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Dunkl operators may be regarded as differential-difference operators parameterized by finite reflection groups and multiplicity functions. In this paper, the Littlewood--Paley square function for Dunkl heat flows in $\mathbb{R}^d$ is introduced by employing the full "gradient" induced by the corresponding carr\'{e} du champ operator and then the $L^p$ boundedness is studied for all $p\in(1,\infty)$. For $p\in(1,2]$, we successfully adapt Stein's heat flows approach to overcome the difficulty caused by the difference part of the Dunkl operator and establish the $L^p$ boundedness, while for $p\in[2,\infty)$, we restrict to a particular case when the corresponding Weyl group is isomorphic to $\mathbb{Z}_2^d$ and apply a probabilistic method to prove the $L^p$ boundedness. In the latter case, the curvature-dimension inequality for Dunkl operators in the sense of Bakry--Emery, which may be of independent interest, plays a crucial role. The results are dimension-free., Comment: Comments welcome!

This paper proves the conjectures (previously proved in the case n = 0 ) that for any Coxeter system ( W , S ) and any natural number n, the set of n-small roots for W is bipodal and the set of n-low elements of W is a Garside shadow. The proof here uses special cases ( k = 3 ) of properties (notably, their existence) of certain maximal rank k reflection subgroups of W, for non-negative integers k.

Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion’s drift via the corresponding scale function. In the static version the diffusion’s drift can be chosen at each point in [0,1], whereas in the dynamic version we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem.

In this paper, a unique one-dimensional double anti-PT-symmetric ring optical waveguide network (1D DAPTSROWN) is designed whose refractive index satisfies n ( x ) = − n ∗ ( − x ) . The extraordinary optical characteristics of the network are studied by means of the generalized Floquet-Bloch theorem, three-material network equation and generalized eigenfunction method. Due to the physical difference between the anti-PT-symmetric and PT-symmetric optical waveguide networks, the previous methond of the PT-symmetric optical waveguide network is not applicable to the anti-PT-symmetric optical waveguide network designed in this paper. Thus, based on the previous method and the network equation, we propose a connection function to identify the extremum mode points in the anti-PT-symmetric optical waveguide network. At the extremum mode point, the optical waveguide network can produce extraordinary ultra-strong transmission, ultra-strong reflection, and ultra-strong photonic localizations. The corresponding calculated values in this paper arrives at 1 0 28 , which is much larger than 1 0 12 (the best result reported previously). This shows that the anti-PT-symmetric network may have potential in applications in designing optical filters, optical amplifiers and so on.

This paper demonstrates an electronically scanned reflectarray antenna based on liquid crystal (LC). The LC-based reflectarray element was designed as a periodically loading of parallel H-shaped polygons on two metal layers. To realize a tunable reflection phase and reduce the inhomogeneity effect of LC, an 8-μm-thick LC layer was designed as a varactor rather than a substrate. In simulations, the adjustable reflection-phase range of the proposed element was 180° in the frequency band 21–21.5 GHz. The design concept was verified on a reflectarray prototype containing 26 rows of the basic elements. In addition, a 32-channel control circuit was designed and fabricated for biasing. The measured results confirmed a tunable phase range of 1500 at 23.8 GHz. The disagreements between the simulated and measured results are discussed and a test process is proposed. As a proof of concept, the main beam was steered to 0°, -40°, and -60° in one plane. The result confirmed the high beam-steering capability of the proposed reflectarray with measured gains above 18 dB at 23.8 GHz. This work provides useful references for the design and measurement of LC-based reflectarray antennas.

Reflection modulation based on reconfigurable intelligent surface (RIS) is considered to be a promising information transfer mechanism without requiring any additional radio frequency chains. However, existing reflection modulation schemes consider manipulating the ON/OFF states of RIS elements, which suffers from power loss. In this paper, we propose a new scheme, called RIS-aided quadrature reflection modulation (RIS-QRM), for harvesting the reflection power based on an RIS-aided downlink multiple-input single-output (MISO) wireless system. To this end, RIS-QRM partitions RIS elements into two subsets for reflecting impinging signals into two orthogonal directions as well as passive beamforming and encodes its local data onto the element partition options. A closed-form expression for the unconditional pairwise error probability of RIS-QRM in Rician fading is derived assuming the maximum-likelihood detection. Moreover, we propose a low-complexity detection method with compromised performance for decoupling the joint search of the constellation symbol and the RIS element partition. Computer simulation results corroborate the effectiveness of RIS-QRM and validate the analytical results. It is shown that RIS-QRM is able to improve the error performance of the additional bits delivered by the RIS without deteriorating that of the bits carried on the constellation symbol, as compared to ON/OFF-based schemes.

Reconfigurable intelligent surfaces (RISs) are capable of enhancing the capacity of wireless networks at a low cost. In practical RIS-assisted communication systems, the acquisition of channel state information (CSI) and RIS reflection optimization constitute a pair of challenges. In this paper, a low complexity channel estimation and passive beamforming design is proposed. First of all, we conceive a low-complexity framework for maximizing the achievable rate of RIS-assisted multiple input multiple-output (MIMO) systems having discrete phase shifts at each RIS element. In contrast to existing solutions, the proposed arrangement partitions the channel training stage into several phases, where the RIS reflection coefficients are pre-designed and the effective superposed channel is estimated instead of separately training the source-destination and source-RIS-destination links. Based on this, the active beamformer can be designed at low complexity and the RIS reflection optimization is performed by selecting that one from the pre-designed training set which maximizes the achievable rate. Secondly, we propose novel techniques for generating the training set of RIS reflection coefficients. The theoretical performance of the proposed scheme is analyzed and compared to the optimal RIS configuration. Finally, our simulation results demonstrate that the proposed framework is more competitive than its existing counterparts when relying on imperfect CSI, especially for rapidly time varying channels having short channel coherence time.

An optical fiber sensor is proposed and experimentally demonstrated for simultaneous measurement of high temperature and transverse load. The sensor is designed by splicing a silica capillary tube (SCT) to a single-mode fiber (SMF) and then heating the SCT to form an air bubble. SCT simultaneously functions as a Fabry Perot (F-P) microcavity and an anti-resonant reflection waveguide. These sensing mechanisms lead to high contrast sensitivity values of temperature and transverse load (1.89pm/°C,190.48pm/N and 24.93pm/°C, 16.68pm/N). Remarkably, the temperature sensitivity of this sensor is eleven times higher than that of the current fiber-tip micro-cavity (2.1 pm/°C). The sensor is also more advantageous in quantitative production and practical application due to its low cost, ease of fabrication, good mechanical strength, and convenient reflection probe.

In this paper, we propose a deep neural network for single image reflection removal. More specifically, we design a convolutional-grid module and take it as the building block of a feature fusion pyramid. The module leverages the combination effect of the grid topology to create a rich ensemble of receptive fields. Embedding the modules into a pyramidal architecture further expands the coverage of receptive fields. Another benefit of the pyramid is to fuse the multi-scale features learned by the modules locating at the ascending and descending pathways. The rich diversity of features helps the neural network analyze the contexts around overlapping objects at various spatial ranges and harvest the cues for layer separation. The proposed work also exploits useful semantic cues from the hyper-column descriptors generated by a pre-trained VGG-19 model to reduce the ambiguity of layer separation. In light of the low correlation between background and reflection layers, we design a channel-correlation based conditional discriminator to penalize residual reflection. The discriminator uses channel-wise attention to screen the features that can distinguish real background images from estimated ones. This paper also presents a task-driven regularization strategy. The high sensitivity of semantic segmentation to reflection is exploited for assessing the completeness of reflection removal. Training with this regularization strategy can boost the performance of both reflection removal and high-level task. The comparison against state-of-the-art algorithms on four public benchmark datasets demonstrates that this work exhibits superior performance in handling the complex reflections in wild scenarios. The proposed network architecture is also applicable to haze removal, which is another ill-posed layer separation problem, and has shown encouraging performance.

Rational excogitation of microstructure and chemical constituents is a superior means of constructing electromagnetic wave (EMW) absorption materials with high performance. In this study, a kind of honeycomb-like NiFe2O4@Ni@C composite is prepared via an uncomplicated polymerization, pyrolysis and etching. Porous structure and internal cavity of NiFe2O4@Ni@C contribute to the numerous reflection and scattering of EMW. The strong ferromagnetic resonance of NiFe2O4 core and the multiple relaxation processes of porous carbon shell strongly promote the EMW loss. Additionally, the synergistic effect can improve impedance matching. The results demonstrate that the minimum reflection loss (RL) of honeycomb-like NiFe2O4@Ni@C composites is −65.33 dB at 13.63 GHz. The effective absorption bandwidth (EAB) is 3.68 GHz when the matching thickness is 4.95 mm. The mechanism of EMW dissipation of the honeycomb-like NiFe2O4@Ni@C composites is attributed to multiple reflections and scattering, conductive loss, interfacial polarization and ferromagnetism resonance. This work provides a tactic for the excogitation and synthesis of a low cost, light weight and efficient EMW absorber.

The effects of irradiation time (IT), laser power (LP), and spot diameter (SD) on the damage caused to quartz ceramics under continuous-wave laser irradiation were investigated through an orthogonal experiment. The experimental results show that the LP has the dominant effect on the depth of an ablation pit, while the SD has the greatest impact on the diameter of the ablation centre. The diameter and depth of the ablation pit were both positively correlated to the irradiation energy. The bubbles and molten silica transition layer affected the laser beam's reflection and transmission properties, leading to the incident laser beam scattering into the entire ablation pit and forming an elliptical ablation pit. Furthermore, a 3D finite element (FE) model considering a dynamic heat source was developed to simulate the laser damage process. The shape and dimension of the ablation pit predicted by the FE model were consistent with those obtained through the experiment, demonstrating the effectiveness and rationality of the model. The FE analysis results show that the different ablation rates in the radial and depth directions significantly influence the morphology of the ablation pits. The temperature gradient in the transition region increases while the thickness of the transition region decreases as the LP increases. This indicates that a large LP will lead to greater thermal stress in this area and result in more microcracks.

The helicity asymmetry parameter τ in the Cameron decomposition indicates the degree to which a scatterer deviates from being an ideal symmetric scatterer. However, the solving procedure of τ can only be expressed in terms of single-look Sinclair scattering matrix. In this paper, we extend the helicity τ to a generalized helicity parameter τg, which is appropriate for both the single-look and multi-look PolSAR data. For single-look data, the generalized helicity τg is equivalent to the previous helicity τ. In addition, we investigate the relationships among the classical helix/helicity definitions, including the Cameron helicity, the Krogager helix component, and the Yamaguchi helix component. To achieve this, we represent the Cameron and Krogager decompositions in terms of the unified CTD model in the format of coherency matrix and revise the expression of Krogager decomposition contributions in function of Huynen parameters. Results show that essentially the Cameron helicity and Krogager helix are two kinds of representation of reflection asymmetry under the same decomposition model, and the Yamaguchi helix contribution is always larger than the Krogager helix contribution. Single-look PolSAR data from L-band ESAR is used for demonstration in this paper. Several multi-look datasets are generated by 1×3, 3×3, 3×5, 5×5, 5×7, 7×7, 7×9, and 9×9 boxcar average. Two techniques are taken to mitigate reflection symmetry assumption based on helix component and helicity angle respectively. It will be shown that the technique with the generalized helicity τg performs best in terms of efficiency and stability.

To satisfy the requirement of the sub-6 GHz bands coverage and the 44 MIMO specification for 5G era, a dual-band four-antenna module covering partial 5G bands N78 (3.4~3.6 GHz) and N79 (4.8~4.9 GHz) is proposed for 5G terminal applications. Based on quarter-circle-shaped dual-mode slotted PIFA, the two target bands are covered by the fundamental TM11 mode and a hybrid higher-order mode combined by quasi-TM11 and quasi-TM0,1/2 modes. The four-antenna module is composed by four such PIFA elements that are arranged in a sequentially rotated layout. It presents a circular shape with a diameter of 39.4 mm and is with a low profile of 1.2 mm. The measured results show that the reflection coefficients of the four elements basically cover the target bands; across N78 and N79, the isolations are better than 8.5 dB and 17.6 dB for the neighboring elements, and 19.4 dB and 18.5 dB for the diagonal elements; the average total efficiencies of the four elements are between 38.3%~39.5% for N78 and 39.3%~42.6% for N79; all the ECCs are lower than 0.42.

This work presents a technique for dielectric property retrieval through Debye parameter reconstruction from open-ended coaxial probe (OECP) response. Debye parameters were obtained with the application of a deep learning (DL) model to the reflection coefficient response of the OECP when terminated with a material under test. The OECP was modelled with the well-known admittance technique from 0.5 to 6 GHz with 20 MHz resolution. A dataset was generated using the admittance technique and obtained data was utilized to design the DL model. As part of the standard procedure, the dataset was separated to train, validate, and test parts by allocating the 80%, 10%, and 10% of the dataset to each section, respectively. Obtained percent relative error for Debye parameters were 1.86±3.01%, 3.33±9.52%, and 2.07±7.42% for $\epsilon _{s}$ , $\epsilon _\infty $ and $\tau $ , respectively. To further test the constructed DL model, OECP responses were measured at the same frequency band when it was terminated with five different standard liquids, four mixtures, and a gel-like material. Reconstructed Debye parameters from the DL model were used to retrieve the complex dielectric properties and obtained results were compared with the literature data. Obtained mean percent relative error was ranging from 1.21±0.06 to 10.89±0.08 within the frequency band of interest.

In this paper, several computer simulations have been carried out using lumerical FTDT software. As a result, the optimal layer thicknesses for antireflection coatings SiC/MgF2 and SiC/ZnO/MgF2 deposited on the surface of polished silicon were determined. Among the considered coatings, the double layer structure SiC (60 nm) + MgF2 (110 nm) has the lowest reflection (

The modelling of the reflection coefficient with simulation base reviled the optimum ratios of the thicknesses of the Porous Si/DLC (PS/DLC) and SiO2/TiO2 layers have been presented. Encouraging results were obtained with the following layer parameters: n(DLC) = 2.4, d(DLC) = 50 nm; and n(PS) = 2.2, d(PS) = 100 nm. Reflection in a range of 550–600 nm was less than 0.4%. The following parameters were obtained for two-layer SiO2/TiO2 system: n(TiO2) = 2.1, d(TiO2) = 150 nm; n(SiO2) = 1.5, d(SiO2) = 90 nm. The reflection was about 0.5% in a range of 550–600 nm. Have been clearly shown that significant reducing of reflection (up to 34.5%) in the visible range, thereby increasing the efficiency of solar cells is possible.

Metallic mirror coatings with high reflectivity using Au thin films deposited onto a Borosilicate BK7 glass substrates by a sputtering technique using ionic coating system (KIC-1A) were investigated. In order to facilitate the process of calculating the relationship between deposition duration and thin film thickness to reach to a certain thickness, so we have described and calculated the relationship between deposition duration and thin film thickness by theoretical analysis and then simulated by polynomial function. This study showed the relationship between the reflection and thin film thickness, where the highest value of the reflective coatings of 90.5% was obtained at thin film thickness of 153 nm.

To compare the accuracy of the equivalent keratometry reading (EKR) from a color LED corneal topographer (Cassini) with that of other no-history formulas for intraocular lens (IOL) power calculation in eyes with previous myopic excimer laser surgery.Centro de Oftalmología Barraquer, Barcelona, Spain.Retrospective case series.The refractive outcomes of the Cassini EKR entered into the Haigis formula were compared with those of the Barrett True-K, Haigis-L, and Shammas-PL formulas and the Triple-S method combined with the Haigis formula. Optimized lens constants for virgin eyes were used. The mean prediction error (PE), the median absolute error (MedAE), and the percentage of eyes with a PE within ±0.25 diopter (D), ±0.50 D, ±0.75 D, and ±1.00 D were calculated.The study comprised 37 patients (37 eyes). The Haigis-L, Shammas-PL, and Barrett True-K no-history methods produced a myopic mean PE that was significantly different from zero (P.001, P.001 and P = .004, respectively), whereas the mean PEs of Cassini EKR and the Triple-S combined with the Haigis formula were not different from zero (P.05). Repeated-measures analysis of variance disclosed a significant difference among the PE of all methods (P.0001). The MedAE of the Cassini EKR, Barrett True-K, Haigis-L, Shammas-PL, and Triple-S was, respectively, 0.34 D, 0.34 D, 0.49 D, 0.48 D, and 0.31 D (P = .0026).The performance of the combination of standard Haigis formula with Cassini EKR was comparable to other no-history formulas in eyes with previous myopic excimer laser surgery.

This work, for the first time, presents an absorptive frequency-tunable substrate-integrated waveguide (SIW) filter. For the filter design, an absorptive bandpass filter prototype tailored to an SIW structure has been formulated. The proposed absorptive bandpass filter prototype is capable of having a return loss larger than 20 dB at all frequencies although it has a simple matching circuit. The filter prototype has been attained by comprehensive formula-based synthesis of a new matching circuit equivalent to an existing one. To validate our filter prototype, a second-order absorptive bandpass filter that can alter its center frequency has been designed, fabricated, and measured. This article demonstrates approaches to find physical dimensions by comparing each section of the filter structure with the corresponding part of the prototype. The fabricated absorptive bandpass filter has a compact structure by virtue of its simple matching section. The frequency-tunable SIW resonators allow our absorptive bandpass filter to adjust its center frequency from 1.76 to 2.69 GHz while having absorptive performance. The measured reflection of the filter centered at 2.50 GHz is smaller than -10 dB between 1.56 and 3.27 GHz (2.10:1). It is shown that theory, simulation results, and measured responses are in good agreement.

Surface plasmon resonance (SPR) is used to infer information about a sample that is in contact with an Au-coated glass slide coupled to the SPR prism. Shifts in the angle of the "SPR minimum reflection" can be related to changes in the refractive index (and/or thickness) of the sample that is in contact with the Au film, which can then be used to determine the concentration of an analyte in that sample. Here, we show that by depositing a layer of poly(N-isopropylacrylamide-co-acrylic acid) [p(NIPAm-co-AAc)] microgel on the SPR's Au film, with a subsequent layer of Au deposited on top of the microgels, the sensitivity of SPR to changes in solution properties can be enhanced. We investigated the sensitivity of the SPR to changes in the temperature of water in contact with the SPR's Au film as a function of the microgel immobilization density and the thickness of the Au layer deposited on the microgel layer. The data revealed that the SPR's Au film densely coated with microgels, with 5 nm of Au deposited, exhibited the maximal enhancement. The plasmon coupling effect between the additional Au film on the microgels and the SPR's Au film was further confirmed by 3D finite difference time domain simulations.

Hard/soft nanocomposites (NCs) of SrNi0.02Zr0.02Fe11.96O19 (SrNiZr)/MFe2O4 (M = Mn, Co, Cu, and Zn) were prepared using a one-pot sol-gel auto-combustion technique. All produced samples showed smooth M − H curves and single peaks on the dM/dH against H curves. This indicates that complete exchange-coupled effects between phases were achieved. Furthermore, the squareness ratio SQR=(Mr/Ms) was obtained and found to be higher than 0.5 at 300 K. This refers to the occurrence of excellent exchange coupling behavior among the soft and hard ferrites, and their structures consist of a single magnetic domain. The electrodynamic parameters were investigated in the 2–18 GHz frequency band using a coaxial line. The dependences of the real and imaginary parts of μ and e as a function of frequency were determined from the measured S-parameters. A strong correlation between the chemical composition of the soft magnetic phase and the electrodynamic parameters of the composite was observed. This was analyzed in terms of the atomic weight and configuration of the electronic shells of the A-cation in the soft phase. The electromagnetic absorption (EMA) of the investigated composites was estimated from the reflection losses calculated from μ and e. The maximal EMA value was observed.

A Fabry-Perot interferometer (FPI) temperature sensor was proposed by splicing a self-made hollow core anti-resonance fiber (HC-ARF) between two single mode fibers (SMFs). The HC-ARF was 2 mm long and one SMF was 20 mm in length. The SMF end face was coated with an Au film. When temperature varied from 45 °C to 85 °C, a sensitivity of 81.1 pm/°C was obtained at the waveband of 1550 nm∼1555 nm. When temperature varied from 35 °C to 95 °C, a sensitivity of 138.8 pm/°C was obtained at the waveband of 1571 nm∼1581 nm. Theoretical analysis suggested that the sensitivity of this proposed sensor can be easily adjusted by varying the length of the Au-coated SMF via the Vernier effect, which was confirmed by a subsequent experiment where the SMF length was varied from 20 mm to 170 mm. This work offers a simple sensitivity control method, and the proposed sensor is easy to manufacture, compact in structure, and convenient in performance control, which can be applied for a wide range of biological and chemical applications.

The concepts of Booleanization and of smallest dense quotient are explored in the context of d-frames. These two notions coincide for frames, but bitopologically they turn out to be different. The approach followed here is different from that in (Moshier in On Isbell’s density theorem for bitopological pointfree spaces I 273:106962, 2020), in which the smallest dense extremal epimorphism of a d-frame is described. Here, we consider the lattice of all quotients of a d-frame, extremal and nonextremal. Here, it is shown that for corrigible d-frames there is a smallest dense quotient, and it is shown that this coincides with the Booleanization of a d-frame: this is a construction which, as in the frame theoretical case, gives us the Boolean reflection of a d-frame in a suitable subcategory of the category of d-frames.

A novel planar dielectric polarizer made of a low-profile high dielectric constant material is proposed. Two anisotropic anti-reflection layers are used on both sides to provide impedance transformation and anisotropy simultaneously. The proposed design uses a high-dielectric-constant material to reduce the overall thickness without severe reflections. The unit cells of the middle layer and the anti-reflection layer use separate periods for better adapting to the fabrication limitation. A polarizer prototype centered at 24 GHz is designed, fabricated, and measured. The prototype is 3D-printed by commercial fused-deposition-modeling (FDM) technology using a material with a dielectric constant of 10. Experiments show the prototype has a 25% operating bandwidth and a thickness of 0.52λ0 (λ0 is the wavelength in the free space). The design methodology widens the choice for material selection and reduces the dimensions of the dielectric polarizer.

Novel X-ray methods are transforming the study of the functional dynamics of biomolecules. Key to this revolution is detection of often subtle conformational changes from diffraction data. Diffraction data contain patterns of bright spots known as reflections. To compute the electron density of a molecule, the intensity of each reflection must be estimated, and redundant observations reduced to consensus intensities. Systematic effects, however, lead to the measurement of equivalent reflections on different scales, corrupting observation of changes in electron density. Here, we present a modern Bayesian solution to this problem, which uses deep learning and variational inference to simultaneously rescale and merge reflection observations. We successfully apply this method to monochromatic and polychromatic single-crystal diffraction data, as well as serial femtosecond crystallography data. We find that this approach is applicable to the analysis of many types of diffraction experiments, while accurately and sensitively detecting subtle dynamics and anomalous scattering.

Let $\mathrm{k}_{0}$ be a field and $W$ a finite orthogonal reflection group over $\mathrm{k}_{0}$. We prove Serre's splitting principle for cohomological invariants of $W$ with values in Rost's cycle modules (over $\mathrm{k}_{0}$) if the characteristic of $\mathrm{k}_{0}$ is coprime to $|W|$. We then show that this principle for such groups holds also for Witt- and Milnor-Witt $K$-theory invariants., 20 pages

An idea of a colored glaze is presented in this study to hide and dispose all the obstacles of using solar systems as facades integrated with buildings. This aim is achieved by designing multilayer optical interference filters by using Mat lab program . Appropriate dielectric materials, namely NdF3 of high refractive index (nH =1.6) and ThF4 of low refractive index (nL =1.5143) were employed. Quarter wave thicknesses of high (H) and low (L) refractive index were deposited on a microscopic slide substrate with n=1.513 and 550 nm design wavelength (l°). Two optical models were designed, which are Air//HL//glass and Air//LH//glass, for even numbers of layers (2-32 layers). The challenge in this study is to find the most efficient design which has lower solar reflectance (Rsol.) and higher solar transmittance (Tsol.) to raise the efficiency of the solar systems and, in parallel, obtain the colored reflection to achieve the esthetic appearance of the buildings integrated with the solar system facades. The Tsol. value was high (94-95 %), whereas the Rsol. was very low (4-5 %). Hence, the efficiency of the solar system was increased. The two optical models exhibited green color reflectance in the visible region. The first design, i.e. Air/HL/glass, showed higher values of Rvis. and the merit factor (M) than the second model, resulting in a higher potential of coloration. The first design requires fewer materials and layers, thus, it is more cost-effective as compared to the second one.

To evaluate through roughness parameters measurement the penetration of calcium phosphate stabilized by casein phosphopeptides (CPP-ACP) in the subsurface zone of the incipient caries lesions known in dentistry as white spot lesion (WSL). To our knowledge, there is no data about roughness parameters to evaluate the demineralization-remineralization process in the body of the lesion. WSL was generated in vitro in 10 dental samples and sectioned in half of them (longitudinal section). CPP-ACP was applied on the WSL (3 minutes daily for 60 days). Roughness parameters (Rp and Ra) were measured on the longitudinal section with a laser scanning confocal microscope in the reflection acquisition mode (CLSRM), either in the WSL or sound enamel, before and after applying CPP-ACP. CLSRM is a non-contact method able to detect small irregularities more precisely due to the small spot of laser illumination (0.5 μm). Mixed linear models were carried out, using the treatment as a fixed factor and the tooth as a random factor (significance level 5%). Rp and Ra values in WSL area before applying the remineralization protocol (WSL pre) were significantly higher than in the sound enamel of the same samples. After applying CPP-ACP, Rp and Ra values decreased significantly with respect to the WSL pre and were similar to the values of these parameters in sound enamel. roughness parameters were used as an indirect way to measure the porosity of WSL at subsurface level. The decrease of these parameters could be interpreted as the remineralization of WSL by the ability of CPP-ACP to penetrate the body of the lesion. Clinical significance: WSL is characterized by the loss of minerals from the enamel and an increase in porosity at the subsurface level. The effectiveness of remineralizing substances would be determined by their ability to penetrate the body of the lesion and reduce porosity.

The theoretical focus of neoclassical economics experienced a significant change in the 1970s–1980s. General equilibrium theory lost its dominant position in theoretical economic studies, with its role of setting the research agenda taken over by what this article calls the “new microeconomic theories,” principally decision theory, game theory, and mechanism design. Mainstream economists, post-Keynesians, and historians of economic thought each give a different explanation of the hows and whys of that change, but all miss some critical methodological implications. That change, as this article discusses, shows that neoclassical economics has turned from “grand theory” toward “small models” with empirically delimited utility and that the ideology of marketism lacks a valid scientific foundation. This interpretation can help illuminate the deeper dynamics of the postwar development of neoclassical economics and provide insights for a new political economy that can come to grips with political-economic practices that cannot be fully grasped by the neoclassical tradition.

We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules X and Y. This bijection fixes the common indecomposable summands of X and Y and sends indecomposable projective (resp., injective) summands of exactly one module to non-projective (resp., non-injective) summands of the other. Moreover, this bijection interchanges the two possible non-isomorphic complements of an almost complete tilting module.

Red quantum dot (QD) films were applied to a conventional white light-emitting-diodes (LEDs) module consisting of 72 LEDs for improving color-rendering properties. Total three QD films with different QD concentrations, two diffuser plates, and six optical configurations were combined and investigated to find an optimized optical structure. QD films formed a red peak near 630 nm in the spectrum which significantly increased the overall color rendering index (CRI). The lateral optical cavity formed by a vertical QD wall and the vertical cavity formed by the diffuser plate and the reflection film in the lighting module played an important role in the improvement of the color-rendering properties. Especially, the adoption of the lateral optical cavity formed by the QD wall was an effective way to improve both efficiency and color rendering properties of the LED lighting. The present result suggests a new possibility of designing high-CRI LED light sources whose color properties can be tuned easily by simply applying and relocating QD components in conventional LED lightings.

The object of this research is the ordinary legal consciousness in the Russian folk tales. The subject of this research is the phenomenon of legal archetype of equivalence in the Russian folk tales. The author analyzes the key approaches towards studying the legal archetype, and provides definition to this phenomenon. Analysis is conducted on the attributes and varieties of the legal archetype, legal aspects of social existence and ordinary legal consciousness reflected in the Russian folk tales. Special attention is given to the clear elements of manifestation of legal consciousness: knowledge, values, attitudes, and motives. The archetype of equivalence in the Russian folk tales is viewed through the prism of retribution, reward for service, help, and exchange. The conclusion is made on the existence of basic attributes of legal archetypes, such as generic nature, frequency, and universality. It is stated that the legal archetype of equivalence is reflected in the representations of personal or property retribution, reward for good conduct of actions, fair exchange of things, magic objects, and symbols. The article advances a thought that the legal archetype of equivalence is a universal archetype, which is reflected in not only the representations of justice, but also the norm and measure, wrongdoing, retribution, agreement, etc. This is why it has fundamental meaning for other legal archetypes.

This work exploits the potential of a novel simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) in improving the security in a multiple-input single-output (MISO) network, where three transmission protocols, namely, energy splitting (ES), mode selection (MS), and time splitting (TS), are studied. The objective is to maximize the weighted sum secrecy rate (WSSR) by jointly designing the beamforming (BF) and the transmitting and reflecting coefficients (TARCs). A path-following based technique is first developed to covert the non-convex problem and design the BF and the TARCs in an alternating manner. Then, for the ES scheme, the TARCs are solved by a penalty concave convex procedure (PCCP) method. Besides, the proposed method is extended to the MS by solving a mixed-integer problem. While for the TS scheme, a two-layer optimization method is proposed. Finally, the simulation results validate the superiority of STAR-RIS.

Active millimeter-wave (mmWave) imaging illuminates a scene with a source of mmWave energy and forms images based on the reflected energy. When imaging objects (such as packaged goods in commerce) that have a mixture of opaque and translucent parts, two-sided reflection imaging can be used to overcome the occlusion by the opaque objects that would plague a transmission imaging approach. However, the two-sided reflection imaging approach suffers from wavelength-dependent beat patterns when coherently combining the images from each side. We present and experimentally verify an approach to successfully mitigate this image beat pattern. The presented two-sided $K$ -band 3-D mmWave imaging system achieves system resolutions of ${\delta }\text {x} = 17.07$ mm, ${\delta }\text {y} = 4.62$ mm, and ${\delta }\text {z} = 7.26$ mm, with an accuracy of 0.8 mm in the y- and z-directions. It is shown that the system is not only capable of producing beat-pattern-free 3-D images of the products inside an optically opaque corrugated cardboard shipping box but also the two-sided approach with image beat pattern correction showing an increased image volume even if portions of the scene are occluded.

A novel tunable reflectionless dual-passband filter (T-RDBPF) based on a single multi-mode resonator and absorptive networks is proposed firstly with independently tunable passbands, no reflection at full band, as well as absorbed harmonic signals. By increasing the admittance radios between parallel resonant paths in the multi-mode resonator, two individually controlled passbands with independent poles can be achieved. To correspond to the resonant poles, two series resonant loops are employed to generate independent zeros in the absorptive network, thus consecutive reflection absorptivity for all tuning states is realized. Without deploying any other structure, the absorptive network for out-of-band signals being equivalent to a resistor, is reused to provide an additional transmission path to absorb multiple harmonics. Then, both the transmission and reflection of harmonics are suppressed. Measurement results show that the proposed tunable reflectionless filter features two independent tuning ranges of 1.45–1.95 GHz ( ${f} _{1}$ ) and 2.45–3 GHz ( ${f} _{2}$ ), a minimum absorption level of −6 dB @ ${f} _{1}$ & −7.3 dB@ ${f} _{2}$ from DC to 6 GHz, a minimum harmonic absorption of −5.8 dB (S11) and −13.9 dB (S21) @ up to $7.4{f} _{1}$ respectively.

A reflection approach utilizing an open-ended rectangular waveguide (ORW) for dielectric constant characterization of low-loss slab materials is presented. A calibration technique is proposed to reduce the effects of the higher order mode fields in dominant-mode analysis. In addition, the effects of undesired reflections caused by the finite-sized flange are also reduced in the extraction of the dielectric constant. Moreover, a small perturbation is introduced in the calculation of the reflection coefficient to eliminate the singularities as well. The dielectric constant of material under test (MUT) is extracted utilizing the measured reflection coefficient by assuming that the loss tangent of MUT is zero. Simulation results are presented to validate the calibration process. The selection of suitable airgap thickness and the effects of lossy MUT are also discussed. The measured dielectric constants of MUT made of polymethyl methacrylate (PMMA) and polytetrafluoroethylene (PTFE) are presented as well, which agrees excellently with the results achieved from the free-space method.

Boundary reflection derivation method has been proposed in order to clarify intracellular structure change among the cell wall, membrane, and cytoplasm in the frequency range from 1 MHz to 3 GHz. This method is composed of three steps, which are 1) dielectric properties extraction of dispersed medium $\varepsilon _{\mathrm {dis}}^{\ast }$ and yeast cells $\varepsilon _{\mathrm {cell}}^{\ast }$ ; 2) dielectric properties fitting of cell wall $\varepsilon _{\mathrm {wall}}^{\ast }$ , membrane $\varepsilon _{\mathrm {mem}}^{\ast }$ , cytoplasm $\varepsilon _{\mathrm {cyto}}^{\ast }$ , and intracellular components $\varepsilon _{\mathrm {IC}}^{\ast }$ by a multishelled sphere model; and 3) reflection coefficients calculation at boundaries between cell wall and membrane $\Gamma _{\text {wm}}^{\ast }$ , and between membrane and cytoplasm $\Gamma _{\text {mc}}^{\ast }$ . With this method, $\Gamma _{\text {wm}}^{\ast }$ and $\Gamma _{\text {mc}}^{\ast }$ in living (LC) and dead (DC) yeast cell solutions with various volume concentrations are calculated from experimental impedances. $\Gamma _{\text {wm}}^{\ast \text {DC}}$ shows a difference as compared with $\Gamma _{\text {wm}}^{\ast \text {LC}}$ in GHz range. $\Gamma _{\text {wm}}^{\ast \text {LC}}$ and $\Gamma _{\text {mc}}^{\ast \text {LC}}$ illustrate electromagnetic waves penetrate yeast cell membrane and cytoplasm in GHz range nevertheless they are reflected in MHz range.

Frente al surgimiento del Pacto Educativo Global propuesto por el papa Francisco, el artículo presenta un ensayo sobre la relación entre la educación religiosa -concebida en el bachillerato- y la reflexión de esta formación en los jóvenes egresados ​​de la PUC-Rio. El análisis se basó en dos encuestas realizadas a estudiantes de la PUC-Rio durante un período de 12 años, en 2006 y 2018. Por medio del análisis y comparaciones realizadas, verificamos cambios significativos en relación con la creencia, imagen y experiencia de Dios. Nuestra evaluación propone que las encuestas a los estudiantes son excelentes mecanismos para escuchar atentamente a los jóvenes y se pueden implementar en otros niveles escolares: primaria y secundaria.

Desde la entrada en vigencia del Código Orgánico Integral Penal, se ha venido formulando estudios que permitan visibilizar lo que implica el tipo penal lavado de activos, en el presente se cavila acerca de lo que implica el onus probandi y cómo se invierte la carga de la prueba, lo que desde el punto de vista del garantismo del Ecuador es atentatoria del efectivo goce de los derechos, aunque se trate del adecuado funcionamiento del sistema económico, no puede soslayarse la tutela judicial efectiva de los derechos ni el debido proceso.

The building cooling load is calculated in most standards using the sol-air temperature (Tsol-air), which depends on the surface properties and the building configuration. This study presents an experimental and numerical analysis to find a relationship between the aspect ratio of the courtyard and the Tsol-air at different height levels. Besides, the influence of the surface reflection factor on the Tsol-air is analyzed. The results show that the Tsol-air inside the courtyard differs compared to the usual outside facade. This difference is increased by increasing the aspect ratio of the courtyard and can reach up to 60 °C at low levels of the deep courtyards. It is also found that the courtyard geometry is much more important than the thermal behavior of the materials and the Tsol-air within the deep courtyard is less affected by the reflection factor of materials.

We construct embeddings of Bers slices of ideal polygon reflection groups into the classical family of univalent functions $\Sigma$. This embedding is such that the conformal mating of the reflection group with the anti-holomorphic polynomial $z\mapsto\overline{z}^d$ is the Schwarz reflection map arising from the corresponding map in $\Sigma$. We characterize the image of this embedding in $\Sigma$ as a family of univalent rational maps. Moreover, we show that the limit set of every Kleinian reflection group in the closure of the Bers slice is naturally homeomorphic to the Julia set of an anti-holomorphic polynomial., Comment: Figure 1 added to illustrate the main result, and some other minor changes to the introduction

“The definition of insanity is doing the same thing over and over again but expecting different results.” This quote by Albert Einstein highlights our need for new formats of communication to address the knowledge-action gap regarding climate change and other sustainability challenges. This includes reflection, and communication spaces, as well as methods and approaches that can catalyze the emergence of transformative change and action. In this article we present and reflect on experiments we carried out at international climate negotiations and conferences.

This paper concerns the reflection of harmonic functions, w(x,y), defined in a neighborhood of a real-analytic curve in the plane subject to the Robin condition, aw+b∂nw=φw, on that curve. Here a a...

We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We use completions to show that reflection subgroups are quasiconvex, as are one-ended Coxeter subgroups of a 2-dimensional RACG. We provide an algorithm that determines whether a given one-ended, 2-dimensional RACG is isomorphic to some finite-index subgroup of another given RACG. In addition, we answer several algorithmic questions regarding quasiconvex subgroups. Finally, we give a new proof of Haglund's result that quasiconvex subgroups of RACGs are separable., Comment: 44 pages, 7 figures. Incorporated referee's comments, added references and new examples. To appear in Journal of Combinatorial Algebra

Introduction. Philosophy of culture one of the aspects of the subject field has an understanding of real cultural practice, based on multivariate reassessments of cultural traditions. The axiological component of the philosophy of culture affects the fundamental moral and ethical values of a person and society that contribute to social activity. The purpose of the article is to show the continuity of the ideological and practical volunteer movement, the importance of social activity of young people. Materials and Methods. In the article, the authors used the methodology of cultural and comparative analysis, the historical and philosophical approach to the problem, and the method of comparative studies. Among the historical foundations of axiology, there is a distinction between what is due and what is, concepts that unite ideas about ethics, human activity itself and its evaluation. The anarcho-communitarian construction of Prince Kropotkin’s ethics makes a significant contribution to this outline of reasoning, sets the guidelines for healthy human relations. The results of the Study. The principles of the evolutionary development of mutual assistance and support, solidarity and altruism, developed by the ethical philosopher and natural scientist Kropotkin in natural science and ethical works, in fact, were not only the theoretical basis of the philosophy of culture, but can also serve as guidelines for the practical activities and axiology of modern volunteers of the XXI century. Discussion. The article considers volunteerism as a continuation of a significant value tradition of mutual assistance and support, which has its historical incarnations. Solidarity, justice, altruism, instinct and the moral sense of a person – these are the main concepts of Kropotkin ethics as a doctrine of morality in its broadest sense. This year, the Russian scientific community is celebrating the centenary of the passing of P. A. Kropotkin. In this regard, it is particularly relevant to develop the principles of mutual assistance and support, which are practically in demand in the context of the cornavirus pandemic. Conclusions. The principles of the evolutionary development of mutual assistance and support, solidarity and altruism, developed by the ethical philosopher and natural scientist Kropotkin in natural science and ethical works, in fact, were not only the theoretical basis of the philosophy of culture, but also the practical activity of the axiology of modern volunteers of the XXI century, a manifestation of human social activity.

The downscaling of nonlinear optical devices is significantly hindered by the inherently weak nonlinearity in regular materials. Here, we report a giant third-harmonic generation discovered in epitaxial thin films of V-VI chalcogenide topological insulators. Using a tailored substrate and capping layer, a single reflection from a 13 nm film can produce a nonlinear conversion efficiency of nearly 0.01%, a performance that rivals micron-scale waveguides made from conventional materials or metasurfaces with far more complex structures. Such strong nonlinear optical emission, absent from the topologically trivial member in the same compound family, is found to be generated by the same bulk band characteristics that are responsible for producing the band inversion and the nontrivial topological ordering. This finding reveals the possibility of obtaining superior optical nonlinearity by examining the large pool of newly discovered topological materials with similar band characteristics.

Zinc-substituted magnesium titanate ZnxMg1−xTiO3 (x = 0.00–0.10, δx = 0.025) solid solutions were synthesized using auto-ignition combustion process and characterized for structural, dielectric and reflection properties. X-ray diffraction analysis discovered the creation of single-phase MgTiO3. Scanning electron microscopy (SEM) indicated the existence of low porosity closely packed grains. The study of the dielectric properties indicated that for ZnxMg1−xTiO3 with x = 0.05, a reasonably great combination of the relative permittivity (ɛr) with value 16.60, loss tangent (tanδ) of 0.9 × 10−3 and temperature coefficient of resonant frequency (τf) of − 41.37 ppm/°C at 10 kHz was observed. The electromagnetic reflection analysis at microwave frequencies (12.4–26.5 GHz) revealed that composition x = 0.05 shows maximum 90% reflection bandwidth of 5.60 GHz in the Ku frequency band and 4.59 GHz in the K frequency band. These materials with low to intermediate relative permittivity, low losses, and a minor negative temperature coefficient of resonant frequency might be utilized as a resonator, antenna, and filter substrate for next-generation communication devices.

With absorption and interference cancellation, lossy metamaterials can achieve broadband electromagnetic wave absorption. However, the design of such metamaterial absorbers (MMAs) is very complicate, because tremendous meta-atoms and their configuration parameters need to be determined. The conventional methods, such as parameter sweep and adjoint-based optimization, suffer from slow convergence and local minimum problem. In this letter, a deep neural network (DNN) is used to map the configuration parameters of a type of meta-atom onto its reflection coefficients. The DNN well predicts the reflection coefficients and is applied to design the MMA under the demand of −10 dB backscattering reduction (BSR) covering the microwave S to Ku bands with the smallest thickness. By globally searching the configuration parameter space using particle swarm optimization (PSO) algorithm, which automatically cooperates the absorption and phase cancelation (or diffusion) of meta-atoms, we obtain the optimized configuration of the meta-atoms and corresponding filling ratios. The designed MMA realizes −10 dB absorption bandwidth covering 2.2–18 GHz with the thickness only 4 mm, which is further verified by experiments. The performance of our absorber is better than other similar absorbers reported. Our letter provides a useful method for ultrathin broadband MMA design, which can also be applied to other functional devices based on metamaterials.