Porous hierarchical structure has been widely used in engineering for its high specific strength and stiffness, improved corrosion-resistance and multifunctionality. The design of multi-scale topology optimization for such structures has been a hot topic during the past two decades. In this paper, a new hybrid MMC-density topology optimization method of cellular structures with quasi-periodic microstructures is proposed. The so-called ‘quasi-periodic’ means the microstructures in different macro points have similar topology but with different parameters. The key idea is to describe the microstructural topology using MMC and describe the micro layout using the variable density. Sensitivities of the structural compliance with respect to the two types of design variables are derived and gradient optimization method is applied to update the design variables. The presented numerical examples show that the quasi-periodic cellular structures have better performance than single-scale structures and periodic cellular structures. Numerical examples demonstrate the effectiveness of the proposed approach.

We address the problem of finding a unique graph embedding that best describes a graph's "topology". This issue is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default "topology" of periodic graphs.

A critical discussion on the computation of the dispersion diagram in periodic one-dimensional guiding structures is carried out. In particular, an analysis is presented of the pros and cons of combined methods that make use of full-wave simulations done with commercial software packages with further analytical post-processing based on simplifications brought by an equivalent circuit model of the structure. Some of the most common methods reported in the literature are reviewed and their advantanges and limitations highlighted. Our discussion is complemented with several selected numerical examples in order to discuss the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between the two halves of a symmetric unit cell of the periodic structure.

Three-dimensional flexible piezoresistive porous sensors have been used in health diagnosis and wearable devices. By utilizing 3D printed sacrificial mold casting with highly conductive polymer composites, porous sensors with high conductivity and complex structures were achieved. Traditional conductive polymer composites are usually heated using external heat sources, which are time and energy consuming. However, in this study, conductive porous sensors with triply periodic minimal surface (TPMS) structures were manufactured using self-resistance electric heating by utilizing the conductive nature of the polymers. The porous structures were designed based on Diamond (D), Gyroid (G), and I-WP (I) unit cells of the TPMS. The use of self-resistance electric heating has improved the compression performance and piezoresistive response of the structures. Among these structures, the D-based structure exhibited the maximum response strain (61 %), with a corresponding resistance response value of 0.97, which increased by 10.26 % compared to that of the structures heated by using the external heat sources. This study offers a new perspective on designing and optimizing porous materials with specific functionalities, particularly in the realm of flexible and portable piezoresistive sensors.

Laser-induced periodic surface structures (LIPSS) have gained significant attention due to their ability to modify the surface morphology of materials at the micro-nanoscale and show great promise for surface functionalization application. In this study, we specifically investigate the formation of LIPSS in silicon substrates and explore their impact on Surface-Enhanced Raman Spectroscopy (SERS) applications. This study reveals a stepwise progression of LIPSS formation in silicon, involving three distinct stages of LIPSS: 1) integrated Low-Spatial-Frequency LIPSS (LSFL) and High-Spatial-Frequency LIPSS (HSFL), 2) principally LSFL and 3) LSFL at the edge of the irradiated spot, elucidating the complex interplay between laser fluence, pulse number, and resulting surface morphology. Furthermore, from an application standpoint, these high-quality multi-scale periodic patterns lead to the next step of texturing the entire silicon surface with homogeneous LIPSS for SERS application. The potential of LIPSS-fabricated silicon substrates for enhancing SERS performance is investigated using thiophenol as a test molecule. The results indicate that the Au-coated combination of LSFL and HSFL substrate showcased the highest enhancement factor (EF) of 1.38 × 10^6. This pronounced enhancement is attributed to the synergistic effects of Localized Surface Plasmon Resonance (LSPR) and Surface Plasmon Polaritons (SPPs), intricately linked to HSFL and LSFL characteristics. These findings contribute to understanding LIPSS formation in silicon and their applications in surface functionalization and SERS, paving the way for sensing platforms.

In this research, a design method for the graded triply periodic minimal surface (TPMS) structures with lightweight, high-strength, and high sound absorption properties is proposed. The graded TPMS structures are controlled by linear, quadratic, and sine functions. Uniform TPMS and graded TPMS were manufactured by laser powder bed fusion (LPBF) with AlSi7Mg powder, and an acoustic impedance tube test, compression test, and digital image correlation (DIC) test were ap-plied to obtain the sound absorption and compression properties. The sound absorption coefficient of a uniform Gyroid increases as the number of layers and surface thickness increase, and it in-creases as element size decreases. The sound absorption peak shifts to low frequencies as the number of layers increases. The sound absorption property of Type-Ⅰ graded TPMS is superior to the Type-Ⅱ, and the G-LinearⅠ has the highest sound absorption properties among the three functions. It reveals that the graded TPMS has superior sound absorption performance at low and medium frequencies. The compression and DIC results of graded TPMS also show excellent mechanical properties and energy absorption characteristics.

Although the spanwise periodicity within the gap between two tandem circular cylinders has been observed by some researchers, there is a lack of systematic study on the properties of this pe-riodicity. For the spanwise periodicity within the gap, this study aims to ascertain its characteris-tics, its influences on the flow field, and its variation trend with increasing spacing ratio. By nu-merically simulating the flow around two tandem circular cylinders with a diameter ratio of d/D=0.6 and seventeen spacing ratios (L/D=1.00~6.00) at Re=3900, this study shows four flow re-gimes: Reattachment Flow (L/D=1.00~3.15), Bi-stable Flow (L/D=3.24), Intermittent Lock-in Co-shedding (L/D= 3.30~3.50) and Subharmonic Lock-in Co-shedding (L/D=4.00~6.00). Further, de-pending on the spanwise periodicity length of the time-averaged flow structures (i.e. Pz) within the gap, Reattachment Flow is, for the first time, subdivided into three new sub-flow regimes: Small-scale Periodic Reattachment (L/D=1.00~1.50, Pz/D=(0, 4]), Large-scale Periodic Reattachment (L/D=2.00~2.25, Pz/D>4) and Non-periodic Reattachment (L/D=2.50~3.15, no spanwise periodicity). The formation mechanisms are elaborated by analyzing the combined effect of both the L/D value and the spanwise-averaged time-averaged reattachment angle of the downstream cylinder. Moreover, this study proves that the newly-defined Small-scale Periodic Reattachment and Large-scale Periodic Reattachment are responsible for the pronounced asymmetry of the flow along the transverse direction within the gap. In addition, detailed flow properties and statistical pa-rameters are provided for each flow regime, such as velocity, vorticity, force coefficient, separa-tion/reattachment angle, Strouhal number and Q-criterion.

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

A multisystem chronic autoimmune disorder, Sjogren syndrome, is characterized by lymphocytic infiltrates in the exocrine glands. Keratoconjunctivitis sicca and xerostomia are the two pathognomic findings in Sjogren syndrome. Here, we present a case of a 30-year-oldan old Indian woman presenting with primary Sjogren syndrome. The clinical features, diagnostic modalities, treatment options, and management of complications have been discussed.

Background: The purpose of this review is to clarify the natural course of Benign Paroxysmal Torticollis (BPT) and to update the relationship of this disorder with migraine. BPT belongs to a group of “episodic syndromes that may be associated with migraine” and is diagnosed when according to diagnostic criteria of the International Classification of Headache Disorders, 3rd edition. It is present in infants and young children and it is an underdiagnosed manifestation, because it is not well recognized and in most cases with a benign evolution, but requires careful differential diagnosis. It was first described by Snyder in 1969 as a movement disorder, a cervical dystonia consequent to labyrinthic disorder.Materials and methods: The PubMed and Web of Science databases were consulted from 1968 to 2024, according to the Preferred Reporting Items for Systematic reviews and Meta-Analyses guidelines ,2020.( PRISMA)Results: 113 articles were identified, 86 selected and 20 considered for the purpose of this review. The clinical studies were considered in relation to evolution, cognitive and motor development, to genetic and not genetic etiology, to the relationship with migraine with and without aura, vestibular migraine, hemiplegic migraine, and paroxysmal vertigo.

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

We propose a novel electrochemical system to form precipitation patterns of Cu-Fe-based Prussian blue analogues (Cu-Fe PBA) in agarose gels, using an applied voltage to produce reactant ions. The spatiotemporal evolution, spatial distribution, and crystallite morphologies of the precipitates were investigated by visual inspection, Fe Kα intensity distribution measurements, and optical and scanning electron microscope observations. The precipitation patterns and their evolution depended on the applied voltage. Multicolored periodic precipitation bands were stochastically formed under cyclic alternating voltage (4 V for 1 h and then 1 V for 4 h per cycle). The distances between adjacent bands were randomly distributed (0.30 ± 0.25 mm). The sizes and shapes of the crystallites generated in the gel were position-dependent. Almost cubic but fairly irregular crystallites (0.1–0.8 μm) were formed in the periodic bands, whereas definitely cube-shaped crystallites (1–3 μm) appeared close to the anode. These cube-like reddish-brown crystallites were assigned to Cu-FeII PBA. In some periodic bands, plate-like blue crystallites (assigned to Cu(OH)2) were also present. Future issues for applications of the observed periodic banding were discussed.

Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.

Classical numerical methods for solving ordinary differential equations often produce less accurate results when applied to problems with oscillatory or periodic behaviour. To adapt them for such problems, they are usually modified using the exponential fitting technique. This adaptation allows for the construction of new methods from their classical counterparts. The new methods are usually more accurate, efficient and suitable for handling the oscillatory or periodic behaviour of the problem. In this work, we construct a two-parameter exponentially-fitted Taylor method suitable for solving oscillatory or periodic problems that possess two frequencies. The construction algorithm is based on a proposed six-step flowchart discussed by authors in related literature. Two standard test problems were used to illustrate the accuracy and performance of the proposed method.

In this paper, we introduce a simple yet powerful and working version of the molecular dynamics code using the Python 3.9 language. The code contents are published in the link given in the appendix 1. The structure and components of the program is given in detail using flowcharts and code snippets. The program consists of major features like velocity verlet integrator, thermostats, COM removal, input and output modules, virial, pressure, and other thermodynamic quantities estimation etc. The author believes that this program will be helpful to graduate students who perform research in molecular dynamics simulations who intend to write their own code instead of the sophisticated open source packages.

We study the crossed Andreev reflection and the nonlocal transport in the staggered graphene/superconductor/periodic line defect superlattice (LDGSL) junctions. The staggered pseudospin potential in the left graphene electrode suppress the local Andreev reflection, while the elastic cotunneling of K′ valley electrons is inhibited due to the exclusive rightward motion of K valley electrons in the right LDGSL electrode, thereby enabling the realization of perfect intravalley crossed Andreev reflection for incident electrons from the K′ valley. Meanwhile, the intravalley elastic cotunneling occurs while both local Andreev reflection and crossed Andreev reflection are completely eliminated for incident electrons in the K valley. Furthermore, the probability of intervalley crossed Andreev reflection scattering is significantly lower than that of intravalley CAR scattering across a broad range of incident angles and electron energies. Our results are helpful for designing the flexible and high-efficiency Cooper pair splitter based on the valley degree of freedom.

Abstract: A perspective is provided which illustrates the central role of quantum mechanics in the structure and periodically varying properties of atoms and in the formation of molecules. Despite having only about one hundred basic building blocks for all substances, chemistry is a subtle discipline due to it’s fundamentally quantum mechanical origin. The atoms, and their behavior as systematized in the Periodic Table, intimately reflect mechanisms natural to quantum mechanics but foreign to classical mechanics. Given their very small mass, the electrons form atomic structures only predictable by the use of quantum mechanics. Thereby the foundation of chemistry is totally dominated by quantum effects which are generally known only empirically, e.g. as in the Periodic Table. Recently these quantum effects have increasingly become known computationally, but not necessarily understood physically and therefore still challenge students and users of chemistry. In order to provide physical insight we extract here, from known facts and relations of quantum mechanics, but without reliance on detailed mathematics or numerical analysis, a simplest, yet fully consistent, physical explanation of atomic structure and periodically variable reactivity. Atomic reactivity is found to arise due to dynamical constraints on electron motion which lead to degeneracy in the atomic energy spectrum. There is a strong correlation between energy degeneracy and reactivity with the inert gas atoms found to display no degeneracy. Chemical bonding follows as a means of atomic reactivity relaxation and reduction of energy degeneracy, achieved by permanent electron rearrangement (ionic bonding) or by oscillatory electron motion between atoms (covalent bonding). Ionic bonding is directly related to the variable stability of atomic structures which extends from neutral atoms to atomic ions. These stable ions then form molecular structures by electrostatic attraction in neutral ionic clusters. The covalent bonding mechanism is fundamentally dynamical and interatomic since it depends directly on the facility with which electrons can move between atomic centers in a molecule. Both the ionic and the covalent mechanism, interatomic displacement and oscillation of electrons, are active in any bond between atoms of different species.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.

The vibration feature of weak gear fault is often covered in strong background noise, which makes it necessary to establish weak feature enhancement methods. Among the enhancement methods, stochastic resonance (SR) has the unique advantage of transferring noise energy to weak signals and has a great application prospection in weak signal extraction. But the traditional SR potential model cannot form a richer potential structure and may lead to system instability when the noise is too great. To overcome these shortcomings, the article presents a periodic potential underdamping stochastic resonance (PPUSR) method after investigating the potential function and system signal-to-noise ratio (SNR). In addition, system parameters are further optimized by using ant colony algorithm. Through simulation and gear experiments, the effectiveness of the proposed method was verified. We concluded that compared with the traditional underdamped stochastic resonance (TUSR) method, the PPUSR method had a higher recognition degree and better frequency response capability.

In this paper, an icosahedral non – body centered model to simulate the periodic structure of homogeneous particulate composites, by predicting the particle arrangement, is presented. This model has yielded three different variations which correspond at three different deterministic particle configurations. In addition, the concept of boundary interphase between matrix and inclusions was taken into account. Thus, the influence of particle vicinity was examined in parallel with the interphase concept on the thermomechanical properties of the overall material. Next, by the use of this model the authors derived a closed – form expression to estimate the thermal conductivity of this type of composites. To test the validity of the model, the theoretical values arising from the proposed formula were compared with other theoretical predictions obtained from several accurate formulae found in the literature and an adequate accordance was observed.

In this paper, a geometric body-centered model to simulate the periodic structure of unidirectional fibrous composites is presented. To this end, three prescribed configurations are introduced to predict in a deterministic manner the arrangement of internal and neighboring fibers inside the matrix. Thus, three different representative volume elements (RVEs) are established. Furthermore, the concept of the interphase has been taken into account, stating that each individual fiber is encircled by a thin layer of variable thermomechanical properties. Next, these three unit cells are transformed in a unified manner to a coaxial multilayer cylinder model. This advanced model includes the influence of fiber contiguity in parallel with the interphase concept on the thermomechanical properties of the overall material. Then, by the use of this model, the authors propose explicit expressions to evaluate the longitudinal and transverse thermal conductivity of this type of composite. The theoretical predictions were compared with experimental results, as well as with theoretical values yielded by some reliable formulae derived from other workers, and a reasonable agreement was found.

The article is focused on detailed framework process for hierarchized construction of periodic freight train paths (PFTPs) – allocation of pre-arranged railway capacity to freight rail operators. The framework process considers fluctuations in demand for capacity from freight rail opera-tors, so the quality of a freight train path is related with its construction priority. Introduced framework process aims to offer freight rail operators attractive train paths, with low number of scheduled stops, and this way enhance competitiveness and decrease energy consumption of freight railway as a factor for sustainable development. The proposed generic process is in-tended for all time horizons of capacity allocation. Correctness of the framework process is tested on the example of mainline Prague – Dresden, in the context of prospective (denser) mod-el passenger timetable.

We deal with Ulam stability of second order periodic linear differential equations with periodic damping. Necessary and sufficient condition for the Ulam stability of second order periodic linear differential equations is obtained by giving an Ulam stability theorem and an Ulam instability theorem. These results extend the conclusions in relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is given.

The two main strategies used in this study are the binary representation and the decomposition of a natural number into many compound functions of odd function and even function. The Collatz conjecture regarding odd even numbers in number theory can be examined and discussed using them in this way: The sequence created by the finite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 85 years.

Fish oil rich in docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), vitamin D₃ and natural astaxanthin sustainably extracted from anchovy fillet leftovers using biobased limonene only, can be conveniently stabilized by adsorption on periodic mesoporous silicas. The simplicity of the process, the high load of entrapped fish oil, and the biocompatible nature of silica support numerous forthcoming applications of this new class of “Omeg@Silica” materials.

A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.

Silicates are among the most abundant and important inorganic materials, not only in the Earth’s crust but also in the interstellar medium in the form of micro-/nano-particles or embedded in the matrices of comets, meteorites and other asteroidal bodies. Although the crystalline phases of silicates are indeed present in Nature, amorphous forms are also highly abundant. Here we report a theoretical investigation of the structural, dielectric and vibrational properties of the amorphous bulk for forsterite (Mg₂SiO₄) as a silicate test case by a combined approach of classical molecular dynamics (MD) simulations for structure evolution, and periodic quantum mechanical DFT calculations for electronic structure analysis. Using classical MD based on an empirical partial charge rigid ionic model within a melt-quenching scheme at different temperatures performed with the GULP 4.0 code amorphous bulk structures for Mg₂SiO₄ were generated using as initial guess the crystalline phase. This has been done for bulks with three different unit cell sizes adopting a super-cell approach; i.e., 1×1×2, 2×1×2 and 2×2×2. The radial distribution functions indicated a good degree of amorphisation of the structures. Periodic B3LYP-geometry optimizations performed with the CRYSTAL14 code on the generated amorphous systems were used to analyze their structure, to calculate their high frequency dielectric constants (ε_∞), and to simulate the IR, Raman and reflectance spectra, which were compared with the experimental and theoretical crystalline Mg₂SiO₄. The most significant changes of the physico-chemical properties of the amorphous systems compared to the crystalline ones are presented and discussed (e.g., larger deviations in the bond distances and angles, broadening of the IR bands, etc.), which are consistent with their disordered nature. It is also shown that by increasing the unit cell size the bulk structures present larger degree of amorphisation.

Children with history of prematurity are at higher risk of complications, comorbidities and iron deficiency. In this study we assess the prevalence of restless sleep disorder, as well as that of periodic leg movements during sleep (PLMS) in these children. Retrospective chart review of sleep studies in children aged 1-18 years, with history of prematurity. Only diagnostic studies in children without diagnosis of a genetic syndrome or airway surgery or tracheostomy were included. Three groups were compared, children with PLMS index&gt;5, children with restless sleep disorder (RSD), and children with neither elevated PLMS index nor RSD. During the study, 2,577 sleep studies were conducted. Ninety-two studies fit our criteria and were included in analysis. Median birth age was 31 weeks, interquartile range (IQR) 27-34 weeks. Thirty-two (34.8%) children were referred for restless sleep and 55 (59.8%) for snoring; after polysomnography 18% were found to have PLMS index &gt;5/hour, 14% fit the criteria for RSD. There were no statistically significant differences in polysomnographic parameters between the children with RSD, PLMS and the remaining group, except for lower obstructive apnea/hypopnea index (Kruskal-Wallis ANOVA 8.621, p=0.0135) in the RSD group (median 0.7, IQR 0.3-0.9) than in the PLMS (median 1.7, IQR 0.7-3.5), or than in the nonRSD/nonPLMS group (median 2.0, IQR 0.8-4.5). There was elevated frequency of RSD and elevated PLMS in children with history of prematurity that might be linked to the increased risk of iron deficiency in premature infants. These new results add new knowledge on the prevalence of RSD in these children.

Global warming has been increasing heat stress threat in animals which can be monitored by Temperature Humidity Index (THI). The present study describes the relationship of THI, calculated using 35 years period weather station data, and production performances of dairy cattle in a se-lected area of Bangladesh. The month January and June were identified as the coolest and hottest, respectively. Based on this outcome, every year in the month of January and June production performances of 10 crossbred cows with homogenous characteristics were monitored for a period of 5 years. The average THIMEAN value was found 17% higher in June as compared to January, and with this increment of THIMEAN average milk production was decreased 24.4% (p<0.05). The milk fat and protein content were also reduced (p<0.05) by 14.5 and 15.2%, respectively suggesting negative correlation as like as milk production. However, ash content was increased 15.3% that indicates a positive correlation. In addition, multiple regression analysis revealed each point increase in THIMEAN and rectal temperature, there was a decrease in milk yield 0.04 and 1.17 kg ECM, respectively. In contrary, each point increase in THIMEAN resulted 0.059 C increase of rectal temperature. Taken together, THIMEAN value calculated using metrological station data has distinct relationship with the production performances of lactating crossbred dairy cows.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

Autoinflammatory disorders encompass a wide range of conditions with systemic and neuro-logical symptoms, which can be acquired or inherited. These diseases are characterized by an abnormal response of the innate immune system, leading to an excessive inflammatory reac-tion. On the other hand, autoimmune diseases result from dysregulation of the adaptive im-mune response. Disease flares are characterized by systemic inflammation affecting the skin, muscles, joints, serosa, and eyes, accompanied by unexplained fever and elevated acute phase reactants. Autoinflammatory syndromes can present with various neurological manifestations, such as aseptic meningitis, meningoencephalitis, sensorineural hearing loss, and others. Early recognition of these manifestations by general neurologists can have a significant impact on the prognosis of patients. Timely and targeted therapy can prevent long-term disability by reducing chronic inflammation. This review provides an overview of recently reported neuroinflam-matory phenotypes, with a specific focus on genetic factors, clinical manifestations, and treatment options. General neurologists should have a good understanding of these important diseases.

Due to the numerous heat sources in electronic equipment, the periodic nature of stream-wise flow occurs in a cooling channel so often, necessitating the development of an effective technique to improve the heat-cooling convection in such a situation. This paper investigates thermal convection enhancement in a heated-block duct through the periodic boundary conditions using the element-by-element (EBE) treatment in a semi-implicit projection finite element method (FEM) through preconditioned conjugate gradient (PCG) solver. This paper used the time-mean Nusselt number ratio, friction factor, and thermal performance to study how installing rectangular cylinders in the channel works with periodic boundary conditions varying Reynolds numbers (100, 175, and 250). The outcomes show that the rectangular cylinders installed stream-wise above an upstream block promote thermal convection in the heated-block duct. However, increasing the number of rectangular cylinders can raise friction factor. As a result, the case for periodic boundary conditions with a rectangular cylinder above every two blocks has the best thermal performance.

Fouling represents a bottleneck problem for promoting the use of membranes in filtration and separation applications. It becomes even more persistent when it comes to the filtration of fluid emulsions. In this case, a gel-like layer that combines droplets, impurities, salts, and other materials form at the membrane's surface, blocking its pores. It is, therefore, a privilege to combat fouling by minimizing the accumulation of these droplets that work as seeds for other incoming droplets to cluster and coalesce with. In this work, we explore the use of the newly developed and novel periodic feed pressure technique (PFPT) in combating the fouling of ceramic membranes upon the filtration of oily water systems. The PFPT is based on alternating the applied transmembrane pressure (TMP) between the operating one and zero. A PFPT cycle is composed of a filtration half-cycle and a cleaning half-cycle. Permeation occurs when the TMP is set at its working value, while the cleaning occurs when it is zero. Three PFPT patterns were examined over two feeds of oily water systems with oil contents of 100 and 200ppm, respectively. The results show that the PFPT is very effective in minimizing the problem of fouling compared to a non-PFPT normal filtration. Furthermore, the overall drops in permeate flux during the cleaning half cycles are compensated by appreciable enhancement due to the significant elimination of fouling development such that the overall production of filtered water is even increased. Inspection of the internal surface of the membrane post rinsing at the end of the experiment proves that all PFPT cycles maintained the ceramic membranes as clean after a 2-hours operation. This can ensure a prolonged lifespan of the ceramic membrane use and a continuous greater permeate volume production. The advantage of the PFPT is that it can be implemented on existing units with minimal modification, ease of operation, and saving energy.

In the context of all-digital radar systems, phase-modulated continuous wave (PMCW) based on pseudorandom binary sequences (PRBSs) appears a prominent candidate modulation scheme for applications such as autonomous driving. Among the reasons for that are its simplified transmitter architecture and lower linearity requirements, e.g., compared to orthogonal-frequency division multiplexing radars, as well as its high velocity unambiguity and multiple-input multiple-output operation capability that are characteristic of digital radars. For appropriate operation of a PMCW radar, choosing a PRBS whose periodic autocorrelation function (PACF) has low sidelobes and high robustness to Doppler shifts is paramount. In this sense, this article performs an analysis of Doppler shift tolerance of the PACFs of typically adopted PRBSs in PMCW radar systems supported by simulation and measurement results. To accurately measure the Doppler-shift-induced degradation of PACFs, peak power loss ratio (PPLR), peak sidelobe level ratio (PSLR), and integrated-sidelobe level ratio (ISLR) were used as metrics. Furthermore, to account for effects on targets whose ranges are not multiples of the range resolution, oversampled PACFs are analyzed.

This paper addresses the study of the stress field in composites continua with the multiscale approach of the DECM (Discrete Element modeling with the Cell Method). The analysis focuses on composites consisting of a matrix with inclusions of various shapes, to investigate whether and how the shape of the inclusions changes the stress field. The purpose is to provide a numerical explanation for some of the main failure mechanisms of concrete, which is precisely a composite consisting of a cement-based matrix and aggregates of various shapes. Actually, while extensive experimental campaigns detailed the shape effect of concrete aggregates in the past, so far it has not been possible to model the stress field within the inclusions and on the interfaces accurately. The reason for this lies in the limits of the differential formulation, which is the basis of the most commonly used numerical methods. The Cell Method (CM), on the contrary, is an algebraic method that provides descriptions up to the micro-scale, independently of the presence of rheological discontinuities or concentrated sources. This makes the CM useful for describing the shape effect of the inclusions, on the micro-scale. When used together with a multiscale approach, it also models the macro-scale behavior of periodic composite continua, without losing accuracy on the micro-scale. The DECM uses discrete elements precisely to provide the CM with a multiscale approach.

Flow over a cluster of three equally spaced circular cylinders was studied by numerical simulation on base of the turbulent mode k-kl-ω for two incidence angles β=0° and 60°, at different Reynolds number,in this paper, flow interference pattern characteristics between cylinders, characteristics of force parameters and Strouhal number of each cylinder with different spacing ratios ranging from 1.5 to 4 at Re 8×104, 2×105and 2×106 had been obtained. At incidence angle β=0° and 60°, the wake was nearly symmetric if S/D≥2.0; at β=60°,S/D=1.5 and Re=2×105, the asymmetric periodic flow pattern occurred in the wake region which leaded to the significant effect on the surface mechanical parameters and Strouhal number which was found for the first time; the periodic flow regime of the wake region also occurred at S/D=1.35 and 1.5, without the same phenomenon at S/D=1.7 and 2.0; the phenomenon of periodic flow regime of the wake region was intrinsic and related to Reynolds number and space ratio. in addition, characteristics of force parameters of three cylinders mainly were affected by the interference between cylinders, at 1.5&lt;S/D&lt;4, which leaded to that the drag coefficient of three cylinders reduced with different Reynolds numbers. At incidence angle 60°, in subcritical and critical regime, the Strouhal numbers of the upstream cylinders were more than that of single cylinder, and with the enlargement of spacing ratio, the Strouhal number decreased; for the downstream cylinder , the Strouhal number is far less than that of single cylinder and with the enlargement of spacing ratio, the Strouhal number increases, which were another prominent flow inference influence. The results indicated the effect of flow interference between cylinders subjected to a cross flow over a cluster of three equally spaced cylinders on the flow pattern,surface mechanical parameters and Strouhal number.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

We use binary string to represent a natural number and show the composite procedure of odd-number and even-number functions, thus we propose full binary directed tree to represent the set of natural numbers and give another partition the natural number set to three sets: pure odd, pure even and mixed number. For the Collatz conjecture we make use of the parity of a natural number to analyse the sequence of iteration (or composite) of Collatz function and reduced Collatz function analog to the inverse function. We give tabular and binary strings to the algebra expression to state the sequence of Collatz, this is the key topic to proof the conjecture: the discrete powers of 2 can be changed to ultimately continuous powers of 2, finally get to pure even number and to the smallest number 1. The sequence created by the infinite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 87 years.

The exceptional performance of graphene has driven the advancement of its preparation technique and application. Laser-induced graphene (LIG), as a novel graphene preparation technique, has been applied in various fields. Graphene periodic structures created by LIG technique exhibit superhydrophobic characteristics and can be used for deicing and anti-icing applications, which are significantly influenced by the laser parameters. The laser surface treatment process was simulated by a finite element software analysis (COMSOL Multiphysics) to optimize the scanning parameter range, and the linear array surface structure were subsequently fabricated by the LIG technique. The generation of graphene was confirmed by Raman spectroscopy, and energy-dispersive X-ray spectroscopy. The periodic linear array structure were observed by Scanning electron microscopy (SEM) and confocal laser imaging (CLSM). In addition, CLSM testings, contact angle measurements, and delayed icing experiments were systematically performed to investigate the effect of scanning speed on surface hydrophobicity. The results show that the high quality and uniform graphene can be achieved using the laser scanning speed of 125 mm/s. The periodic linear array structures can obviously increase the contact angle and suppress delayed icing. Furthermore, these structures have the enhanced ability of the electric heating deicing, which can reach 100°C and 240°C within 15 s and within 60 s under the DC voltage power supply ranging from 3 to 7 V, respectively. These results indicate that the LIG technique can be developed to provide an efficient, economical, and convenient approach for preparing graphene and the hydrophobic surface array structure based on LIG has considerable potential for deicing and anti-icing applications.

\abstract{The existence of vorticies is well known in fluid mechanics and particularly in turbulence theory. In the context of the millennium problem of the Clay Institute on the existence (or not) of Global solutions in time of the Periodic Navier Stokes equations (PNS) results are now proposed to confirm that Global solutions do not exist in the general case of PNS defined on $\mathbb{T}^3$. This corresponds to part ($D$) proposition in the Navier Stokes problem as posted by C.Fefferman. Recent work has shown that for the Euler equations defined on the 3-Torus there exists a H\"older continuous solution for the third component of velocity $v_3$ at the center of each cell or cube of the 3-Torus Lattice. It has also been determined that as the kinematic viscosity changes from the corresponding value at $\nu=0$ to the fully viscous case for the Periodic Navier Stokes equations (PNS) at the value $\nu=1$ the solution reaches a peak ($\frac{\partial v_3}{\partial y_3} = 0$ ) in $y_3$. (third component of $\vec{r}=(y_1,y_2,y_3)$ in Cartesian co-ordinates) Here in the viscous case there exists a dipole which is not centered at the center of the cell of the Lattice. This immediately implies that since the dipole by definition has an equal in magnitude positive and negative peak in the third component of velocity, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere $\|\vec{r}\|=1$ and where a given cell of dimensions $[-1,1]^3$ is circumscribed on a sphere of radius $1$. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of $v_3$ wrt to surface normal $\vec{n}$ is zero including at $y_i, i=1\dots 3$ is zero at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. Here $\frac{\partial v_3}{\partial \vec{n}}= \vec{n}\cdot \nabla v_3$. Also a boundary condition on the sphere shows rotation of sphere. Finally as a result, on the sphere a solution for $v_3$ is obtained which is proven to be H\"older continuous and it is proven that it is possible to extend H\"older continuity on the sphere uniquely to all of the interior of the ball.}

In this paper, we present a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations. After the convergence analysis, we study the stability of this class by using the tools of complex discrete dynamics. This allows us to select those elements of the class with lower dependence on initial estimations. We verify by means of numerical tests that the stable members on quadratic polynomials perform better than the unstable ones, when applied to other non-polynomial functions. We also compare the performance of the best elements of the family with known methods, such as the schemes by Newton or Chun, among others, showing robust and stable behaviour.

The main result of this work is the estimation of the entropy mode accompanying a wave disturbance, observed at the atmosphere heights range of 90-120km. The study is the direct continuation and development of recent results on diagnosis of the acoustic wave with the separation on direction of propagation. The estimation of the entropy mode contribution relies upon the measurements of the three dynamic variables (the temperature, density and vertical velocity perturbations) of the neutral atmosphere measured by the method of the resonant scattering of radio waves on the artificial periodic irregularities of the ionospheric plasma. The measurement of the atmosphere dynamic parameters has been carried out on the SURA heating facility. The mathematical foundation of the mode separation algorithm is based on the dynamic projecting operator technique. The operators are constructed via the eigenvectors of the coordinate evolution operator of the transformed system of balance equations of the hydro-thermodynamics.

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists in a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

Fourier expansions by the polyharmonic-Neumann eigenfunctions showed improved convergence compared to the Fourier expansions by the classical trigonometric system due to the rapid decay of the corresponding Fourier coefficients. Based on this evidence, we investigate interpolations on a finite interval that are exact for the polyharmonic-Neumann eigenfunctions and show the same benefits. Further, we improve the convergence of the interpolations by applying the idea of quasi-periodicity, where the basis functions are periodic on a slightly extended interval. We show that those interpolations have much better convergence rates away from the endpoints of the approximation interval. Moreover, the interpolations are more accurate on the entire interval. We prove those properties for a specific case of the polyharmonic-Neumann eigenfunctions known as the modified Fourier system. For other basis functions, we provide evidence based on the results of numerical experiments.

Tantalum oxide thin films are deposited by DC reactive magnetron sputtering from a tantalum metallic target and oxygen as reactive gas. The reactive gas pulsing process (RGPP) is implemented to produce TaOx compounds with tunable chemical compositions. The argon mass flow rate is maintained constant whereas that of the oxygen gas is pulsed during the deposition. A constant pulsing period T = 10 s is used and the introduction time of the oxygen gas, namely the tON injection time, is systematically changed from 0 to 100 % of the pulsing period T. As the tON injection time increases, the chemical composition of as-deposited TaOx films is continuously changed from pure metallic tantalum to the over-stoichiometric Ta2O5 material. Analysis of the crystallographic structure by X-ray diffraction shows that the films adopt the body-centered cubic structure (metallic Ta) for the lowest tON injection time values (oxygen stoichiometry x &lt; 1.0) and become amorphous for the longest tON injection times. It is shown that the tON injection time is a key parameter to produce either homogeneous tantalum oxides, or periodic Ta/TaOx multilayers with alternations close to 3 nm. Similarly, optical transmittance spectra of the film/glass substrate system are recorded in the visible region and the electrical conductivity of the films is measured vs. temperature. Both exhibit a gradual evolution from metallic (300K = 8.17105 S m-1 with a null optical transmittance in the visible range) to semi-conducting (300K = 1.97103 S m-1 with a semi-transparent behavior) and finally to dielectric properties (300K &lt; 10-5 S m-1 for interferential films) as a function of the oxygen concentration in the films.

Inspired by amazing result obtained by Semay [1], this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication [2] but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq|^3/2 = πG/√2[(Σ^N_i=1 Σ^N_j=i+1 m_im_j)³/(Σ^N_k=1 m_k)]^1/2. This formulae is, of course, consistent with the Kepler's third law of 2-body system, and exact same as Semay's quantum result for identical bodies.

The effective macroscopic model describing interactions of a viscous compressible heat-conducting fluid and a two-level fine bristly thermoelastic structure is derived from microstructure by means of the Allaire–Briane multi-scale convergence method. This new model naturally generalizes the isothermal formulation earlier constructed by the authors in 2020, see in Siberian Electronic Mathematical Reports, vol. 17 (https://doi.org/10.33048/semi.2020.17.100). In applications, the established model can be used, for example, in description, with account of heat transfer phenomemon, of airflow near surface of plant’s leaf, in simulation of epithelium surfaces of blood vessels, and in design of biotechnological devices operating in liquids.

We show that the compound samarium hexaboride is a strong topological insulator using the eigenvalues of the space inversion operator in the low-energy limit of the periodic Anderson model. Additionally, we assume the presence of the ferromagnetic exchange interaction (M). A Dirac cone like feature in the surface state energy spectra is observed for M equals zero in a certain parameter range. For M not equal to zero, there is no Kramers degeneracy. We have been able to show that this phase corresponds to the quantum anomalous Hall state by calculating Berry curvature and the Chern number. Using Floquet theory, we further show that the access to a novel state with broken time reversal symmetry is possible due to the normal incidence of circularly polarized optical field on the surface of the compound despite M being absent.

Universal gravitation is investigated with principles of foundational classical (Newtonian) physics. The results reveal gravitation an atomic field action; hence, Newton’s law, although absolutely valid, unavoidably misleads in creating the impression of matter rather than waveform action. Six force constants fully define gravitation: (i) a waveform torque field ; (ii) an expansion force field ; (iii) a centripetal force field ; (iv) a matter-wave torque field (the force fields , and constitute gravitational inertial rest frame); (v) a Galilean acceleration field and (vi) nuclear inverse mass-squared centripetal force constant The inertial rest frame force constants sum up to give observational G = 2.266 + 2.61 + 2.61cos46^o) x 10^-11 = 6.689 x 10^-11 m³ kg^-1 s^-2. Notably, the procedure is able to account also for observational inclination of galaxies and their aligned conjunctions. An attempt is made to account for angular momentum quantization and rectilinear, parabolic or elliptic profile of objects in gravitational acceleration. Same quantitative expression, , defines the photon and gravitation thus uniquely unifying gravitation, electricity and magnetism; furthermore, the expression reveals the photon packed with tremendous energy amounting to some . It is argued that: (i) neither mass nor gravitation curves spacetime; (ii) the principles that sustain cosmic time-scale dynamic equilibrium, scale invariance and inertia are incompatible with quantum gravitation; and (iii) the cosmic vacuum field comprises gravitational (photonic) waves, hence the interferometer likely measures shock waves.

In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

In the work, the nuclei structure was modeled by a system of shells consisting of combinations of spherical and annular vortices. Having connected the spin and the magnetic moments of the nuclei with the dynamics of the outer shell of the nucleus, we determined its type and carried out a semiempirical calculation of the parameters of its structure for stable and unstable nuclear isotopes in the sequence of the order number Z from 1 to 37. Comparison of the obtained nuclear sizes with the radii of the electron shells of atoms made it possible to reveal a definite correlation. On the basis of it, it was concluded that the periodic law of Mendeleyev can determine the patterns in the change in the structure of the atomic nucleus.

We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.

Large-area nanostructuring of glasses using intense laser beam remains a difficult task due to the extreme non-linear absorption of the laser energy by the material. Precise optimization of the process parameters is essential for fabricating nanostructures with large area coverage. In this study, we report the findings on creating high spatial frequency LIPSS (HSFL) on borosilicate glass through direct laser writing, using a femtosecond laser with a wavelength λ = 800 nm, pulse duration τ = 35 fs, and repetition frequency frep = 1 kHz. The orientation of the HSFL was found to be parallel to the electric field vector. We measured the single pulse ablation threshold (Fth=3.87±0.26 J/cm2) and incubation factor (S=0.68±0.03) of Borosilicate glasses for precise control for large area surface structuring. Single-spot experiments indicate that uniform LIPSS formation is limited by melt formation inside the irradiated area for higher fluence and a larger number of irradiated laser pulses. The orientation of the scan axis with the laser beam polarization is found to be significantly influencing the uniformity of the large area processing. We found that the orientation of the scan axis with the laser beam polarization significantly affects the uniformity of large-area processing, with redeposition and melt formation being higher when the scan axis is perpendicular to the laser beam polarization. Large-area processing of the borosilicate glass surface is done by line-by-line scanning over the surface with a scan orientation parallel to the laser beam polarization. The optical characterization reveals that the transmittance and reflectance of the borosilicate glass decreased significantly after processing. Also, the wettability of the surface has been changed from hydrophilic to super hydrophilic after processing. These chemical contamination-free and uniformly distributed structures have potential applications in optics, microfluidics, photovoltaics, and biomaterials.

For any odd positive integer $x$, define $(x_n)_{n\geqslant 0} $ and $(a_n )_{n\geqslant 1} $ by setting $x_{0}=x, \,\, x_n =\cfrac{3x_{n-1} +1}{2^{a_n }}$ such that all $x_n $ are odd. The 3x+1 problem asserts that there is an $x_n =1$ for all $x$. Usually, $(x_n )_{n\geqslant 0} $ is called the trajectory of $x$. In this paper, we concentrate on $(a_n )_{n\geqslant 1} $ and call it the E-sequence of $x$. The idea is that, we consider any infinite sequence $(a_n )_{n\geqslant 1} $ of positive integers and call it an E-sequence. We then define $(a_n )_{n\geqslant 1} $ to be $\Omega-$convergent to $x$ if it is the E-sequence of $x$ and to be $\Omega-$divergent if it is not the E-sequence of any odd positive integer. We prove a remarkable fact that the $\Omega-$divergence of all non-periodic E-sequences implies the periodicity of $(x_n )_{n\geqslant 0} $ for all $x_0$. The principal results of this paper are to prove the $\Omega-$divergence of several classes of non-periodic E-sequences. Especially, we prove that all non-periodic E-sequences $(a_n )_{n\geqslant 1} $ with $\mathop {\overline {\lim } }\limits_{n\to \infty } \cfrac{b_n }{n}>\log _23$ are $\Omega-$divergent by using the Wendel's inequality and the Matthews and Watts's formula $x_n =\cfrac{3^n x_0 }{2^{b_n }}\prod\limits_{k=0}^{n-1} {(1+\cfrac{1}{3x_k })} $, where $b_n =\sum\limits_{k=1}^n {a_k } $. These results present a possible way to prove the periodicity of trajectories of all positive integers in the 3x + 1 problem and we call it the E-sequence approach.

GaN ultraviolet photodetector with metal-semiconductor-metal structure is achieved by growing on a periodic trapezoid column-shape patterned sapphire substrate using metalorganic chemical vapor deposition. Under 5-V reverse bias, the photodetector fabricated on such patterned sapphire substrate exhibits a lower dark current, a higher photocurrent, and a 476 % enhancement in the maximum responsivity as compare with those of the photodetector fabricated on conventional flat sapphire substrate. It is also found that the much larger UV-to-visible rejection ratio and the fact that responsivity drops in a smaller cut-off region are observed from photodetector fabricated by using a periodic trapezoid column-shape patterned sapphire substrate. These phenomena may all be attributed to the reduction of threading dislocation density and the improved quality of GaN film, as well as the internal reflection and/or scattering effect on the interface between GaN film and the periodic trapezoid column-shape pattern of the substrate.

In this study, an optimized multi-material system was designed and developed to print samples in various applications, including biomedical fields (e.g., mandibular bone loss). To improve the mechanical and biological properties of scaffolds utilized for dental bone loss applications, a multi-material setup was devised, which employs digital light processing technology. This setup consists of a linear system comprising two resin vats and one ultrasonic cleaning tank, enabling the integration of diverse materials and structures to optimize the composition of the scaffold. This approach was used to print multi-material PLLA scaffolds containing 20 wt.%. HA on the interior side, and PLLA containing 1 wt.% GO on the exterior surface of the scaffold, which were evaluated mechanically and biologically after printing. The scaffold was designed using a triply periodic minimal surface (TPMS) lattice structure, which is known to possess favorable mechanical and biological properties. Various multi-material samples were successfully printed and evaluated to illustrate the multiple-material setup's potential for ensuring proper function, cleaning, and adequate interface bonding. By numerically evaluating several TMPS structures, a novel Gyroid TPMS scaffold with a nominal porosity of 50% was developed and validated experimentally. The biological properties of the scaffolds were also evaluated, including surface morphology, (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) MTT assay, and cell adhesion. Based on the results, multi-material components with the least contaminations with suitable mechanical and biological properties were successfully printed. By combining PLLA-HA and PLLA-GO, this innovative technique holds tremendous potential for enhancing the effectiveness of regenerative procedures in the field of dentistry.

This paper proposes a radiation pattern synthesis of the almost periodic antenna arrays including mutual coupling effects (that extracted by the Floquet analysis according to our previous work), which principally has a high directivity and large bandwidth. For modeling the given structures, the moment method combined with the Generalized Equivalent Circuit (MoM-GEC) is proposed. The artificial neural network (ANN) as a powerful computational model has been successfully applied to the antenna array pattern synthesis. The results showed that the multilayer feedforward neural networks are rugged and can successfully and efficiently resolve various distinctive complex almost periodic antenna patterns (with different source amplitudes) (in particular, both periodic and randomly aperiodic structures are taken into account). However, the artificial neural network (ANN) is capable of quickly producing the synthesis results using generalization with the early stopping (ES) method. A significant time gain and memory consumption are achieved by using this given method to improve the generalization (called early stopping). To justify this work, several examples are developed and discussed.

The understanding of various health-oriented vital sign data generated from body sensor networks (BSN) and discovery of the association between the generated parameters is an important task that may assist and promote important decision making in healthcare. For example, in a smart home scenario where the occupants’ health status is continuously monitored remotely, it is essential to provide required assistance when an unusual or critical situation is detected in their vital sign data. In this paper, we present an efficient approach to mine the incomplete (partial) periodic patterns obtained from BSN data. In addition, we employ a correlation test on the generated patterns and introduce the productive-associated partial periodic frequent patterns as the set of correlated partial periodical frequent items. The combination of these measures has the advantage of empowering healthcare providers and patients for quality of diagnosis, and also for better treatment and smart care, especially for the elderly people at smart home. We developed an efficient algorithm named PPFP-Growth (Productive Periodic Frequent Pattern growth) to discover all productive associated partial periodic patterns using these measures. PPFP-Growth is efficient, and the productiveness measure removes uncorrelated periodic items. An experimental evaluation on synthetic and real datasets shows the efficiency of the proposed PPFP-Growth algorithm, and can filter a huge number of partial periodic patterns to reveal only the correlated ones.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

For the KdV-Burgers equations on cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equations describe a medium which is both dissipative and dispersive. Symmetries, invariant solutions and conservation laws are investigated. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock and a median of the oscillating part is found.

Abstract: A new method for constructing exact solutions of the General Relativity equations for a dusty matter with fractal property is proposed. This method allows to find the solution of the GR-equations in terms of matter velocities : the connection coefficients and the Ricci tensor of space-time are expressed in terms of matter velocities; the metric tensor and the matter density are found as functions of velocity from the GR-equations. The connection coefficients and the Ricci tensor are invariant with respect to the discrete scaling transformation of velocity , where is constant. Therefore, the found solution can be used to simulate the fractal properties of the cosmic web in terms of matter velocities. This solution includes isotropic and anisotropic distributions of matter density. In an isotropic case, there is a class of exact solutions including both the well-known Friedmann’s solution and a solution with a periodic distribution of the matter density in space. This last solution may be used to simulate the quasi-periodic distribution of matter in the cosmic web. It is possible that, the cosmic web and its fractal properties are the space-time primary properties. These properties are described with a deformation tensor of the space-time.

Patients with sAID are a population at high risk of severe COVID outcomes but evidence on the efficacy of SARS-CoV-2 vaccination in this group of patients is scarce. To investigate the efficacy of SARS-CoV-2 vaccination in patients with systemic autoinflammatory diseases (sAID) receiving interleukin-1 inhibition is important. Vaccination responses from 100 sAID patients most of whom were treated with IL-1inhibitors (N=96) and 100 healthy controls (HC) were ana-lyzed. After 2nd SARS-CoV-2 vaccination, sAID patients showed similar anti-SARS-CoV-2 anti-body responses (mean (SD): 6.7 (2.7)) compared to HC (5.7 (2.4)) as well as similar neutralizing antibodies (85.1 ±22.9% vs. 82.5 ±19.7%). Anti-SARS-CoV-2 antibody responses and neutralizing antibodies were similar in sAID patients after SARS-CoV-2 infection and double vaccination. Furthermore, while antibodies increased after 1st and 2nd vaccination in sAID patients they did not further increase after 3rd and 4th vaccination. No difference was found in antibody responses between anakinra and anti-IL-1 antibody treatments and also the additional use of colchicine or other drugs did not impair vaccination responses. Primary and booster SARS-CoV-2 vaccination lead to protective antibody responses in sAID patients, which are at the same level of vaccination responses in HC and in sAID patients after SARS-CoV-2 infection. Immunomodulatory treatments used in sAID do not seem to affect antibody responses to the SARS-CoV-2 vaccine.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

This study investigates the effectiveness of a range of timber-based solutions for seismic and energy retrofitting of existing masonry buildings. These solutions are designed not only to prevent structural collapse during earthquakes but also to create integrated interventions that enhance thermo-physical performance and reduce emissions in existing buildings. Various case scenarios were considered and both mechanical and energetic behavior post-intervention were evaluated. Timber-engineered products serve as foundational components for the retrofit approach, encompassing one-dimensional vertical elements (strong-backs) and various types of panels (cross-laminated timber panels, laminated veneer lumber panels, and oriented strand board panels). The analyzed retrofit techniques share a common principle, involving the attachment of these timber-based elements to the building's wall surfaces through mechanical point-to-point connections. The proposed solutions integrate strong-backs and timber panels with membranes and insulation layers, yielding cohesive and highly effective interventions. Finite element modeling was employed to analyze the mechanical and thermal responses of the retrofitted walls. A comprehensive comparative analysis of various techniques was conducted to determine the most effective solution for each specific scenario.

The article analyzes the problems connected with ensuring the coordinated operation of slipway drives that arise during the launch of a ship. The dynamic model of load of the electric drive of the ship's cart is obtained taking into account the peculiarities of the construction of the ship-lifting complex, which allows to analyze the influence of external factors and random influences during the entire process of launching the ship. A linearized mathematical model of the dynamics of a complex vessel movement in the process of descent in the space of states is developed, which allows to identify the mode of operation of the multi-drive system, taking into account its structure. The analysis of efficiency of application of recurrent methods of identification (stochastic approximation and least squares) of the parameters of the linearized model in the space of states is carried out. A decision support system has been developed in the automated system of operational control by the module for estimating the situation and the control synthesis to ensure a coherent motion of a complex ship-carts object in a two-phase environment.

In this paper, we introduce a new formulation based on Floquet (Fourier) spectral analysis combined with a spectral modulation technique (and its spatial form) to study strongly coupled sublattices predefined in the infinite and large finite extent of almost periodic antenna arrays (e.g metasurfaces). This analysis is very relevant for dense massive MIMO, intelligent surfaces, 5G, and 6G applications (used for very small areas with a large number of elements such as millimeter and terahertz waves applications). The numerical method that is adopted to model the structure is the method of moments simplified by equivalent circuits MoM GEC. Other numerical methods (as the ASM array scanning method and windowing Fourier method) used this analysis in their kernel that to treat periodic and pseudo-periodic (or quasi-periodic) arrays.

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.

We delve into the axion-dilaton model within the supergravity framework, with a specific focus on the intricacies of domain wall construction and stability. Employing holographic vitrification, we unravel the dynamics of domain wall formation in gauge theories featuring periodic vacuum structures. Our model, incorporating a QCD-like axion term and a stabilizing dilaton, undergoes scrutiny for conductivity variations under weak disorder. The investigation reveals the model's resilience, manifesting near-perfect conductivity under mild disorder conditions. However, the rigorous mathematical motivation for the holographic setup demands further elucidation. The scattered nature of our results prompts the necessity for a more systematic interpretation of QCD phenomena and conductivity transitions. This study contributes to the mathematical understanding of the axion-dilaton model's behavior, highlighting the imperative for a refined holographic framework and a more coherent interpretation of observed phenomena.