We discuss the role of the opposing principles of order and disorder in physical and biological systems in determining stability, growth and evolution and bring forth the potential role of a cosmic ordering agency. We analyze its role in decreasing entropy by coarse-graining and hence in determining the initial low entropy state of the big bang universe. Since all physical and biological systems have either cycles of order and disorder alternating, or may have chaotic evolution with non-linear laws, the same is expected of the dynamics of the whole universe as well. The entropy of the initial state of the universe could be low because of the reduction of degrees of freedom (DoF) as one moves from physical encoding to neural encoding and then on to psychic encoding of information in a nested manner by coarse-graining. It is by such encoding that this cosmic agency enables the universe to pass through the big crunch phase and then rolls it out as the big bang universe from the initial state of low entropy.

To obtain drop-in fuel properties from non-feed biomass, we herein report the catalytic hydrotreatment of microalgae biocrude, produced from hydrothermal liquefaction (HTL) of Spirulina. Our contribution focuses on the effect of temperature, initial H2 pressure, and residence time on the removal of heteroatoms (O and N). In contrast to common hydrotreating experimental protocols at batch scale, we devised a set of two-level factorial experiments and studied the most influential parameters affecting the removal of heteroatoms. It was found that up to 350 °C, the degree of deoxygenation (de-O) is mainly driven by temperature, whereas the degree of denitrogenation (de-N) also relies on initial H2 pressure and temperature-pressure interaction.Based on this, complete deoxygenation was obtained at mild operating conditions (350 °C), reaching a concurrent 47 % denitrogenation. Moreover, three optimized experiments are reported with 100 % removal of oxygen. In addition, the analysis by GC-MS and Sim-Dis gives insight to the fuel quality. The distribution of heteroatom N in lower (<340 °C) and higher (>340 °C) fractional cuts is studied by a fractional distillation unit following ASTM D-1160. Final results show that 63-68 % of nitrogen is concentrated in higher fractional cuts.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

Sustainability in material purchasing is a growing area of research. Goods purchasing decisions strongly affect transportation path flows, vehicle consolidation, inventory levels and related obsolescence costs. Within a global sourcing context, companies experience the need of new decision making approaches capable to consider a large variety of factors, also linked with society and environment. Environmental impact assessment has become a key requirement for materials purchasing and transportation decisions since global warming is a rising concern both in academic and industrial researches. In fact, it is well known that the freight transport industry is responsible for large amounts of carbon emissions contributing to global warming. In this paper, we initially analyse and compare the environmental economic policies established by the International Governments in relation to the carbon trading systems adopted. Then, we develop a multi-objective lot sizing approach useful in practice to define the sustainable quantity to purchase when a Cap and Trade mitigation policy is present. We further analyse the model behaviour according to different carbon price values by demonstrating that carbon prices are still far too low to motivate managers towards sustainable purchasing choices.

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams-Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches

Despite the successes earned in cataloguing and finding the role of the most of molecular components in living matter, the “biochemical and molecular” perspective, popular in biology, medicine and genetics, is unable to give account for crucial topics as the faculty of living systems to “feel”, to “perceive” what a given stimulus implies (means, indeed) for their survival. Condensed matter physics too, if bounded to a local, short-range, and perturbative approach, fails dramatically. This is also due to the role commonly assigned to water – actually the main constituent of living matter – deemed for long time to be merely chemical (as “solvent” or a reactant/product). Nonetheless, today many evidences show how living matter can be right conceived as a super-structured coherent water-based matrix, suggesting that the characterization of bio(electro)chemical and physical processes undertaken at molecular level in living matter, would let us unable to answer a question like this: what allows an amoeba, moreover without any neurons, to “know” to get closer to a nutrient or escape away from a toxin? I propose that to pursue such a fundamental inquiry it’s necessary an essentially relational approach, that is: to consider the living being at its grounding as the outcome of a physical history of relationships where symmetry-breakings, dissipation and coherence yield the emergence of the living state of matter, conceivable only as a time-dependent open process, and not as a portraited “body”. The effective tools to build up such an approach may be retrieved in far-from-equilibrium thermodynamics (TD), symmetry-breakings and gauge-fields theory, science of complexity, within the framework of a Quantum Field Theory. Indeed, within a field-view of matter, and of water especially, as it has been developed by a Quantum Electrodynamic (QED) description of condensed matter, it’s possible to give account for a physical basis too such an epistemologically elusive, though crucial, feature of living systems (i.e.: perception and meaning). The emerging landscape allows some important meditations about adaptation, evolution, ecodynamics, and about different conceptions of complexity and “information” in living realm. Furthermore, some neuroscientific themes like consciousness, qualia and their links to artificial intelligence could be supplied with due insights.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

Proteins having a variety of functions play many essential roles in maintaining various life activities in organisms. Various methods, by which new protein functions can be artificially produced, have progressed rapidly upon development in recombinant DNA technology and effective screening techniques. However, the obtainable scope of the new functions has been restricted in a narrow range, because only functions of presently existing proteins can be used. On the other hand, it has been considered that it would be impossible to create an entirely new protein, which does not show any meaningful homology with any other amino acid sequences of previously existing proteins. The reason is because one amino acid sequence for a protein cannot be selected out from an extraordinary large amino acid sequence diversity as ~10130. As a matter of course, it is impossible to design an amino acid sequence of a protein in advance and a gene encoding the protein cannot be also formed through random process. Nevertheless, extant organisms have generated a variety of entirely new proteins in some way to make full use of them. This means that extant organisms have equipped a mechanism with which entirely new proteins can be produced under the present core life system composed of protein, tRNA (genetic code) and gene. In this article, first I introduce the mechanism, with which entirely new proteins are created in extant organisms, and further propose a novel strategy for application of the mechanism to protein engineering through creation of entirely new proteins, which could contribute to development of various industries.

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

Brazil, Russia, China, India, and the Republic of South Africa (BRICS) represent developing economies facing different energy and economic development challenges. The current study aims to forecast energy consumption in BRICS at aggregate and disaggregate levels using the annual time series data set from 1992 to 2019 and to compare results obtained from a set of models. The time-series data are from the British Petroleum (BP-2019) Statistical Review of World Energy. The forecasting methodology bases on a novel Fractional-order Grey Model (FGM) with different order parameters. This study contributes to the literature by comparing the forecasting accuracy and the forecasting ability of the FGM(1,1) with traditional ones, like standard GM(1,1) and ARIMA(1,1,1) models. Also, it illustrates the view of BRICS's nexus of energy consumption at aggregate and disaggregates levels using the latest available data set, which will provide a reliable and broader perspective. The Diebold-Mariano test results confirmed the equal predictive ability of FGM(1,1) for a specific range of order parameters and the ARIMA(1,1,1) model and the usefulness of both approaches for energy consumption efficient forecasting.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

Complex models have received significant interest in recent years and are being increasingly used to explain the stochastic phenomenon with upward and downward fluctuation such as the stock market. Different from existing semi-variance methods in traditional integer dimension construction for two variables, this paper proposes a simplified multi-factorized fractional dimension derivation with the exact Excel tool algorithm involving the fractional center moment extension to covariance, which is a complex parameter average that is a multi-factorized extension to Pearson covariance. By examining the peaks and troughs of gold price averages, the proposed algorithm provides more insight into revealing underlying stock market trends to see who is the financial market leader during good economic times. The calculation results demonstrate that the complex covariance is able to distinguish subtle differences among stock market performances and gold prices for the same field that the two variable covariance may overlook. We take the London, Tokyo, Shanghai, Toronto and Nasdaq as the representative examples.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

Chivalry is a concept that is both familiar and distant to many Japanese. There is no other social class in the world that resembles knights as much as the samurai in Japan. However, why is it that there is such a gap between knights and warriors, even though they are both warriors with the same social status and honor? This paper reviews the legal debates on the deposed sovereigns’ rights have emerged since 20th century. Among them, the right to appoint knights by heads of deposed royal families is one of the focal points. The author begins with a comprehensive review of legal debates on the subject. Six principles on the appointment are extracted from the review. Then, a comparison between chivalry and Bushido, the Japanese Samurai code, was carried out.

Soft-Core architecture for Analogue to Digital Converter (ADC) sampling is useful for mixed signal applications. Soft-core architecture for cutting edge odd or even ADC sampling with interface to block RAM memory has not been found. Soft-core architecture as a concept has become popular due to the advantage of customization for different applications as compared to general-core architecture suited for single application. The latest generation of piece wise sampling is odd sampling and was introduced in the second decade of the 20th century. Odd and even order sampling techniques are analogue in nature driven by a tuned (tuned for odd or even) mixer. This paper proposes a third-generation piece wise sampling with soft-core architecture that enables an option to select both odd and even while interfacing to memory mapping. The proposed odd/even has superior SNR performance of 6 dB as compared to existing architecture such as Mod-∆ which recorded worst performance of 18 dB. Advances in soft-core technology have allowed a niche odd/even switching field to be identified and studied, the study has also been extended to include memory architecture.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane BnHm+n is extended here, with the B3LYP/cc-pVDZ model, to pure conjugated carbon systems with the example of buckminsterfullerene C60 with the corresponding icosahedral isoelectronic system closo-borane B60H60, and the fluorine substituted systems B60F30H30 and B60F60 , all with icosahedral Ih symmetry. All systems correspond to energy minima in the potential energy hypersurface, except for B60(F30)in(H30)out . Selected electronic structure methods are used to characterize all systems: molecular electrostatic potentials (MEP), atomic charges, bond orders, and topological properties of the electron density within quantum theory of atoms-in-molecules (QTAIM) and electron-localization function (ELF) theory. In the particular case of B60H60 we use the recently developed Hückeloid model to characterize this system. The stability of the energy minimum icosahedral structure B60F60 could have an origin in F···F attractive interactions of the inner fluorine atoms of the cage.

An in-depth study of the failure of granular materials, which is known as a mechanism to generate defects, can reveal the facts about the origin of the imperfections such as cracks in the carbon anodes. The initiation and propagation of the cracks in the carbon anode, especially the horizontal cracks below the stub-holes, reduce the anode efficiency during the electrolysis process. In order to avoid the formation of cracks in the carbon anodes, the failure analysis of coke aggregates can be employed to determine the appropriate recipe and operating conditions. In this paper, it will be shown that a particular failure mode can be responsible for the crack generation in the carbon anodes. The second-order work criterion is employed to analyze the failure of the coke aggregate specimens and the relationships between the second-order work, the kinetic energy, and the instability of the granular material are investigated. In addition, the coke aggregates are modeled by exploiting the discrete element method (DEM) to reveal the micro-mechanical behavior of the dry coke aggregates during the compaction process. The optimal number of particles required for the failure analysis in the DEM simulations is determined. The effects of the confining pressure and the strain rate as two important compaction process parameters on the failure are studied. The results reveal that increasing the confining pressure enhances the probability of the diffusing mode of the failure in the specimen. On the other hand, the increase of strain rate augments the chance of the strain localization mode of the failure in the specimen.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

Damage in concrete structures initiates as the growth of diffuse microcracks that is followed by damage localisation and eventually leads to structural failure. Weak changes such as diffuse microcracking processes are failure precursors. Identification and characterisation of these failure precursors at an early stage of concrete degradation and application of suitable precautionary measures will considerably reduce the costs of repair and maintenance. To this end, a reduced order multiscale model for simulating microcracking-induced damage in concrete at the mesoscale levelis proposed. The model simulates the propagation of microcracks in concrete using a two-scale computational methodology. First, a realistic concrete specimen that explicitly resolves the coarse aggregates in a mortar matrix was generated at the mesoscale. Microcrack growth in the mortar matrix is modelled using a synthesis of continuum micromechanics and fracture mechanics. Model order reduction of the two-scale model is achieved using clustering technique. Model predictions are calibrated and validated using uniaxial compression tests performed in the laboratory.

NMR Spectroscopy is used, in the temperature range 180-350K, to study local order and transport in liquid water (pure and confined) and its solutions with glicerol and methanol at different molar fractions. Being the liquid water thermodynamic dominated by polymorphism (two coexisting liquid phases: high- and low-density HDL and LDL) - with the LDL due to the hydrophilic HB interactions, originating in the supercooled regime the tetrahedral networking and the liquid-liquid transition – we focused our interest to hydrophobic effects (HE) on these. Nowadays, if compared to the hydrophilicity, little is known about hydrophobicity so that the main purpose of this study is to gain new information on it. We measured the relaxation times (T1 and T2) and the self-diffusion (DS). From the times we took advantage of the NMR property to follow the behaviors of each molecular component (the hydrophilic and hydrophobic groups) separately; they are studied directly and DS in terms of the Adam-Gibbs model: obtaining the configurational entropy (Sconf ) and the specific heat contributions (CP,conf ). Due to the HE all the studied quantities, behave differently. For water-glycerol the HB interaction is dominant for all the conditions, whereas for water-methanol are observable two different T-regions above and below 265 K, dominated respectively by the hydrophilicity and hydrophobicity. A situation linked to the water polymorphism. Below this temperature, where the LDL phase and the HB networking develops and grows, the times and CP,conf change behaviors leading to maxima and minima. Above it, where the HB becomes weak and less stable and the HDL dominates, the hydrophobicity determines the solution properties.

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein-Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. In Bohm's ontological interpretation, black hole radiation, and the analogous tunneling process of quantum transmission through an ER bridge, are classically allowed if the dynamics are modified to include such a quantum potential. The 4th-order extension of general relativity required to generate the quantum potential is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero. Quantum transmission through the classically non-traversable bridge is replaced by classical transmission through a traversable wormhole. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then the classical wormhole transmission effect gives the ontological nonlocal connection between the particles posited in Bohm's interpretation of their entanglement. It is hypothesized that higher-derivative extensions of classical gravity can account for the nonlocal part of the quantum potential generally.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

To date, theoretical analyses have provided several useful methods/algorithms for studying transition states and non-covalent interactions. Potential Energy Scan (PES) is one such method that has found wide application in the physicochemical community. Analyzing the PES profiles of the catalytic system of FeBr3 in Electrophilic Aromatic Substitution (EAS) with molecular halogens, one can notice an obvious difference from the modern textbook mechanisms proposed in this area of study. Moreover, the newly presented Graphic Methodology (GM) allows a simple and reliable transition state determination even for very weakly bound charge transfer complexes using second-order derivatives as an efficient tool in the graphical analysis. Relative errors that can be reduced to a few parts per thousand in transition state estimation make this method a potentially very useful tool in further graphical studies of non-covalent interactions. Studies performed using high-precision semiempirical methods suggest that the process of halonium ion quenching proceeds along a completely different pathway, suggesting a possible novel transition metal-nonmetal catalytic system involved in the EAS electrophilic quenching step. The results presented here strongly suggest a future GM application that is widely used and the introduction of pseudo and pre-transition states as new terms in the description of non-covalent interactions.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of finitely generated groups. The DNA ‘word’ in the binding domain -the motif- may be seen as the generator of a finitely generated group Fdna on four letters, the bases A, T, G and C. It is shown that, most of the time, the DNA-binding motifs have subgroup structure close to free groups of rank three or less, a property that we call ‘syntactical freedom’. Such a property is associated to the aperiodicity of the motif when it is seen as a substitution sequence. Examples are provided for the major families of TFs such as leucine zipper factors, zinc finger factors, homeo-domain factors, etc. We also discuss the exceptions to the existence of such a DNA syntactical rule and their functional role. This includes the TATA box in the promoter region of some genes, the single nucleotide markers (SNP) and the motifs of some genes of ubiquitous role in transcription and regulation.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

Integrating large-scale wind energy in modern power systems is demanding more efficient mathematical models to properly address classical assumptions in power system problems. In particular, there are two main assumptions in power system problems with wind integration that have not been adequately studied yet; First, non-linear AC power flow equations have been linearized in most of the literature. Such simplifications can lead to inaccurate power flow calculations that may result in other technical issues. Second, wind power uncertainties are inevitable and have been mostly modelled using the traditional uncertainty modelling approaches, that may not be suitable for large-scale wind power integration. In this paper, we address both challenges: we present a tight second-order conic relaxation (SOCR) for optimal power flow (OPF) problem, and simultaneously, implement the new effective budget of uncertainty approach for uncertainty modelling that determines the maximum wind power admissibility first and then addresses the uncertainty in the model. To the best of our knowledge, this is the first study that proposes an effective robust second-order conic programming (ERSOCP) model that simultaneously addresses the issues of power flow linearization and wind power uncertainty with the new paradigm on the budget of uncertainty approach. Our numerical results show the merit of the proposed model against traditional linearized power flow equations as well as traditional uncertainty modelling approaches.

The effects of mixing orders of tannic acid (TA), starch and α-amylase on the enzyme inhibition of TA were studied, including mixing TA with α-amylase before starch addition (order 1), mixing TA with pre-gelatinized starch before α-amylase addition (order 2) and co-gelatinizing TA with starch before α-amylase addition (order 3). It was found that the enzyme inhibition was always highest for order 1 because TA could bind with the enzyme active site thoroughly before digestion occurred. Both order 2 and 3 reduced α-amylase inhibition through decreasing binding of TA with the enzyme, which resulted from the non-covalent physical adsorption of TA with gelatinized starch. Interestingly, at low TA concentration, α-amylase inhibition for order 2 was higher than order 3, while at high TA concentration, the inhibition was shown with opposite trend, which arose from the difference in the adsorption property between the pre-gelatinized and co-gelatinized starch at the corresponding TA concentrations. Besides, both the crystalline structures and apparent morphology of starch were not significantly altered by TA addition for order 2 and 3. Conclusively, although a polyphenol may have an acceptable inhibitory activity in vitro, the actual effect may not reach the expected one when taking processing procedures into account.

The aim of the paper is to provide an overview of the monastic houses operated on the northernmost periphery of Roman Catholic Europe during the Middle Ages. The intention is to debunk the long-held theory of Iceland and Norse Greenland’s supposed isolation from the rest of the world, as it is clear that medieval monasticism reached both of these societies, just as it reached their counterparts elsewhere in the North Atlantic. During the Middle Ages, fourteen monastic houses were opened in Iceland and two in Norse Greenland, all following the Benedictine or Augustinian Order.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

This paper deals with the analysis of trends in road accidents on major highways in Brazil. Using updated time series techniques, our results indicate that a low degree of long memory was detected in the series with shocks having transitory effects over time. We further find that the number of accidents taking place in Brazil has been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

The article is dedicated to the role of polychrome solutions of the architectonic order in the concept of the Baroque façade. The ancient principles of designing architectural structures, inherited from the Renaissance were subjected to reinterpretations in order to impart different expressive values. The arrangements of façades, initially balanced or even horizontal, were replaced by ambiguous bivalent compositions. Vertical layouts began to dominate in the Baroque. Appropriately selected polychrome of the elements of the order could emphasize the compositional expression. The relationship between the layout of the polychrome in a given architectural order and the expression of a work of art has been established for quite a long time. However, the generally available data on color schemes of architectural structures in baroque buildings are still not fully organized. The paper analyses examples of Baroque façades preserved in their original state and revalorized in recent years after thorough conservator’s research in the field of architecture and color. The examples are mainly designed in the so-called great order, i.e. pertaining largely to church façades. In the Baroque, the vertical direction of the composition was strongly emphasized by multiplying or applying perspective arrangements of supports, and finally by embattled entablatures. The decisive field of change became the shaping of the coloristic decoration of the entablature – decisions regarding the material and color separation of elements of the frieze above the supports. The uniform color of all vertical elements of the façade structure guaranteed an unambiguous verticality of the composition.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

In this work we present the results obtained with an artificial neural network (ANN) which we trained to predict the expected output of high-order harmonic generation (HHG) process, while exploring a multi-dimensional parameter space. We argue on the utility and efficiency of the ANN model and demonstrate its ability to predict the outcome of HHG simulations. In this case study we present the results for a loose focusing HHG beamline, where the changing parameters are: the laser pulse energy, gas pressure, gas cell position relative to focus and gas cell length. The physical quantity which we predict here using ANN is directly related to the total harmonic yield in a specified spectral domain (20-40 eV). We discuss the versatility and adaptability of the presented method.

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.

An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.

An overview of the chemical compounds forming the rare smectic T phases is cited with references to the historical context. Thermodynamics (transition temperatures, enthalpies) along with the factors (stereochemical constraints, electrostatic interactions, aliphatic chain stacking, intermolecular forces) contributing to the adoption of tetragonal scaffolds are also discussed. Characteristic optical microscopy textures and x-rays diffraction patterns are presented. In parallel, a comparison of the geometrical parameters such as distances between atoms, molecular areas, volumes, and lattice parameters with the closest two-dimensional and three-dimensional organizations, is performed.

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and triggered the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

Reading is a complex cognitive task involving processes from different systems. The present work aims to identify some points of divergence reported in the reading literature and discuss them in a new experimental paradigm framework. Inspired by the paradigms of perceptual identification and rapid parallel presentation (RPVP), we emphasize that the originality of our experimental paradigm lies in the recruitment of multi-stable Arabic percepts within the region where low-level processing occurs (i.e., the visual span area). With good flexibility, the current paradigm has reached higher-order processing levels. In agreement with previous works highlighting the parafoveal-on-foveal effect, results suggest parallel word processing. Furthermore, they suggest a rapid extraction of syntactic and semantic information from words in sentences while attributing an advantage to semantic processing in the emergence of the sentence superiority effect.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

We report on the application of femtosecond laser micromachining to the fabrication of complex glass microdevices, for high-order harmonic generation in gas. The three-dimensional capabilities and extreme flexibility of femtosecond laser micromachining allow us to achieve accurate control of gas density inside the micrometer interaction channel. This device gives a considerable increase in harmonics generation efficiency if compared with traditional harmonic generation in gas jets. We propose different chip geometries that allow to control the gas density and driving field intensity inside the interaction channel to achieve quasi-phase matching conditions in the harmonic generation process. We believe that these glass micro-devices will pave the way to future downscaling of High-order Harmonic Generation beamlines.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Sentinel-2 provides the opportunity to map the snow cover at unprecedented spatial and temporal resolution at global scale. Here we calibrate and evaluate a simple empirical function to estimate the fractional snow cover (FSC) in open terrain using the normalized difference snow index (NDSI) from 20 m resolution Sentinel-2 images. The NDSI is computed from flat surface reflectances after masking cloud and snow-free areas. The NDSI-FSC function is calibrated using Pléiades very high resolution images and evaluated using independent datasets including SPOT 6/7 satellite images, time lapse camera photographs, terrestrial lidar scans and crowd-sourced in situ measurements. The calibration results show that the FSC can be represented with a sigmoid-shaped function 0.5×tanh(a×NDSI+b)+0.5 where a = 2.65 and b = -1.42 yielding a root mean square error of 25%. Similar RMSE are obtained with different evaluation datasets with a high topographic variability. With this function, we estimate that the confidence interval on the FSC retrievals is 38% at the 95% confidence level.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

A comprehensive presentation of a variety of biologically sounding properties of genomes is present; chloroplast genomes are used as a biological matter. Triplet frequency composition is the general issue standing behind the properties. Besides, the new alignment-free error-tolerant method of sequences comparison highly efficient for in/del mismatches is present, for transposons search. Triplet frequency dictionaries determined for a genome, or for a part of that latter were studied through various clustering techniques. The interplay between triplet composition and function reveals on tRNA genes unambiguously shows the prevalence of the function encoded in tRNA gene over the phylogeny: the genes gather into the clusters comprising the genes encoding the same amino acid; more exactly, few gene families exhibit fine cluster pattern corresponding the synonymous codons of amino acid. Previously reported symmetry in chloroplast genomes is shown for a set of gymnosperm: that is mirror symmetry, rotational symmetry, and the second Chargaff's parity rule asymmetry. A family of transposons was found in gymnosperm chloroplast genomes. This family is revealed through the novel comparison method based on convolution calculation, for a set of DNA sequences.

In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

One of the problems, which make it difficult to solve the mystery of the origin of life, would be how life emerged in chemically complex messy environments on the primitive Earth. It is considered that three main points contributed to open the way to the emergence of life. (1) A characteristic inherent in [GADV]-amino acids, which are easily produced with prebiotic means. (2) Protein 0th-order structure or [GADV]-amino acid composition generating water-soluble globular protein with some flexibility, which can be produced even by random joining of [GADV]-amino acids. (3) Formation of versatile [GADV]-microspheres, which can grow, divide, proliferate even without genetic system, was the emergence of proto-life. (4) [GADV]-microspheres with a higher proliferation ability than others could be selected. The proto-Dawin evolution made it possible to proceed forward to creation of the core life system composed of (GNC)n gene, anticodon stem-loop tRNA or AntiC-SL tRNA (GNC genetic code) and [GADV]-protein. (5) Eventually, the first genuine life with the core life system emerged. Thus, the formation processes of [GADV]-protein and (GNC)n gene in chemically complex messy environments were the steps to the emergence of genuine life.

Understanding the mechanism, how entirely new (EntNew) gene/protein or the first ancestral gene/protein of a family was created, should be one of the most important issues in the biological sciences. However, the mechanism is totally unknown still now. On the other hand, it is well known that mature protein is generally rigid and one catalytic center exists on the protein. Creation of such a mature EntNew gene/protein should be, of course, carried out through random process, because it cannot be designed in advance. However, the EntNew gene/protein never be created by random polymerization of the respective monomeric units, because of the extraordinary large sequence diversities of ~10¹⁸⁰ and ~10¹³⁰, respectively. Protein 0^th-order structure or a specific amino acid composition, in which immature but water-soluble protein can be produced even through random process, holds the key for solving the difficult problem. As it was fragmentally described in the previous papers how and where EntNew gene/protein was created, I describe in detail in this review three processes generating EntNew gene/protein with some flexibility under three genetic codes, the universal genetic code, SNS primitive code and GNC primeval code, and discuss why the mature gene/protein could be created through the processes.

We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.

This note addresses a fundamental problem in matrix theory on establishing and characterizing range equalities for matrix expressions that involve generalized inverses. We first establish a group of necessary and sufficient conditions for the matrix range equality ${\rm range}(D_1 - C_1A_1^{\dag}B_1) = {\rm range}(D_2 - C_2A_2^{\dag}B_2)$ to hold, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of matrix. We then give several groups of range equalities with extrusion properties for multiple matrix products associated with two matrices and their conjugate transposes and Moore--Penrose inverses.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

Background. The treatment of coronary stenosis relies on invasive high risk surgical assessment to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaque causing stenosis. Non-invasive methods are therefore a need of the times. This study proposes an extensible mathematical description of the coronary vasculature that permits rapid estimation of the coronary fractional flow reserve. Methods. By adapting an existing closed loop model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simula-tions generated flow and pressure information which was used to compute fractional flow re-serve under a spectrum of conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis stratified the influence of model parameters on the index. The model was simulated as coupled non-linear ordinary differential equations and numerically solved us-ing an implicit higher order method. Results. Large vessel stenosis affected fractional flow re-serve. The model predicts that the presence, rather than severity, of microvascular disease affect coronary flow deleteriously. Sensitivity analysis revealed that heart rate may not affect the index. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential in reducing the index. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

^{We consider the collective pricing orders in a minimum supply chain that is composed of a monopolistic manufacturer and many retailers that belong to the same chain store firm. The retailers have the freedom to raise or lower the local price. The chain store firm sets up the commercial rules for local retail stores to maximize its total payoff. The monopolistic manufacturer firm controls the total quantity supplied for the market to achieve maximum benefits. We applied the two dimensional Ising model in statistical physics to map the collective distribution of microscopic strategy of local retailers into the macroscopic total payoff of the chain store firm. The local stores choose to raise the price or lower the price based their own mind when the supply in market surpasses the demand. When the supply in market is far less than the demand, the stores synchronously raise prices, even though a local store only have the incomplete information of their nearest neighboring supermarket. We find the critical equation for the balance point between the action of supplier and the action of chain store management based on game theory and statistical physics. The critical equation can identify the Nash equilibrium point of the non-cooperative game between the manufacturer and the chain-store seller, and reveal different levels of collective operations. This statistical physics method also holds for more complicate supply chains and economic systems.}

In the study of materials and macromolecules by first-principle methods, the bond order is a useful tool to represent molecules, bulk materials and interfaces in terms of simple chemical concepts. Despite the availability of several methods to compute the bond order, most applications have been limited to small systems because a high spatial resolution of the wave function and an all-electron representation of the electron density are typically required. Both limitations are critical for large-scale atomistic calculations, even within approximate density-functional theory (DFT) approaches. In this work we describe our methodology to quickly compute delocalization indices for all atomic pairs, while keeping the same representation of the wave function used in most compute-intensive DFT calculations on high-performance computing equipments. We describe our implementation into a post-processing tool, designed to work with Quantum ESPRESSO, a popular open-source DFT package. In this way we recover a description in terms of covalent bonds from a representation of wave function containing no explicit information about atomic types and positions.

In addition to the canonical loss-of-function mutations, mutations in proteins may additionally result in gain-of-function through the binary activation of cryptic ‘structural capacitance elements’. Our previous bioinformatic analysis allowed us to propose a new mechanism of protein evolution - structural capacitance – that arises via the generation of new elements of microstructure upon mutations that cause a disorder-to-order (DO) transition in previously disordered regions of proteins. Here we propose that the DO transition is a necessary follow-on from expected early codon-anticodon and tRNA acceptor stem-amino acid usage, via the accumulation of structural capacitance elements - reservoirs of disorder in proteins. We develop this argument further to posit that structural capacitance is an inherent consequence of the evolution of the genetic code.

Since 1974, when Heinz von Foerster made the distinction between “the cybernetics of observed systems” as first-order cybernetics (1oC) and “the cybernetics of observing systems” as second-order cybernetics (2oC), cybernetics has been dominated by this observer-centric paradigm that he claimed cannot be extended meaningfully to a third-order. Rather than attempting to extend his paradigm, we derive an alternative, model-centric paradigm from first principles of regulation that naturally extends to three orders, where the third order is ethical regulation. We thus consider a type of regulator that requires a third model and a third observer: If the third model is a model of acceptable (ethical) situations, then a third observer is a necessary element of the system’s “conscience” that prevents or detects any violations of the model of ethical situations. In this paradigm, the cybernetics of systems that are designed to exhibit ethical behaviour can be characterized as third-order cybernetics (3oC). By being able to extend the paradigm to include ethical systems, the model-centric paradigm brings clarity and utility that is not possible using the philosopher-friendly observer-centric paradigm and its under-specified (abstract) observers. Finally new definitions for cybernetics are proposed that clearly differentiate between the science and the philosophy, of cybernetics.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structural elements (SSEs), which we deduce by calculating the nematic order parameter, $P_2$. We find that the folded structures are nematic droplets with a broad distribution of $P_2$. We argue that non-zero values of $P_2$, leads to an arrangement of the SSEs that can resist mechanical forces, which is a requirement for allosteric proteins. Such proteins, which resist mechanical forces in some regions while being flexible in others, transmit signals from one region of the protein to another (action at a distance) in response to binding of ligands (oxygen, ATP or other small molecules).

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

When a rotary machine is running, from which the acquired vibro-acoustic signals enable to reveal its operation status and health condition. The study proposed a DSP-based adaptive angular-velocity Vold-Kalman filtering order tracking (AV2KF_OT) algorithm with an online real-time nature for signal interpretation and machine condition monitoring. Theoretical derivation and numerical implementation of computation schemes are briefly introduced. An online real-time monitoring system based on the AV2KF_OT algorithm, which was implemented through both a digital signal processor and a user interface coded by using LabVIEW, was developed. Two experimental tasks were applied to justify the proposed technique, including (i) the detection of startup on the fluid-induced whirl performed through a journal-bearing rotor rig, and (ii) the separation of close orders from the measured signals of a multifunction transmission-element ball-bearing bench.

This article presents a unique set of voltage and current data from a public building and acquired using a hybrid measurement solution that combines Python and Grafana. The transversal purpose consists of contributing to the community with a vision of the quality of the supply more oriented to the monitoring of the state of the network, providing a more realistic vision, which allows a better understanding, and the adoption of the best decisions to achieve the efficient energy management and thus optimize the operation and maintenance of power systems. The work focuses on higher order statistical estimators that, combined with exploratory data analysis techniques, improve the characterization of the shape of the stress signal. These techniques and data, together with the acquisition and monitoring system, present a unique combination in the line of low-cost measurement solutions. It also incorporates the underlying benefit of the contribution to industrial benchmarking. The paper also includes a computational comparison between Python and LabVIEW to elicit the performance of the measurement solution.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

Mixing is considered as a critical process parameter (CPP) during process development due to its significant influence on reaction selectivity and process safety. Nevertheless, mixing issues are difficult to identify and solve owing to their complexity and dependence on knowledge of kinetics and hydrodynamics. In this paper, we proposed an optimization methodology using Computational Fluid Dynamics (CFD) based compartmental modelling to improve mixing and reaction selectivity. More importantly, we have demonstrated that through the implementation of surrogate-based optimization, the proposed methodology can be used as a computationally non-intensive way for rapid process development of reaction unit operations. For illustration purpose, reaction selectivity of a process with Bourne competitive reaction network is discussed. Results demonstrate that we can improve reaction selectivity by dynamically controlling rates and locations of feeding in the reactor. The proposed methodology incorporates mechanistic understanding of the reaction kinetics together with an efficient optimization algorithm to determine the optimal process operation and thus can serve as a tool for quality-by-design (QbD) during product development stage.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

Antimicrobial resistance (AMR) has been a serious threat to human health, and combination therapy is proved to be an economic and effective strategy to fight the resistance. However, the abuse of drug combinations would conversely accelerate the spread of AMR. In our previous work, it had been concluded that the mutant selection indexes (SIs) of one agent against a specific bacterial strain are closely related to the proportions of two agents in a drug combination. To discover probable correlations, predictors and laws for further proposing feasible principles and schemes guiding the AMR-preventing practice, here three aspects were further explored. First, the power function (y=ax^b, a > 0) correlation between the SI (y) of one agent and the ratio value (x) of two agents in a drug combination was further established based on the mathematical and statistical analyses for those experimental data, and two rules a₁ × MIC₁ = a₂ × MIC₂ and b₁ + b₂ = -1 were discovered from both equations of y=a₁x^b1 and y=a₂x^b2 respectively for two agents in drug combinations. Simultaneously, it was found that one agent with larger MPC alone for drug combinations show greater potency for narrowing itself MSW and preventing the resistance. Second, a new concept as mutation-preventing selection index (MPSI) was proposed and used for evaluating the mutation-preventing potency difference of two agents in drug combinations, and the positive correlation between the MPSI and the mutant prevention concentration (MPC) or minimal inhibitory concentration (MIC) was subsequently established. Inspired by this, the significantly positive correlation, contrary to previous reports, between the MIC and the corresponding MPC of antimicrobial agents against pathogenic bacteria was established using one hundred and eighty-one of data pairs reported. These results together of above three aspects indicate that the MPCs in alone and combination are very important indexes for drug combinations to predict the mutation-preventing effects and the trajectories of collateral sensitivity, and while the MPC of an agent can be roughly calculated from its corresponding MIC. Subsequently, the former conclusion was further verified and improved by the antibiotic exposure to forty-three groups designed as different drug concentrations and various proportions. The results further proposed that the C/MPC for the agent with larger proportion in drug combinations can be considered as a predictor and is the key to judge whether the resistance and the collateral sensitivity occur to two agents. Based on these above correlations, laws, and their verification experiments, some principles were proposed, and a diagram of the mutation-preventing effects and the resistant trajectories for drug combinations with different concentrations and ratios of two agents was presented. Simultaneously, the reciprocal of MPC alone (1/MPC), proposed as the stress factors of two agents in drug combinations, together with their SI in combination, is the key to predict the mutation-preventing potency and control the trajectories of collateral sensitivity. Finally, a preliminary scheme for antimicrobial combinations preventing the AMR was further proposed for subsequent improvement research and clinic popularization, based on the above analyses and discussion. Moreover, some similar conclusions were speculated for triple or multiple drug combinations.

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana-Baleanu fractional derivatives without singular and local kernel having strong memory. The human blood is considered as base fluid dispersing carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes(MWCNTs )) into it to form blood-CNTs nanofluid. The nanofluids are considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood-SWCNTs by reason of higher thermal conductivity whereas, this trend is opposite in case of velocity profile due densities difference.

In magneto-photoluminescence (magneto-PL) spectra of quasi-two dimensional islands (quantum dots) having seven electrons and Wigner-Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts and jumps of the energy of the emission components for filling factors &gt;1 (B&lt;10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock-Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, Majorana anyon origin of the states having even , i.e., composite fermions, which provide new opportunities for topological quantum computing.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which are also BICs in a laser-written second-order topological lattice, and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such an HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

The diverse socio-economic and environmental impacts that the set-up of a new photovoltaic installation has must be weighed carefully in order to reach the best possible solution. Among the different photovoltaic systems there are several classification criteria, depending on the technology, application and the size of the modules that define them. The size (installed nominal capacity) stands out as an impartial and critical measure in the decision making process. In this article we use a multi-criteria decision making method to analyse the responses of five experts to a detailed questionnaire in which several different criteria are correlated with various photovoltaic installation sizes. The limitation associated to the low number of experts is addressed with a robustness and sensitivity analysis. With this study we seek first, to apply and demonstrate the feasibility of a methodology which combines technical information with multi-criteria decision making methods, and second, to obtain a clear result oriented that increases the benefits of a forthcoming photovoltaic installation of modules in distributed generation adding up to 1GW total peak power in standard conditions. We observe a consistent result in which smaller photovoltaic modules are the ideal solution that maximises the socio-economic benefits of any installation. If a decision has to be taken about the type of photovoltaic plant to be installed, the conclusion is clear: given a certain size, small, easily scalable installations are the best solution for stake-holders, for the inhabitants, and for the environment.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

Change orders have received considerable attention from researchers thus far, but none have considered pricing strategies of change orders through the interaction between general contractors and subcontractors. Previous studies found that contractors’ opportunistic bidding considering beyond-contractual reward (BCR) in the execution stage can be reduced by improving the construction management system and strengthening the supervision of contractors’ performance. However, the BCR remains in ecology of construction engineering. This study proposes an integrated evolutionary game theory-system dynamics model (ET-SD model) and simulates the pricing strategy of change orders between general contractors and subcontractors to explore the root cause of BCR phenomenon. Sensitivity analysis on the evolutionary dynamics of payoff is explored. Results reveal that change orders with BCR maintain Nash equilibrium and evolutionary stable strategy (ESS) unless changing the payoff structure between general and subcontractors’ pricing strategies. This study presents important managerial insights from the evolutionary game perspectives, nature of change orders, and payoff of the alternative.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

Centromeres, the chromosomal loci where spindle fibers attach during cell division to segregate chromosomes, are typically found within satellite arrays in plants and animals. Satellite arrays have been difficult to analyze because they comprise megabases of tandem head-to-tail highly repeated DNA sequences. Much evidence suggests that centromeres are epigenetically defined by the location of nucleosomes containing the centromere-specific histone H3 variant cenH3, independently of the DNA sequences where they are located; however, the reason that cenH3 nucleosomes are generally found on rapidly evolving satellite arrays has remained unclear. Recently, long read sequencing technology has clarified the structures of satellite arrays and sparked rethinking of how they evolve, while new experiments and analyses have helped bring both understanding and further speculation about the role these highly repeated sequences play in centromere identification.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation. The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts. Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society. Application of the quantum-like model of Frhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and internet based sources.