-saving performance. The existing air-balancing methods are usually based on a hybrid duct system ...model, including a data-driven duct system model between terminal flow and static pressure, and an ASHRAE damper model between static pressure and terminal damper angle. Most of these methods only focus on how to improve the accuracy of the former part whereas neglecting the latter. However, the ASHRAE damper model cannot exactly reflect the actual dampers characteristics in practice and may lead to unavoidable modelling error. To fix this issue, this paper proposes a full data-driven duct system (FD3S) model to directly reveal the relationship between the terminal flow and terminal damper angle in the whole duct system. Therefore, the desired terminal damper angle under the design flow conditions can be more accurately predicted. Besides, since the proposed method directly models the relationship between terminal flow and terminal damper angle, it avoids installing extra pressure sensors and reduces the operation cost. Moreover, the complexity of the proposed FD3S model is greatly reduced compared with the previous hybrid model. Finally, the experimental results demonstrate the effectiveness of the proposed method.
An on-chip Ruthroff-type balun fabricated in tsmc(TM) 0.18 mu m CMOS technology has been realised and used in a single balanced mixer. By using the phase compensation line and appropriately choosing ...the characteristic impedance of transmission lines, the balun was realised with a minimum insertion loss of 0.71 dB and the 1 dB bandwidth over a frequency range from 3.2 to 8.4 GHz. The compact size of 0.088 mm super( 2) is achieved owing to the short length of the transmission line winding, approximately 1/18 lambda sub( g), and the adoption of broadside-coupled and spiral-shape structures. A simple single balanced mixer with the Ruthroff-type balun was then designed to demonstrate the capability of the broadband and low-loss balun. A minimum conversion loss of 12.48 dB with a 3 dB bandwidth from 2.5 to 7 GHz was measured at the LO drive of only 6 dBm. The chip area, including pads, is 0.49 mm super( 2).
This paper presents a vertically and horizontally folded half-wavelength resonator in a three-dimension environment and its application to a balanced bandpass filter (BPF). Benefiting from the ...multilayered resonator based on the transmission line theory and low temperature co-fired ceramic (LTCC) technology, the proposed balanced BPF can obtain compact size and good performance. For demonstration, a LTCC balanced BPF centred at 2.45GHz has been designed using the proposed resonator, and the size of the circuit is 6.0 x 5.0 x 1.6 mm^sup 3^.
A balanced pulse generator with high voltage amplitude and pulse width in the picoseconds region is described. It can operate well at the pulse repetition frequency (PRF) up to 500 kHz. The proposed ...generator contains four NPN silicon power transistors operating in avalanche mode and a pair of pulse shaping circuits which effectively utilise the transition characteristics of a step recovery diode. Measurement results are presented, which show the output of the generator are balanced pulses with peak values of ±46 V at 100 kHz PRF and approximately 330 ps full-width at half-maximum in width. PUBLICATION ABSTRACT
The major objective of this study, based on critical review and experimental studies, was to develop a reliable thermodynamic model for the NdaF system at 25 degree C. The SIT model was used to ...convert concentration constants reported in the literature to constants at zero ionic strengths for cross comparison and selection of reliable values. The critically evaluated thermodynamic constants for the formation of NdF2+ and NdF 2 + were then used to interpret the extensive NdF3(cr) solubility data in NaF and NH4F solutions, ranging in concentrations from extremely low values to as high as 1.0 molADTkga1, equilibrated for different periods ranging up to as long as 72 days. These efforts have resulted in $ \log_{10} \beta_{n}0} $ log 10 I2 n 0 for the reaction Nd3+ + nFa a NdF n 3an of (3.81 A- 0.10), (5.89 A- 0.77), and <12.48 for n values of 1a3, respectively. The $ \log_{10} K_{\text{sp}}0} $ log 10 K sp 0 for the solubility of NdF3(cr) (NdF3(cr) a Nd3+ + 3Fa) was determined to be (a20.49 A- 0.37). Because (1) Nd is an excellent analog for trivalent actinidesaAn(III) (i.e., Pu(III), Am(III), and Cm(III)), and (2) the available data for the An(III)aF system, especially the solubility products of AnF3(cr), are of extremely poor quality, the critical literature review in combination with the experimental NdaF system data have been used to assign thermodynamic constants for the An(III)aF reactions until good quality specific data for them becomes available.
Thermal and state-of-charge (SOC) imbalances are well known to cause nonuniform aging in batteries. This paper presents the electrothermal control of a multilevel converter-based modular battery to ...address this issue. The modular battery provides a large redundancy in synthesizing terminal voltage, which gives extra degrees of freedom in control on cell level. There are multiple tightly coupled control objectives including the simultaneous thermal and SOC balancing as well as battery terminal voltage control. The main purpose of this paper is to devise an electrothermal control scheme for cases where full future driving information is not accessible. The control scheme is based on decomposition of controller into two orthogonal components, one for voltage control and the other for balancing control. This problem decomposition enables the application of constrained linear quadratic model predictive control scheme to solve the balancing problem elegantly. The control scheme is thoroughly evaluated through simulations of a four cell modular battery. The results show that a rather short prediction horizon is sufficient to achieve robust control performance.
Voltage balancing between series-connected cells of rechargeable lithium-ion batteries is important for battery life, autonomy, and safety. Active balancing is the designated choice for applications ...that are sensitive to energy losses and maximized autonomy. First, a well-known next-to-next balancing technique is presented and its design and operating limitations are analyzed. Then, the paper focuses on an evolution of the converter's architecture offering better performances while being more compact, requiring fewer and smaller filtering needs and still, being simple to implement. The experimental results of the balancing operation of a pack of eight cells connected in series show demonstrative and satisfactory results.
PDF
