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This review explores the most recent advancements in transformer-based data fusion techniques in agricultural remote sensing (RS), with a particular focus on soil analysis. Utilizing a systematic, data-driven approach, we demonstrate that transformers have significantly outperformed conventional deep learning and machine learning methods since 2022, achieving prediction performance between 92% and 97%. The review is specifically focused on soil analysis, due to the importance of soil condition in optimizing crop productivity and ensuring sustainable farming practices. Transformer-based models have shown remarkable capabilities in handling complex multivariate soil data, improving the accuracy of soil moisture prediction, soil element analysis, and other soil-related applications. This systematic review primarily focuses on 1) analysing research trends and patterns in the literature, both chronologically and technically, and 2) conducting a comparative analysis of data fusion approaches, considering factors such as data types, techniques, and RS applications. Finally, we propose a roadmap for implementing data fusion methods in agricultural RS., Comment: 14 pages, 9 figures, 4 tables, Journal

In this paper, a multimode smart nonlinear circuit (MSNC) for wireless communications (Tx and Rx modes) as well as energy harvesting (EH) and power saving is presented. The proposed MSNC is designed at 680 MHz and has three ports, which are connected to an antenna, and T/R (transceiver) and power-saving modules. According to the input/output power level, the proposed MSNC has three modes of operations; Receiving (Rx), power saving and transmitting (Tx), for low (<-25 dBm), mid (>-25 dBm and <0 dBm) and high (>5 dBm) power ranges, respectively. In the power-saving mode, when the received power is greater than the sensitivity of the Rx module, the excess power is directed to the energy harvesting load (power storage), while the receiving direction is still in place. The fact that the proposed MSNC can manage the received power level smartly and without any external control, distinguishes the proposed MSNC from other EH circuits. The proposed MSNC operates within a power range from -50 dBm to +15 dBm, demonstrates an efficiency of more than 60% in the power-saving mode, and has acceptable matching over a large frequency range. The design procedure of the proposed MSNC along with the theoretical, simulation and measurement results are presented in this paper. Good agreement between theory, simulation and measurement results confirms the accuracy of design procedure.

This paper presents an efficient dual-band rectifier for radiofrequency energy harvesting (RFEH) applications at FM and GSM bands. The single-port rectifier circuit, which comprises a 3-port network, optimized T-matching circuits and voltage doubler, is designed, simulated and fabricated to obtain a high RF-to-DC power conversion efficiency (PCE). Measurement results show PCE of 26% and 22% at -20 dBm, and also 58% and 51% at -10 dBm with a maximum amount of 69% and 65% at -2.5 dBm and -5 dBm, with single tone at 95 and 925 MHz, respectively. Besides, the fractional bandwidth of 21% at FM and 11% at GSM band is achieved. The measurement and simulation results are in good agreement. Consequently, the proposed rectifier can be a potential candidate for ambient RF energy harvesting and wireless power transfer (WPT). It should be noted that a 3-port network as a duplexer is designed to be integrated with single-port antennas which cover both FM and GSM bands as a low-cost solution. Moreover, based on simulation results, PCE has small variations when the load resistor varies from 10 to 18 k$\Omega$. Therefore, this rectifier can be utilized for any desired resistance within the range, such as sensors and IoT devices.

This paper presents a highly sensitive microwave sensor for dielectric sensing. One of the main disadvantages of microwave resonant-based sensors is cross-sensitivity originated by time-dependent uncontrolled environmental factors such as temperature that affect the material under test (MUT) behavior, leading to undesirable frequency shifts and, hence, lower accuracy. However, this work eliminates the unwanted errors using the differential measurement technique by comparing two transmission resonance frequencies during a unit test setup to measure the permittivity of MUT over time. The proposed structure comprises a spiral resonator with an extended horizontal microstrip line (EH-ML) coupled to a microstrip transmission line (MTL). Creating EH-ML within the structure comprises two primary contributions: enhanced sensitivity resulting from stronger fringing fields generated by increasing the effective area and improved resolution due to higher resonance frequencies caused by a lower total capacitive coupling effect. The proposed sensor is fabricated and tested using MUTs with a permittivity of less than 80 to verify the performance. In this regard, a frequency detection resolution (FDR) of 44MHz and a sensitivity of 0.85% are achieved at a maximum permittivity of 78.3. The results of theoretical analysis, simulation, and measurement are in relatively good agreement. Consequently, the proposed highly sensitive microwave sensor offers significant advantages, such as low complexity in design and fabrication. It also offers high resolution and precision in a wide range of permittivity, which can be an attractive candidate for dielectric sensing in health, chemical and agriculture applications.

In this paper, a compact multi-service antenna (MSA) is presented for sensing and communication using a reconfigurable complementary spiral resonator. A three turns complementary spiral resonator (3-CSR) is inserted in the ground plane of a modified patch antenna to create a miniaturized structure. Two Positive-Intrinsic-Negative (PIN) diodes (D1, D2) are also integrated with the 3-CSR to achieve frequency reconfiguration. The proposed structure operates in three different modes i.e., dual-band joint communication and sensing antenna (JCASA), dual-band antenna, and single-band antenna. The required mode can be selected by changing the state of the PIN diodes. In mode-1, the first band (0.95-0.97 GHz) of the antenna is dedicated to sensing by using frequency domain reflectometry (FDR), while the second band (1.53-1.56 GHz) is allocated to communication. The sensing ability of the proposed structure is utilized to measure soil moisture using FDR. Based on the frequency shift, permittivity of the soil is observed to measure soil moisture. In mode-2 and mode-3, the structure operates as a standard dual and single band antenna, respectively, with a maximum gain of 1.5 dBi at 1.55 GHz. The proposed planar structure, with its simple geometry and a high sensitivity of 1.7%, is a suitable candidate for precision farming. The proposed structure is versatile and capable of being utilized as a single or dual-band antenna and also measuring permittivity of materials within the range of 1-20. Hence, it is adaptable to a range of applications.

A software-defined 2-bit Programmable Transmit Metamaterial (PTM) array surface with beam steering capabilities is proposed for indoor dynamic Wireless Power Transfer (DWPT) applications. The novel metamaterial unit cell structure is designed based on transmission phase, amplitude, and electric field response to model DWPT using PTM. Theoretical analysis of the electric field (e-field), coupling effect, and current distribution at the metamaterial interface enhances the intelligence and reconfigurability of the PTM lens. The modeled 2-bit 6x6 array PTM is designed to operate at a frequency of 4 GHz. The reconfigurable architecture comprises a fixed system with a single-layer PTM lens capable of 60{\deg} beam scanning. The PTM lens, along with a distribution board, is fabricated and experimentally tested. The results between simulation and measurements are in good agreement. The system enables dynamic optimisation of the beam pattern to track the positions of mobile users with minimal software-hardware complexity. This novel work presents a low-cost experiment achieving an average 90.7% beamforming accuracy throughout the analytical and measurement processes of DWPT for movable users, utilizing a programmable transmit metamaterial array.

In this paper, a compact microstrip forward broadside coupler (MFBC) with high coupling level is proposed in the frequency band of 3.5-3.8 GHz. The coupler is composed of two parallel pixelated transmission lines. To validate the designstrategy, the proposed MFBC is fabricated and measured. The measured results demonstrate a forward coupler with 3 dB coupling, and a compact size of 0.12 {\lambda}g x 0.10{\lambda}g. Binary Particle Swarm Optimization (BPSO) design methodology and flexibility of pixelation enable us to optimize the proposed MFBC with desired coupling level and operating frequency within a fixed dimension. Also, low sensitivity to misalignment between two coupled TLs makes the proposed coupler a good candidate for near-field Wireless Power Transfer (WPT) application and sensors.

A miniaturized linearly-polarized patch antenna is presented for Wireless Power Transfer (WPT) at 1. 8 GHz. The proposed antenna consists of a patch element and a 3-turn Complementary Spiral Resonator (3-CSR) with antenna dimension of 50 mm x 50 mm. 3-CSR is inserted in the ground plane to reduce the antenna size. This modification also increased the impedance bandwidth from 43 MHz (1.78-1.83 GHz) to 310 MHz (1.69-2.0 GHz) . Moreover, antenna is fabricated and simulated and measured results are in good agreement. Additionally, a rectifier and matching circuits are designed at -10 dBm to realize a rectenna (rectifying antenna) for WPT application. Rectenna efficiency of 53.6 % is achieved at a low input power of -10 dBm.

A new compact quad-band notch filter (QBNF) based on the extended composite right and left-handed transmission line (E-CRLH TL) has been presented. As known, E-CRLH TL behaves like a quad-band structure. A microstrip TL which is loaded with an open-ended E-CRLH TL is presented as a QBNF. Four unwanted frequencies were used in a dual-band LTE receiver as four notch frequencies which must be eliminated (0.9 GHz, 1.3 GHz, 2.55 GHz, and 3.35 GHz). Also, this QBNF can be applied to simultaneous wireless power and data transfer (SWPDT) system to isolate the wireless power circuit from the data communication circuit. A design technique for the proposed QBNF is presented and its performance is validated using full-wave simulation results and theoretical analysis. The main advantage of this design is an overall rejection greater than 20dB at selected unwanted frequencies. Good agreements between the full-wave simulation and equivalent circuit model results have been achieved which verified the effectiveness of the proposed circuit model. The proposed QBNF is designed on an FR-4 substrate and the dimension of the proposed QBNF is 20X22 mm.

Capacitive coupling wireless power transfer (CCWPT) is one of the pervasive methods to transfer power in the reactive near-field zone. In this paper, a flexible design methodology based on Binary Particle Swarm Optimization (BPSO) algorithm is proposed for a pixelated microstrip structure. The pixel configuration of each parallel plate (43x43 pixels) determines the frequency response of the system (S-parameters) and by changing this configuration, we can achieve the dedicated operating frequency (resonance frequency) and its related |S21| value. Due to the large number of pixels, iterative optimization algorithm (BPSO) is the solution for designing a CCWPT system. However, the output of each iteration should be simulated in electromagnetic simulators (e.g., CST, HFSS, etc.), hence, the whole optimization process is time-consuming. This paper develops a rapid, agile and efficient method for designing two parallel pixelated microstrip plates of a CCWPT system based on deep neural networks. In the proposed method, CST-based BPSO algorithm is replaced with an AI-based method using ResNet-18. Advantages of the AI-based iterative method are automatic design process, more efficient, less time-consuming, less computational resource-consuming and less background EM knowledge requirements compared to the conventional techniques. Finally, the prototype of the proposed simulated structure is fabricated and measured. The simulation and measurement results validate the design procedure accuracy, using AI-based BPSO algorithm. The MAE (Mean Absolute Error) of prediction for the main resonance frequency and related |S21| are 110 MHz and 0.18 dB, respectively and according to the simulation results, the whole design process is 3629 times faster than the CST-based BPSO algorithm.

Discrete Fractional Fourier Transforms (DFrFT) are universal mathematical tools in signal processing, communications and microwave sensing. Despite the excessive applications of DFrFT, implementation of corresponding fractional orders in the baseband signal often leads to bulky, power-hungry, and high-latency systems. In this paper, we present a passive metamaterial coupled lines network (MCLN) that performs the analog DFrFT in real-time at microwave frequencies. The proposed MCLN consists of M parallel microstrip transmission lines (TLs) in which adjacent TLs are loaded with interdigital capacitors to enhance the coupling level. We show that with proper design of the coupling coefficients between adjacent channels, the MCLN can perform an M-point DFrFT of an arbitrary fractional order that can be designed through the length of the network. In the context of real-time signal processing for realization of DFrFT, we design, model, simulate and implement a 16x16 MCLN and experimentally demonstrate the performance of the proposed structure. The proposed innovative approach is versatile and is capable to be used in various applications where DFrFT is an essential tool. The proposed design scheme based on MCLN is scalable across the frequency spectrum and can be applied to millimeter and submillimeter wave systems.

This paper presents a Time-Domain Transmissometry Soil Moisture Sensor (TDT-SMS) using a Dispersive Phase Shifter (DPS), consisting of an interdigital capacitor that is loaded with a stacked 4-turn Complementary Spiral Resonator (S4-CSR). Soil moisture measurement technique of the proposed sensor is based on the complex permittivity sensing property of a DPS in time domain. Soil relative permittivity which varies with its moisture content is measured by burying the DPS under a soil mass and changing its phase difference while excited with a 114 MHz sine wave (single tone). DPS output phase and magnitude are compared with the reference signal and measured with a phase/loss detector. The proposed sensor exhibits accuracy better than +-1.2 percent at the highest Volumetric Water Content (VWC=30 percent) for sandy-type soil. Precise design guide is developed and simulations are performed to achieve a highly sensitive sensor. The measurement results validate the accuracy of theoretical analysis and design procedure. Owning the advantages of low profile, low power consumption, and high sensitivity makes the proposed TDT-SMS a good candidate for precision farming and IoT systems.

In this paper, a very compact and low insertion loss metamaterial band-pass filter (MBPF) at the center frequency of f0=730 MHz is proposed, based on the rectangular-shape 4 turn complementary spiral resonators (4 CSR). The proposed MBPF consists of an interdigital capacitor as a series capacitance in the top layer, leading to improve the stopband performance in the pass band range of 700 to 760 MHz, which makes it suitable for wireless power transfer (WPT) systems by rejecting unwanted signals. In order to validate the performance of the proposed technique, the MBPF is fabricated on the RO-4003 substrate and great agreement is achieved between simulated and measured results. The stop band attenuations of greater than 52 dB and 20 dB are obtained around the 0.8xfcl (lower cutoff frequency) and 1.2xfcu (upper cutoff frequency), respectively.

A highly efficient and compact quad band energy harvester (QBEH) circuit based on the extended composite right and left handed transmission lines (ECRLHTLs) technique is presented.The design procedure based on ECRLHTLs at four desired frequency bands is introduced to realize a quad band matching network (QBMN).The proposed QBEH operates at four frequency bands f1=0.75 GHz,f2=1.8 GHz,f3=2.4 GHz and f4=5.8 GHz. The simulations and experimental results of the proposed QBEH exhibit overall (end to end) efficiency of 55percent and 70percent while excited at four frequency bands simultaneously with negative 20dBm (10 microWatt) and negative 10dBm (100 microWatt) input power, respectively.Due to applying multi band excitation technique and radio frequency (RF) combining method in the QBEH circuit, the sensitivity is improved, and sufficient power is generated to realize a self sustainable sensor (S3) using ambient low level RF signals.A favorable impedance matching over a broad low input power range of negative 50 to negative 10 dBm (0.01 to 100 microWatt) is achieved, enabling the proposed QBEH to harvest ambient RF energy in urban environments. Moreover, an accurate theoretical analyses based on the Volterra series and Laplace transformation are presented to maximize the output DC current of the rectifier over a wide input power range.Theoretical, simulation and measurement results are in excellent agreement, which validate the design accuracy for the proposed quad band structure.The proposed new energy harvesting technique has the potential to practically realize a green energy harvesting solution to generate a viable energy source for low powered sensors and IoT devices, anytime, anywhere.

This paper presents a highly sensitive differential soil moisture sensor (DSMS) using a microstrip line loaded with triangular two turn resonator(T2 SR) and complementary of the rectangular two turn spiral resonator(CR2 SR),simultaneously.Volumetric Water Content (VWC) or permittivity sensing is conducted by loading the T2 SR side with dielectric samples.Two transmission notches are observed for identical loads relating to T2 SR and CR2 SR.The CR2 SR notch at 4.39 GHz is used as a reference for differential permittivity measurement method.Further, the resonance frequency of T2 SR is measured relative to the reference value. Based on this frequency difference,the permittivity of soil is calculated which is related to the soil VWC.Triangular two turn resonator (T2 SR) resonance frequency changes from 4 to 2.38 GHz when VWC varies 0 percent to 30 percent.The sensor's operation principle is described through circuit model analysis and simulations.To validate the differential sensing concept, prototype of the designed 3 cell DSMS is fabricated and measured.The proposed sensor exhibits frequency shift of 110 MHz for 1 percent change at the highest soil moisture content (30 percent) for sandy type soil.This work proves the differential microwave sensing concept for precision agriculture.

Slant-polarized Multi Input Multi Output (MIMO) antennas are able to improve the performance of mobile communication systems in terms of channel capacity. Especially, the implementation of MIMO configurations for automotive applications requires to consider high gain, wideband, low-profile and affordable antennas in the communication link. In this work design, simulation and measurement of a new dual-band slant-polarized MIMO antenna with HPBW (Half Power Beam Width) of around 900 are presented. Then, four replicas of the proposed antenna set are placed at four different poles (North, South, West and East) to cover 3600 around the vehicle as an omni-directional pattern. In the real world scenario, the proper antenna set is selected to communicate with the intended user. Each slant MIMO antenna set consists of two inclined (450) low band (LB: 700 to 900 MHz) and two inclined high band (HB: 1.7 to 2.7 GHz) log-periodic antennas. The measured gain of LB and HB antennas are 7 dBi and 8 dBi, respectively. Great agreement between simulation and measurement results confirms the accuracy of the design and simulation procedures of antenna system using optimization algorithm (Genetic method). The proposed antenna is also measured in the field for industrial applications.

This paper presents a pixelated cubic antenna design with enhanced isolation and diverse radiation pattern for vehicular applications. The design consists of four radiating patches to take advantage of a nearly omnidirectional radiation pattern with enhanced isolation and high gain. The antenna system with four patches has been pixelated and optimized simultaneously to achieve desired performance and high isolation at 5.4 GHz band. The antenna achieved measured isolation of more than -34 dB between antenna elements. The overall isolation improvement obtained by the antenna is about 18 dB compared to a configuration using standard patch antennas. Moreover, isolation improvement is achieved through patch pixelization without additional resonators or elements. The antenna achieved up to 6.9 dB realized gain in each direction. Additionally, the cubic antenna system is equipped with an E-shaped GPS antenna to facilitate connectivity with GPS satellite. Finally, the antenna performance has been investigated using a simulation model of the vehicle roof and roof rack. The reflection coefficient, isolation and radiation patterns of the antenna remains unaffected. The antenna prototype has been fabricated on Rogers substrate and measured to verify the simulation results. The measured results correlate well with the simulation results. The proposed antenna features low-profile, simple design for ease of manufacture, good radiation characteristics with multidirectional property and high isolation, which are well-suited to vehicular applications in different environments.

This paper introduces a highly efficient rectenna (rectifying antenna) using a binary optimization algorithm. A novel pixelated receiving antenna has been developed to match the diode impedance of a rectifier, eliminating the need for a separate matching circuit in the rectenna's rectifier. The receiving antenna configuration is fine-tuned via a binary optimization algorithm. A rectenna is designed using optimization algorithm at 2.5 GHz with 38% RF-DC conversion efficiency when subjected to 0 dBm incident power, with an output voltage of 815mV. The proposed rectenna demonstrates versatility across various low-power WPT (wireless power transfer) applications.

Recent advancements in RF technologies, especially Internet of Things (IoT) devices, require compact and integrated RF circulators or transmit-receive (TR) switches for efficient resource use. Although conventional techniques are crucial in managing signal flow to prevent signal interference to sensitive receiver components, they have some drawbacks, such as limited isolation, low switching speed, complex circuitry, bulkiness, and high cost. This work presents a smart, miniaturized, nonlinear TR switch capable of operating over a wide frequency range (0.8 - 1.3 GHz), making it suitable for IoT frequency bands. The switch achieves high isolation, low insertion loss, and intelligent transitions between transmitter and receiver without requiring external control or bias pins.

A novel digital reconfigurable 2_bit metamaterial, equipped with a substrate integrated feeding system, is designed for industrial quality control applications within the terahertz frequency range. The proposed feeding mechanism facilitates azimuthal beam steering, spanning from negative 90 degree to positive 90 degree, thereby enabling the reconfiguration of beam patterns within the digital metamaterial. Utilizing the phase distribution concept and comprehensive analysis of coupling and the e_field effect on individual unit cells, the metamaterial array spacing is meticulously designed. Operational at 0.7 THz, the system offers versatile reconfigurability, supporting single, dual, and multibeam modes. Through meticulous optimization, the system demonstrates an impressive negative 138 degree to positive 138 degree beam steering capability. This dynamic beamforming ability, transitioning seamlessly from a singular beam to multibeam configurations, requires minimal software-hardware integration for scanning and inter_satellite links, thus presenting significant potential for enhancing product quality within industrial environments and satellite communication.

In this paper, a joint sensing and communication system is presented for smart agriculture. The system integrates an Ultra-compact Soil Moisture Sensor (UCSMS) for precise sensing, along with a Pattern Reconfigurable Antenna (PRA) for efficient transmission of information to the base station. A multiturn complementary spiral resonator (MCSR) is etched onto the ground plane of a microstrip transmission line to achieve miniaturization. The UCSMS operates at 180 MHz with a 3-turn complementary spiral resonator (3-CSR), at 102 MHz with a 4- turn complementary spiral resonator (4-CSR), and at 86 MHz with a 5-turn complementary spiral resonator (5-CSR). Due to its low resonance frequency, the proposed UCSMS is insensitive to variations in the Volume Under Test (VUT) of soil. A probe-fed circular patch antenna is designed in the Wireless Local Area Network (WLAN) band (2.45 GHz) with a maximum measured gain of 5.63 dBi. Additionally, four varactor diodes are integrated across the slots on the bottom side of the substrate to achieve pattern reconfiguration. Six different radiation patterns have been achieved by using different bias conditions of the diodes. In standby mode, PRA can serve as a means for Wireless Power Transfer (WPT) or Energy Harvesting (EH) to store power in a battery. This stored power can then be utilized to bias the varactor diodes. The combination of UCSMS and PRA enables the realization of a joint sensing and communication system. The proposed system's planar and simple geometry, along with its high sensitivity of 2.05 %, makes it suitable for smart agriculture applications. Moreover, the sensor is adaptive and capable of measuring the permittivity of various Material Under Test (MUT) within the range of 1 to 23.

Immersive Virtual Reality typically requires a head-mounted display (HMD) to visualize the environment and hand-held controllers to interact with the virtual objects. Recently, many applications display full-body avatars to represent the user and animate the arms to follow the controllers. Embodiment is higher when the self-avatar movements align correctly with the user. However, having a full-body self-avatar following the user's movements can be challenging due to the disparities between the virtual body and the user's body. This can lead to misalignments in the hand position that can be noticeable when interacting with virtual objects. In this work, we propose five different interaction modes to allow the user to interact with virtual objects despite the self-avatar and controller misalignment and study their influence on embodiment, proprioception, preference, and task performance. We modify aspects such as whether the virtual controllers are rendered, whether controllers are rendered in their real physical location or attached to the user's hand, and whether stretching the avatar arms to always reach the real controllers. We evaluate the interaction modes both quantitatively (performance metrics) and qualitatively (embodiment, proprioception, and user preference questionnaires). Our results show that the stretching arms solution, which provides body continuity and guarantees that the virtual hands or controllers are in the correct location, offers the best results in embodiment, user preference, proprioception, and performance. Also, rendering the controller does not have an effect on either embodiment or user preference., Comment: Presented in CHI'24

The silicon T centre's narrow, telecommunications-band optical emission, long spin coherence, and direct photonic integration have spurred interest in this emitter as a spin-photon interface for distributed quantum computing and networking. However, key parameters of the T centre's spin-selective optical transitions remain undetermined or ambiguous in literature. In this paper we present a Hamiltonian of the T centre TX state and determine key parameters of the optical transition from T$_0$ to TX$_0$ from a combined analysis of published results, density functional theory, and new spectroscopy. We resolve ambiguous values of the internal defect potential in the literature, and we present the first measurements of electrically tuned T centre emission. As a result, we provide a model of the T centre's optical and spin properties under strain, electric, and magnetic fields that can be utilized for realizing quantum technologies., Comment: 9 pages and 6 figures in the main manuscript. 10 pages and 6 figures in the supplementary information

It is well known that for Auslander algebras, the category of all (finitely generated) projective modules is an abelian category and this property of abelianness characterizes Auslander algebras by Tachikawa theorem in 1974. Let $n$ be a positive integer. In this paper, by using torsion theoretic methods, we show that $ n $-Auslander algebras can be characterized by the abelianness of the category of modules with projective dimension less than $ n $ and a certain additional property, extending the classical Auslander-Tachikawa theorem. By Auslander-Iyama correspondence a categorical characterization of the class of Artin algebras having $ n $-cluster tilting modules is obtained. Since higher Auslander algebras are a special case of higher Auslander-Gorenstein algebras, the results are given in the general setting as extending previous results of Kong. Moreover, as an application of some results, we give categorical descriptions for the semisimplicity and selfinjectivity of an Artin algebra. Higher Auslander-Gorenstein Algebras are also studied from the viewpoint of cotorsion pairs and, as application, we show that they satisfy in two nice equivalences.

This paper is devoted to study the relationship between two important notions in ring theory, category theory, and representation theory of Artin algebras; namely, Gabriel topologies and higher Auslander(-Gorenstein) algebras. It is well-known that the class of all torsionless modules over a higher Auslander(-Gorenstein) algebra is a torsion-free class of a hereditary torsion theory that is cogenerated by its injective envelope and so by Gabriel-Maranda correspondence we can define a Gabriel topology on it. We show that higher Auslander(-Gorenstein) algebras can be characterized by this Gabriel topology. This characterization can be considered as a higher version of the Auslander-Buchsbaum-Serre theorem that is considered as one of the most important achievements of the use of homological algebra in the theory of commutative rings. Among some applications, the results also reveal a relation between the projective dimension of a module and the projective dimensions of the annihilator ideals of its objects over higher Auslander algebras., Comment: arXiv admin note: text overlap with arXiv:2402.17293

Throughout this paper $G$ is a fixed group, and $k$ is a fixed field. All categories are assumed to be $k$-linear. First we give a systematic way to induce $G$-precoverings by adjoint functors using a 2-categorical machinery, which unifies many similar constructions of $G$-precoverings. Now let $\mathcal{C}$ be a skeletally small category with a $G$-action, $\mathcal{C}/G$ the orbit category of $\mathcal{C}$, $(P, \phi) : \mathcal{C} \rightarrow \mathcal{C}/G$ the canonical $G$-covering, and $\mathrm{mod}\mbox{-} \mathcal{C}$, $\mathrm{mod}\mbox{-} (\mathcal{C}/G)$ the categories of finitely generated modules over $\mathcal{C}, \mathcal{C}/G$, respectively. Then it is well known that there exists a canonical G-precovering $(P., \phi.) : \mathrm{mod}\mbox{-} \mathcal{C} \rightarrow \mathrm{mod}\mbox{-} (\mathcal{C}/G)$. By applying the machinery above to this $(P., \phi.)$, new $G$-precoverings $(\mathrm{mod}\mbox{-} \mathcal{C}) / S \rightarrow (\mathrm{mod}\mbox{-} \mathcal{C}/G)/S'$ are induced between the factor categories or localizations of $\mathrm{mod}\mbox{-} \mathcal{C}$ and $\mathrm{mod}\mbox{-} \mathcal{C}/G$, respectively. This is further applied to the morphism category $\mathrm{H}(\mathrm{mod}\mbox{-} \mathcal{C})$ of $\mathrm{mod}\mbox{-} \mathcal{C}$ to have a $G$-precovering $\mathrm{fp}(\mathcal{K}) \rightarrow \mathrm{fp}(\mathcal{K}')$ between the categories of finitely presented modules over suitable subcategories $\mathcal{K}$ and $\mathcal{K}'$ of $\mathrm{mod}\mbox{-}\mathcal{C}$ and $ \mathrm{mod}\mbox{-} \mathcal{C}/G$, respectively.

In the era of digital medicine, medical imaging serves as a widespread technique for early disease detection, with a substantial volume of images being generated and stored daily in electronic patient records. X-ray angiography imaging is a standard and one of the most common methods for rapidly diagnosing coronary artery diseases. The notable achievements of recent deep learning algorithms align with the increased use of electronic health records and diagnostic imaging. Deep neural networks, leveraging abundant data, advanced algorithms, and powerful computational capabilities, prove highly effective in the analysis and interpretation of images. In this context, Object detection methods have become a promising approach, particularly through convolutional neural networks (CNN), streamlining medical image analysis by eliminating manual feature extraction. This allows for direct feature extraction from images, ensuring high accuracy in results. Therefore, in our paper, we utilized the object detection method on X-ray angiography images to precisely identify the location of coronary artery stenosis. As a result, this model enables automatic and real-time detection of stenosis locations, assisting in the crucial and sensitive decision-making process for healthcare professionals., Comment: The results in the article need fundamental corrections

In this research, we present a Python-based solution designed to simulate a one-dimensional quantum system that incorporates multiple Dirac $\delta -$% potentials. The primary aim of this research is to investigate the scattering problem within such a system. By developing this program, we can generate wave functions throughout the system and compute transmission and reflection amplitudes analytically and numerically for an infinite range of combinations involving potential strengths, potential separations, and the number of potential centers in the form of the Dirac $\delta -$functions. Furthermore, by modifying the code, we investigate the so-called "transmission resonances" which yields the energy of the quantum particles undergoing a perfect transmission. Subsequently, our research is extended by considering impurities in the system., Comment: 14 pages and 12 figures, final version accepted for publication in Physica Scripta