We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

We present a new penalized method for estimation in sparse logistic regression models with group structure. Group sparsity suggests us to consider the Group Lasso penalty. Being different from penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over the existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. This asymptotic phenomena is observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem.

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply "expectation," traditionally the probability-weighted outcome, regarded since the seventeenth century as the mathematical definition of "expectation." However, when considering the "expectation" of an individual confronted with a finite sequence of outcomes, particularly existential outcomes (e.g., a trader with a limited time to perform or lose his position in a trading operation), we find this individual "expects" the median terminal outcome over those finite trials, with the classical seventeenth-century definition being the asymptotic limit as trials increase to this. Since such finite-sequence "expectations" often differ in values from the classic one, so do the optimal allocations (e.g., growth-optimal). We examine these for fat-tailed distributions. The focus is on implementation, and the techniques described can be applied to all distributional forms.

A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase separations. The results on the evolution of the distribution function and other characteristics of the ensemble, which in the zero volume fraction approximation are asymptotically in good agreement with the theory and the experiment, have been obtained. The peculiarity of the created program complex is the possibility of its adaptation to the description of the decomposition of multicomponent multiphase systems. Fig. 6, list of references - 19 titles.

On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

Abstract-Digital Phase Plane is presented in this paper. For constant input second order digital systems with arbitrary initial conditions for arbitrary quantizaters, this digital phase plane shows, in plot form, the state trajectory and the asymptotic stability, including the existence and the position of arbitrary period limit cycles.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

We review extrapolation methods for calculation of critical points and indices from the perturbative expansions by means of Pad\'{e}-based techniques and their various post-Pad\'{e} extensions by means of root and factor approximants. Factor approximants are applied to finding critical points. Roots are employed within the context of finding critical index. Additive self-similar approximants are discussed and $DLog$ additive recursive approximants are introduced as their generalization. They are applied to the problem of interpolation.

In this study, we investigate spectral structure of conformable Sturm-Liouville problems and with this end, we obtain representation of solutions under different initial conditions and asymptotic formulas for eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Also, we compare the solutions with graphics with different orders, different eigenvalues, different potentials and so, we observe the behaviors of eigenfunctions. We give an application to the α-orthogonality of eigenfunctions and reality of eigenvalues for conformable Sturm-Liouville problems defined by [15] in the last section.

Microstructured optical fibres (MOFs) are a new type of optical fibres that possess a wide range of optical properties and many advantages over common optical fibres. Those are provided by unique structures defined by a pattern of periodic or quasi-periodic arrangement of air holes that run through the fibre length. In recent years, MOFs have opened up new possibilities in the field of optics and photonics, enabling the development of advanced devices and novel optical systems for different applications. The key application areas of PCFs vary from telecommunications and high-power energy transmission to quantum optics and sensing. The stack-and-draw method is a standard manufacturing technique for MOFs, where a preform is first manually created and then drawn in a high-tech furnace into a fibre with the required final dimensions and position of the air holes. Since in the manufacturing process experimenters can control only a few parameters, mathematical models and numerical simulations of the drawing process are highly requested. They not only allow to deepen the understanding of physical phenomena occurring during the drawing process, but they also accurately predict the final cross-section shape and size of the fibre. In this manuscript, we assume thermal equilibrium between the furnace and the fibre and propose a functional form of the fibre temperature distribution. We utilise it with asymptotic mass, momentum, and evolution equations for free surfaces already available in the literature to describe the process of fibre drawing. By doing so, the complex heat exchange problem between the fibre and the furnace need not be solved. The numerical results of the whole asymptotic model overall agree well with experimental data available in the literature, both for the case of annular capillaries and for the case of holey fibres.

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N<1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N<-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

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.

In the present paper, a measure of the influence of irregularities of the underlying surface (for instance, the real terrain profile) on the dynamics of air flow is estimated. It is shown that these irregularities significantly perturbing the pressure, density, velocity and temperature of air flow; for perturbed pressure, density, velocity and temperature of air flow the closed formulas in the Fourier integral form are obtained. In addition, in the present paper, it is proved that due to these perturbations, at a certain altitude of the atmosphere some surface of the "sturdy wall" form appears, on which the vertical and horizontal components of the air flow velocity become infinitesimal and infinitely large, respectively.

Spatial regression models have garnered significant attention across several disciplines, including functional magnetic resonance imaging analysis, econometrics, home price analysis, and many other domains. The phenomenon of sparsity is often found in nature, when a limited number of factors contribute significantly to the overall variation. Spatial regression models frequently use sparsity to indicate less complex computational and more superficial covariance structures. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach for estimating the vector of regression coefficients in the spatial error model, taking into consideration of the prior knowledge that some coefficients are insignificant and there is multicollinearity among the regressors. It also introduces pretest and shrinkage ridge estimators for spatial error regression models, evaluating their performance compared to traditional maximum likelihood estimators. It also assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes.

Random Forest (RF) is a widely used data prediction and variable selection technique. However, the variable selection aspect of RF can become unreliable when there are more irrelevant variables than relevant ones. In response, we introduced the Bayesian Random Forest (BRF) method specifically designed for high-dimensional datasets with a sparse covariate structure. Our research demonstrates that BRF possesses the oracle property, which means it achieves strong selection consistency without compromising efficiency or bias.

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 work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

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

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

The work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/(2r^2) is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying the angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l + 1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.

The objective of this study is to examine a nonparametric estimate , using the kernel approach, of the conditional distribution function of a scalar response variable that is given a random variable whose values take place in a separable real Hilbert space. The observations will be dependent on one another in a quasi-associated fashion. The pointwise practically perfect consistencies with rates of this estimator are established by us under some broad conditions. The study’s major objective is to investigate the convergence rate of the proposed estimator and its application in the convergence rate and asymptotic normality of the hazard function. The asymptotic normality of the developed estimator is established precisely. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

In this paper, we study a one-dimensional Bresse-Cattaneo system with infinite memories and time-dependent delay term (the coefficient of which is not necessarily positive) in the internal feedbacks. First, it is proved that the system is well-posed by means of the Hille-Yosida theorem under suitable assumptions on the relaxation functions. Then, without any restriction on the speeds of wave propagations, we establish the exponential or general decay result by introducing suitable energy and Lyapunov functionals.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.

This work emphasizes some geometrical properties of the Maxwell--Bloch equations. Based on these properties the closed-form solutions of their equations are established. Thus, the Maxwell-Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the Optimal Homotopy Asymptotic Method (OHAM). A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure could be successfully applied for more dynamical systems with geometrical properties.

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

The aim of this paper is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random. The estimators are constructed by the kernel method, and some asymptotic properties such as probability convergence rates of the nonparametric component and asymptotic distribution of the parametric and nonparametric components are established under certain conditions. Next, the performances and the superiority of these estimators are presented and examined using a study on simulated data and on real data by carrying out a comparison between our semi-functional partially linear model with MAR estimator (SFPLRM), the semi-functional partially linear model with the full-case estimator (SFPLRC) and the nonparametric functional model estimator with MAR (FNPM). The results show that the proposed estimators outperform existing estimators as the number of random missing data increases.

The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.

By defining a constant probabilistic orbit of and iterated functions, the stability dynamics of these functions in possible interactions through connectivity provides the formation of a dynamic fixed point as a metric space between both iterated functions. The presence of a dynamic fixed point identifies qualitatively phases of iteration time lengths and interaction orbits of the event. Qualitative results show that the greater the average distance from one of the functions to the fixed point of the other (all possible solutions), the higher the iteration expression on time (false asymptotic effect) of one of the functions and in the opposite hand, the lower the average distance, the higher orbit’s interactions proximity between iterated functions (stability). This feature reveals asymptotic (well-defined) behavior between functions f and g within a well-defined Lyapunov stability.

The Chen circuit system, a three-dimensional autonomous system with intriguing dynamics, has gained considerable attention due to its potential applications in diverse scientific fields. In this article, a Chen circuit-like system is defined and a comprehensive dynamics has been studied. The system exhibits chaotic dynamics, limit cycles, and bifurcations, making it a captivating subject of study. By employing numerical simulations and analytical techniques, we explore the system's stability and identify critical parameter values leading to qualitative changes. Notably, we delve Hopf bifurcations, which give rise to stability changes and the emergence of limit cycles. Furthermore, we analyze the fractal dimension of the system's attractor, providing insights into its complexity and self-similarity. Through a systematic examination of the Chen circuit-like system, we deepen our understanding of its intricate dynamics and offer valuable insights into the underlying mechanisms. The findings contribute to the field of dynamical systems and hold potential implications in areas such as chaos-based secure communications, signal processing, and nonlinear control. This work serves as a valuable reference for researchers and practitioners interested in the dynamics and bifurcation analysis of nonlinear systems.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the SIR-type epidemiological model that we developed for viral diseases with long-term immunity memory pandemic. This is a large-scale model containing 15 nonlinear ODE equations, and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions.

Reporting on CSR activities has become the essence of reporting for modern business entities. In this regard, particular attention is paid to public interest companies. Therefore, the following paper aims to answer the question of whether there are differences in the linguistic structure of the studied CSR reports in three selected industry indices on the Warsaw Stock Exchange (WSE) in Poland, i.e. WIG-energy index, WIG-fuel index, WIG-mining index and their relationship with the performance of selected companies. The study was conducted on a purposely selected sample of companies between 2013 and 2018. A total of 138 CSR reports and 138 annual separate financial statements prepared in accordance with international balance sheet law were collected. The study was carried out based on a panel regression model. It was found that CSR reports contained similar average percentages of parts of speech such as nouns and adjectives. When linking the economic performance of companies, expressed with selected indices, to the information on the implementation of CSR concepts, it was revealed that the results are more likely to describe business performance when it is satisfactory.

In a single-center, retrospective study, 22 cases were enrolled and divided into two groups: those who underwent surgical wide excision (group A) and those who did not (group B). The study included 13 cases in group A and 9 cases in group B. In group A, 6 cases solely underwent surgical wide excision, while 7 cases received additional treatments like radiotherapy or chemotherapy. Conversely, in group B, 4 cases received chemotherapy, 4 cases received radiotherapy, and 1 case was managed through observation alone. The mean follow-up time was 60.15 months in group A and 43.44 months in group B, with no significant difference observed. In group A, 9 cases resulted in mortality, whereas 6 cases died within the follow-up period in group B. Lesion-free intervals post-operation were observed predominantly in group A, while 7 cases in group B never experienced freedom from skin lesions. Kaplan-Meier survival curve analysis demonstrated a significant difference between the survival curves of the two groups (P = 0.046). Among non-HIV Kaposi’s sarcoma patients, surgical wide excision appears to have a role in treatment. Patients in group A exhibit a more favorable outcome in the survival curve analysis.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

In the design of multi-loop Networked Control Systems (NCSs) wherein each control system is characterized by heterogeneous dynamics and associated with certain set of timing specifications and constraints, appropriate metrics need to be employed for the synthesis of control and networking policies to efficiently respond to the requirements of each control loop. Majority of the design approaches for sampling, scheduling and control policies include either time-based or event-based metrics to perform pertinent actions in response to the changes of the parameters of interest. We specifically focus in this article on Age-of-Information (AoI) as a recently-developed time-based metric and threshold-based triggering function as a generic event-based metric. As the NCS model, we consider multiple heterogeneous stochastic linear control systems that close their feedback loops over a shared-resource communication network. We investigate the co-design across the NCS, and discuss the pros and cons with AoI and ET approaches in terms of asymptotic control performance measured by linear-quadratic Gaussian (LQG) cost functions. In particular, sampling and scheduling policies combining AoI and stochastic event-triggered metrics are proposed. It is argued that pure AoI functions that generate decision variables solely upon minimizing the average age irrespective of control systems dynamics may not be able to improve the overall NCS performance even compared with pure randomized policies. Our theoretical analyses are successfully validated through several simulation scenarios.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

The problem of normal impact of a rigid sphere onto a Maxwell viscoelastic solid half-space is considered. The first-order asymptotic solution is constructed in the framework of Hunter’s model of viscoelastic impact [Hunter, S. C., 1957. Energy absorbed by elastic waves during impact. Journal of the Mechanics and Physics of Solids, 5(3), 162–171.]. In particular, simple analytical approximations have been derived for the maximum contact force and the time to achieve it. A linear regression method is suggested for evaluating the instantaneous elastic modulus and the mean relaxation time from a set of experimental data collected for different impactors and impact velocities.

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.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

For the treatment of cancer and other diseases, therapeutic targeting of non-coding RNAs (ncRNAs) such as microRNAs (miRNAs) and long non-coding RNAs (lncRNAs) is an attractive approach. RNA-based therapeutics have been extensively researched over the past decade, with antisense oligonucleotides and small interfering RNAs being the most commonly used. Some of these have even gained FDA approval. However, the results of trials have been mixed, with some studies reporting strong effects while others have shown limited effectiveness or toxicity. Alternative treatments, such as antimiRNAs, are currently in clinical trials. There is growing interest in the use of lncRNA-based therapies. This Perspective discusses the main challenges of ncRNA therapeutics, including specificity, delivery and tolerability. It also highlights emerging approaches that aim to improve their success.

Non-compliant (NC) structures are often encountered in building construction in developing countries. This is a condition whereby erected buildings do not follow regulatory standards, especially in the provision of reinforcements. Therefore, under an earthquake load, the structures do not have sufficient resistance against such load. The structural elements of the building, which often have NC conditions, are the beam-column joints because they do not contain adequate shear reinforcements due to installation difficulty. This study aims to determine the structural performance of the reinforced concrete (RC) frame, which has a reinforcement deficiency in the beam-column joints. Numerical simulation was conducted on the Kakaletsis structure model by modifying the reinforcement details at the joints to represent the NC conditions. The non-linear modeling and analysis of the structural model were carried out using ATENA software. The analysis showed that the reduction in shear reinforcements in the NC model joint caused a decrease in load-carrying capacity by about 26.04%. A shift was also observed in the collapse pattern, i.e., from the beam to the end of the column, causing global failure and reducing the undamaged but increasing more severely damaged condition. This showed that the NC structure, due to the non-conformance of reinforcement, significantly reduced the structure's performance.

An exhaustive list of thirteen instances of reports confirming experimentally the relativistic Doppler relation, are examined. For those involving longitudinal Doppler, the non-relativistic relation is seen to be confirmed, within the reported experimental accuracies, to the same degree as the standard relativistic relation. Higher values of the speed of the emitter would be required to examine further the claimed confirmations. For those reports involving saturation spectroscopy, there is much confusion over the appropriate Doppler relation to be used, together with some serious analytical flaws. For the two cases that involve transverse Doppler, there are seen to be either serious faults in the theoretical part, or intrusion from the first order effect. Therefore, the reported conclusions - that the results for the experiments confirm the relativistic SR relation - cannot be justified by any of the experimental works.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{F}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We show that the public, secret and channel keys become indistinguishable to the eavesdropper under matrix multiplication. Remarkably, for achieving a 512-bit security level, the public key is 1024 bits and the private key is 768 bits, making them the smallest keys among post-quantum key exchange algorithms. Also, we discuss how to achieve key authentication, interdomain certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest only is considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

Nonionizing millimeter-waves (MMW) interact with cells in a variety of ways. Here the inhibited cell division effect was investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm2 safety standards. Irradiation using a power density of about 1.0 mW/cm2 , SAR over 5-6 hours on 50 cells/μl samples of Saccharomyces cerevisiae model organism resulted in 62% growth rate reduction compared to the control (sham). The effect was specific for 85-105 GHz range, and was energy and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deleted cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause permanent genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm2) and compared to that of a compact waveguide (17.17 mW/cm2) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. We have shown that non-thermal MMW radiation has potential for future use in treatment of yeast related diseases and other targeted biomedical outcomes.

Nonionizing millimeter-waves (MMW) are reported to interact with cells in a variety of ways. Possible mechanisms of the inhibited cell division effect were investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm² safety standards. ~1.0 mW/cm² exposure over 5-6 hours treatment on 50 cells/μl samples of Saccharomyces cerevisiae model organism, resulted in 62% growth rate reduction compared to control (sham). The effect was specific for 85-105 GHz range and energy dose and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deletion cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm²) and compared to that of a compact waveguide (17.17 mW/cm²) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. Combinations of MMW mediated Structure Resonant Energy Transfer (SRET), membrane modulations eliciting signaling effects, and energetic resonance with biomolecules were indicated to be responsible for the observations reported. Our results provide novel mechanistic insights enabling innovative applications of nonionizing radiation procedures for eliciting targeted biomedical outcomes.

Non-isocyanate polyurethane synthesis by non-Sn catalysis is an essential challenge toward green polyurethane synthesis. Bismuth compounds are attractive candidates due to their low cost, low toxicity, and availability to urethane chemistry. We applied various Bi catalysts to the self-polycondensation of a bishydroxyurethane monomer and found BiCl3 to be an excellent catalyst through optimization. The catalytic activity and price of BiCl3 are comparable to those of Bu2SnO, while its toxicity is significantly low. BiCl3 is, therefore, a promising alternative to Sn-based catalysts in non-isocyanate polyurethane synthesis.

Wine is a processed beverage that offers high nutritional and health benefits. It is produced from grape must, which undergoes fermentation by yeasts (and sometimes lactic acid bacteria) to create a product that is highly appreciated by consumers worldwide. However, if only one type of yeast, specifically Saccharomyces cerevisiae, were used in the fermentation process, the resulting wine would lack aroma and flavor and may be rejected by consumers. To produce wine with a desirable taste and aroma, non-Saccharomyces yeasts are necessary. These yeasts contribute volatile aromatic compounds that significantly impact the wine’s final taste. They promote the release of primary aromatic compounds through a sequential hydrolysis mechanism involving several glycosidases unique to these yeasts. This review will discuss the unique characteristics of these yeasts (Schizosaccharomyces pombe, Pichia kluyveri, Torulaspora delbrueckii, Wickerhamomyces anomalus, Metschnikowia pulcherrima, Hanseniaspora vineae, Lachancea thermotolerans, Candida stellata, and others) and their impact on wine fermentations and co-fermentations. Their existence and the metabolites they produce enhance the complexity of wine flavor, resulting in a more enjoyable drinking experience.

Post-quantum public cryptosystems introduced so far do not define an scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based in Lizama’s non-invertible Key Exchange Protocol which can be used to implement a public key infrastructure (PKI), secure, scalable, interoperable and efficient. We show functionality of certificates across different certification domains. Finally, we discuss that non-invertible certificates can exhibit Perfect Forward Secrecy (PFS).

It is well established in literature that the public debt and economic growth bear positive and non-linear relationship. However, in recent literature, evidence of no causal relationship is found when accounted for endogeneity in case of advanced economies (Panizza & Presbitero, 2014). Chudik, Mohaddes, Pesaran, & Raissi, (2017) analyse the data on forty countries and find no evidence of universally applicable threshold effect in the relationship between debt and growth. These advancements in the debt-growth literature provides the motivation to re-explore the relationship between public debt and economic growth under non-linearity and endogeneity in context of developing economies of South Asia including Pakistan, India, Bangladesh and Sri-Lanka for the period 1980-2014. There exists a significant, positive but nonlinear relationship between the public debt and economic growth for the selected set of developing countries when accounted for endogeneity and non-linearity. The negative association between the public debt and economic growth for SAARC region is found when the debt level is higher than 61% of GDP which is quite lower than developed economies (90% of GDP). Individual threshold levels for debt-to-GDP ratio divulge that Sri Lanka, Pakistan and India need to control their public borrowings as their current debt levels are higher and/or around the respective threshold levels.

Non-alcoholic steatohepatitis (NASH), which is the most severe manifestation of non-alcoholic fatty liver disease (NAFLD), has been recognized as a major hepatocellular carcinoma (HCC) catalyst. However, the molecular mechanism of NAFLD-NASH-HCC sequence remains unclear and a specific and effective treatment for NASH has not yet been established. The progress in this field depends on the availability of reliable preclinical models which show the steady progress to NASH, liver cirrhosis, and HCC. However, most of NASH mouse models that have been described to date develop NASH generally for more than 24 weeks and there is an uncertainty of HCC development. To overcome such shortcomings of experimental NASH studies, we established a novel NASH-HCC mouse model with very high reproducibility, generality, and convenience. We treated male C57BL/6J mice with a newly developed choline-deficient and methionine-restricted high-fat diet (CDMRHFD) for 60 weeks. Treatment of CDMRHFD for 3 weeks revealed marked steatosis, lobular inflammation, and fibrosis, histologically diagnosed as NASH. Liver cirrhosis was observed in all mice with 36-week treatment. Liver nodule emerged at 12 weeks of the treatment, and diameter >2 mm liver tumors developed in all mice at 24 weeks of the treatment. In conclusion, our rapidly progressive and highly reproducible NASH-liver cirrhosis-HCC model is helpful for preclinical development and research on the pathogenesis of human NAFLD-NASH-HCC. Our mouse model would be useful for the development of novel chemistry for NASH-HCC-targeted therapies or HCC prevention strategies.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

(1) Background: Although multiple studies have reported on the therapeutic effects of Atezo+Bev for the treatment of NASH-related liver cancer, few studies have focused on its effect on liver reserve. Here, we aimed to compare the changes in hepatic reserve during the Atezo+Bev treatment of NAFLD/NASH-related HCC and of non-NAFLD/non-NASH-related HCC. (2) Methods: We retrospectively compared the changes in ALBI score in 109 patients with NAFLD/NASH or non-NAFLD/non-NASH during 12 weeks of treatment with Atezo+Bev for advanced HCC between September 2019 and January 2022. PSM was performed, and the OS, PFS, and PPS of the two groups were compared. (3)Results: The ALBI after 12 weeks of Atezo+Bev treatment was significantly worse in the NAFLD/NASH group than in the non-NAFLD/non-NASH group. Analysis of the 24 propensity score-matched pairs of cases with NAFLD/NASH or non-NAFLD non-NASH yielded similar results. The prognoses of the two groups were similar with respect to OS and PFS, but the NAFLD/NASH group had a significantly shorter PPS. The 24 matched pairs had similar OS and PFS, but the PPS of the NAFLD/NASH group was shorter. (4)Conclusion: Atezo+Bev treatment may worsen hepatic reserve, and there-fore life expectancy, in patients with NAFLD/NASH-related liver cancer.

This article develops a duality principle and a related convex dual formulation suitable for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a model in non-linear elasticity.

The connection of two phenomena - non-conservative friction forces and dissipation-induced instability can lead to many interesting engineering problems. The paper studies general material-dependent damping influence on dynamical instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on a minimal and complex model of a disc brake. A complex system including material-dependent damping is defined in the commercial finite element software. The finite element model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and a disc damping variations on system stability by complex eigenvalue analysis. Analyzes show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

Near-fault ground motions can cause severe damage to civil structures, including bridges. Safety assessment of these structures for near fault ground motion is usually performed through Non-Linear Dynamic Analyses, while faster methods are often used. IMPAb (Incremental Modal Pushover Analysis for Bridges) permits to investigate the seismic response of a bridge by considering the effects of higher modes, which are often relevant for bridges. In this work, IMPAb is applied to a bridge case study considering near-fault pulse-like ground motion records. The records were analyzed and selected from the European Strong Motion Database and the pulse parameters were evaluated. In the paper results from standard pushover procedures and IMPAb are compared with nonlinear Response-History Analysis (NRHA), considering also the vertical component of the motion, as benchmark solutions and incremental dynamic analysis (IDA). Results from the case study demonstrate that the vertical seismic action has a minor influence on the structural response of the bridge. Therefore IMPAb, which can be applied considering vertical motion, remains very effective conserving the original formulation of the procedure, and can be considered a well performing procedure also for near-fault events.

Abrasive Water Jet Machining (AWJM) is a non-conventional machining process that, unlike other methods, is deemed superior because of its applicability, versatility, and no heat-affected zones in the target material. The main objective of this paper was to develop a cheap, practical model for a low-pressure water jet cutting machine and provide some empirical test data for cutting delicate materials. Proper design calculations were performed and are included for both the water jet machine and the two-axis numerical control. Finite Element Analysis results validate the structural integrity of beams and columns in AWJM. Computational Fluid Dynamic analysis of the nozzle shows good agreement with the theoretical calculations regarding the pressure and velocity of the water-abrasive mixture exiting the nozzle. Modal analysis in ANSYS was done to mitigate potential failure due to resonance induced by vibrations. Limited testing on various thicknesses of polystyrene foam ranging from 1-5 mm thickness and rubber sheet of 1 mm thickness showed that even low pressure of 25-30 bar was sufficient to produce a kerf without any burr. However, extensive testing to report optimized parameters like nozzle transverse speed, standoff distance, abrasive flow rate, etc for working at low-pressure ranges is still a consideration for future investigation.

Postprandial glucose levels between 4 and 7.9 hours (PPG4–7.9h) correlate with mortality from various diseases including hypertension, diabetes, cardiovascular disease, and cancer. This study aimed to assess if predicted PPG4–7.9h could diagnose diabetes. Two groups of participants were involved: Group 1 (4420 participants) had actual PPG4–7.9h, while Group 2 (8422 participants) lacked this measure but had all the diabetes diagnostic measures. Group 1 underwent multiple linear regression to predict PPG4–7.9h using 30 predictors, achieving accuracy within 11.1 mg/dL in 80% of the participants. Group 2 had PPG4–7.9h predicted using this model. Receiver operating characteristic curve analysis showed that predicted PPG4–7.9h could diagnose diabetes with an accuracy of 87.3% in Group 2, with a sensitivity of 75.1% and specificity of 84.1% at the optimal cutoff of 102.5 mg/dL. Simulation on 10,000 random samples from Group 2 revealed that 175 participants may be needed to investigate PPG4–7.9h as a diabetes diagnostic marker with a power of at least 80%. In conclusion, predicted PPG4–7.9h appears to be a promising diagnostic indicator for diabetes. Future studies seeking to ascertain its definitive diagnostic value might require a minimum sample size of 175 participants.

Turbulent dissipation is a central issue in the star and galaxy formation process. Its fundamental property of space-time intermittency, well characterised in incompressible laboratory experiments, remains elusive in cosmic turbulence. Progress requires the combination of state-of-the-art modelling, numerical simulations and observations. The power of such a combination is illustrated here where the statistical method intended to locate extrema of velocity shears in a turbulent field is applied to numerical simulations of compressible magneto-hydrodynamical (MHD) turbulence dedicated to dissipation scales and to a nearby turbulent diffuse molecular cloud. We demonstrate that short-spacing increments of observables can detect strongly dissipative structures. In our simulations, we compute structure functions of various synthetic observables and show that they verify Extended Self-Similarity. This allows to compute their intermittency exponents and we show how they could help constraining some properties of the underlying three-dimensional turbulence. In observations of a turbulent cloud close to the Sun in our Galaxy, a remarkable coherent structure of velocity shear extremum is disclosed . At the location of the largest velocity shear, this coherent structure is found to foster 10 × more carbon monoxide molecules than standard diffuse molecular gas, an enrichment supported by models of non-equilibrium warm chemistry triggered by turbulent dissipation. The power of the combination between modelling and observations is also illustrated by observations of the CH+ cation that provide unique quantitative informations on the kinetic energy trail in the massive, multi-phase and turbulent circum-galactic medium of a galaxy group at redshift z = 2.8.

In this paper is presented the design and syntheis of a dynamic output feedback neural network controller for a non-holonomic mobile robot. First the dynamic model of a non-holonomic mobile robot is presented, in which these constraints are considered for the mathematical derivation of a feasable representation for this kind of robot. Then two control strategies are provided based on kinematic control for this kind of robot. The first control strategy is based on driftless control, this means, that considering that the velocity vector of the mobile robot is orthogonal to its restriction a dynamic output feedback and neural network controller is designed in order that the control action would be zero only when the velocity of the mobile robot is zero. The Lyapunov stability theorem is implemented in order to find a suitable control law. Then another control strategy is designed for trajectory tracking purposes, which similar to the driftless controller, a kinematic control scheme is provided but suitable to implement in more sophisticated hardware. In both control strategy a dynamic control law is provided along with a feedforward neural network controller, so in this way, by the Lyapunov theory the stability and convergence to the origin of the mobile robot position coordinates is ensured. Finally, two numerical experiment are presented in order to validate the theoretical results synthetized in this research study. Discussions and conclusions are provided in order to analyze the results found in this research study.

Non-vertebrate species represent about ~95% of known metazoan (animal) diversity. They remain to this day relatively unexplored genetically, but understanding their genome structure and function is pivotal for expanding our current knowledge of evolution, ecology and biodiversity. Following the continuous improvements and decreasing costs of sequencing technologies, many genome assembly tools have been released, leading to a significant amount of genome projects being completed in recent years. In this review, we examine the current state of genome projects of non-vertebrate animal species. We present an overview of available sequencing technologies, assembly approaches, as well as pre and post-processing steps, genome assembly evaluation methods, and their application to non-vertebrate animal genomes.

Background: Thousands of genetic variants have been associated with hematological traits, though target genes remain unknown at most loci. Also, limited analyses have been conducted in African ancestry and Hispanic/Latino populations; hematological trait associated variants more common in these populations have likely been missed. Methods: To derive gene expression prediction models, we used ancestry-stratified datasets from the Multi-Ethnic Study of Atherosclerosis (MESA, including N=229 African American and N=381 Hispanic/Latino participants, monocytes) and the Depression Genes and Networks study (DGN, N = 922 European ancestry participants, whole blood). We then performed a transcriptome-wide association study (TWAS) for platelet count, hemoglobin, hematocrit, and white blood cell count in African (N = 27,955) and Hispanic/Latino (N = 28,324) ancestry participants. Results: Our results revealed 24 suggestive signals (p < 1×10^(-4)) that were conditionally distinct from known GWAS identified variants and successfully replicated these signals in European ancestry subjects from UK Biobank. We found modestly improved correlation of predicted and measured gene expression in an independent African American cohort (the Genetic Epidemiology Network of Arteriopathy (GENOA) study (N=802), lymphoblastoid cell lines) using the larger DGN reference panel; however, some genes were well predicted using MESA but not DGN. Conclusions: These analyses demonstrate the importance of performing TWAS and other genetic analyses across diverse populations and of balancing sample size and ancestry background matching when selecting a TWAS reference panel.

The quality and shelf-life of NCS (Non-centrifugal sugar) mainly depend on the moisture content present in it. NCS formed by the current practice of open sun drying contains moisture substantially greater than the acceptable level of 3%. This paper presents the work taken up to design a tunnel dryer to attain require moisture content in granular NCS for various load conditions. Initially, an experimental investigation had been carried out on a laboratory scale dryer to achieve required moisture content (< 3%) for various load conditions. This experimental data was used for validating two drying models and found that one of the models is best suitable for designing an industrial-scale dryer. For various load conditions on each tray and dryer exit temperature, nine different cases were arrived at. The number of trucks, trays, drying time and energy requirements were computed using the suitable theoretical model. Tunnel dryer with a length of 18 m, a height of 1.2 m, a width of 1 m, number of trucks of 18 and 24 number of trays on each truck was found to be the suitable dryer to dry 1 tone of NCS based on the minimum energy requirement of 176.49 MJ, and a minimum drying time of 68 minutes.

Untranslated regions (UTRs) of flaviviruses contain a large number of RNA structural elements involved in mediating the viral life cycle, including cyclisation, replication, and encapsidation. Here we report on a comparative genomics approach to characterize evolutionarily conserved RNAs in the 3'UTR of tick-borne, insect-specific and no-known-vector flaviviruses in silico. Our data support the wide distribution of previously experimentally characterized exoribonuclease resistant RNAs xrRNAs within tick-borne and no-known-vector flaviviruses and provide evidence for the existence of a cascade of duplicated RNA structures within insect-specific flaviviruses. On a broader scale, our findings indicate that viral 3'UTRs represent a flexible scaffold for evolution to come up with novel xrRNAs

The aim of the study was to identify factors associated with non-adherence to tuberculosis (TB) preventive treatment among contacts with latent TB infection of new cases of pulmonary TB cases reported in Catalonia in 2019-2021. All contacts aged 18 years or older with a latent TB infection who received a TB preventive treatment were included in the study. The Chi square test and the odds ratios (OR) were used to assess the association between non-adherence to TB preventive treatment and the study variables, considering a p < 0.05 as statistically significant. Multiple logistic regression analysis was used to detect the in-dependent factors associated with TB preventive treatment non-adherence, considering a p < 0.05 as statistically significant. The percentage of non-adherence to TB preventive treatment found in this study was 23.7%. A multivariable logistic regression analysis determined that the following factors were significantly associated with TB preventive treatment non-adherence among adult contacts: “exposure at school or workplace” (aOR = 3.34), “exposure to an index case without laboratory confirmation of TB” (aOR = 2.07), “immigrant contact” (aOR = 1.81), “male gender” (aOR = 1.75) and “exposure duration <6 hours per week or sporadic exposure” (aOR = 1.60). By contrast, the factor “short-term TB preventive treatment regimen” (aOR = 0.38) was significantly associated with a lower treatment non-adherence. Adherence to TB preventive treatment should be improved among adult contacts of TB pulmonary cases with latent TB infection by recommending short-term treatment regimens and by developing health education activities, with a greater focus on contacts with factors associated with treatment non-adherence.

Non-alcoholic beer (NAB) or low alcoholic beer (LAB) are taking over the market with a growing sale. Sus-tainable recycling and valorization of exhausted brewer’s spent grains (BSG) coming from craft beer is a relevant issue in brewing process. In this work, recycled BSG and BSG+GJ (supplemented with 10% grape juice) were used as wort-substrate to inoculate already selected non-conventional yeasts to produce NABLAB craft beer. Results showed that wort composed by only recycled BSG produced appreciate NAB beers (ethanol from 0.12% to 0.54 % v/v) while the addition of 10% of grape juice made LAB beers (ethanol from 0.82 to 1.66 % v/v). As expected, volatile compounds production was highest with the addition of grape juice. Lachancea thermotolerans confirmed the lactic acid production and, as Saccharomyces cerevisiae, is characterized by (in both worts) ethyl butyrate and isoamyl acetate, while Torulaspora delbrueckii produced relevant amounts of exanol, phenylethyl acetate and β-phenyl ethanol (wort added with grape juice). Wickeramhomyces anomalus and Pichia kluyvery showed consistent volatile production but only in wort with grape juice addition where a fermentation activity was exhibited. The overall results indicated that reused BSGs, non-conventional yeasts and grape juice is a suitable strategy for specialty NABLAB beer.

With increased vulnerabilities and vast technology landscapes, it is extremely critical to build systems which are highly resistant to cyber-attacks, to break into systems to exploit. It is almost impossible to build 100% secure authentication & authorization mechanisms merely through standard password / PIN (With all combinations of special characters, numbers & upper/lower case alphabets and by using any of the Graphical password mechanisms). The immense computing capacity and several hacking methods used, make almost every authentication method susceptible to cyber-attacks in one or the other way. Only proven / known system which is not vulnerable in spite of highly sophisticated computing power is, human brain. In this paper, we present a new method of authentication using a combination of computer’s computing ability in combination with human intelligence. In fact this human intelligence is personalized making the overall security method more secure. Text based passwords are easy to be cracked ^[6]. There is an increased need for an alternate and more complex authentication and authorization methods. Some of the Methods ^{[7] [8]} in the category of Graphical passwords could be susceptible, when Shoulder surfing/cameras/spy devices are used.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

Previous studies demonstrate the critical importance of non-coding RNAs interfacing with chromatin-modifying machinery resulting in promoter-enhancer-based gene regulation and raise the possibility that many other enhancer-like RNAs may operate via similar mechanisms. Critically, more than 80% of the disease-linked variations identified in genome-wide studies are located in the non-coding regions of genomes, especially non-coding RNA, suggesting non-coding RNAs are relevant to disease. Thus, a critical path forward for understanding non-coding RNAs' role, especially long non-coding RNAs, is to understand the genomic regions' transcriptional regulation, especially non-coding regions. Here, we developed a user-friendly R package called SomaGene for studying and identifying enhancer-like non-coding RNAs with enriched somatic mutations in the cancer genome. SomaGene accepts different genomic variants (whole genome/exome somatic point mutations, structural variations, copy number variations) to identify those RNAs that significantly mutated in diseases (e.g., cancer). It then uses multiple publicly available genomics and epigenetics datasets including ENCODE epigenomics annotations, FANTOM5 tissue-specific expression profiles, disease-associated genome-wide association SNPs, and tissue-specific eQTL pairs to identify those RNAs with potentially enhancer function. SomaGene, as a powerful R package, can provide the opportunity to cancer scientists to study the roles of non-coding RNAs in different cancer genomes.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Numerical models widely used for hydrocarbon phase behavior and compositional flow simulations are based on assumption of thermodynamic equilibrium. However, it is not uncommon for oil and gas-condensate reservoirs to exhibit essentially non-equilibrium phase behavior, e.g., in the processes of secondary recovery after pressure depletion below saturation pressure, or during gas injection, or for condensate evaporation at low pressures. In many cases the ability to match field data with equilibrium model depends on simulation scale. The only method to account for non-equilibrium phase behavior adopted by the majority of flow simulators is the option of limited rate of gas dissolution (condensate evaporation) in black oil models. For compositional simulations no practical yet thermodynamically consistent method has been presented so far except for some upscaling techniques in gas injection problems. Previously reported academic non-equilibrium formulations have a common drawback of doubling the number of flow equations and unknowns compared to the equilibrium formulation. In the paper a unified thermodynamically-consistent formulation for compositional flow simulations with non-equilibrium phase behavior model is presented. Same formulation and a special scale-up technique can be used for upscaling of an equilibrium or non-equilibrium model to a coarse-scale non-equilibrium model. A number of test cases for real oil and gas-condensate mixtures are given. Model implementation specifics in a flow simulator are discussed and illustrated with test simulations. A non-equilibrium constant volume depletion algorithm is presented to simulate condensate recovery at low pressures in gas-condensate reservoirs. Results of satisfactory model matching to field data are reported and discussed.

GCTs are developmental tumors and likely to reflect ontogenetic and teratogenetic determinants. The objective was to identify syndromes with or without congenital anomalies and non-syndromic defects as potential risk factors. Patients with extracranial GCTs (eGCTs) registered in MAKEI 96/MAHO 98 between 1996 and 2017 were used. According to Teilum's holistic concept malignant and benign teratomas were registered. We used a case control study design with Orphanet as a reference group for syndromic defects and the Mainz birth registry (EUROCAT) for congenital anomalies at birth. Co-occurring genetic syndromes and/or congenital anomalies were assessed accordingly. Odds ratios and 95% confidence intervals were calculated and p-values for Fisher’s exact test with Bonferroni correction if needed. A strong association was confirmed for Swyer (OR 338.6, 95% CI 43.7-2623.6) and Currarino syndrome (OR 34.2, 95% CI 13.2-88.6). We additionally found 17 isolated cases of eGCT with a wide range of syndromes, however not significantly associated following Bonferroni correction. All these cases pertained to girls. Regarding non-syndromic defects, no association with eGCTs could be identified. In our study we confirmed a strong association for Swyer and Currarino syndromes with additional congenital anomalies.

Meat serves as a vital component of the human diet, offering a rich source of protein and essential trace elements. China stands as both a significant producer and consumer of meat on a global scale, leading the world in terms of total meat production and consumption. As the standard of living within the country continues to rise, there is a growing emphasis on the nutritional value and safety of meat consumption. The tenderness of meat is a critical factor influencing its overall quality. Traditionally, tenderness has been assessed through shear force testing, a method that is inherently destructive, inefficient, and results in considerable sample wastage. In light of these drawbacks, non-destructive testing techniques have emerged as a preferred alternative, promising greater accuracy, efficiency, and convenience without compromising the integrity of the samples. This paper delves into the application of five advanced non-destructive testing technologies in the realm of meat tenderness assessment. These include near-infrared spectroscopy, hyperspectral imaging, Raman spectroscopy, airflow optical fusion detection, and nuclear magnetic resonance detection. Each technology is scrutinized for its respective strengths and limitations, providing a comprehensive overview of their current utility and potential for future development. Moreover, the integration of these techniques with the latest advancements in artificial intelligence (AI) technology is explored. The fusion of AI with non-destructive testing offers a promising avenue for the development of more sophisticated, rapid, and intelligent systems for meat tenderness evaluation. This integration is anticipated to significantly enhance the efficiency and accuracy of quality assessment in the meat industry, ensuring a higher standard of safety and nutritional value for consumers. The paper concludes with a set of technical recommendations aimed at guiding the future direction of non-destructive, AI-enhanced meat tenderness detection, thereby contributing to the ongoing improvement of the meat industry in China and beyond.

Despite significant milestones in armed conflict research generally and climate security research specifically, methodologically tight explanation of naturally caused armed conflict still leaves much to be desired. In this article we unpack the black box of the climate-security nexus and advance causal modelling of armed conflict. To infer effects of natural causes on armed conflict outcomes, we apply recent advances in causal methods to conflict outcomes that have been non-experimentally observed across Iraqi municipalities. Retrieval of an entire empirical causal structure of climate-conflict pathways allows us to corroborate the existence of a cause-and-effect relationship between climatological, environmental, and demographic variables and armed conflict. We confirm that soil temperature, population density, and variability of latent energy cause an increase in fatalities, while rice production decreases fatalities. We discuss our findings, their limitations, and future research directions, and reflect on their relevance for policy interventions.

Background: Despite scientific advances, the management of procedural pain in neonates remains suboptimal. Applying adequate therapy to control pain during the neonatal period is a moral and ethical act. In recent decades, ample evidence has accumulated regarding the risks, associated with both untreated pain and the use of more aggressive analgesic therapy. Thus, the emphasis in neonatal clinical practice is on non-aggressive pain management techniques, including homeopathic agents. The efficacy and safety of homeopathic agents for reducing procedural pain in neonates is the subject of the present study. Materials and Methods: Healthy full-term newborn babies with an average age of 72-84 hours were included. They were divided into three study groups: group (A) – not anesthetised, /n= 67/, group (B) – anesthetised with Arnica D30 /n=40/ and group (C)- anesthetised with Sol.Glucose 25% /n=40/. The severity of the pain was assessed using the multimodal - Neonatal Infant Pain Scale (NIPS) and the unimodal - Neonatal Facial Coding System (NFCS) scale. Assessments were done 30s before, 30 seconds after, and 5 minutes after the painful stimulus caused by the heel prick. Heart rate, transcutaneous oxygen saturation, respiratory rate and blood pressure were examined at the same intervals. The results obtained were processed statistically by descriptive analysis and ANOVA at a significance level of p&lt; 0.05. Results: 5 minutes after heel prick both scales showed a statistically significant lower score in those given Arnica D30, compared to those who received Sol.Glucose 25%. When monitoring the physiological indicators, we found a significant increase in the heart rate 30 seconds after the procedure.5 minutes after the heel prick we recorded significantly respiratory rate and systolic blood pressure in all three groups compared to pre-procedural values. Conclusions: Arnica D30 has better analgesic effects compared to Sol.Glucose 25% for newborn babies after heel prick tests.

Approximately 300 million non-cardiac surgeries are performed each year. Perioperative mortality after non-cardiac surgery is estimated at 2% in patients over 45 years of age . Half of these deaths are attributable to cardiovascular complications, and most to perioperative myocardial infarction (MINS). Before introduction of cardiac biomarkers the diagnosis of postoperative myocardial infarction was based on symptoms and electrocardiographic changes and its incidence was largely underestimated. The incidence of MINS when standard troponin assay is used ranges between 8 and 19% but increases to 20-30% whit high sensitivity troponin assays. Higher troponin values sugegsting myocardial injury , both with or without definite diagnosis of myocardial infarction, are associated with increased 30 day and 1-year mortality . Diagnostic and therapeutic strategies are reported .

Malnutrition problems are related to diets that lack one or more essential elements, which it is extremely important to food enrichment to improve the content of compounds effective for health. The objective of this study is to evaluate the effect of the addition of Ca2+, K+ and Mg2+ on the induction of nutraceutical quality in grafted tomatoes grown in the NFT (Nutrient Film Technique) system. In the experiment, two factors were evaluated: plants with and without grafting and the foliar application of 10 ml L−1 Ca2+, 4 ml L−1 K+ and 10 ml L−1 Mg2+ cations separately for each case, in addition to the control. The treatments were evaluated using a completely randomized design, with 5 repetitions per treatment. The interactive effects between grafting and foliar application of Ca2+ induced a greater content lycopene, β-carotene and total flavonoids in fruits of tomato. The interactive effects between the graft and the Mg2+ foliar applications obtained the best results in the phenol content. As regards, capacity DPPH and ABTS, the graft decreased concentration, increasing the content of these through foliar applications of calcium. Regarding the enzymatic variables, graft factor increased activity catalase, glutathione peroxidase and phenylalanine ammonium lyase, obtained the best results graft interaction and foliar application of calcium and magnesium. The results obtained demonstrate the influence of the use of grafts and foliar applications of cal-cium and magnesium as tools that could improve the nutraceutical quality content of tomato crop