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.

The aim of this work is to study the zonally asymmetric stratopause that occurred in the Arctic winter of 2019/2020, when the polar vortex was particularly strong and there was no sudden stratospheric warming. Aura Microwave Limb Sounder temperature data were used to analyze the evolution of the stratopause with a particular focus on its zonally asymmetric wave 1 pattern. There was a rapid descent of the stratopause height below 50 km in the anticyclone region in mid-December 2019. The descended stratopause persisted until mid-January 2020 and was accompanied by a slow descent of the higher stratopause in the vortex region. The results show that the stratopause in this event was inclined and lowered from the mesosphere in the polar vortex to the stratosphere in the anticyclone. It was found that the vertical amplification of wave 1 between 50 km and 60 km closely coincides in time with the rapid stratopause descent in the anticyclone. Overall, the behavior contrasts with the situation during sudden stratospheric warmings when the stratopause reforms at higher altitudes following wave amplification events. We link the mechanism responsible for coupling between the vertical wave 1 amplification and this form of zonally asymmetric stratopause descent to the unusual disruption of the quasi-biennial oscillation that occurred in late 2019.

The process of senescence (aging) is largely determined by the action of wild-type genes. For most organisms, this does not reflect any adaptive function of senescence, but rather evolutionary effects of declining selection against genes with deleterious effects later in life. To understand aging requires an account of how evolutionary mechanisms give rise to pathogenic gene action and late-life disease, that integrates evolutionary (ultimate) and mechanistic (proximate) causes into a single explanation. A well-supported evolutionary explanation by G.C. Williams argues that senescence can evolve due to pleiotropic effects of alleles with antagonistic effects on fitness and late-life health (antagonistic pleiotropy, AP). What has remained unclear is how gene action gives rise to late-life disease pathophysiology. One ultimate-proximate account is T.B.L. Kirkwood’s disposable soma theory. Based on the hypothesis that stochastic molecular damage causes senescence, this reasons that aging is coupled to reproductive fitness due to preferential investment of resources into reproduction, rather than somatic maintenance. An alternative and more recent ultimate-proximate theory argues that aging is largely caused by programmatic, developmental-type mechanisms. Here ideas about AP and programmatic aging are reviewed, particularly those of M.V. Blagosklonny (the hyperfunction theory) and J.P. de Magalhães (the developmental theory), and their capacity to make sense of diverse experimental findings is described.

Background: Pediatric Rapid Response Teams (RRTs) are expected to significantly lower pediatric mortality in healthcare settings. This study evaluates RRTs' effectiveness in decreasing cardiac arrests and unexpected Pediatric Intensive Care Unit (PICU) admissions. Methods: A quasi-experimental study (2014-2017) at King Abdulaziz University Hospital, Jeddah, Saudi Arabia, involved 3,261 pediatric inpatients, split into pre-intervention (1,604) and post-intervention (1,657) groups. The intervention entailed pediatric specialists collaboratively managing acute decompensations following set protocols. Results: RRT was activated 471 times, primarily for respiratory distress (29.30%), sepsis (22.30%), clinical anxiety (13.80%), and hematological abnormalities (6.7%). Family concerns triggered 0.1% of activations. Post-RRT implementation, unplanned PICU admissions significantly reduced (RR = 0.552, 95% CI 0.485-0.628, P < 0.0001), and non-ICU cardiac arrests were eliminated (RR = 0). Patient care improvement was notable, with a -9.61 coefficient for PICU admissions (95% CI: -12.65 to -6.57, P < 0.001) and a -1.641 coefficient for non-ICU cardiac arrests (95% CI: -2.22 to -1.06, P < 0.001). Sensitivity analysis showed mixed results for PICU admissions, while zero-inflation Poisson analysis confirmed a reduction in non-ICU arrests. Conclusions: The deployment of pediatric RRTs is associated with fewer unexpected PICU admissions and non-ICU cardiopulmonary arrests, indicating improved PICU management. Further research using robust scientific methods is necessary to conclusively determine RRTs' clinical benefits.

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.

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.

A simple bounded stochastic motion is employed for modelling equity price dynamics under shocks, where the prices are constrained to lie between two positive bounds. While the stochastic process has an inaccessible boundary, the other boundary is quasi-bounded, implying that the boundary can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the boundary can thus provide an indicator of possible risk of equities under price shocks. Empirical calibration of model parameters of the proposed process for equities can be performed easily due to the availability of an analytically tractable probability density function which generates fat-tailed distributions consistent with empirical observations. The volatility and mean-reversion of the S&P500 dynamics calibrated by the process is positively and negatively co-integrated respectively with the VIX index representing the level of market distress. The process captures the high likelihood of Hertz’s default about two months earlier, using only information until that point, and before the firm filed for Chapter 11 bankruptcy in May 2020 as a result of the Covid-19 pandemic. Empirical calibration of the process for GameStop’s stock price shows that the short squeeze of the stock occurred when the condition for breaching an upper boundary was met on 14 January 2021, i.e., about two weeks before major short sellers closed out their positions with significant losses. The trading volume of the stock was positively co-integrated with the probability leakage ratio.

The application of the sensors optical fiber in the areas of scientific instrumentation and industrial instrumentation is very attractive due to its numerous advantages. In the industry of civil engineering for example, quasi-distributed sensors made with optical fiber are used for reliable strain and temperature measurements. Here, a quasi-distributed sensor in the frequency domain is discussed. The sensor consists of a series of low-finesse Fabry-Perot interferometers where each Fabry-Perot interferometer acts as a local sensor. Fabry-Perot interferometers are formed by pairs of identical low reflective Bragg gratings imprinted in a single mode fiber. All interferometer sensors have different cavity length, provoking the frequency-domain multiplexing. The optical signal represents the superposition of all interference patterns which can be decomposed using the Fourier transform. The frequency spectrum is analyzed and sensor´s properties were defined. Following, a quasi-distributed sensor was numerically simulated. Our sensor simulation considers sensor properties, signal processing, noise system and instrumentation. The numerical results show the behavior of resolution vs. signal-to-noise ratio. From our results, the Fabry-Perot sensor has high resolution and low resolutions. Both resolutions are conceivable because the FDPA algorithm elaborates two evaluations of Bragg wavelength shift

In this paper, quasi-static axial compression tests are performed on the nodal Moso bamboos to study the size effect on energy absorption of the bamboos and the damage pattern of the multiple bamboo columns. Experimental results show that under the same moisture content, growth age and growing environment, the specific energy absorption (SEA) of the test samples increases with the increase of the out-diameter and thickness of the bamboo columns, indicating that size effect exists for energy absorption of the Moso Bamboos. For the multiple bamboo columns, there are mainly three failure modes for the constituent single bamboo columns: splitting above the node, splitting below the node and splitting through the node. Also, the tensile tests are conducted on three kinds of dog-bone shaped bamboo samples to investigate the macroscopic tensile fracture mode in the longitudinal direction of Moso bamboos. Results show that there is no direct relationship between the fracture pattern and moisture content of the bamboos, as well as the growth age of the bamboos. However, the tensile loading rate and the shape of the dog-bone shaped bamboo sample could affect the macroscopic fracture pattern of the bamboos in some cases.

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.

Induction heating (IH) technology is widely recognized and utilized in residential applications due to its high efficiency and safe operating characteristics. Resonant inverter circuits are widely used in IH systems because of their high efficiency and ability to perform soft-switching. Among the various resonant inverters used in IH systems, the single-switch quasi-resonant (SSQR) inverter topology is typically preferred for low-cost and low-output-power applications. Despite its cost advantage, the SSQR topology has a relatively narrow soft-switching range, which can be unstable depending on the electrical parameters of the load and the resonant converter circuit. Accurately determining the capacitance value of the resonant capacitor and the inductance value of the induction coil, which are the key circuit elements of the SSQR induction cooker, is crucial for designing a reliable, efficient, and durable cooking system. In other words, there exists a critical relationship between the resonant converter circuit parameters, load characteristics, and safe operating conditions. Additionally, when considering closed-loop control methods used for power control and safety, selecting appropriate resonant circuit elements becomes vital in ensuring both reliable and efficient operation. This paper focuses on a novel and simplified design method for the SSQR inverter utilized in household appliances. The proposed method and its advantages in terms of the safe operating area of the switch are theoretically investigated and verified through simulations and prototype circuits.

Tick-borne encephalitis virus (TBEV) is a pathogenic, enveloped, positive-stranded RNA virus in the family Flaviviridae. Structural studies of flavivirus virions have primarily focused on mosquito-borne species with only one cryo-electron microscopy (cryo-EM) structure of a tick-borne species published. Here, we present a 3.3 Å cryo-EM structure of the TBEV virion of the Kuutsalo-14 isolate, confirming the overall organisation of the virus. We observe conformational switching of the peripheral and transmembrane helices of M protein, which can explain the quasi-equivalent packing of the viral proteins and highlights their importance in stabilizing the membrane protein arrangement in the virion. The residues responsible for the M protein inter-actions are highly conserved in TBEV but not in the structurally studied Hypr strain, nor in mosquito-borne flaviviruses. These interactions may compensate for the lower number of hydrogen bonds between E proteins in TBEV compared to the mosquito-borne flaviviruses. The structure reveals two lipids bound in the E protein, which are important for virus assembly. The lipid pockets are comparable to those recently described in mosquito-borne Zika, Spondweni, Dengue, and Usutu viruses. Our results thus advance the understanding of tick-borne flavivirus architecture and virion-stabilising interactions.

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.

The paper proposes an approach to determine the optimal number of medical specialists in the region. According to the author's theoretical model, in order to maximize public welfare, the marginal contribution of the last physician recruited to the growth of the public utility function should be equal to the marginal cost of attracting him and providing conditions for his work. To empirically assess the contribution of physicians to the number of lives saved, the CVD mortality rate is modeled using the instrumental variable method. On average, a 1% increase in the number of cardiologists is associated with a 0.6% decrease in cardiovascular mortality. At the level of provision with cardiologists in the amount of 1 per 100 thousand people, their marginal contribution to the number of lives saved is not less than 129 per 100 thousand people, with a further decrease by 5 people with the increase in the level of provision by 1 unit. The use of the obtained results will increase the validity of managerial decisions and in determining the optimal level of doctors when choosing between alternative possibilities of spending money on hiring doctors of different profiles or other expenses, especially in the case of limited resources.

The pore-throat radius of shale oil reservoir is extremely small, and it is difficult to accurately obtain the absolute permeability and oil-water two-phase relative permeability of actual oil reservoir through conventional core experiments. However, these parameters are very important for reservoir numerical simulation. In this paper, a method for characterizing flow parameters based on pore network model that considers differential pressure flow and diffusion flow is proposed. Firstly, a digital core was reconstructed using focused ion beam scanning electron microscopy (FIB-SEM) from the Gulong shale reservoir in the Songliao Basin, China, and a pore network model was extracted. Secondly, quasi-static single-phase flow and two-phase flow equations considering diffusion were established in the pore network model. Finally, pore throat parameters, absolute permeability, and oil-water two-phase permeability curves were calculated, respectively. The results show that the pore throat distribution of Gulong shale reservoir is mainly concentrated in the nanometer scale, the mean pore radius is 87 nm, the mean throat radius is 41 nm, and the mean coordination number is 3.97; The calculated permeability considering diffusion is 0.000124mD, which is approximately twice the permeability calculated without considering diffusion; The irreducible water saturation of the Gulong shale reservoir is approximately 0.26, and the residual oil saturation is approximately 0.73. The method proposed in this paper can provide an important approach for characterizing the flow parameters of similar shale oil reservoirs.

A quasi-two-dimensional (quasi-2D) modelling approach is introduced to mimic transverse mixing of an inflow into a river from one of its banks, either an industrial outfall or a tributary. The concentrations of determinands in the inflow vary greatly from those in the river, leading to very long mixing lengths in the river downstream of the inflow location. Ideally, a two-dimensional (2D) model would be used on a small scale to capture the mixing of the two flow streams. However, for large-scale applications of several hundreds of kilometres of river length, such an approach demands too many computational resources and too much computational time, especially if the application will at some point require ensemble input from climate-change scenario data. However, a one-dimensional (1D) model with variables varying in the longitudinal flow direction but averaged across the cross-sections is too simple of an approach to capture the lateral mixing between different flow streams within the river. Hence, a quasi-2D method is proposed in which a simplified 1D solver is still applied but the discretisation of the model setup can be carried out in such a way as to enable a 2D representation of the model domain. The quasi-2D model setup also allows secondary channels and side lakes in floodplains to be incorporated into the discretisation. To show proof-of-concept, the approach has been tested on a stretch of the lower Athabasca River in Canada flowing through the oil sands region between Fort McMurray and Fort MacKay. A dye tracer and suspended sediments are the constituents modelled in this test case.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging material seem to be promising due to their low weight, structure and production price. Based on the review, the linear low-density polyethylene material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a Constitutive material model to be used in future design by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of the linear low-density polyethylene under static and dynamic loading. The quasi-static measurement is realized in two perpendicular principal directions and is supplemented by a test measurement in the 45 degrees direction, i.e. exactly between the principal directions. The quasi-static stress-strain curves are analyzed as an initial step for dynamic strain rate dependent material behavior. The dynamic response is tested in the drop tower using a spherical impactor hitting the flat material multi-layered specimen at two different energy levels. The strain rate dependent material model is identified by optimizing the static material response obtained in the dynamic experiments. The material model is validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

To improve the understanding of soil–pile interaction of laterally loaded piles, the quasi-static test of pile group foundation in silty clay with 5 foundation piles arranged in cross shape is carried out. The direct measurement-based p–y curves at different depths showed nonlinear behavior, in which the initial stiffness and ultimate soil reaction increased as the depth increased. The loading displacement amplitude corresponding to the failure of each foundation pile in the high axial compression reinforced concrete pile group foundation is given as follows: the front-end nappe foundation pile (#3 pile) is 6mm, the middle pile is 16mm, the front-end nappe foundation pile is 20mm, and the loading displacement amplitude of side pile is 24mm. In silty clay, due to the existence of pile group effect, the edge effect has little effect on the horizontal foundation bed coefficient of foundation pile in pile group, while the influence of masking effect on the horizontal foundation bed coefficient of each foundation pile in pile group is not related to the position of pile, but only to the existence of masking effect, and the influence of different columns of masking effect on the horizontal foundation bed coefficient is the same.

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

The independent set, IS, on a graph $G=(V,E)$ is $V^{*}\subseteq V$ such that no two vertices in $V^{*}$ have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. $V^{*}\subseteq V$ is a vertex cover, i.e. VC of $G=(V,E)$ if every $e\in E$ is incident upon at least one vertex in $V^{*}$ . $V^{*}\subseteq V$ is dominating set, DS, of $G=(V,E)$ if $\forall v\in V$ either $v\in V^{*}$ or $\exists u\in V^{*}$ and $(u,v)\in E$ . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if $k=\Theta (log\mid V\mid )$ then MIS, MVC and MDS can be computed in polynomial time and if $k=O\left({(log\mid V\mid )}^{\alpha }\right)$ , where $\alpha <1$ , then MCV and MCD can be computed in polynomial time. If $k=\Theta \left({(log\mid V\mid )}^{1+ϵ}\right)$ , for $ϵ>0$ , then MIS, MVC and MDS require quasi-polynomial time. If $k=\Theta (log\mid V\mid )$ then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

Rubble stone masonry walls are widely diffused in most of the cultural and architectural heritage of historical cities. The mechanical response of such material is rather complicated to predict due to their composite nature. Vertical compression tests, diagonal compression tests, and shear-compression tests are usually adopted to experimentally investigate the mechanical properties of stone masonries. However, further tests are needed for the safety assessment of these ancient structures. Since the relation between normal and shear stresses plays a major role in the shear behavior of masonry joints, governing the failure mode, triplet test configuration was here investigated. First, the experimental tests carried out at the laboratory (LPMS) of the University of L'Aquila on stone masonry specimens were presented. Then, the triplet test was simulated by using the Total Strain Crack Model, which reflects all the ultimate states of quasi-brittle material such as cracking, crushing and shear failure. The goal of the numerical investigation was to evaluate the shear mechanical parameters of the masonry sample, including strength, dilatancy, normal and shear deformations. Furthermore, the effect of (i) confinement pressure and (ii) bond behavior at the sample-plates interfaces were investigated, showing that they can strongly influence the mechanical response of the walls.

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.

Previous studies generally reckon that the full converter-base wind power generation (FCWG) is a ’decoupled’ power source from the grid, which hardly participates in electromechanical oscillations. However, it is found recently that strong interaction could be induced which might incur severe resonance incidents in electromechanical dynamic timescale. In this paper, the participation of FCWG in electromechanical dynamics is extensively investigated, and particularly, an unusual transition of electromechanical oscillation mode (EOM) is uncovered for the first time. The detailed mathematical models of open-loop and closed-loop power systems are firstly established, and modal analysis is employed to quantify the FCWG participation in electromechanical dynamics, with two new mode identification criteria, i.e., FCWG dynamics correlation ratio (FDCR) and quasi-electromechanical loop correlation ratio (QELCR). On this basis, the impact of different wind penetration levels and controller parameter settings on the participation of FCWG is investigated. It is revealed that if an FOM has a similar oscillation frequency to the system EOMs, there is a high possibility to induce strong interactions between FCWG dynamics and system electromechanical dynamics of the external power systems. In this circumstance, an interesting phenomenon may occur that an EOM may be dominated by FCWG dynamics, and hence is transformed into a quasi-EOM, which actively involves the participation of FCWG quasi-electromechanical state variables.

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.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

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.

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.