Matrices and their inverses allow accurate calculations to be produced quickly and compactly and can be used to control any process represented by a system of equations. Singular matrices require extensive workarounds (costing time and money) to solve these systems of equations because they have no inverse. Finding their inverse involves division by zero. Nevertheless, recently a new number set called semi-structured complex numbers was developed to enable division by zero in algebraic equations. The aim of this research was to demonstrate that the inverse of a singular matrix can be found using semi-structured complex numbers. This research reveals (1) Singular matrices and their inverses can be used to find a unique solution to a pair of simultaneous equations that appear to have infinitely many solutions or appear to have no solution; (2) Singular matrices map coordinates in projective space to coordinates in Euclidean space and their inverse maps coordinates in Euclidean space to coordinates in projective space; (3) the inverse of a singular matrix proves that parallel lines in Euclidean space do not intersect but in projective space intersect at a “point at infinity” and (4) collinear lines that intersect at infinitely many points in Euclidean space only intersect at one point in projective space.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

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

In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices $A$ and $B$. $A$ is said to be C-S orthogonal to $B$ if $A^{\tiny\textcircled{S}}B=0$ and $BA^{\tiny\textcircled{S}}=0$, where $A^{\tiny\textcircled{S}}$ is the generalized core inverse of $A$. The characterizations of C-S orthogonal matries and the C-S additivity are also provided. And the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.

People have long had a problem: the equations of motion that reflect the laws of physics are invariance under time inversion, while there always are irreversible processes for gases compose of microscopic particles. This article solves this problem. The point is that we should distinguish between the concepts of the equation of motion and motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a frictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion processes is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We give a physical explanation for the detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases.

The paper deals with the Compound Inverse Rayleigh distribution, shown to constitute a proper model for the characterization of the probability distribution of extreme values of wind-speed, a topic which is gaining growing interest in the field of renewable generation assessment, both in view of wind power production evaluation and the wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model - already proven to be a valid model for extreme wind-speeds - by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity to interpret different field data is illustrated, also by means of numerous numerical examples based upon real wind speed measurements. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. In practice, the method allows to express one’s prior beliefs both in terms of parameters, as customary, and/or in terms of probabilities. The results of a large set of numerical simulations – using typical values of wind-speed parameters - are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Deep Learning is a recent and important addition to the computational toolbox available for image reconstruction in fluorescence microscopy. We review state-of-the-art applications such as image restoration, super-resolution, and light-field imaging, and discuss how the latest Deep Learning research can be applied to other image reconstruction tasks such as structured illumination, spectral deconvolution, and sample stabilisation. Despite its successes, Deep Learning also poses significant challenges, has often misunderstood capabilities, and overlooked limits. We will address key questions, such as: What are the challenges in obtaining training data? Can we discover structures not present in the training data? And, what is the danger of inferring unsubstantiated image details?

In this paper, a new millimeter wave 3D imaging radar is proposed. The user just needs to move the radar along a circular track, a high resolution 3D imaging can be generated. The proposed radar uses the movement of itself to synthesize a large aperture in both the azimuth and elevation directions. It can utilize inverse Radon transform to resolve 3D imaging. To improve the sensing result, compressed sensing approach is further investigated. The simulation and experimental result further illustrated the design. Because a single transceiver circuit is needed, a light, affordable and high resolution 3D mmWave imaging radar is illustrated in the paper.

One of the possible mechanisms causing significant emissions of methane into the atmosphere within the Arctic shelf may be the decomposition of gas hydrates. Their accumulations within the Arctic shelf formed during Ice Age almost simultaneously with the formation of permafrost, which contributed to the emergence of a zone of stable existence of gas hydrates. The subsequent flooding of the Arctic shelf led to the degradation of the permafrost and the violation of the conditions for the existence of hydrates. To assess the state of the stability zone, methods of mathematical numerical modeling are used. Standard seismic methods are widely used to localize gas hydrates, but monitoring their physical state requires the development of fundamentally new approaches based on solving multiparameter inverse seismic problems. In particular, the degree of attenuation of seismic energy is one of the objective parameters for assessing the consolidation of gas hydrates: the closer they are to the beginning of decomposition, the higher the attenuation, and hence the lower the quality factor. Thus, the methods of seismic monitoring of the state of gas hydrates in order to predict the possibility of developing dangerous scenarios should be based on solving a multi-parameter inverse seismic problem. This publication is devoted to the presentation of this approach.

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform adaptive filtering techniques and algorithms normally used in adaptive control, especially when the plant is nonlinear. The deeper the controller the better the inverse function approximation, provided that the nonlinear plant have an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to parameter change of the nonlinear plant in that, under such change, the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. Settling times and rise times of the step response are shown to improve in the DL-based AIC system.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

Industrial manipulators and parallel robots are often used for tasks like drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows to completely remove the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient-descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

Electrolysis stands as a pivotal method for environmentally sustainable hydrogen production. However, the formation of gas bubbles during the electrolysis process poses significant challenges by impeding the electrochemical reactions, diminishing cell efficiency, and dramatically increasing energy consumption. Furthermore, the inherent difficulty in detecting these bubbles arises from the non-transparency of the wall of electrolysis cells. Additionally, these gas bubbles induce alterations in the conductivity of the electrolyte, leading to corresponding fluctuations in the magnetic flux density outside of the electrolysis cell, which can be measured by externally placed magnetic sensors. By solving the inverse problem of the Biot-Savart Law, we can estimate the conductivity distribution as well as the void fraction within the cell. In this work, we study different approaches to solve the inverse problem including Invertible Neural Networks (INNs) and Tikhonov regularization. Our experiments demonstrate that INNs are much more robust to solving the inverse problem than Tikhonov regularization when the level of noise in the magnetic flux density measurements is not known or changes over space and time.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation, and errors in structural installation. Therefore, coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks, this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing integrated antenna structure verify the efficient of the method on the reconstruction accuracy of the structural body displacement field.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Social distancing is a recommended solution by the World Health Organisation (WHO) to minimise the spread of COVID-19 in public places. The majority of governments and national health authorities have set the 2-meter physical distancing as a mandatory safety measure in shopping centres, schools and other covered areas. In this research, we develop a Deep Neural Network-based Model for automated people detection, tracking, and inter-people distances estimation in the crowd, using common CCTV security cameras. The proposed DNN model along with an inverse perspective mapping technique leads to a very accurate people detection and social distancing monitoring in challenging conditions, including people occlusion, partial visibility, and lighting variations. We also provide an online infection risk assessment scheme by statistical analysis of the Spatio-temporal data from the moving trajectories and the rate of social distancing violations. We identify high-risk zones with the highest possibility of virus spread and infection. This may help authorities to redesign the layout of a public place or to take precaution actions to mitigate high-risk zones. The efficiency of the proposed methodology is evaluated on the Oxford Town Centre dataset, with superior performance in terms of accuracy and speed compared to three state-of-the-art methods.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

G-protein-coupled receptors (GPCRs) are ubiquitous sensors and regulators of cellular functions. Each GPCR exists in complex aggregates with multiple resting and active conformations. Designed to detect weak stimuli, GPCRs can also activate spontaneously, resulting in basal ligand-free signaling. Agonists trigger a cascade of events leading to an activate agonist-receptor-G protein complex with high agonist affinity. However, the ensuing signaling process can further remodel the receptor complex to reduce agonist affinity, causing rapid ligand dissociation. The acutely activated ligand-free receptor can continue signaling, as proposed for rhodopsin and  opioid receptors, resulting in robust receptor activation at low agonist occupancy with enhanced agonist potency. Continued receptor stimulation can further modify the receptor complex, regulating sustained ligand-free signaling - proposed to play a role in opioid dependence. Basal, acutely agonist-triggered, and sustained elevated ligand-free signaling could each have distinct functions, reflecting multi-state conformations of GPCRs. This review addresses basal and stimulus-activated ligand-free signaling, its regulation, genetic factors, and pharmacological implications, focusing on opioid and serotonin receptors, and the growth hormone secretagogue receptor (GHSR). Ligand-free signaling of intracellular 5-HT2A receptors could mediate therapeutic effects of psychedelic drugs. Research avenues are suggested to close gaps in our knowledge of ligand-free GPCR signaling.

The reliability of concrete cable-stayed bridge structure is time variant. This is due to strength deterioration and time-variant mechanical and environmental loadings. Demands for keeping concrete cable-stayed bridge structure in functional and reliable states require maintenance interventions. Limited financial resources require optimal maintenance strategies. These strategies have to consider the effects of uncertainties not only on the structural reliability deterioration but also on the maintenance interventions. By analyzing variation of concrete cable-stayed concrete cable-stayed bridge liabilities and benefit expectation through different maintenance programs, on the condition of satisfying the concrete cable-stayed bridge performance, with the maximum expected benefit as the target to discuss repair and reinforcement strategies for the concrete cable-stayed bridges in service. The method takes into account the present performance and future expected benefit, optimizing the performance of the concrete cable-stayed bridge and the expected benefit through determination policies of concrete cable-stayed concrete cable-stayed bridge maintenance program. The proposed method also includes an advanced cost model which takes into account the interaction between costs of maintenance interventions and their effect on reliability. Examples are presented demonstrating the application of the proposed method to a stock of existing deteriorating concrete cable-stayed bridges under various maintenance scenarios.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two architectures (unrolling the loop) were developed and analyzed. The algorithm recovers sources located at the boundary separating two homogeneous media that make up a two-dimensional non-homogeneous region from measurements on the boundary of such region. The problem of recovering these sources is an ill-posed inverse problem as small errors in the measurement can produce important changes in the source location. Inverse source problems have many applications in different areas, such as engineering and medicine, making the proposed implementation important. The first architecture (mode one) allows considering different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (mode two) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems such as inverse electrocardiography or electroencephalography. The architectures were tested on four FPGAs of the 7 Series of Xilinx: Spartan-7 xc7s100fgga484, Virtex-7 xc7v585tffg1157, Kintex-7 xc7k70tfbg484, and Artix-7 xc7a35tcpg236. The two FPGA implementations of the algorithm were validated using synthetic examples implemented in MATLAB. The results presented here can be extended to concentric spheres and complex geometries.

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.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

We present a MATLAB-based, open source reconstruction software for Hybrid Imaging problem arising from Current Density Impedance Imaging (CDII) and Acoustic-Electrical Impedance Tomography (AEIT), utilizing mixed finite element method solver of Darcy toolbox {\tt DarcyLite}~. For a formulation of hybrid inverse problems in impedance tomography the successive substitution iterative schemes are adapted and an reconstruction algorithm is developed. The problem formulation is a class of hybrid imaging modality which is current density impedance imaging or Acoustic-Electrical Impedance Tomography. The proposed algorithm is implemented numerically in two dimensions.

Helmholtz energy of ice VII-X is determined in a pressure regime extending to 450 GPa at 300 K using local basis functions in the form of b splines. The new representation for the equation of state is embedded in a physics-based inverse theory framework of parameter estimation. Selected pressures as a function of volume from 14 prior experimental studies and two theoretical studies constrain the behavior of Helmholtz energy. Separately measured bulk moduli, not used to construct the representation, are accurately replicated below about 20 GPa and above 60 GPa. In the intermediate range of pressure, the experimentally determined moduli are larger and have greater scatter than values predicted using the Helmholtz representation. Although systematic experimental error in the experimental elastic moduli is possible and likely, the alternative hypothesis is a slow relaxation time associated with changes in proton mobility or the ice VII to X transition. A correlation is observed between anomalies in the pressure derivative of the predicted bulk modulus and previously suggested higher-order phase transitions. Improved determinations of elastic properties at high pressure would allow refinement of the current equation of state. More generally, the current method of data assimilation is broadly applicable to other materials in high-pressure studies.

We tested the possibility of using “adverse events count” (AEC) as a drug-risk indicator and side-effect severity indicator. Data from 3938 adverse event (AE) reports for COVID-19 vaccines (Comirnaty, Moderna, Vaxzevria, and Janssen) and 6869 AE reports for other medicines were collected from the Bulgarian Drug Agency database (01.01.2018–31.03.2022). AEC was modeled with zero-adjusted negative binomial (ZANBI) and zero-adjusted Poisson inverse Gaussian (ZAPIG) regression models, which account for zero absence and overdispersion. The models’ fit was checked with residual diagnostic plots and parametric correspondence to normality. Explanatory variables were: age, sex, sequence number (order of submission), severity of AE, and vaccine type. Average AEC was higher in severe vs. non-severe AE, and in females vs. males; it decreased with age and was lower in Comirnaty than other vaccines. Variability of AEC for COVID-19 data decreased with sequence number in severe AE and increased in non-severe AE. Full ZANBI models had greater sensitivity than parametric ZANBI or ZAPIG models. Results showed correlation between AEC and AE severity, suggesting AEC as a simple and reliable measure of drug-risk and side-effect severity for clinicians and regulators, especially for COVID-19 vaccines.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses the relationship between stability and the Gaussian curvature, as well as the connections between queueing theory, information geometry, , Riemannian geometry, and the Theory of Relativity.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

Despite great technical capabilities, the theory of non-contact temperature measurement is usually not fully applicable to the use of measuring instruments in practice. While black body calibrations are in practice well established and easy to accomplish, this calibration protocol is never fully applicable to measurements of real objects under real conditions. Currently, the best approximation to real world radiation thermometry is grey body radiation thermometry, which is supported by most measuring instruments to date. Nevertheless, the metrological requirements necessitate traceability, therefore real body radiation thermometry is required for temperature measurements of real bodies. This article documents the current state of temperature calculation algorithms for radiation-thermometers and the creation of a traceable model for radiation thermometry of real bodies that uses a digital twin model of the system of measurement to compensate for the loss of data, caused by spectral integration, which occurs when thermal radiation is absorbed on the active surface of the sensor. To solve this problem, a hybrid model with variable scalar inputs is proposed, in which the scalar input parameters are calculated to correspond to the system of measurement. The method for calculating the effective parameters is proposed and verified with the theoretical model of non-contact thermometry. The sum of effective instrumental parameters is presented for different temperatures to show that the rule of radiation thermometry of grey bodies, according to which the sum of instrumental emissivity and instrumental reflectivity equals to 1, does not hold in radiation thermometry for real bodies. Using the derived models of radiation thermometry, the uncertainty of radiation thermometry due to the uncertainty of spectral emissivity is analysed by simulated measurements along the temperature ranges of various radiation thermometers, enabling traceable non-contact temperature measurements with known measurement uncertainty under any known conditions.

Recent advances in nanomaterials have been heavily influenced by low-dimensional nanocarbon allotropes. In particular, carbyne has attracted attention for its potential as a true one-dimensional carbon chain with sp1 hybridization. To maximize the capabilities of this material, we employ a focused data-driven inverse design approach based on the carbon nanomaterials genome concept. This involves using deep learning neural network models to identify key descriptors tied to desired properties, enabling property prediction and reverse engineering of nanocarbons. Our iterative approach entails: (i) gathering growth/property data on nanostructures; (ii) identifying informative numerical/categorical predictors; (iii) developing deep learning models mapping descriptors to properties; (iv) refining models with new insights; (v) determining required descriptors/conditions for target properties via inverse mapping; (vi) validating models by synthesizing predicted nanostructures; and (vii) enhancing models with validation data. This allows uncovering hidden growth-property connections, precisely tuning nanocarbons for desired attributes. We introduce new methodologies including exciting synergistic effects, synchronizing atomic vibrations, active screen plasma, energy-driven transformations, surface acoustic micro/nano-manipulation, doping and directed self-assembly to expose relationships and integrate insights into the inverse design flow. This research promises to accelerate discovery of next-generation low-dimensional nanocarbons with exceptional properties and applications.

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

This paper first explains the theory of the origin of force from a new perspective, explaining that the origin of all forces is caused by the "missing of energy in the time dimension" (non-conservation in a certain period of time), and constructs a unified theory of force on this basis. Then, through the unified theory of force, the following phenomena are reinterpreted: (1) The common origin of the inverse square law of gravitation and electromagnetic force; (2) The origin of the repulsive force of electrons and protons at small distances; (3) The mystery of the rotation curve of galaxies and the new explanation of "dark matter"; (4) explain the origin of the magnetic field; (5) Predict that moving magnets have the same radiation effect as charged particles (electron magnetic moments also have radiation effects); (6) Reinterpret Maxwell's displacement current; (7) Reinterpret synchrotron radiation and bremsstrahlung; (8) Explain that the strong and weak forces are short-range forces; (9) Predict the true structure of black holes and the origin of gravitational waves;(10) Possible explanation for the origin of the speed of light.

The swift progress in low-dimensional nanocarbons, specifically in the realm of the authentic one-dimensional carbon chain featuring sp¹ hybridization, has unveiled exciting prospects for integrating them into cutting-edge technologies across diverse industries. To fully harness their potential, precise control over the growth process is necessary to obtain desired nanostructure and functionality. However, optimizing properties through traditional approaches has been challenging due to complex interactions. To address this, we implement a focused data-driven strategy for nanocarbon inverse design by leveraging a state-of-the-art data-driven nanocarbon genome approach (NCGA). By uncovering relationships between growth parameters and resultant traits, this serves as an expedient catalyst in engineering nanostructures with tailored attributes. We introduce an extensive array of technological approaches aimed at precisely controlling the growth process. These methods encompass stimulating and precisely adjusting synergistic effects, coordinating atomic vibrations at a collective level through the implementation of multilayer nano-interfaces, harnessing the potential of active screen plasma surface engineering, utilizing nano-patterning and allotropic phase transformations, incorporating heteroatom doping, and effectively directing self-assembly. These aim to unlock nanomaterials' latent potential and reveal novel neural pathways within the data-driven NCGA, enhancing its predictive capabilities. Specifically, triggering self-organization during growth can potentially unlock previously unexplored neural pathways. The data-driven NCGA offers a paradigm shift, accelerating discovery and design of nanocarbons with optimized, application-specific properties.

This paper introduces an innovative nanotechnology-based approach that provides a pathway to enhance the energy release efficiency of nanoenergetic materials (nEMs) by harnessing self-synchronized collective atomic vibrations and phonon wave resonance within the transition domains between nanocomponents, without altering the material composition. The key innovation involves incorporating finely-tuned 2D-ordered linear-chain carbon-based multilayer nano-enhanced interfaces as programmable nanodevices into the transition domains using advanced multistage processing and assembly techniques. These programmable nanodevices enable precise control over self-synchronized collective atomic vibrations and phonon wave propagation, leading to synergistic effects. To activate and optimize these effects, a combination of various methods is employed, including energy-driven initiation of allotropic phase transformations, surface acoustic wave-assisted micro/nano-manipulation, heteroatom doping, directed self-assembly using high-frequency electromagnetic fields, and data-driven inverse design approaches. By leveraging a data-driven inverse design strategy and uncovering hidden structure-property relationships, we maximize energy release efficiency using the carbon nano-materials genome approach derived from multifactorial neural network-based predictive models. This approach not only unlocks new functionalities in nEMs but also improves environmental performance and safety levels. By pioneering transformative pathways for nEMs through harnessing phonon wave resonance in low-dimensional nanocarbon transition interfaces, this research brings significant advancements in the field.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

Power sources that can consistently deliver high levels of energy over extended periods are crucial for various space applications. Among the many methods of energy generation, direct heat-to-electricity conversion without intermediate steps or moving components shows particular promise but also presents significant challenges. The aim of this research is to address these challenges by enhancing the energy efficiency of thermionic conversion, which transforms thermal energy into electrical energy, through the development and utilization of a novel class of emission nanomaterials known as multilayer carbyne-enriched 3D-shaped nano-interfaces. By manipulating the topological, physicochemical, and functional characteristics of these interfaces, we seek to optimize their thermionic conversion capabilities. Building on the recent discovery of collective atomic vibrations called phonon waves within transition domains of multilayer nanostructures, we have devised a new approach to enhance the efficiency of thermionic energy converters. This involves unlocking the predictive functionality of 2D-ordered linear-chain carbon-based multilayer emitters through the excitation and fine-tuning of collective atomic vibrations and nanoarchitecture. To achieve this, we propose employing a combination of techniques that leverage interface effects, enable phonon wave propagation, facilitate energy exchange, and capitalize on synergistic effects offered by the multilayer nano-enhanced interfaces. The resulting devices for thermionic energy conversion have the potential to significantly surpass the efficiency of existing plasma thermionic converters by several orders of magnitude. Moreover, these electricity-generating sources based on thermionic conversion represent fundamental options for the advancement of Lunar and Martian research missions, opening up possibilities for sustainable energy production in extraterrestrial environments.

Synthetic Aperture RADAR (SAR) is a radar imaging technique in which the relative motion of the sensor is used to synthesize a very long antenna and obtain high spatial resolution. Standard SAR raw data processing techniques assume uniform motion of the satellite (or aerial vehicle) and a fixed antenna beam pointing sideway orthogonally to the motion path, assumed rectilinear. Despite SAR data processing is a well established imaging technology that has become fundamental in several fields and applications, in this paper a novel approach has been used to exploit coherent illumination, demonstrating the possibility of extracting a large part of the ancillary data information from the raw data itself, to be used in the focusing procedure. In this work an effort has been carried out to try to focus the raw SAR complex data matrix without the knowledge of anyof the parameters needed in standard focusing procedures as Range Doppler (RD) algorithm, ω - K algorithm and Chirp Scaling (CS) algorithm. All the literature references regarding the algorithms needed to obtain a precise image from raw data use such parameters that refer both to the SAR system acquisition geometry and its radiometric specific parameters. In [12], authors introduced a preliminary work dealing with this problem and able to obtain, in the presence of a strong point scatterer in the observed scene, good quality images, if compared to the standard processing techniques. In this work the proposed technique is described and performances parameters are extracted to compare the proposed approach to RD.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.