Symmetrical Arrangement Research Articles

Collatz Conjecture

This paper presents an analysis of the number of zeros in the binary representation of natural numbers. The primary method of analysis involves the use of the concept of the fractional part of a number, which naturally emerges in the determination of binary representation. This idea is grounded in the fundamental property of the Riemann zeta function, constructed using the fractional part of a number. Understanding that the ratio between the fractional and integer parts of a number, analogous to the Riemann zeta function, reflects the profound laws of numbers becomes the key insight of this work. The findings suggest a new perspective on the interrelation between elementary properties of numbers and more complex mathematical concepts, potentially opening new directions in number theory and analysis.This analysis has allowed to understand that the Collatz sequence initially tends towards a balanced symmetric arrangement of zeros and ones, and then it collapses, realizing the scenario of the Collatz conjecture.

Structures and NMR Solution Dynamics of Diorganotin Complexes with Bulky Quadridentate Salen‐ and Salphen‐Type Schiff Bases (N2O2) Incorporating Diazenylpyridyl Side Arms

AbstractA series of six complexes [n‐Bu2Sn(L1)]⋅S (S=Benzene/toluene, mixed/partial) (1), [Ph2Sn(L1)]n⋅S (S=Benzene) (2), [Bz2Sn(L1)] (3), [n‐Bu2Sn(L2)]n (4), [Ph2Sn(L2)] (5) and [Bz2Sn(L2)] (6) were synthesized using diorganotin(IV) oxide precursors and two new bis‐Schiff bases containing N2O2 donor atoms. The Schiff bases, H2L1 and H2L2, were prepared by reacting ethane‐1,2‐diamine or benzene‐1,2‐diamine with 2‐hydroxy‐5‐(pyridin‐3‐yldiazenyl)benzaldehyde in absolute ethanol. Compounds 1–6 were characterized by IR and NMR spectroscopies, as well as by solid‐state single‐crystal X‐ray diffraction (except for 3 and 6). In all the complexes the bis‐Schiff bases occupy the equatorial positions and the R groups are in axial sites. However, while 1 and 5 are discrete molecules where the tin atoms adopt distorted octahedral geometries, 2 and 4 are monoperiodic polymers with the metal cations in pentagonal bipyramidal environments. Although solid state crystallographic results revealed asymmetrical molecular configurations, solution NMR studies proved symmetric arrangements for all the compounds. Tin NMR spectroscopy confirmed that all complexes are six‐coordinate in solution, despite variations in solid‐state coordination. Further analysis using Hirshfeld surface and fingerprint plots provided insights into intermolecular interactions in compounds 1, 2, 4, and 5. This comprehensive study underscores the structural diversity and solution‐state dynamics of organotin(IV) complexes synthesized using novel Schiff bases.

Locating method of buried PE pipeline based on vibration signal analysis

Abstract This paper proposes a buried PE gas pipeline positioning method based on vibration signal analysis. Firstly, the collected signal is denoised using the Dual-tree complex wavelet transform (DTCWT) method, and then the delay time of the denoised collected signal is extracted through the cross-correlation function to locate the buried PE pipeline. A simulation model is established on this theoretical basis, and sensor asymmetric and symmetric arrangements are simulated in COMSOL to observe the peak values of the collected signal in the time domain, determining the relationship between the time difference of the two signals and the pipeline position. Through simulation, it is known that the pipeline location can be judged by the magnitude of the delay time. The method proposed in this paper addresses the shortcomings of existing pipeline positioning methods and provides a basis for future pipeline positioning.

Application of the FDTD Method for Multivariate Analysis of the Influence of Conductivity and the Arrangement of Hollows Inside Bricks on the Values of Electric Field Intensity

The article contains a numerical analysis of the effects of electromagnetic wave propagation in an area containing a non-ideal, non-uniform, and absorbing dielectric. The analysis concerned the influence of the structure of the building material and its electrical parameters on the electric field intensity. The analysis took into account the variability of the number of hollows in the brick, the width of hollows, as well as the arrangement of these hollows relative to each other using the example of two types of bricks. The article also provides the most commonly used values of electrical parameters for building materials (brick, plaster). For this reason, the article includes results for different values of conductivity (0–0.2 S/m). The FDTD (Finite Difference Time Domain) method was used for multivariate analysis. The aim was to verify the correctness of the numerical assumptions adopted. Using the example of the most commonly used wall structure in construction, the results obtained using the FDTD method were compared with values obtained using another numerical method, the finite element method (FEM). The influence of an additional layer of plaster on the considered wall on the electric field was also checked. The analysis showed that a symmetrical arrangement of bricks results in higher values of the electric field by an average of 20%. Of course, this depends on the length of the hollows and the number of holes. The highest field values occur at low conductivities (0–0.04 S/m). A brick wall with a larger number of hollows and a symmetrical brick arrangement shows the highest electric field intensity, especially for hollow sizes (0.009–0.015 m).

Laser-induced fluorescence spectroscopic investigation of Echium amoenum decoction

Herbs containing medicinal ingredients with nutritional value have recently gained attention as an alternative to synthetic drugs. Aside from their pharmaceutical worthiness, a variety of naturally occurring chromophores with specific optical properties have made them valuable sources of natural pigments for many biophotonic applications. Echium Amoenum (EA) is one of the colorful flowers that has been used in traditional medicine for a long time. To our knowledge, although several studies have been carried out on the characterization of EA ingredients and their chemical activities, information on EA fluorescence is still lacking. Here, laser induced fluorescence (LIF) features of the decoction of EA petals were evaluated and found to be highly dependent on the excitation wavelength, EA concentration, and detection geometry. The abundance of pigments, the boundaries of their absorption/emission spectral regions, and the corresponding energy transfer ascertain the contribution of certain chromophores to the cumulative fluorescence activity. Upon deconvolution of the LIF spectra, it was revealed that the different emission bands of rosmarinic acid (corresponding to its dissociated forms) and the luminescent activity of luteolin and β-carotene mainly determine the quantum distribution of the fluorescence of EA. Angular measurement of LIF in a symmetric cylindrical arrangement revealed the presence of the inner filters mainly due to the reabsorption of LIF photons by anthocyanins (flavone, pelargonidin, delphinidin and cyanidin) and carotenoids. We hope that the obtained results will be useful in various fields of photochemistry and biophotonics.

Identifying crystal structures beyond known prototypes from x-ray powder diffraction spectra

The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we present a scheme to resolve powder diffraction data into crystal structures with precise atomic coordinates by screening the space of all possible atomic arrangements, i.e., structural prototypes, including those not previously observed, using a pre-trained machine learning (ML) model. This involves (i) enumerating all possible symmetry-confined ways in which a given composition can be accommodated in a given space group, (ii) ranking the element-assigned prototype representations using energies predicted using the Wyckoff representation regression ML model [Goodall , ], (iii) assigning and perturbing atoms along the degree of freedom allowed by the Wyckoff positions to match the experimental diffraction data, and (iv) validating the thermodynamic stability of the material using density-functional theory. An advantage of the presented method is that it does not rely on a database of previously observed prototypes and is, therefore capable of finding crystal structures with entirely new symmetric arrangements of atoms. We demonstrate the workflow on unidentified x-ray diffraction spectra from the ICDD database and identify a number of stable structures, where a majority turns out to be derivable from known prototypes. However, at least two are found not to be part of our prior structural data sets. Published by the American Physical Society 2024

A Wideband and Compact Millimeter-Wave Antenna Array Fed by Printed Ridge Gap Waveguide for 5G Applications

This paper proposes a printed ridge gap waveguide (PRGW)-based 2 × 2 millimeter-wave antenna array with broad bandwidth and compact aperture. A dual-resonance element consisting of a quarter circular and a quarter annular patch is initially designed. Subsequently, to reduce the cross polarization (XP) radiation and enhance the gain of the proposed antenna, a four-element array with symmetric arrangement is developed, leading to a decline in the normalized XP levels from -4.5 to -18.9 dB and from -4.4 to -18.7 dB in the xoz and yoz planes, respectively. In addition, a pair of parasitic shorted half-circular patches is loaded to improve the antenna gain in the highfrequency range. Finally, a PRGW feeding network is designed and applied to provide differential feeding for the planar array. To validate the reflection and radiation performance, an array prototype is fabricated, and experimental verification is conducted. Measurement results show that a -10-dB impedance bandwidth of 14.3% (26.0–30.0 GHz) is realized for the prototype, and an average realized gain of 9.8 dBi with low XP radiation is achieved by the proposed array.

Chirality-Mediated 1D-to-2D Phase Transition in Hybrid Lead Halide Perovskites.

Dimensionality engineering plays a pivotal role in optimizing the performance, ensuring long-term stability, and expanding the versatile applications of lead halide perovskites (LHPs). Currently, the manipulation of LHP dimensions primarily occurs during the synthesis stage, a procedure hampered by constraints, including synthetic complexity and irreversibility. This investigation successfully achieved a transition from one-dimensional (1D) to two-dimensional (2D) structures in chiral LHPs by applying hydrostatic pressure. Remarkably, this pressure-induced transition in dimensionality is absent in the racemic analogue due to the staggered arrangement of inorganic chains and the elevated steric hindrance posed by the organic cations. Notably, the hydrogen bonding between organic cations and the inorganic framework adopts a symmetrical arrangement in the racemic system but a helical configuration along the 1D chain direction in the chiral counterparts. This distinct helical arrangement induces a consequential distortion in the inorganic moiety, resulting in the emergence of a spin-polarized Rashba-Dresselhaus texture that explains the chirality's electronic spin origin. Furthermore, both experimental and density functional theory calculation results demonstrate that the 1D-to-2D phase transition in chiral halide perovskites can induce significant modifications in the electronic structures and associated optical emissions. In summary, the findings unveil novel avenues for manipulating optoelectronic properties in chiral perovskites through dimensionality engineering.

The influence of the bounding surface on the structural ordering of short chains of oligoetherimides.

In this study, we have conducted a comparative analysis of the structural ordering of short oligoetherimide chains (dimers) near the bounding surface, depending on the structure of that surface. In order to clarify the possibility of oligoetherimide ordering along the symmetry axes of graphene, two types of bounding surfaces were considered: graphene, with a regular discrete position of interaction centers (carbon atoms), and a smooth, structureless impermeable wall. The chemical structures of the considered dimers consist of two repeating units of BPDA-P3, ODPA-P3, or aBPDA-P3 thermoplastic polyetherimides. Using all-atom molecular dynamics simulations, the process of structural ordering of the dimers near the surface of the graphene or wall was established. The ODPA-P3 and BPDA-P3 dimers form an ordered state near the graphene surface, while the aBPDA-P3 dimers do not demonstrate structural ordering. The simulation results confirmed that the ordering direction of the BPDA-P3 and ODPA-P3 dimers near the graphene surface is chosen randomly. Comparison of the oligoetherimide structure formed near the attracting wall without a symmetrical location of the interaction centers shows the similarity of the ordering of dimers near the graphene surface and the wall. As in the case of the graphene surface, the ordering of oligoetherimide molecules near the structureless wall demonstrates one direction of ordering. Therefore, we confirmed that the key factor for the onset of ordering is the presence of a confining surface, rather than the symmetrical arrangement of interaction centers in the substrate structure.

Synthesis of fullerite (100) through epitaxy on a complex intermetallic surface

We report the first epitaxial growth of bulk-like C60(100) plane stabilized by a size-matching effect on the surface of a complex intermetallic compound. As characterized by low energy electron diffraction (LEED) and scanning tunneling microscopy (STM) techniques, the adsorption of C60 on Au–Si–Ho(100) surface is disordered at room temperature but ordered when the substrate is held at elevated temperature (669 K). In the submonolayer regime, different superstructures are observed depending on the fullerenes coverage. Upon completion of the first monolayer of C60, the thin film of c(1 × 1) superstructure is structurally equivalent to a (100) surface plane of the face-centered cubic structure of C60 bulk crystal. This structure is unusual for C60 monolayers on metal surfaces and appears to be favored by an almost perfect match between the most preferred C60 intermolecular distance and the distances separating specific adsorption sites of the large unit cell compound. The adsorption site selection is dictated by a local symmetry matching between the pentagonal fullerene facets and pseudo-five-fold symmetric atomic arrangements on the substrate. After the completion of the first monolayer, further deposition of C60 at 387 K results in the growth of a (100) oriented thicker epitaxial fullerite crystal.

A compact 6‐shaped high isolation MIMO antenna for 28 GHz 5G applications

SummaryThis study presents the design, fabrication, and measurement of a novel MIMO antenna for 28 GHz 5G applications. The design includes two compact antennas with dimensions of 12.8 × 12.8 × 1.6 mm3, placed side by side in a symmetrical arrangement. The antenna being considered operates within the 28 GHz frequency range and has excellent characteristics in terms of reflection coefficient, isolation, and impedance matching. The measurements conducted encompassed both single and MIMO setups and focused on important parameters such the reflection coefficient, transmission coefficient, gain, and efficiency. The MIMO antenna exhibited a reflection coefficient of −62.52 dB at a frequency of 27.93 GHz, while the transmission coefficient was found to be −37.23 dB. The antenna attained a gain of 6.02 dB relative to an isotropic radiator (dBi) and exhibited a maximum efficiency of 90.73%, encompassing a bandwidth of 4.45 MHz (MHz). The simulated envelope correlation coefficient (ECC) was found to be less than 0.003, indicating a very low error rate. Additionally, the antenna attained a diversity gain of 9.998 dB. The suggested MIMO antenna is very suitable for 5G applications operating at 28 GHz.

Mechanical properties of a novel negative Poisson's ratio gradient structure

A novel cellular structure is proposed based on bionic structure with negative Poisson's ratio characteristic, and the cell is periodically expanded in the in-plane direction to create a new honeycomb structure. The influence of gradient changes of the structural parameters on the load-bearing capacity and damping characteristics of the structure is investigated through a combination method of finite element numerical simulations and experiments. The results indicate that the concentric gradient arrangement of cell wall thickness and angle parameters, and the symmetrical gradient arrangement of cell height, wall thickness and angle parameters have the most significant influence on the static bearing capacity of the structure. In contrast, the gradient arrangement under the corner circle diameter has minimal effect on the static bearing capacity of the structure. Under the same conditions, the peak values of the transmissibility of C2 (large angle at constraint end and loading end, and smaller angle in the middle) and C3 structures (angle gradually increases from the loading end to the constraint end) are significantly reduced between the frequency 2 Hz and 1024 Hz. The peak values of the transmissibility of the structures C2 and C3 are respectively decreased by 20% and 25% compared to that of the non-gradient structure. This shows that the vibration damping effect of these two structures is better. The structure with the gradient change and the structure without the gradient change of the new honeycomb structure can both achieve certain vibration reduction and isolation from the middle to high frequency range.

Nanoscale particle-droplet coalescence-induced jumping on superhydrophobic surfaces: Insights from molecular dynamics simulations

The removal of solid particles from superhydrophobic surfaces via coalescence-induced droplet jumping has gained increasing attention. However, the underlying mechanisms, especially the nanoscale dynamics of particle-droplet coalescence, remain largely underexplored. In our research, we employ molecular dynamics simulations to investigate the influences of the radius, wettability, and arrangement of solid particles on the particle-droplet jumping velocity and energy conversion efficiency. We observe notable rotational motions during the jumping events. Our findings reveal that the arc length of the wetted area on spherical particles and the spreading time of droplets exhibit a power-law relationship. As the particle-to-droplet radius ratio increases, the jumping velocity and energy conversion efficiency initially increase but subsequently decrease. Moreover, enhanced particle wettability leads to an increase in jumping velocity while a slight decrease in translational energy conversion efficiency. The velocities of coalescence-induced particle-droplet jumping at the nanoscale are consistent with predictions from the momentum model. Significantly, our results show that the rotationally symmetric multi-particle arrangements can effectively enhance the jumping velocity and energy conversion efficiency, thus improving particle removal efficiency. Our study not only deepens the understanding of coalescence-induced particle-droplet jumping behaviors, but also provides a foundation for developing more effective particle removal strategies on superhydrophobic surfaces.

A symmetrical arrangement strategy based real-time toolpath planning method for a 5-DoF fully parallel machining robot

A symmetrical arrangement strategy based real-time toolpath planning method for a 5-DoF fully parallel machining robot

Numerical analysis of heat transfer and flow characteristics of the satellite thermal flowmeter and exploration of high-precision calibration methods

The performance of the thermal flowmeter for satellites is numerically studied to optimize. Flow patterns and temperature distributions, affected by buoyancy convection, significantly influence the accuracy of flow-rate measurements in inclined thermal flowmeters. The present study delves into the thermal flowmeter’s flow field and temperature distribution influenced by gravitational effects. When the Reynolds number is low, buoyancy convection causes a significant inconsistency in the measurement result between ground and space. By eliminating the constraint of the symmetrical arrangement of thermocouples and introducing additional thermocouples for high-precision calibration, the measurement accuracy is remarkably improved. Ultimately, arranging the thermocouples asymmetrically reduces the error by 62%. Additionally, integrating two more thermocouples is even more beneficial, reducing the error by 83% compared to the previous study. These improvements would be potential solutions of flow-rate measuring inconsistency between ground and space, aiding the development of a high-precision thermal flowmeter for satellites.

Second type second order slope rotatable designs utilizing symmetrical unequal block arrangements with two unequal block sizes

Kim and Ko developed second order slope rotatable designs (SOSRD) of second type utilizing central composite designs (CCD), in which two numbers are used to represent the positions of star points. In this paper, we suggest second type SOSRD utilizing symmetrical unequal block arrangements (SUBA) with two unequal block sizes. In some cases, the suggested method may develop designs containing fewer design points than second type SOSRD obtained utilizing CCD, pairwise balanced designs (PBD) and balanced incomplete block designs (BIBD). The first order partial derivative's for estimated second order response variance for factors 6≤v≤15 is also obtained.

Frequency shifting of plasmon polariton defect modes in a non-Hermitian finite heterostructure

A finite photonic layered system alternating usual media with a dispersive metamaterial with two central layers in a PT- symmetric arrangement is investigated under the oblique incidence of an electromagnetic wave. We have found a defect mode within the gap, and we have studied its optical properties under the influence of gain and loss distributed in these central layers. As a consequence of PT-symmetry in the system, we find that exceptional points can be attracted to or repelled from each other depending on which side of the frequency band under study. Below the plasmon frequency, repulsion occurs between pairs of exceptional points, while above it they attract each other.

Dynamics of a restricted (6 + 1)-vortex problem

This paper investigates the dynamics of a restricted (6 + 1)-vortex problem. The existence of nested equilateral triangle configurations depends on the position of two triangles, which can be divided into two situations: staggered arrangement and symmetrical arrangement. Firstly, we provide the existence conditions for the configuration and further discuss the stability of the configuration numerically. Secondly, we have established the global dynamics of the restricted point-vortex problem with configurations under different arrangements, including the dynamic behavior of equilibrium points, periodic orbits, homoclinic orbits, and heteroclinic orbits.

ArcaDB: A Disaggregated Query Engine for Heterogenous Computational Environments.

Modern enterprises rely on data management systems to collect, store, and analyze vast amounts of data related to their operations. Nowadays, clusters and hardware accelerators (e.g., GPUs, TPUs) have become a necessity to scale with the data processing demands in many applications related to social media, bioinformatics, surveillance systems, remote sensing, and medical informatics. Given this new scenario, the architecture of data analytics engines must evolve to take advantage of these new technological trends. In this paper, we present ArcaDB: a disaggregated query engine that leverages container technology to place operators at compute nodes that fit their performance profile. In ArcaDB, a query plan is dispatched to worker nodes that have different computing characteristics. Each operator is annotated with the preferred type of compute node for execution, and ArcaDB ensures that the operator gets picked up by the appropriate workers. We have implemented a prototype version of ArcaDB using Java, Python, and Docker containers. We have also completed a preliminary performance study of this prototype, using images and scientific data. This study shows that ArcaDB can speed up query performance by a factor of 3.5x in comparison with a shared-nothing, symmetric arrangement.

Investigations of the physical behavior of Cr2PX (X = C and N) MAX phases through first-principles calculations

MAX phases display an exclusive combination of ceramic and metallic characteristics, which makes them highly promising for various technological applications. This study investigated MAX phases of 211-type based on Cr2PX (X = C and N) by focusing on their physical properties, mainly the magnetic, electronic, and optical behaviors. The results obtained using the “density functional theory (DFT) based full-potential linearized augmented plane wave (FP-LAPW) method” matched those reported in the literature, indicating the reliability of the adopted methodology. The stabilities of the Cr2PX were validated by calculating their cohesive energies and phonon band structures. These compounds demonstrate identical energies for nonmagnetic, ferromagnetic, and antiferromagnetic phases and exhibit symmetrical arrangements of the “density of states (DOS)” for both up and down spins. Moreover, these MAX phases exhibit high optical absorption (∼10−6cm−1) and anisotropic reflectivity spectra, emphasizing the role of crystallographic orientation and their potential for applications in photovoltaics and other optical devices. These findings will provide valuable insights into the properties and behaviors of Cr2PX-based 211-MAX phases, thereby establishing the foundation for further research and potential applications across diverse areas.