Modulation Spaces Research Articles

4D-printed intelligent reflecting surface with improved beam resolution via both phase modulation and space modulation

Recently, intelligent reflecting surfaces (IRSs) have emerged as potential candidates for overcoming the line-of-sight issue in 5 G/6 G wireless communication. These IRSs can manipulate the direction of reflected beams, enabling efficient beam steering to enhance the performance of wireless communication. Each unit cell (or unit structure) of an IRS commonly consists of electrical elements for phase modulation. However, by employing phase modulation alone, an IRS can steer the reflected electromagnetic waves toward only discrete and specific angles, leaving a wide range of out-of-beam areas. In this work, an IRS that uses both phase modulation and space modulation is presented to improve the beam resolution and continuously cover out-of-beam areas that phase modulation alone cannot address. A positive-intrinsic-negative diode is mounted on a unit cell for phase modulation, and a 4D-printed reconfigured structure is fabricated to demonstrate space modulation. The beam-steering function is achieved by alternating the states of the diodes in the same columns, while the beam resolution is improved by controlling the gaps between the columns. The functions are first theoretically and numerically analyzed and then experimentally verified, demonstrating that additional angles of −46°/+50°, −22°/+14°, and −16°/+12° are achieved with space modulation and −60°/+62°, −30°/+22°, and ±16° are achieved by phase modulation alone. The proposed IRS offers the possibility of functional integration in a variety of indoor applications within the wireless communication field.

Full-space trifunctional metasurface with independent control of amplitude and phase for circularly polarized waves

Abstract Flexible and diverse manipulation of electromagnetic (EM) waves in half space (reflection or transmission) has facilitated strong aspiration toward full-space wave control. However, it remains challenging to achieve independent amplitude and phase control, which seriously hinder the real-world applications. Herein, an innovative strategy of trifunctional metasurface is proposed to independently and simultaneously manipulate the amplitude and phase of circular polarized waves in full space. The multifunctional design is composed of double-layer anisotropic metasurface sandwiched with a bandpass frequency selective surface, with a frequency-direction multiplexed paradigm for on-demand control of both amplitude and phase across three independent channels. To validate the concept, a multifunctional metadevice is designed and verified by simulations and experiments, showcasing arbitrary near-field and far-field power modulation in full space. Lateral and axial bifocal metalenses with desired intensity distribution are designed in two reflection channels at 9 GHz, while multibeam generator with desired spatial scatterings and power allocations is designed in transmissive channel at 13 GHz. The finding paves the way for attaining multifunctional metadevices with amplitude and phase modulation in full space, which have potential applications in high-quality imaging and high-capacity communication systems.

Well-posedness for the NLS hierarchy

We prove well-posedness for higher-order equations in the so-called NLS hierarchy (also known as part of the AKNS hierarchy) in almost critical Fourier–Lebesgue spaces and in modulation spaces. We show the jth equation in the hierarchy is locally well-posed for initial data in H^rs(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\hat{H}}}^s_r({\\mathbb {R}})$$\\end{document} for s≥j-1r′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s \\ge \\frac{j-1}{r'}$$\\end{document} and 1<r≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 < r \\le 2$$\\end{document} and also in M2,ps(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^s_{2, p}({\\mathbb {R}})$$\\end{document} for s=j-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s = \\frac{j-1}{2}$$\\end{document} and 2≤p<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le p < \\infty $$\\end{document}. Supplementing our results with corresponding ill-posedness results in Fourier–Lebesgue and modulation spaces shows optimality. Using the conserved quantities derived in Koch and Tataru (Duke Math J 167(17), 3207–3313, 2018), we argue that the hierarchy equations are globally well-posed for data in Hs(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^s({\\mathbb {R}})$$\\end{document} for s≥j-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s \\ge \\frac{j-1}{2}$$\\end{document}. Our arguments are based on the Fourier restriction norm method in Bourgain spaces adapted to our data spaces and bi- and trilinear refinements of Strichartz estimates.

Understanding of linear operators through Wigner analysis

In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the introduction of (quasi-)algebras of Fourier integral operators (FIOs), which encompass FIOs of type I and II. The symbols of these operators belong to (weighted) modulation spaces, particularly in Sjöstrand's class, known for its favorable properties in time-frequency analysis. One of the significant results of our study is demonstrating the inverse-closedness of these symbol classes.Our analysis includes fundamental examples such as pseudodifferential operators and Fourier integral operators related to Schrödinger-type equations. These examples typically feature classical Hamiltonian flows governed by linear symplectic transformations S∈Sp(d,R). The core idea of our approach is to utilize the Wigner kernel to transform a Fourier integral operator T on Rd into a pseudodifferential operator K on R2d. This transformation involves a symbol σ well-localized around the manifold defined by z=Sw.

Error performance of DF cooperative SMTs with I/Q imbalance over Beckmann fading channels

The direct down-conversion principle, which has generally been used in the design of multiple-input multiple-output (MIMO) schemes, including space modulation techniques (SMTs), is attractive to researchers because of its low cost, low power consumption with fewer components, flexible and simple structure. However, hardware imperfections such as in-phase (I) and quadrature-phase (Q) imbalance (IQI) negatively affect the performance of the systems with direct down-conversion in practice. On the other hand, cooperative communication is a promising technology that can be utilized in the design of future wireless networks due to its significant advantages such as increasing system reliability, extending network coverage, reducing channel degradation, and providing high quality of service. In this study, SMT-based methods are integrated into cooperative systems, and a flexible and comprehensive model is presented that is applicable to many channel structures. Specifically, the error performance analysis of space shift keying (SSK), spatial modulation (SM), and quadrature SM (QSM) systems in the presence of IQI in decode-and-forward (DF) cooperative communication is carried out by analytical derivations and computer simulations over generalized Beckmann fading channels. The obtained results show that the performance of SMT-based DF cooperative systems is superior to the conventional schemes, and the effects of receiver IQI can be eliminated by optimal detector designs.

Global well-posedness for the higher order non-linear Schrödinger equation in modulation spaces

We consider the initial value problem (IVP) associated with a higher order non-linear Schrödinger (h-NLS) equation∂tu+ia∂x2u+b∂x3u=2ia|u|2u+6b|u|2∂xu,x,t∈R, with given data in the modulation space Ms2,p(R). Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces Ms2,p(R) for s≥14 and p≥2.

A 3D hydrogel scaffold with adjustable interlayer spacing for the formation of compact myocardial tissue

AbstractThe design and optimization of three‐dimensional tissue scaffolds have presented a persistent challenge for myocardial tissue engineering. While current scaffolds have made strides in mimicking in vivo three‐dimensional environments, the presence of interlayer spacing has limited the formation of densely packed tissue, impeding cell‐to‐cell connections. We proposed a novel dynamic three‐dimensional myocardial tissue engineering scaffold with adjustable interlayer spacing, aiming to improve the uniformity of cell distribution and facilitate effective cell communication. The device was composed of hydrogel scaffolds that were fabricated with poly (ethylene glycol) diacrylate (PEGDA) and flexible elastomer actuators that composed of polyurethane acrylate (PUA). Human induced pluripotent stem cell‐derived cardiomyocytes mixed with gelatin methacryloyl (GelMA) were seeded onto the multi‐layered scaffold with initial spacing of 100–500 μm. Experimental results indicated the seeding efficiency was maximized at an initial spacing of 400 μm. By decreasing the interlayer spacing, cell growth morphology and gap junction protein expression was improved. This work demonstrated the effect of interlayer spacing modulation to the tissue density and provided a potential approach for cultivation of compact and multi‐layered myocardial tissue.

Research on the Modular Design Method and Application of Prefabricated Residential Buildings

As one of the key ways to realize the industrialization and green development of construction, prefabricated construction is conducive to saving resources and energy and improving labor productivity and quality. Aiming to solve the problem of the lack of standardization in the design of prefabricated residential buildings, which leads to the components not being universally used and the industrial characteristics not being fully embodied, while excessive standardization leads to a lack of personalization and flexibility, the modular design theory is applied to the standardized design of prefabricated residential buildings in this study. The application route of modular design theory in the standardized design is constructed, that is, “system decomposition—module design—module combination”. Taking residential buildings within a height of 54 m as an example, each basic functional module is standardized and combined into standard plans. At the same time, the functional space module design based on modular coordination and the module combination design based on the trinity of “modulus, pattern, and mode” are discussed. This research is of great significance for giving full play to the comprehensive benefits of prefabricated concrete structures in quality improvement, cost reduction, and rapid assembly.

Double rectangular-grooves metasurface for highly efficient electric modulation

With the rapid development of optical communication, how to achieve efficient modulation (fast response speed and high modulation depth) of optical signals has attracted more and more attention from researchers. Among all electro-optical modulator (EOM) designs, the electro-optical metasurface is undoubtedly a competitive solution for optical signal modulation in free space. Although current research on electro-optical metasurfaces has realized improving response speed owing to the Pockels effect, there are still difficulties in achieving high modulation depth under CMOS-compatible voltage and developing rational designs of metasurfaces to achieve voltage application that trigger electro-optical effects. In this work, an ultrahigh-Q factor BaTiO3 (BTO) electro-optical metasurface, which consists of a periodic array of rectangular grooves, was designed to provide a feasible solution to address these shortcomings. Based on bound states in the continuum (BIC) theory, ultrahigh-Q factor (2.87 × 105) quasi-BIC (Q-BIC) was obtained around 1550 nm by breaking the in-plane symmetry of the two rectangular grooves in a unit cell, which could significantly deepen the modulation depth. The concave and continuous structure of rectangular grooves made the application of voltage more efficient. The simulation results show that an optical signal modulation in free space with a modulation depth of 100% could be achieved. Multipole decomposition indicated that toroidal dipole (TD) was dominant in this Q-BIC. Our work may further promote the development of electro-optical modulation towards faster and deeper modulation.

Internal Space Modulation of Yolk-Shell FeSe2@Carbon Anode with Peanut-Shaped Morphology Enabling Ultra-Stable and Fast Potassium-Ion Storage.

The poor cycling stability and rate performance of transition metal selenides (TMSs) are caused by their intrinsic low conductivity and poor structural stability, which hinders their application in potassium-ion batteries (PIBs). To address this issue, encapsulating TMSs within carbon nanoshells is considered a viable strategy. However, due to the lack and uncontrollability of internal void space, this structure cannot effectively mitigate the volume expansion induced by large K+, resulting in unsatisfactory electrochemical performance. Herein, peanut-shaped FeSe2@carbon yolk-shell capsules are prepared by modulation of the internal space. The active FeSe2 is encapsulated within a robust carbon shell and an optimal void space is retained between them. The outer carbon shell promotes electronic conductivity and avoids FeSe2 aggregation, while the internal void mitigates volume expansion and effectively ensures the structural integrity of the electrode. Consequently, the FeSe2@carbon anode demonstrates exceptional rate performance (242 mAh g-1 at 10 A g-1) and long cycling stability (350 mAh g-1 after 500 cycles at 1 A g-1). Furthermore, the effect of internal space modulation on electrochemical properties is elucidated. Meanwhile, ex situ characterizations elucidate the K+ storage mechanism. This work provides effective guidance for the design and the internal space modulation of advanced TMSs yolk-shell structures.

Study of ash deposition characteristics of photovoltaic arrays taking into account the effect of photovoltaic module spacing and its effect on output characteristics: Indoor experiment

The problem of ash deposition on the surface of photovoltaic (PV) arrays during actual operation seriously affects their power generation efficiency. Because traditional research does not consider the PV module spacing, it cannot reflect the actual PV array ash deposition problem. This study explored the influence of PV module spacing, combined with different tilt angles and inlet wind speeds, on the characteristics of ash deposition and power output of the PV array through indoor experiments. The study designed a set of experimental equipment for simulating the formation process of ash deposition on the surface of PV arrays and set up an experimental platform to measure the influence of ash deposition on the maximum output power (Pmax), open-circuit voltage (Uoc), and short-circuit current (Isc) of the PV modules. The findings indicate that as the tilt angle increases, the PV array experiences reduced ash deposition and increased output power. Conversely, higher inlet wind speeds lead to greater ash deposition and decreased output power. Moreover, widening the spacing between PV modules results in increased ash deposition and reduced output power. Notably, within the PV array, the front PV module accumulates more ash than the rear module, with larger particle sizes. These research findings have significant implications for optimizing PV array design and enhancing power generation efficiency.

A Novel End-to-End Deep Learning Framework for Chip Packaging Defect Detection.

As semiconductor chip manufacturing technology advances, chip structures are becoming more complex, leading to an increased likelihood of void defects in the solder layer during packaging. However, identifying void defects in packaged chips remains a significant challenge due to the complex chip background, varying defect sizes and shapes, and blurred boundaries between voids and their surroundings. To address these challenges, we present a deep-learning-based framework for void defect segmentation in chip packaging. The framework consists of two main components: a solder region extraction method and a void defect segmentation network. The solder region extraction method includes a lightweight segmentation network and a rotation correction algorithm that eliminates background noise and accurately captures the solder region of the chip. The void defect segmentation network is designed for efficient and accurate defect segmentation. To cope with the variability of void defect shapes and sizes, we propose a Mamba model-based encoder that uses a visual state space module for multi-scale information extraction. In addition, we propose an interactive dual-stream decoder that uses a feature correlation cross gate module to fuse the streams' features to improve their correlation and produce more accurate void defect segmentation maps. The effectiveness of the framework is evaluated through quantitative and qualitative experiments on our custom X-ray chip dataset. Furthermore, the proposed void defect segmentation framework for chip packaging has been applied to a real factory inspection line, achieving an accuracy of 93.3% in chip qualification.

MFAD-RTDETR: A Multi-Frequency Aggregate Diffusion Feature Flow Composite Model for Printed Circuit Board Defect Detection

To address the challenges of excessive model parameters and low detection accuracy in printed circuit board (PCB) defect detection, this paper proposes a novel PCB defect detection model based on the improved RTDETR (Real-Time Detection, Embedding and Tracking) method, named MFAD-RTDETR. Specifically, the proposed model introduces the designed Detail Feature Retainer (DFR) into the original RTDETR backbone to capture and retain local details. Subsequently, based on the Mamba architecture, the Visual State Space (VSS) module is integrated to enhance global attention while reducing the original quadratic complexity to a linear level. Furthermore, by exploiting the deformable attention mechanism, which dynamically adjusts reference points, the model achieves precise localization of target defects and improves the accuracy of the transformer in complex visual tasks. Meanwhile, a receptive field synthesis mechanism is incorporated to enrich multi-scale semantic information and reduce parameter complexity. In addition, the scheme proposes a novel Multi-frequency Aggregation and Diffusion feature composite paradigm (MFAD-feature composite paradigm), which consists of the Aggregation Diffusion Fusion (ADF) module and the Refiner Feature Composition (RFC) module. It aims to strengthen features with fine-grained awareness while preserving a certain level of global attention. Finally, the Wise IoU (WIoU) dynamic nonmonotonic focusing mechanism is used to reduce competition among high-quality anchor boxes and mitigate the effects of the harmful gradients from low-quality examples, thereby concentrating on anchor boxes of average quality to promote the overall performance of the detector. Extensive experiments are conducted on the PCB defect dataset released by Peking University to validate the effectiveness of the proposed model. The experimental results show that our approach achieves the 97.0% and 51.0% performance in mean Average Precision (mAP)@0.5 and mAP@0.5:0.95, respectively, which significantly outperforms the original RTDETR. Moreover, the model reduces the number of parameters by approximately 18.2% compared to the original RTDETR.

Investigating the impact of battery arrangements on thermal management performance of lithium-ion battery pack design

The working temperature is one of the key factors affecting the efficiency and safety performance of automotive power batteries. Current battery pack design primarily focuses on single layout configurations, overlooking the potential impact of mixed arrangements on thermal management performance. This study presents a module-based optimization methodology for comprehensive concept design of Lithium-ion (Li-ion) battery pack. Firstly, the arrangement modules is optimized and performed using particle swarm optimization algorithms considering various arrangement layout (i.e. rectangular, diamond, and staggered arrangements) by taking the intercell spacing and maximum temperature of the modules as design objectives. Secondly, the battery pack configuration design is performed employing a neural network model reflect diverse battery module configurations within the pack, exploring their impact on thermal management performance. The hybrid battery arrangement effectively improves thermal management, and the module spacing helps to enhance heat dissipation. The staggered arrangement has a greater impact on the heat dissipation performance of the battery pack, but the spacing between different modules varies with the position of the modules. When all configuration schemes are staggered modules, the optimal range of the spacing between modules is between 6 and 7 mm. However, the study observes a non-linear relationship between module spacing and the maximum temperature difference within the battery pack. While increasing module spacing initially decreases temperature differences, it eventually reverses, suggesting that spacing alone may not consistently enhance thermal management. Validation with a lithium-ion battery pack case study demonstrates the method’s effectiveness, providing valuable knowledge for future cell and pack designs that employ different battery cell arrangements and diverse cooling strategies.

Factorizations for quasi-Banach time–frequency spaces and Schatten classes

We deduce factorization properties for Wiener amalgam spaces WLp,q, an extended family of modulation spaces M(ω,ℬ), and for Schatten symbols spw in pseudo-differential calculus under e.g. convolutions, twisted convolutions and symbolic products. Here M(ω,ℬ) can be any quasi-Banach Orlicz modulation space. For example we show that WL1,r∗WLp,q=WLp,q and WL1,r#spw=spw when r∈(0,1], r≤p,q<∞. In particular we improve Rudin’s identity L1∗L1=L1.

DFT-spread OTFS-NOMA for downlink integrated positioning and communication

In this article, a non-orthogonal multiple-access (NOMA) transmission system that incorporates discrete Fourier transform (DFT) spread orthogonal time-frequency space (OTFS) modulation is proposed for the downlink integrated positioning and communication (IPAC). This system is designed to decrease the Peak-to-Average Power Ratio (PAPR) within the OTFS-NOMA system while simultaneously serving both communication user (CU) and positioning user (PU) within the same time-frequency resources. Firstly, we demonstrate the applicability of the proposed DFT-spread OTFS-NOMA (DFT-s-OTFS-NOMA) system for downlink transmission. It efficiently serves both the CU and PU concurrently within the same time and frequency resources, thereby increasing spectrum utilization. Subsequently, we develop a two-stage parameter estimation algorithm focusing on accurate positioning parameter estimation for PU and precise channel estimation for CU. Then, the position of the PU is estimated using the time of arrival (TOA) model and the linear least squares (LLS) approach. Simulation demonstrates a 9 dB PAPR reduction in the proposed system compared to the existing OTFS-NOMA system. Additionally, the proposed two-stage positioning method for the PU achieves centimeter-level accuracy in position estimation and near millimeter-per-second-level accuracy in velocity estimation. What is more, the performance of channel estimation and symbol detection, aided by the PU signal in the DFT-s-OTFS-NOMA system, demonstrates resilience against Doppler effects without the need for reliance on pilots. This ensures sustained an effective Bit Error Rate (BER) even in time-variant high mobility scenarios.

Bit Error Rate Performance Improvement for Orthogonal Time Frequency Space Modulation with a Selective Decode-and-Forward Cooperative Communication Scenario in an Internet of Vehicles System.

Orthogonal time frequency space (OTFS) modulation has recently found its place in the literature as a much more effective waveform in time-varying channels. It is anticipated that OTFS will be widely used in the communications of smart vehicles, especially those considered within the scope of Internet of Things (IoT). There are efforts to obtain customized traditional point-to-point single-input single-output (SISO)-OTFS studies in the literature, but their BER performance seems a bit low. It is possible to use cooperative communications in order improve BER performance, but it is noticeable that there are very few OTFS studies in the area of cooperative communications. In this study, to the best of the authors' knowledge, it is addressed for the first time in the literature that better performance is achieved for the OTFS waveform transmission in a selective decode-and-forward (SDF) cooperative communication scenario. In this context, by establishing a cooperative communication model consisting of a base station/source, a traffic sign/relay and a smart vehicle/destination moving at a constant speed, an end-to-end BER expression is derived. SNR-BER analysis is performed with this SDF-OTFS scheme and it is shown that a superior BER performance is achieved compared to the traditional point-to-point single-input single-output (SISO)-OTFS structure.

A Low-complex OFDM based DCO-OTFS modulation for VLC systems

Visible Light Communication (VLC) has emerged as a promising alternative for indoor and vehicular wireless communication, offering several advantages over traditional radio frequency (RF) technology. With the adoption of optical-orthogonal frequency division multiplexing (O-OFDM) schemes, visible light communication (VLC) has become more robust and adaptable in indoor, outdoor, vehicular, and underwear communications. Recently, an orthogonal time frequency space (OTFS) modulation technique has evolved with better performance than OFDM. The recent finding in the context of VLC shows that the OTFS technique shows remarkable advantages over conventional OFDM techniques except for the modem design complexity. This work introduces a low-complexity direct current-biased optical OTFS (DCO-OTFS) modulation based on OFDM. This paper evaluates the proposed system’s performance through simulations, providing evidence of its bit-error-rate (BER), peak-to-average power ratio (PAPR), and complexity behavior. Comparative assessments against the DCO-OFDM system are presented to understand the advantages of the low-complex DCO-OTFS system. The findings reveal that the proposed system not only provides low computational complexity in modem design but also maintains superior error performance, with a notable 10 dB signal-to-noise ratio (SNR) gain over DCO-OFDM along with a superior PAPR, making it a commendable choice for VLC applications.

Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

The main aim of this paper is to prove that the wave front set of aw(x,D)u\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a^w(x,D)u$$\\end{document}, i.e. the action of the Weyl operator with symbol a on u, is contained in the wave front set of u and in the conic support of a in spaces of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}-tempered ultradistributions in the Beurling setting for adequate symbols of ultradifferentiable type. These symbols are not restricted to have order zero. To do so, we prove an almost diagonalization theorem on Weyl operators. Furthermore, an almost diagonalization theorem involving time-frequency analysis leads to additional applications, such as invertibility of pseudodifferential operators or boundedness of them in modulation spaces with exponential growth.

ORBIT SELECTION OF THE SPACE INDUSTRIAL PLATFORM WITH DISTRIBUTED ELECTRICAL-POWER SYSTEM MODULES

Space industrialization is one of the prospective directions in modern aerospace science and engineering for space exploration of new resources and habitats. The key issue is to provide industrial space modules with the required amount of electricity needed. One type of power supply for such modules is the use of distributed power systems, which consist of constellations of spacecraft with contactless power transmission. Given this, the problem of rational orbit selection for their dislocation arises. Considering these problems, the methodology for orbits selection of the space industrial platform with distributed electrical-power system modules is proposed in the paper. This methodology includes orbital translation, attitude, relative dynamics estimation for each power satellite, and its corresponding orbit optimization algorithm. The orbit optimization algorithm includes statistical processing and elements of gradient and coordinate descent methods, allowing us to determine the most significant parameter influencing the duration of the contactless power transmission session. Also, quaternion mathematics is used to estimate the dynamics in the program parameters for targeting the transmitter spacecraft antenna to the receiver spacecraft rectenna. With the approaches mentioned above, the methodology proposed in this paper allows us to form the requirements for the power satellites’ attitude and orbit control system to improve the process of selecting corresponding design parameters of such systems. Thus, the usage of the proposed methodology can allow the designing of the power satellites’ attitude and orbit control system in the conceptual stages of designing.