The purpose of this study is to apply the convergence-confinement method (CCM) based on the assumption of hydrostatic stress to the surrounding rock excavated in a circular tunnel whose rock mass characteristics meet the requirements of the non-linear Hoek-Brown failure criterion. Based on a consistent and rigorous method of theoretical analysis, a closed-form analytical solution for the stress/displacement of the ground reaction induced by the advancing excavation of the tunnel, especially in the elastic and plastic regions, is derived and investigated under the condition of an isotropic stress state. By taking the value of a confinement loss as an explicit analysis process in an incremental manner, not only is the computationally executable analytical solution achieved, but it can also be performed using a simple spreadsheet. The validity of the analytical solution implemented by the incremental procedure was examined with published data to study the effect of nonlinear failure criteria on the ground reaction curve; in particular the mechanical behavior at the intrados of the tunnel, and the distribution of stress/displacement on the cross-section of the tunnel. A comparison between the published results and the solution proposed in this study, which interprets the closed-form by the incremental procedure, shows consistent and favorable trends.

This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in W^m[0; 1] by multiscale orthonormal basis in W¹[0; 1]. We define approximate solution, and obtain the approximate solution of high-order BVPs by using the approximate theory. Moreover, the convergence and stability of the algorithm are improved. At last, several numerical experiments show the feasibility of the proposed method.

Homotopy perturbation and analysis methods have been widely used to obtain both approximate and exact so- lutions to nonlinear problems. In general, these two methods are based on the Taylor series with respect to an embedding parameter. Many researchers have compared the two methods and raised more concerns on the homo- topy perturbation method (HPM) because the homotopy analysis method (HAM) contains a convergence-control parameter ~: For this reason, in this article, a more general form of HPM is introduced as the -homotopy per- turbation method (-HPM), which contains a control parameter : The introduction of parameter  in this new modication gives a better way to adjust and control the convergence region and the rate of the series solution. We conrm through the given examples in this study that the HPM is a special case of the -HPM. The error and convergence analysis of this proposed method are also presented

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector r_m+1 on r_m is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.

Quantum computing is an emerging field that have given a significant impact on optimization. Among the diverse quantum algorithm, the quantum gradient descent has become a prominent technique for solving unconstrained optimization problems. In this paper, we propose a quantum-spectral Polak-Ribi{\'e}re-Polyak (PRP) conjugate gradient approach. The technique is considered as a generalization of the spectral PRP method which employs a $q$-gradient that approximate the classical gradient with quadratically better dependence on the quantum variable $q$. Additionally, the proposed method reduces to the classical variant as quantum variable $q$ gets closer to $1$. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search. This approach is globally convergent with the standard Wolfe line search without any convexity assumption. Numerical experiments are conducted and compared with the existing approach to demonstrate the improvement of the proposed strategy.

In this paper, we introduce and study the notion of rough I₂-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I₂-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

The influence of neutrosophy in the previous period is constantly growing in many areas of science and technology. Moreover, various applications of the neutrosophic approach have become more common in recent years. Our goal in this research is to utilize the neutrosophy to improve the performance of the Dai-Liao conjugate gradient (CG) method. Specifically, in this research, we propose and investigate a new neutrosophic logic system to calculate the key parameter t involved in the Dai–Liao CG iterations. Theoretical analysis and numerical experience indicate that the efficiency and robustness of the new rule for determining t. Combining the neutrosophy and the Dai-Liao conjugate gradient method, we propose and explore a new Dai-Liao CG iterations for solving large-scale unconstrained optimization models. The global convergence is established under common assumptions and the backtracking line search. Finally, by conducting numerical experiments, computational evidence demonstrates that the new fuzzy neutrosophic Dai-Liao conjugate gradient method is computationally effective and robust.

In this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

The research presented in this paper concerns the determination of the attraction basins of the Newton’s iterative method which was used to solve the non-linear systems of observational equations associated with the geodetic measurements. The authors considered simple observation systems corresponding to the intersections, or linear and angular resections, used in practice. The main goal was to investigate the properties of the sets of convergent in the initial points of the applied iterative method. An important issue regarding the possibility of automatic and quick selection of such points was also considered. Therefore, the answers to the questions regarding the geometric structure of the basins, their limitations, connectedness or self-similarity were sought. The research also concerned the iterative structures of the basins, i.e. maps of the number of iterations which are necessary to achieve the convergence of the Newton’s method. The determined basins were compared with the areas of convergence that result from theorems on the convergence of the Newton’s method, i.e. the conditions imposed on the eigenvalues and norms of the matrices of the studied iterative systems. One of the essential results of the research is the indication that the obtained basins of attraction contain areas resulting from the theoretical premises and their diameters can be comparable with the sizes of the analyzed geodetic structures. Consequently, in the analyzed cases it is possible to construct methods that enable quick selection of the initial starting points or automation of such selection. The paper also characterizes the global convergence mechanism of the Newton’s method for disconnected basins and, as a consequence, the non-local initial points, i.e. located far from the solution points.

In the first part of this article, we discuss and generalize the complete convergence introduced by Hsu and Robbins (1947) to the r-complete convergence introduced by Tartakovsky (1998). We also establish its relation to the r-quick convergence first introduced by Strassen (1967) and extensively studied by Lai (1976). Our work is motivated by various statistical problems, mostly in sequential analysis. As we show in the second part, generalizing and studying these convergence modes is important not only in probability theory but also to solve challenging statistical problems in hypothesis testing and changepoint detection for general stochastic non-i.i.d. models.

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than the observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics is connected with the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

The COVID-19 pandemic has obliged Governments all around the world to take confinement and social 13 distancing measures. The reduction of leisure and production activities on beaches and ports have 14 disappeared direct and indirect contamination such as plastics, hydrocarbon spill, microbiological loads, 15 noise level, etc. leading to temporary improved environmental conditions, converting the beaches 16 similar to Marine Protected Areas. Some conditions are briefly analyzed through local surveys and in situ 17 observations in the popular beaches and ports of Salinas, Manta and Galápagos. 97-99 % of surveyed 18 people agreed that beaches have notoriously improved during confinement at least from visual 19 observation. On a scale from 1 (worst) to 5 (best), the beaches were rated 2.23 and 2.83 (less than 20 acceptable) before quarantine, and 4.48 and 4.33 after it for Salinas and Manta respectively. The 21 beaches have less garbage in general and plastic, even though there has been an increase in plastic and 22 face mask production around the world. In Salinas, 72%, and 23 % of surveyed people have seen small 23 pelagic fish, whilst in Manta 75%, and 41% of people saw the same, but also 17% of people have seen 24 whales (humpback and shark-whales) and dolphins practically swimming on the beach. Manta rays, 25 turtles, and other types of species were also observed. In Galapagos beaches, turtles have been 26 observed many more times than usual. The main plausible reason is the decrease in noise level. It is 27 recommended to take this unique opportunity, to construct a baseline data and information on physical, 28 chemical, biological, microbiological coastal oceanographic science, and from them to establish a proper 29 Coastal Zone Management based on beach description, water, and beach quality, human dimension, 30 and economic value indexes. This data and information construction should ideally be done before the 31 beaches are open.

We quantitatively investigated the statistical behaviors of semiflexible polymer chains, which are simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by which new compact formulas are obtained for the confinement free energy and force-confinement-extension relation. These newly derived formulas have been justified by numerical solutions of an eigenvalue problem associated with the Fokker-Planck governing equation and extensive Brownian dynamics simulations based on the so-called Generalized Bead-Rod (GBR) model. We found that, comparing to the classical deflection theory, these new formulas are valid for a much extended range of the confinement-size /persistence-length ratio, and have no adjustable fitting parameters for sufficient long semiflexible chains in the whole deflection regime.

During the pandemic, assisted reproductive treatments suffered from major disruptions in their terms due to the restrictions imposed. The objective of this study is to evaluate the level of anxiety of women whose treatments were either suspended or delayed. Methods: Descriptive cross-sectional study conducted between April and May 2020. The State-Trait Anxiety Inventory was applied in a Spanish adapted version. The research also included social, personal, and work aspects which may be involved in the challenging situation. Results: A total of 115 patients participated in the study (73.7%). Women showed a mean in trait anxiety of 17.79 (SD = 8.80) and a mean in state anxiety of 19.95 (SD = 9.08). Neither the type of treatment nor the time of infertility are predictors of trait anxiety or state anxiety. More age pressure and more worry were associated with more trait and state anxiety (p<0.001). The most common emotional reactions to discontinuation of fertility treatments were sadness and anxiety. Conclusions: Discontinuation of fertility treatments due to confinement restrictions had a negative impact on the mental health of women who were following a process of assisted reproduction treatment, increasing their levels of emotional distress and anxiety.

When liquids are confined into nanometer-scale slit, the induced layering-like film structure allows the liquid to sustain non-isotropic stresses and thus being load-bearing. Such anisotropic characteristics of liquid under confinement arise naturally from the liquids’ wave number dependent compressibility that does not need solidification to take place as a prerequisite. In other words, liquids under confinement can still remain fluidity with molecules being (sub-)diffusive. However, the extensively prolonged structural relaxation time can cause hysteresis of stress relaxation of confined molecules in response to the motions of confining walls and thereby yield the quasi-static stress tensor history-dependent. In this work, by means of molecule dynamics, the discrepancy of stress tensor of a highly confined key base-oil component, i.e. 1-decene trimer, is captured after its relaxation from being compressed and decompressed. The results indicate that among the effects (e.g. confinement, molecular structure, and film density) that can potentially affect confined stress tensor, the ordering status of the confined molecules plays a predominant role.

In this theoretical study we report on molecular electrostatic potential (MEP) of titled molecules confined by repulsive potentials of cylindrical symmetry mimicking a topology. Our calculations show that the spatial restriction significantly changes the picture of MEP of molecules in quantitative and qualitative sense. In particular, the drastic changes of MEP as a function of the strength of spatial confinement are observed for the BrCN molecule. This preliminary study is the first step in the investigations of the behavior of MEP of molecular systems under the orbital compression.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

A total internal reflection photonic crystal fiber (PCF) based on hexagonal core is proposed for gas sensing in a specific wavelength range. The higher sensitivity and lower confinement loss were realized by the structure of the proposed PCF consists of two layers with circular holes rotated hexagonally around a core region and six slotted air-hole in the cladding based on numerical analysis. The simulation results show that the enhancement of the relative sensitivity has been done by enhancing the diameter of the hexagonal shape air-hole cladding (d1) and the hexagonal arranged holes around the central solid core (d0) in this design. Also, the confinement loss has been reduced by enhancing the ratio of length to width of slotted holes (l/w) and decreasing the cladding air-hole diameters (d1). As the refractive index increases, the wavelength shifts toward the long wavelength. And in a certain temperature range, the transmission characteristics of the device does not change with the temperature. The results are helpful for designing high performance PCF for gas sensing applications.

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields.

New analysis regarding the structure of center vortices and their color structure is presented: Using data from gluonic SU(2) lattice simulation with Wilson action a correlation of fluctuations in color space to curvature of vortex fluxes was found. Finite size effects of the S2-homogeneity hint at color homogeneous regions on the vortex surface.

tructural and superconducting properties of high quality Niobium nanofilms with different thicknesses are investigated on silicon oxide and sapphire substrates. The role played by the different substrates and the superconducting properties of the Nb films are discussed based on the defectivity of the films and on the presence of an interfacial oxide layer between the Nb film and the substrate. The X-ray absorption spectroscopy is employed to uncover the structure of the interfacial layer. We show that this interfacial layer leads to a strong proximity effect, specially in films deposited on a SiO2 substrate, altering the superconducting properties of the Nb films. Our results establish that the critical temperature is determined by an interplay between quantum-size effects, due to the reduction of the Nb film thicknesses, and proximity effects.

We construct a novel family of summation-integral type hybrid operators in terms of shape parameter $\alpha\in \lbrack 0,1]$ in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre's K-functional, Lipschitz class, and second-order modulus of smoothness.

Due to the broadening of services from industrial enterprises to customers, the industrial network has gained more significance than what is really thought. As a part of this revolution, this paper tried to introduce the best suitable routing option for the healthcare, banking and internet services industries to optimize the routing department of their enterprises. RIP is not associated with this study, being out of favor in the industries due to hop count limitation. The idea behind doing such a thing is to avoid improper implantation of routing inside the enterprises which causes lack of optimization in routing department. The method which is selected for this paper is qualitative case study of banking, healthcare and internet services industries with unstructured interviews of IT experts of the respected industries in an open-ended questions fashion. The results were illustrated based on the stories and the discussion of the stories is the main contributor to the result of the study. The evaluation results of the stories have illustrated, that EIGRP is a suitable routing option for health care and banking, while OSPF can be suitable for the internet services industry. The implication of the study can be optimized network of industries such as healthcare, banking and internet services and it introduces the best suitable routing option for the demanded industries with the case study method and narrative analysis of the stories, which start from load balancing type and ends to demanded routing protocol, while reaching to demanded routing protocol, it introduces the best suitable routing option of that industry

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

In this paper, we generalize the concept of I-statistical convergence, which is a recently introduced summability method, with an infinite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our definitions. The name of our new method will be A^{I}-lacunary statistical convergence with respect to a sequence of modulus functions. We also define strongly A^{I}-lacunary convergence and we give some inclusion relations between these methods.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

Balanced and coordinated economic development across regions is a critical goal of regional economic development and new-type urbanization in China. However, few studies have examined economic growth convergence clubs at the county level. To extend the research on convergence clubs, this research applies a log t convergence test and a dynamic spatial ordered Probit model (DSOP) to endogenously identify economic growth convergence clubs in counties and to examine the influence of initial states and structures on club convergence probability. The study sample covers 2286 counties of China from 1992 to 2010. The results show significant convergence club patterns at the county levels, resulting in the gradual formation of six convergence clubs. The DSOP estimation results show that per capita fixed assets, population density and industrialization have promoted convergence club formation to varying degrees.

The mass of the nucleons is calculated from first principles by defining the quark as a non-gravitational particle, subject to Dirac’s equation with non-canonical gamma matrices. Unlike the canonical electron-type, this Dirac particle has two real dipole moments, which allows a structural modelling of hadrons. It is shown how such modelling reveals striking correspondences and differences between dually related particles and properties like electrons and quarks, photons and gluons, pions and nucleons, spin and isospin and protons and neutrons. It is a stepping stone to the actual calculation, which competes in precision with lattice QCD. The appendix contains a Lorentz covariance proof of hadrons composed by such particular Dirac-type quarks.

The center vortex model of quantum-chromodynamics can explain confinement and chiral symmetry breaking. We present a possible resolution for problems of the vortex detection in smooth configurations and discuss improvements for the detection of center vortices.

We investigate, whereas the SU(4)/SU(2) model, is viable for describing strong interactions. The existing problems of confinement and asymptotic freedom, two phenomena that can not be described by the SU(3) model, might indicate that we need something "larger" than the SU(3) model. The considered coset SU(4)/SU(2) or the Stiefel manifold V^2(C_4) contains an su(3) algebra, plus additional degrees of freedom that resembes the Feddev-Poppov concept. The richer structure of this coset, give us enough room, to seek for new phenomena, as its dimensionality is 12. The consideration of the SU(4)/SU(2) model flavors firstly the unification of nuclear fields (strong and weak) in an SU(4) model.

Gauge fields control the dynamics of fermions. On the other hand a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum.

Reinforced concrete (RC) columns are often placed under confinement to increase their strength and ductility. Carbon fiber reinforced polymer (CFRP) materials have recently been recognized as favorable confinement systems. At present, a number of national standards and codes dedicated to the design of concrete components strengthened with CFRP in general and CFRP confinement in particular are available. These sets of rules provide design equations for confined reinforced concrete columns with circular and rectangular cross sections. Most of the standards and codes exhibit significant differences, including the used predictive models limitations, observed effects, and covered loading conditions. In this paper, five international standards and design guidelines are introduced and discussed. The purpose is to present a constructive and critical assessment of the state-of-the-art design methodologies available for CFRP confined RC columns and to discuss effects not previously considered properly. Therefore, some recent research efforts and findings from the Leipzig University of Applied Sciences are also introduced. The obtained data is used for a comparative study of the guideline predictive equations. Furthermore, it is shown that some new findings concerning the rupture strength and the maximum strength plus accompanying axial strain of a CFRP confined column are suitable to improve the current guidelines.

In this work a research on pulsed electrochemical micromachining of Stainless Steel is presented. A suitable equipment to study the process is described as well as a fitting procedure to machine and measure the variables involved. A tool of Tungsten with a tip of about 5 mm diameter sunk in an electrolyte of NaNO₃ is used for the process. The pulse on-time must be maintained in the order of ns to achieve a good current confinement, since the tool is active. Some experiments were made to assess the most important variables of the process, as current confinement, surface roughness, material removal rate and efficiency. It is observed that the current confinement get worse when the pulse on-time increases, as well as surface roughness. The material removal rate and the efficiency increase with the voltage amplitude and the pulse on-time. The voltage amplitude must be higher than 12 V so that the phenomenon of passivation disappears. There is a compromise in the choice of the variables, so a suitable combination of parameters is determined so that a good material removal rate with an acceptable result is achieved.

In order to master the structure state of subway shield tunnel, reduce the diseases and avoid the potential safety hazards, the lateral convergence deformation of subway shield tunnels should be predicted. For the non-stationarity small sample size of subway shield tunnel lateral convergence deformation value, the existing prediction models have poor performance in terms of accuracy and stability. In this paper, a lateral convergence model of subway shield tunnel based on Kalman algorithm is constructed based on Kalman filtering theory. The model is efficient, adaptive and robust, and can accurately predict the lateral convergence deformation of subway shield tunnel. Taking the horizontal diameter of 200 rings shield segment in the interval section of a subway tunnel as an example, it is proved that the residuals of the Kalman prediction model are small, the residual distribution conforms to the normal distribution, and the prediction effect is great. The model is suitable for the prediction of more than 5 periods of data, and the prediction accuracy of the model is improved with the increase of the number of data periods. In addition, the Kalman model is compared with GM(1,1) model and GM-Markov model, and RMSE and MAPE are introduced as evaluation indexes. The results show that the Kalman model has higher prediction accuracy and is more suitable for predicting the lateral convergence deformation of subway shield tunnel.

Infant obesity has become one of the most serious global health challenges of our time. The combined prevalence of overweight and obesity has rapidly increased worldwide during the last two decades, especially in some developing countries where obesity is reaching levels on a par with some industrialized countries, or even higher. This fast growth has occurred especially in countries in the midst of rapid social-economic transitions. Most international comparisons focus on the adult population while analyses focusing on the child population are more limited. Using the methodology developed by Phillips and Sul [1], this paper studies the worldwide evolution of infant body mass index (BMI), overweight and obesity prevalence for a large sample of countries during the period 1975-2016. Our results indicate that the figures for BMI or the prevalence of obesity in different countries do not converge, while the opposite is the case for overweight prevalence in children. Furthermore, there is a non-linear relationship between obesity and income or human capital, indicating that low and middle-income countries require a strong initiative for health policies targeting obesity prevention.

As consequence of COVID-19, millions of households suffered mobility restrictions and changes in their lifestyle during several months. The aim of this study was to evaluate the effects of COVID-19 home confinement in food habits, lifestyle and emotional balance of the Spanish population. This cross-sectional study used data collected via an anonymous online questionnaire during the last month before lockdown finished in Spain in a total of 675 participants. 38.8% of the respondents experienced weight gain while 31.1% lost weight during confinement. The increase in body weight was positively correlated with the age (Rs = 0.14, p <0.05) and BMI (Rs = 0.20, p <0.05). We also identified that 39.7% reported poorer quality sleep, it was positively correlated with BMI (Rs = -0.18, p <0.05) and with age (Rs = -0.21, p <0.05). 44.7% of the participants had not performed physical exercise during confinement with differences by sex (p <0.05), by age (p <0.05), by BMI (p <0.05) and sleep quality (p <0.05). According to emotional-eater questionnaire, 21.8% and 11% were classified as emotional eater and very emotional eater, respectively. We emphasize the importance of adopting a healthy lifestyle, as the COVID-19 pandemic nowadays is ongoing.

This paper presents an overview of the principal structural and dynamics characteristics of reverse micelles (RMs) in order to highlight their structural flexibility and versatility, along with the possibility to modulate their parameters in a controlled-manner. The multifunctionality in a large range of different scientific fields is exemplified in two distinct directions: a theoretical model for mimicry of biological microenvironment and practical application in the field of nanotechnology and nano-based sensors. RMs represents a convenient experimental approach that limits the drawbacks of the conventionally biological studies in vitro, while the particular structure confers them the status of simplified mimics of cells by reproducing a complex supramolecular organization in an artificial system. The biological relevance of RMs is discussed in some particular cases referring to the confinement and crowding environment, molecular dynamics of water and cell membrane structure. The use of RMs in different range of applications seems to be more promising due to their structural and compositional flexibility, a high efficiency and selectivity being achieved. The advance in nanotechnology is based on developing new methods of nanomaterials synthesis and deposition. This review highlighting the advantages of using RMs in synthesis of nanoparticles with specific properties and in nano (bio)sensors design.

This interdisciplinary work presents a novel patent pending method of inertial electrostatic confinement (IEC) fusion called the Nuclear Electromagnetic Shaping Accelerator Reactor (NESAR) that addresses all of the major failure problems with currently known methods of IEC fusion. A brief background of previous IEC methods that generate a negative potential well to accelerate ions for fusion will be reviewed and compared to the NESAR method of magnetic confinement. In addition, a direct comparison will be presented between the NESAR and the tokamak method of fusion. The NESAR method of fusion obtains the plasma oscillation and compression capabilities of a tokamak without producing the catastrophic magnetic reconnection disruptions that currently plague tokamaks. Since the NESAR can oscillate charged particles comparable to the tokamak, this work will briefly review the history of the tokamak, how sawtooth magnetic reconnection occurs, and how the NESAR precludes the occurrence of magnetic reconnection. This work will also review the beginnings of a novel theory that has obtained interest from the Defense Advanced Research Projects Agency (DARPA) which is currently interested in possibly supporting further research into the NESAR to explore this new theoretical concept. This novel theory is a unified field theory based upon the trajectory of charged particle movements within the NESAR. The NESAR is the only concept of magnetic confinement in the world that may have the capability to allow charge particles to collectively interact relatively to a solitary location. Due to this possible capability, there is a probability that the confined particles may experience curved trajectories that could allow them to experience the effects of curvature deviation. If curvature deviation occurs with these magnetically confined charged particles; then the deviated acceleration would allow for the electromagnet field to be propelled to a higher dimension that could influence spacetime. Finally, this work will review another theory that explains how pole reversals are observed by the National Aeronautics and Space Administration’s (NASA) coiled magnetic field detectors. This theory requires little to no postulations to be framed and it is purely based upon the trajectory of charged particles within the NESAR, Michael Faraday’s law of induction, and experimental observations of rotating plasmas.

Machine learning offers advanced tools for efficient management of radio resources in modern wireless networks. In this study, we leverage a multi-agent deep reinforcement learning (DRL) approach, specifically the Parameterized Deep Q-Network (DQN), to address the challenging problem of power allocation and user association in massive multiple-input multiple-output (M-MIMO) communication networks. Our approach tackles a multi-objective optimization problem aiming to maximize network utility while meeting stringent quality of service requirements in M-MIMO networks. To address the non-convex and nonlinear nature of this problem, we introduce a novel multi-agent DQN framework. This framework defines a large action space, state space, and reward functions, enabling us to learn a near-optimal policy. Simulation results demonstrate the superiority of our Parameterized Deep DQN (PD-DQN) approach when compared to traditional DQN and RL methods. Specifically, we show that our approach outperforms traditional DQN methods in terms of convergence speed and final performance. Additionally, our approach shows 72.2 % and 108.5 % improvement over DQN methods and RL method respectively in handling large-scale multi-agent problems in M-MIMO networks.

In this article, an iterative method of two step is proposed for finding all roots simultaneously of polynomial equations. The order of convergence of the proposed algorithm is 2m, by using any iterative scheme of order m. Numerical tests are performed to confirm the theoretical results and to compare the proposed scheme with existing methods for finding all roots simultaneously.

We carry out in a thin heterogeneous porous layer, the multiscale analysis of Smoluchowski's discrete diffusion-coagulation equations describing the evolution density of diffusing particles that are subject to coagulate in pairs. Assuming that the thin heterogeneous layer is made of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.

Starting with a particle in the cube system, we investigate the exotic possibility that the quantum numbers (n_x,n_y,n_z) satisfy the Markov equation. We find that the proposed particle in the Markov-cube system follows from a non-classical information entropic space by the quantum potential Q. We study the classical correspondents of the proposed particle in the Markov-cube system. According to our proposition, this particle identified by detailed measurements of the confinement particle-energy levels is an artifact or occurs in nature.

In this work we report recent theoretical calculations of a superconducting island in a strong vortex confinement regime. The obtained results reveal the evolution of superconducting condensate as a function of electron mean-free path (l) with the evolution of an applied magnetic field H0. The results of this study provide an insight about the emergent superconducting properties under such conditions, using the Ginzburg-Landau numerical simulations where spatial variation of thickness d on island, omnipresent in these kind of structures grown on Si (111), is taken into account. These results offer a new route to tailor superconducting circuits by using the controlled bombardment, in order to explore the impact on vortex distribution, phase of order parameter, number of vortices, free energy and the first H1 and second critical field H2.

The purpose of this research has been to provide information about the psychological effects of confinement forced by a prolonged quarantine in a suitable adult sample of 596 Bolivians of both sexes. It was sought to explore the perceptions of the participants about their own emotional state: fears, anxieties, depressions, while they were in isolation to reduce the probability of contagion of COVID 19. Additionally, we were interested in verifying the modulating effects of resilience and self-efficacy on such emotional states. The results indicated, in the same direction of similar studies, significant relationships between high perceived loneliness, high levels of stress and anxiety, with relatively high levels of depression. Likewise, it was clear that stress, perceived loneliness, and anxiety are predictors of depression among those in conditions of forced isolation. Finally, it was found that both resilience and self-efficacy exert a clear moderating effect by attenuating the relationships of perceived loneliness and anxiety, on depression.

The center vortex model of quantum chromodynamic states that vortices, closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using non-trivial center regions, that is, regions whose boundary evaluates to a non-trivial center element, a resolution of this issue seems possible. We use such non-trivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

The QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. % The pion $q \bar q$ eigenstate has zero mass for $m_q=0.$ % % A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto e^{-{Q^2/4 \kappa^2}}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. % The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS$_5$ space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

Promoting the sustainable development of resource-based cities is of great significance to the ecological protection and high-quality development of the Yellow River Basin. Combining the environmental status and economic development, we objectively evaluate the ecological safety level of resource-based cities in the Yellow River Basin, compare and analysis the main factors affecting the ecological safety of different resource-based cities, and formulate precise and differentiated ecological safety protection measures in river basins to achieve high-quality development. Taking the Yellow River Basin as an example, this paper analyses the ecological level of the Yellow River Basin based on the theory of sustainable development, calculates the ecological safety level of 30 resource-based cities in the Yellow River Basin from 2006 to 2020 by TOPSIS model, and makes convergence analysis by classification. Through the DID empirical test of sustainable development planning policy on ecological safety factors, distinguish the development characteristics of different resource-based cities. The results show that: (1) the ecological safety level of resource-based cities in the Yellow River Basin is generally developing well, and there are differences among different types of resource-based cities; (2) the kinetic energy of sustainable development of resource-based cities in the Yellow River Basin is mainly industrial transformation, and the power of science and technology is insufficient; (3) local governments pay limited attention to environmental protection, and the sustainable development planning of resource-based cities in 2013 mainly promotes the adjustment of industrial structure of resource-based cities.

In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. Using this procedure, we achieve a remarkable increase in the order of convergence, raising it from p to p + 3 units, which results in a remarkable improvement in the overall performance. We have conducted comprehensive numerical tests in various scenarios to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes.

Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space Cr((−∞,0];Rn). The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both LG2 and exponential estimates.

Influenced by the quasi-stationary Mei-yu front and the development of mesoscale low vortices on the Mei-yu front, a torrential rain event occurred in Suzhou on July 6, 2020. The 24-hour rainfall recorded by the automatic station exceeded 200 millimeters, with the highest hourly intensity surpassing 70 millimeters, accompanied by thunderstorms and strong winds. This heavy precipitation process was characterized by suddenness, extremity, long duration, high precipitation efficiency, and backward propagation. Using various data sources such as the European ERA5 reanalysis data, ground-based automatic stations, sounding, Doppler weather radar, and wind profile radar, this paper analyzed in detail the circulation characteristics and radar echo structures of this torrential rain event, and further studied the triggering, feature evolution, and maintenance mechanisms of the heavy precipitation.The results show: (1) The continuously strengthening low-level jet stream propagates downward forming an ultra-low-level jet stream. Heavy precipitation is located on the left front side of the jet exit area, where strong convergence and lifting in the boundary layer overlap with the ascending branch of the secondary circulation above the shear line, resulting in heavy precipitation. (2) A supercell storm with intense precipitation produced this heavy rainfall event, characterized by a low centroid of strong echo; echo-free vault, bounded weak echo region, and other supercell structural features. During this event, the high reflectivity factor areas corresponded to high KDP value areas, indicating a large amount of liquid water content. Vertically, the KDP column can track the rainwater mixing ratio well, and its location corresponds to the vicinity of the short-term heavy precipitation occurrence. The high KDP value area mainly consists of numerous precipitation particles, and the vertical vortex wind field structure causes rapid growth of precipitation particles through continuous rolling. Furthermore, it can be found through correlation coefficients (CC) that there are always high-value areas for CC since they correspond to areas of intense precipitation. (3) Continuous triggering of mesoscale convective cloud clusters on the east-west ground convergence line leads to new development and forms a "train effect." Strong frontogenesis in both horizontal and vertical directions triggers and sustains this heavy precipitation event. The significant increase in liquid water and water vapor density has indicative significance for the occurrence of heavy precipitation.

The latest World Atlas of Desertification represents a turning point in the diagnosis of desertification. While it forgoes desertification mapping due to the intrinsic complexity of the phenomenon and the impossibility of measuring it using a single indicator, it introduces the Convergence of Evidence paradigm, which identifies socioeconomic and biophysical variables whose behavior allows pointing out those areas prone to desertification. The Spanish National Action Program Against Desertification (PAND), back to 2008, already implemented a similar approach to identify five “desertification landscapes” within Spain using both socio-economic and climatic information. The PAND was not only pioneering but also, unfortunately, accurate. Desertification in Spain has continued to worsen and the first two decades of the 21st century have consolidated an agri-food model whose dynamics have exacerbated the desertification processes identified in the PAND. Despite its scientific value, the PAND lacked a proper action plan and was completely detached from the diagnosis. As a result the diagnosis it provided was not followed by effective actions to halt desertification in Spain. The Spanish Government's recent declaration of climate and environmental emergency requires a new strategy to combat desertification. This commitment is an excellent opportunity to update the diagnosis of the situation and, more crucially, to unify the different desertification sectoral policies and actions under a single front. We provide here elements for a roadmap to be designed around the pressures, impacts, and drivers that define today's Spanish desertification landscapes to manage them effectively and avoid their further degradation.

The theory of the origin of carcinomas suggests that neoplasias from epithelial tissues are the consequence of the reactivation of developmental programs. It proposes a model in which the epithelial cells undergo cellular transitions due to replicative senescence and inflammation towards a mesenchymal-undifferentiated phenotype with cancerous behavior. The conserved pattern of histological progression and the molecular biology of carcinomas is congruent with the view of cancer as a developmental disease. In support of the theory, the experimental literature regarding the molecular, cellular, and histopathological mechanisms associated with epithelial carcinogenesis were aligned according to the premises of the hypothesis. Thereby identified a generic process in the carcinogenesis of the breast, endometrium, prostate, colon, lung, pancreas, bladder, liver, and cervix. Then, is provided a methodology overview of modeling in systems biology derived from previous research testing the hypothesis. The results illustrate the value of the complex systems approach to recover behavior that cannot be inferred only by traditional methods. Specifically, the model suggests that the consistency in the cell types and the directionality of the observed cellular transitions during epithelial carcinogenesis arise from structural constraints in the molecular networks associated with the carcinomas. Overall, the results of the dynamical analysis agree with the premises of the hypothesis and provide an insightful perspective of the potential mechanisms underlying the cellular plasticity displayed during epithelial carcinogenesis. In an era of big data and yet few advances in the underlying causes of chronic diseases, the manuscript also aims to inspire molecular biologists to integrate existing empirical evidence with systems biology modeling in the pursuit of understanding.

Evolutionary convergence provides natural opportunities to investigate how, when, and why novel traits evolve. Many convergent traits are complex, highlighting the importance of explicitly considering convergence at different levels of biological organization, or ‘multi‐level convergent evolution’. To investigate multi‐level convergent evolution, we propose a holistic and hierarchical framework that emphasizes breaking down traits into several functional modules. We begin by identifying long‐standing questions on the origins of complexity and the diverse evolutionary processes underlying phenotypic convergence to discuss how they can be addressed by examining convergent systems. We argue that bioluminescence, a complex trait that evolved dozens of times through either novel mechanisms or conserved toolkits, is particularly well suited for these studies. We present an updated estimate of at least 94 independent origins of bioluminescence across the tree of life, which we calculated by reviewing and summarizing all estimates of independent origins. Then, we use our framework to review the biology, chemistry, and evolution of bioluminescence, and for each biological level identify questions that arise from our systematic review. We focus on luminous organisms that use the shared luciferin substrates coelenterazine or vargulin to produce light because these organisms convergently evolved bioluminescent proteins that use the same luciferins to produce bioluminescence. Evolutionary convergence does not necessarily extend across biological levels, as exemplified by cases of conservation and disparity in biological functions, organs, cells, and molecules associated with bioluminescence systems. Investigating differences across bioluminescent organisms will address fundamental questions on predictability and contingency in convergent evolution. Lastly, we highlight unexplored areas of bioluminescence research and advances in sequencing and chemical techniques useful for developing bioluminescence as a model system for studying multi‐level convergent evolution.

Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it. Moreover some improvements of EM algorithm are also proposed in the tutorial such as combination of EM and third-order convergence Newton-Raphson process, combination of EM and gradient descent method, and combination of EM and particle swarm optimization (PSO) algorithm.

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers, and m∈{2,3,⋯}. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.

We identify the source of the Mw = 5.6 earthquake that hit west-central Epirus on March 21, 2020 00:49:52 UTC. We use synthetic aperture radar interferograms tied to one permanent Global Navigation Satellite System (GNSS) station (GARD). We model the source by inverting the INSAR displacement data. The inversion model suggests a shallow source on a low-angle fault (39°) dipping towards east with a centroid depth of 8.5 km. The seismic moment deduced from our model agrees with those of the published seismic moment tensors. This geometry is compatible with the Margariti thrust fault within the collision zone between Apulia and Eurasia. We also processed new GNSS data and estimate a total convergence rate between Apulia and Eurasia of 8.9 mm yr-1 , of which shortening of the crust between the Epirus coastal GNSS stations and station PAXO in the Ionian Sea is equivalent to ~ 50% of it or 4.6 mm yr−1. A 60-km wide deformation zone takes up nearly most of the convergence between Apulia-Eurasia, trending N318°E. Its central axis runs along the southwest coast of Corfu, along the northeast coast of Paxos, heading toward the northern extremity of the Lefkada island.

Relying on the USA, Canada and Mexico extract from the cross-national data sample on the environmental affection and cognition of adolescent students (Niankara, 2019), along with seemingly unrelated bivariate weighted ordered probit regression modeling (Niankara and Zoungrana, 2018), this study reports on the convergence of technological awareness and expectations within the context of international trade. We achieve this by adopting a regional perspective in investigating the effects of affective, cognitive and situational factors on youth's awareness and expectations about genetically modified organisms (GMOs) and nuclear power technology (NPT) within the North American free trade block. Identification of model parameters is achieved using maximum simulated likelihood methods. The findings show that although it has been over 20 years as of 2015 that USA, Canada, and Mexico ratified the north American free trade agreement (NAFTA), the diffusion of technology and information within the trade block has not succeeded in homogenizing awareness and expectations about GMOs and Nuclear power technology, as observed in the youth population across the three countries. Indeed, with regards to technological awareness, compared to youth from the USA, those from Canada show 15% (GMOs) and 7.1% (NPT) more awareness respectively; while those in Mexico are respectively 34.4% and 19.5% less aware about GMOs and NPT. With respect to technological expectations, compared to youth from the USA, those from Canada and Mexico are respectively 34.4% and 39.9% more optimistic about GMOs, while 15% and 49.7% more optimistic about NPT. Overall, youth within NAFTA country members are respectively 2.5% and 6.7% more optimistic about GMOs and NPT for every level increase in their awareness about the two technologies.

Centralized/Cloud Radio Access Networks (C-RAN) are deployed in converged fixed-mobile networks to exploit the flexibility coming from joint application of Network Function Virtualization (NFV) and Software Defined Networking (SDN). In this context, optical links connecting C-RAN nodes, possibly based on the Ethernet standards, may carry traffic with different requirements in terms of latency and throughput. This paper considers the problem of traffic aggregation on C-RAN optical Ethernet links with latency control for fronthaul traffic and throughput capability for backhaul traffic. Integrated hybrid nework technique is applied to show how time transparency can be enforced for Ethernet encapsulated Common Public Radio Interface (CPRI) traffic while allowing statistical multiplexing of backhaul traffic. Simulation results show the effectiveness of segmentation of backhaul traffic to allow exploitation of the available bandwidth even with high capacity CPRI options.

This work proposes a hollow-core photonic crystal fiber-based edible oil sensor in the terahertz (THz) range (e.g., 1.0THz ≤ f ≤ 3.0THz) and different sensing characteristics are numerically analyzed. The suggested sensor’s performance was assessed by means of COMSOL Multiphysics, a commercial program that uses the finite element approach. The computational results indicate that the relative sensitivity is 85.591%, 84.648%, 82.625%, 82.683%, and 79.161%, respectively, at f = 2.2 THz, for several types of sunflower oil, mustard oil, coconut oil, olive oil and palm oil; and the corresponding effective areas are 7.22×10-8 um2, 7.09×10-8 um2, 6.83×10-8 um2,7.09×10-8 um2, 6.5231 ×10-8 um2. In addition, the effective material loss for sunflower oil, muster oil, coconut oil, olive oil, and palm oil has been found to be 0.02561 cm-1, 0.027054 cm-1, 0.030322 cm-1, 0.028854 cm-1 ,0.035427cm-1 respectively. Moreover, the proposed sensor also has low confinement loss are 1.55×10-8 dB/m, 1.63×10-8 dB/m, 1.31×10-8 dB/m, 1.99×10-8 dB/m, 4.0345×10-8 dB/m.This proposed sensor can be fabricated using extrusion and 3D-printing technologies, and due to its augmented detecting capabilities, it can be a vital part of oil sensing devices implemented in real life such as industry fields.

This article reveals a best possible design for hybrid dispersion compensating fiber (HyDCF) with high birefringence established on modified broadband compensating structure through S, C and L telecommunication bands. The simulation outcome exhibits relatively higher birefringence of 3.76×10-2 at wavelength of 1550 nm. The suggested fiber also has dispersion compensation characteristics in an inclusive series of wavelengths which covers 1400-1625 nm. The reported design can achieve dispersion quantity of – 606 ps/ (nm.km) at 1550 nm effective wavelength. The reported fiber design matches the relative dispersion slope (RDS) 0.003694 nm-1 similar to single mode fiber at 1550 nm operating wavelength. This fiber demonstrates negatively flattened effective dispersion of – 2.703 ± 0.734 ps/ (nm.km) within 180 nm flat band ranging from 1460-1640 nm wavelength. It is also convenient to optical high bit rate communication systems. The low confinement loss is found 3.756×10-10 dB/m at the operating wavelength. This design also achieves highly nonlinear coefficient of 50.34 W-1km-1. In some cases, it can also be used in sensing applications.

Randomized block Kaczmarz Method and randomized extended block Kaczmarz Method are proposed for solving matrix equation AXB=C, where the matrix A and B may be full rank or rank deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved these methods converge to the solution or least square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations.

Recently, the triple-network convergence system (TNCS) has emerged from the deep integration of the power grid, transportation network, and information network. Fault recovery research in the TNCS is important since this system's complexity and interactivity can expand the faults scale and increase faults impact. Currently, fault recovery focuses primarily on single power grids and cyber-physical systems, but there are certain shortcomings, such as ignoring uncertainties including generator start-up failures and the occurrence of new faults during recovery, energy supply-demand imbalances leading to system security issues and communication delay caused by network attacks. In this study, we propose a recovery method based on the improved TD3 algorithm, factoring in shortcomings of the existing research. Specifically, we establish a TNCS model to analyze interaction mechanisms and design a state matrix to represent the uncertainty changes in the TNCS, a negative reward to reflect the impact of unit start-up failures, a special reward to reflect the impact of communication delay and an improved Actor network update mechanism. Experimental results show that our method obtains the optimal recovery decisions, maximizes restoration benefit in power grid failure scenarios and demonstrates a strong resilience against communication delay caused by DoS attacks.

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

In this study, we describe quark confinement in terms of linear interaction potentials and solve the problem of the net spin of a proton. The three quarks in a proton are assumed to revolve around a common center, and their masses are determined assuming they are Dirac particles. On the basis of these assumptions, the magnetic moment of a proton can be derived. Moreover, the rotation of the quarks is considered, in which an electrical current induces a magnetic field. Thus, the scalar product of the magnetic moment and field describes the linear interaction potential between the quarks, and the mass of the proton can be obtained. The proton mass predicted by this physical model is consistent with experimental values, and no numerical or fitting calculations are required. Furthermore, using the newly derived spins and angular momentum of the three quarks, we derived the net spin of a proton. Additionally, we predicted the mass of a pi-meson from the same model, which agrees with the experimental values.

The Newton-Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb-Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.

This paper proposed a time two-mesh (TT-M) finite difference numerical scheme to improve the efficiency of solving the symmetric regularized long wave (SRLW) equation. The TT-M Crank-Nicolson discretization and finite difference method are employed in time and space approximation respectively. The scheme involves three main steps: firstly, the time interval is divided into coarse and fine time meshes, then the nonlinear system is solved on the coarse time mesh; secondly, coarse numerical solutions on the fine time mesh are computed using an interpolation formula based on the solutions derived in the step one; lastly, the TT-M finite difference numerical solutions can be obtained through constructing the linearized fine time mesh system using Taylor’s formula. Compared to the currently existing TT-M numerical methods, the novelty of this study is that the nonlinear term including derivatives is linearized by Taylor’s formula for a function with three variables, whose error analysis is more complex. Finally, some numerical examples, including computational time and accuracy, preservation of conservation laws, are given to verify the efficiency of the scheme. By comparing it with the standard nonlinear finite difference scheme, this method can reduce CPU time without sacrificing accuracy.

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

This paper examines whether the Great Recession has altered the disparities of the US regional health care expenditures. We test the null hypothesis of convergence for the US real per capita health expenditure for the period 1980-2014. Our results indicate that the null hypothesis of convergence is clearly rejected for the total sample as well as for the pre-Great Recession period. Thus, no changes are found in this regard. However, we find that the Great Recession has modified the composition of the estimated convergence clubs, offering a much more concentrated picture in 2014 than in 2008, with most of the states included in a big club, and only 5 (Nevada, Utah, Arizona, Colorado and Georgia) exhibiting a different pattern of behavior. These two estimated clubs diverge and, consequently, the disparities in the regional health sector have increased.

The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article.

In this paper, we present a three-step sixth-order iterative schemes to estimate the solutions of a nonlinear systems of equations, for predicting the shear strength of a reinforced concrete beam. This procedure is designed by means of a weight function technique. The values for the parameters of this system were randomly selected inside the prescribed ranges by technical standards for structural concrete; moreover, some of this parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The efficiency of the new class is compared with other current schemes, with very good results.

This study used a two-stage network data envelopment analysis model to measure the water use efficiency of 108 cities in the Yangtze River Economic Belt in the initial water use and wastewater treatment phases from 2009 to 2019. We used the Dagum Gini coefficient to decompose the urban water use efficiency of six major urban clusters in the Yangtze River Economic Belt. We also used σ convergence and β convergence types to test the convergence characteristics of urban water use efficiency of six major urban clusters in the Yangtze River Economic Belt. This study found that the overall low level of water use efficiency in cities in the Yangtze River Economic Zone mainly stems from the low level of water use efficiency in the wastewater treatment stage. The 108 cities in the Yangtze River Economic Zone are divided into four types based on the average values of water use efficiency in the initial use and wastewater treatment phases; the highest number of cities are in the double-low category, with low average values of water use efficiency in the initial use and wastewater treatment phases. During the study period, spatial differences in urban water use efficiency in the Yangtze River Economic Zone narrowed, with the differences stemming mainly from hyperdensity, followed by intra- and inter-regional differences. Meanwhile, there is convergence in urban water use efficiency in the Yangtze River Economic Belt; significant β convergence in the urban agglomerations of the Yangtze River Delta, Jianghuai, middle reaches of the Yangtze River, Chengdu–Chongqing, and Central Yunnan; and insignificant β convergence in the Central Qian urban agglomeration. After considering control factors, such as industrial structure, financial development level, environmental regulation, economic development level, and science and education development level, the water use efficiency of the six major urban clusters in the Yangtze River Economic Belt converges faster, but the influence of these control factors on the water use efficiency of each urban cluster is heterogeneous. Research results have reference value for the development of improvement strategies on differentiated urban water use efficiency in the Yangtze River Economic Belt.

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 Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

Arguments of Mises and Hayek, who opposed the planned economy (PE), are used in the paper as a starting point for establishing the objective area of effective application of the PE. The abstract model of PE, based on the definitions of Mises and Hayek, leads to the conclusion that for the effective use of PE, it must be a part of mixed economy and it must produce a limited amount of essential goods of irreducible demand. These goods must be distributed among all members of society free of charge, evenly, without competition. Examples of a mixed economy are given that meet this requirement. Calculations of the personal benefit in the transition to a mixed model of the economy have been carried out. The positive and negative qualities of the planned and market methods of organization are considered. Mixed economy model combines these qualities in optimal construction. An analytical framework has been introduced for the construction of product characterization curves. Such curves provide criteria for determining the efficiency of manufacturing of this product in a planned economy. The general economic prerequisites for the usability of the PE are clarified. The applicability and advantages of the PE for the organization of the universal basic income (UBI) system are demonstrated. The possibility of using PE to solve the problem of guaranteed employment is mentioned.

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980s. On the other hand, deep learning methods have boosted the capacity of machine learning algorithms and are now being used for non-trivial applications in various applied domains. But training a fully-connected deep feed-forward network by gradient-descent backpropagation is slow and requires arbitrary choices regarding the number of hidden units and layers. In this paper, we propose near-optimal neural regression trees, intending to make it much faster than deep feed-forward networks and for which it is not essential to specify the number of hidden units in the hidden layers of the neural network in advance. The key idea is to construct a decision tree and then simulate the decision tree with a neural network. This work aims to build a mathematical formulation of neural trees and gain the complementary benefits of both sparse optimal decision trees and neural trees. We propose near-optimal sparse neural trees (NSNT) that is shown to be asymptotically consistent and robust in nature. Additionally, the proposed NSNT model obtain a fast rate of convergence which is near-optimal up to some logarithmic factor. We comprehensively benchmark the proposed method on a sample of 80 datasets (40 classification datasets and 40 regression datasets) from the UCI machine learning repository. We establish that the proposed method is likely to outperform the current state-of-the-art methods (random forest, XGBoost, optimal classification tree, and near-optimal nonlinear trees) for the majority of the datasets.

Not only does this paper present a novel type-2 fuzzy system for identification and behavior prognostication of an experimental solar cell set and a wind turbine, but also it brings forward an exquisite technique to acquire an optimal number of membership functions and the corresponding rules. It proposes a seven-layered NCPRT2FS. For fuzzification in the first two layers, Gaussian type-2 fuzzy membership functions with uncertainty in the mean, are exploited. The third layer comprises rule definition and the forth one embeds fulfillment of type reduction. The three last remained layers are the ones in which resultant left–right firing points, two end-points and output all get assessed correspondingly. It should not be neglected off the nutshell that recurrent feedback at the fifth layer exerts delayed outputs ameliorating efficiency of the suggested NCPRT2FS. Later in the paper, a modern structural learning, established on type-2 fuzzy clustering, is held forth. An adaptively rated learning back-propagation algorithm is extended to adjust the parameters ensuring the convergence as well. Eventually, solar cell photo-voltaic and wind turbine are deemed as case studies. The experimental data are exploited and the consequent yields emerge so persuasive.

To mitigate the spread of the COVID-19 coronavirus, some countries have enforced more stringent non-pharmaceutical interventions in contrast to those widely adopted (for e.g. the state of Kuwait). In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies such as the total confinement of highly populated areas has also been implemented. In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host may be infected if in close spatial proximity of the infectious host. Our focus is only on the short-time scale prior to the infectious period, so that no further transmission is assumed. We find that the level of infection depends heavily on the population dynamics, and increases in the case of slow population diffusion, but remains stable for a high or super-diffusive population. Also, we find that the confinement of homogeneous or overcrowded sub-populations has minimal impact in the short term. Finally, we discuss the possible implications of our findings for total confinement in the context of the current situation in Kuwait.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

This study identified, analysed, and prioritised significant factors for standardising the Korean smart city project evaluation system. We analysed the efficiency and productivity of companies currently providing smart city services to consider both policy and practical aspects. The prioritisation of smart city planning reflects the latest trends in South Korea, where urban planning is moving towards smart city planning. Furthermore, the capacity building of public-private/private-private partnerships indicate the importance of business scalability. This indicates that smart city services are only stabilised when the private sector is involved and leads the project, rather than focusing on public development. The feasibility of building intelligent facilities indicates that smart city projects should be implemented after securing cost-benefit feasibility. The results were used as the basis for building an evaluation system, showing that in smart city convergence alliances, small- and medium-sized enterprises achieved the highest efficiency by reducing inputs to 81% and 86%, under the assumptions of constant and variable returns to scales, respectively. As the operational aspect is more problematic than the technical aspect, policy alternatives are necessary for smooth business progress, including increased flexibility of laws and institutions and the activation of policies that temporarily relieve regulations to demonstrate smart city projects.

Because of the rapid advancement in the use of photovoltaic (PV) energy systems, it has become critical to look for ways to improve the energy generated by them. The extracted power from the PV modules is proportional to the output voltage. The relationship between output power and array voltage has only one peak under uniform irradiance, whereas it has multiple peaks under partial shade circumstances (PSC). There is only one global peak (GP) and many local peaks (LPs), where the typical maximum power point trackers (MPPT) may become locked in one of the LPs, significantly reducing the PV system's generated power and efficiency. The metaheuristic optimization algorithms (MOAs) solved this problem, albeit at the expense of the convergence time, which is one of these algorithms' key shortcomings. Most MOAs attempt to lower the convergence time at the cost of the failure rate and the accuracy of the findings because these two factors are interdependent. To address these issues, this work introduces the dandelion optimization algorithm (DOA), a novel optimization algorithm. The DOA's convergence time and failure rate are compared to other modern MOAs in critical scenarios of partial shade PV systems to demonstrate the DOA's superiority. The results obtained from this study showed substantial performance improvement compared to other MOAs, where the convergence time is reduced to 0.4 s with zero failure rate compared to 0.9 s, 1.25 s, and 0.43 s for other MOAs under study. The optimal number of search agents in the swarm, optimal initialization of search agents, and optimal design of the dc-dc converter is introduced for optimal MPPT performance.

This paper presents a numerical study on the vertical (axial) and lateral (flexure) behavior of CFST (Concrete-Filled Steel Tube) columns with active hoop prestress; this transverse prestressing effect is achieved by bolting together two steel half-tubes. This study refers to new construction only (i.e., no retrofit). 12 prototype CFST column specimens (segments) are analyzed. These specimens differ in the prestressing force (3 levels) and in the gravity loading ratio (4 levels); they are selected to represent typical ground columns of mid-rise buildings. The structural behavior of these column specimens is simulated with a nonlinear model implemented in Abaqus; the concrete and steel behavior are described with a damage-plasticity and a plasticity model, respectively. Finally, the interface concrete-steel interaction is represented by a hard (compression-only) surface-to-surface contact model. The calculations involve three consecutive loading steps: (i) transverse prestress, (ii) axial force, and (iii) lateral loading (shear force and bending moment). The structural behavior of the CFST columns is deeply examined and discussed; the results show that their axial-flexural capacity is adequate. Noticeably, it is concluded that the overall benefits of prestressing the columns are only modest. Preliminary studies on the aforementioned mid-rise buildings equipped with the CFST columns show that their gravity and wind capacities are largely enough; conversely, their seismic capacity is sufficient for moderate seismic ground motions only.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

Currently, energy security and environmental degradation are the two biggest challenges before humanity that can be surmounted with the use of green and sustainable biofuels produced from lignocellulosic crops. In the future, to ensure adequate and cost-effective supply of biofuels, it requires a sufficient amount of amenable and quality lignocellulosic feedstocks. Therefore, agricultural yields of lignocellulosic biomass crops should be substantially increased by intense genetic maneuvering of key gene regulatory mechanisms and signaling pathways that control plant biomass yield. Recently, numerous miRNAs families are identified, characterized, and validated across the plant kingdom. Plant microRNAs (miRNAs) are 21 to 24 nucleotides long, non-coding small RNAs, act as regulators of their target genes via inducing modifications in transcription, translation, and epigenome. MiRNAs represent many hallmark characteristics like sequence-specific regulation, tissue, and species-specific expression, evolutionary conservation, and functional diversity. They coordinate well physiological and life cycle processes in plants under adverse environmental conditions. Hence, miRNAs offer accurate, precise, and efficient regulatory switches in the miRNA-targeted genetic networks. It is evident from the study of the miR156 family and its target SQUAMOSA PROMOTER BINDING PROTEIN-LIKE (SPL) genes network that controls highly significant agronomic traits in crop plants. The miR156/SPL module acts as a master circuit that synchronizes many intricate complex biological functions such as growth and development, and metabolic processes by sensing internal and external environmental signals in plants. Therefore, miR156 can prove a potential target for miRNAs based plant biotechnology to harmonize complex biofuel traits and improve biomass yield in lignocellulosic biomass crops.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

The relative force strengths of the Coulomb forces, gravitational forces, dark matter forces, weak forces and strong forces are compared for the dark matters, leptons, quarks, and normal matters (p and n baryons) in terms of the 3-D quantized space model. The quark confinement and asymptotic freedom are explained by the CC merging to the A(CC=-5)₃ state. The proton with the (EC,LC,CC) charge configuration of p(1,0,-5) is p(1,0) + A(CC=-5)₃. The A(CC=-5)₃ state has the 99.6% of the proton mass. The three quarks in p(1,0,-5) are asymptotically free in the EC and LC space of p(1,0) and are strongly confined in the CC space of A(CC=-5)₃. This means that the lepton beams in the deep inelastic scattering interact with three quarks in p(1,0) by the EC interaction and weak interaction. Then, the observed spin is the partial spin of p(1,0) which is 32.6 % of the total spin (1/2) of the proton. The A(CC=-5)₃ state has the 67.4 % of the proton spin. This explains the proton spin crisis. The EC charge distribution of the proton is the same to the EC charge distribution of p(1,0) which indicates that three quarks in p(1,0) are mostly near the proton surface. From the EC charge distribution of neutron, the 2 lepton system (called as the koron) of the koron is, for the first time, reported in the present work.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

The search algorithm based on symbiotic organisms’ interactions is a relatively recent bio-inspired algorithm of the swarm intelligence field for solving numerical optimization problems. It is meant to optimize applications based on the simulation of the symbiotic relationship among the distinct species in the ecosystem. The modified SOS algorithm is developed to solve independent task scheduling problems. This paper proposes a modified symbiotic organisms search based scheduling algorithm for efficient mapping of heterogeneous tasks to access cloud resources of different capacities. The significant contribution of this technique is the simplified representation of the algorithm's mutualism process, which uses equity as a measure of relationship characteristics or efficiency of species in the current ecosystem to move to the next generation. These relational characteristics are achieved by replacing the original mutual vector, which uses an arithmetic mean to measure the mutual characteristics with a geometric mean that enhances the survival advantage of two distinct species. The modified symbiotic organisms search algorithm (G_SOS) aimed to minimize the task execution time (Makespan), response, degree of imbalance and cost and improve the convergence speed for an optimal solution in an IaaS cloud. The performances of the proposed technique have been evaluated using a Cladism toolkit simulator, and the solutions are found to be better than the existing standard (SOS) technique and PSO.

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

That birds are maniraptoran theropod dinosaurs is now considered an evolutionary consensus. An “open” (i.e., completely, or substantially perforate) acetabulum is considered an important synapomorphy verifying the bird-dinosaur nexus. Here I present anatomical evidence from morphological aspects of the acetabulum and its important appurtenances, the supracetabular crest and the antitrochanter, that the hip anatomy differs substantially between dinosaurs and birds and for the current hypothesis of origins to be correct unlikely anatomical reversals would have been required. Given the thin bone of the acetabular walls and the varied tissue, both hard and soft, in the acetabular region and especially the lower part of the basin, it is apparent that many avian skeletons exhibit some anatomical loss of soft tissue and thin bone, some perhaps related to changes in gait, but also in part related to the dramatic trend in bone reduction associated with flight, especially in more advanced crown taxa. Many basal birds and early diverging neornithines tend to have a nearly closed or various levels of partially closed acetabula, thus rendering the current terms “open” or “closed” acetabula inaccurate; they should be modified or replaced.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.