Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

Wave energy converter (WEC) arrays deployed in coastal regions may create physical disturbances potentially resulting in environmental stresses. Presently, limited information is available on the nature of these physical disturbance or the resultant effects. A quantitative Spatial Environmental Assessment Tool (SEAT) for evaluating potential effects of wave energy converter (WEC) arrays on nearshore hydrodynamics and sediment transport is presented for the central Oregon coast (USA) through coupled numerical model simulations of an array of WECs. Derived climatological wave conditions were used as inputs to the model to allow for the calculation of risk metrics associated with various hydrodynamic and sediment transport variables such as maximum shear stress, bottom velocity, and change in bed elevation. The risk maps provided simple, quantitative, and spatially-resolved means of evaluating physical changes in the vicinity of a hypothetical WEC array in response to varying wave conditions. Near-field risk of sediment mobility was determined to be moderate in the lee of the densely spaced array, where the potential for increased sediment deposition could result in benthic habitat alteration. Modifications to the nearshore sediment deposition and erosion patterns were observed near headlands and topographic features, which could have implications for littoral sediment transport. The results illustrate the benefits of a risk evaluation tool for facilitating coastal resource management at early market marine renewable energy sites.

The field of smart materials is attaining global industrial importance rapidly. The ionic polymer metal metaIl composites withheld there importance in this field. They are not only used as biocompatible devices but also in the field of thin and conformal bio coatings. The nafion 117 is unstable at elevated temperatures and its water intake resistance is low, so the nafion 117 is coated with the noble material to increase its thermal stability and water resistant property. The high cost of noble metal make its too costly to use in day to day applications so parylene has been used as substitute for noble metal in order to reduce the cost. The high thermal stability and water intake property if parylene make its suitable for the same. Multiple chemical treatments like plasma ionization and others have been done on the parylene coated nafion to increase its desirable properties considerably. The low adhesion rate between parylene and nafion 117 has been increased upto the certain extend by the use of ionized plasma. This paper reviewed the plasma chemical treatment of paryelene coatings for the biocompatible devices and provides an insight knowledge on classification, structure and thermal stability of the parylene coatings.

We propose a neural-network-based watermarking method that introduces the quantized activation function that approximates the quantization of JPEG compression. Many neural-network-based watermarking methods have been proposed. Conventional methods have acquired robustness against various attacks by introducing an attack simulation layer between the embedding network and the extraction network. The quantization process of JPEG compression was replaced by the noise addition process in the attack layer of the conventional methods. In this paper, we propose a quantized activation function that can simulate the JPEG quantization standard as it is in order to improve the robustness against the JPEG compression. Our quantized activation function consists of several hyperbolic tangent functions and is applied as an activation function for neural networks. Our network was introduced in the attack layer of ReDMark proposed by Ahmadi et al. to compare it with their method. That is, the embedding and extraction networks had the same structure. We compared the usual JPEG compressed images and the images applying the quantized activation function. The results showed that a network with quantized activation functions can approximate JPEG compression with high accuracy. We also compared the bit error rate (BER) of estimated watermarks generated by our network with those generated by ReDMark. We found that our network was able to produce estimated watermarks with lower BERs than those of ReDMark. Therefore, our network outperformed the conventional method with respect to image quality and BER.

Motion related human activity recognition using wearable sensors can potentially enable various useful daily applications. So far, most studies view it as a stand-alone mathematical classification problem without considering the physical nature of human motions. Consequently, they suffer from data dependencies and encounter the dimension disaster problem and the over-fitting issue, and their models are never human-readable. In this study, we start from a deep analysis on natural physical properties of human motions, and then propose a useful feature selection method to quantify each feature's classification contribution capability. On one hand, the "dimension disaster" problem can be avoid to some extent, due to the affined dimension of key features; On the other hand, over-fitting issue can be depressed since the knowledge implied in human motions are nearly invariant, which compensates the possible data inadequacy. The experiment results indicate that the proposed method performs superior to those adopted in related works, such as decision tree, k-NN, SVM, neural networks.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et.\ al. This approach modifies Wigner's method by introducing an arbitrary timelike unit vector $n^\mu$ on which one induces a representation of $SL(2,C)$, rather than induce on the spacetime momentum $p^\mu$. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^\mu,p^\mu),(\zeta^\mu,\pi^\mu)\}$, inducing a representation on the momentum $\pi^\mu$, thus providing a novel dynamical interpretation of the timelike unit vector $n^\mu = \pi^\mu / M$. Studying the unitary representations of the Poincar\'e group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments.

In this paper, several classes of rough Marcinkiewicz integral operators along surfaces of revolution on product spaces are investigated. We prove the Lp boundedness of these operators when their kernels functions belong to a class of functions related to a class of functions introduced by Grafakos-Stefanov. The results in this paper extend and improve several known results on Marcinkiewicz integrals.

Abstract The value of the mass of the particles is one more mystery that current theories cannot predict, so they have to be determined experimentally. In this paper we will see how the quantization of 4D space gives rise to the quantization of mass and, in turn, the quantization of mass implies that space-time is discrete.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

The research was aimed at comparing the fire characteristics of different types of pepper in the context of designing explosion prevention. The following characteristics were studied: explosion pressure pmax and Kst at selected concentrations, ignition temperature of the deposited dust layer from the hot surface and minimum initiation energy. The comparison of the chemical properties of the used types of pepper was performed using TG/DSC. Results of the measurements suggest that different types of peppers exhibit different explosion characteristics. Each of the samples reached the maximum value of the explosion pressure, and their rate of pressure rise increased at different concentrations. The volume of the explosion chamber used also influenced the explosion characteristics. It is a consequence of the fact that the explosion characteristics strongly depend on the mechanism of action of a particular igniter. The minimum effect on the safety characteristics was observed when measuring the minimum initiation energy and the minimum ignition temperature of dust layer from the hot surface. The results of the measurements suggest that different types of peppers exhibit different explosion characteristics. This information should then be considered in explosion prevention.

The aim this text to present the confined covariant quark model (CCQM) and review its applications to the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we review also. The physics principles are in detail exposed for the CCQM, the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering successively three categories of decay processes: leptonic, semileptonic and non-leptonic.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

The present study evaluated the effect of Prosthechea karwinskii leaves extract on antioxidant enzymes superoxide dismutase (SOD) and catalase (CAT) in a model of obese rats with insulin resistance to know its nutraceutical potential on insulin resistance and oxidative stress. Obesity and insulin resistance were induced in rats by administering 40% sucrose in water. Once the model was established, four groups were evaluated (control, obese, obese administered with extract, and obese administered with metformin), and the indices of insulin resistance and the activity of antioxidant enzymes were measured. In addition, compounds in the extract were identified with UHPLC-ESI-qTOF-MS/MS. The glucose, insulin, triglycerides, and insulin resistance indicators (HOMA-IR and TyG) increased in obese rats. The activity of the antioxidant enzymes evaluated increased in the obese group, apparently as an adaptive response to oxidative stress to inhibit reactive oxygen species formed by hyperglycemia. Administration of P. karwinskii extract and metformin reduced glucose, insulin, triglyceride levels, insulin resistance indicators and antioxidant enzymes to values like those of the control group. This study shows the nutraceutical potential of P. karwinskii extract as an ingredient in the formulation of food supplements or functional foods to help treat diseases related to insulin resistance and oxidative stress.

Canonical quantization is a wonderful procedure for selected problems, but there are many problems for which it fails. Affine quantization is a different procedure that has shown that it can solve many problems that canonical quantization cannot. Here, words like succeed and fail refer to whether the quantization results are correct or incorrect. This paper offers two simple examples that serve to introduce affine quantization, and compare studies of two different quantization procedures. Brief comments about field theory and gravity problems undergoing quantization by affine procedures completes the paper.

We present a geometric field theory in which the action and field equation are constructed from an ultra-high-density vector field and its covariant derivative and have full general covariance in a higher-dimensional spacetime. The field equation is the simplest possible generalisation of the Poisson equation for gravity consistent with general covariance and the equivalence principle. It contains the Ricci tensor and metric acting as operators on the vector field. If the covariant derivative is diagonalisable across a neighbourhood under real changes of coordinate basis, spacetime coincides with a product manifold. The dimensionalities of the factor spaces are determined by its eigenvalues and hence by its algebraic invariants. Tensors decompose into multiplets which have both Lorentz and internal symmetry indices. The field equation has a `classical vacuum' solution which is a product of Minkowski spacetime and an Einstein manifold. A worked example is provided in six dimensions. Away from this classical vacuum, connection components in appropriate coordinates include $SO(N)$ gauge fields. The Riemann tensor includes their field strength. Unitary gauge symmetries act indirectly on tensor fields and some or all of the unitary gauge fields are found amongst the $SO(N)$ gauge fields. Symmetry restoration occurs at the zero-curvature `decompactification limit', in which all dimensions appear on the same footing.

Shrimp is the most important aquaculture industry. Therefore, we determined the effect of nitrifying-probiotic bacteria on water quality, growth, survival, immune response and intestinal microbiota of Litopenaeus vannamei cultured without water exchange. In vitro, only B. licheniformis used TAN, nitrites and nitrates since nitrogen bubbles were produced. TAN decreased significantly in the treatments with bacilli and LAB, but no differences were observed in nitrites. Nitrates were significantly higher in the treatments with bacteria. The final weight and survival of shrimp in the bacterial treatments increased significantly and superoxide anion increased significantly only in LAB treatment. The activity of phenoloxidase decreased significantly in the treatment with LAB and with the mixture of bacilli and LAB. Shrimp treated with bacilli in the water showed lower species richness. The gut bacterial community after treatments was significantly different from that of the control. Linoleic acid metabolism was positively correlated with final weight and superoxide anion, whereas quorum sensing was correlated with survival. Thus, bacilli and LAB in the water of hyperintensive culture systems act as nitrifers, modulate the intestinal microbiota and immune response, and improve the growth and survival of shrimp. This is the first report on Pediococcus pentosaceus and Leuconostoc mesenteroides as nitrifying bacteria.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.

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

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

In a previous work by the author it was shown that the Koopman-von Neumann formulation of classical mechanics (KvN) exhibits quantum interference. As such it was there claimed that KvN ought to be considered as a proper quantum mechanical theory in a similar sense as ordinary non-relativistic quantum mechanics (OQM) is. In this article this claim is made manifest by showing that KvN and OQM can be taken as merely inequivalent representations resulting from one and the same quantization scheme. Of course, as the typical notion of quantization necessitates the canonical commutation relations (CCR) to hold, which they do not in KvN, the concept needs to be properly revised. To justify such a revision the typical reasons for necessitation the CCR, reductionism and quantization as 'turning brackets to commutators', are examined and found insufficient.

We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born--Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

The goal of this study is to create regression models estimating the daily Penman–Monteith reference evapotranspiration (PMR) using latitude–temperature data for the state of Sinaloa, Mexico. Daily series of minimum–maximum temperature (1979–2017) were obtained from seven weather stations in Sinaloa. The reference evapotranspiration was calculated by the methods of Penman–Monteith using empirical equations (PMC), Hargreaves (HAC), and PMR. Prior to calculating PMC, the incident solar radiation (SR) was calculated. From the Acaponeta station (2005–2008, 2011–2013 and 2015–2017), all complete observed variables were obtained: mean temperature, incident solar radiation (SRg), average relative humidity and average wind speed at a height of 10 m. The data from the eight weather stations were provided by the National Meteorological Service and the National Water Commission. The daily observed Penman–Monteith reference evapotranspiration (PMO) was calculated. For validation, three simple linear regressions (SLR) were applied: SR vs SRg, PMC vs PMO and PMR vs PMO. hypothesis tests were applied to each SLR: Pearson correlation (Pr) vs critical Pearson correlation (Pcr). All rP were significantly different from zero (> |0.576|): SRg vs SR (Pr = 0.951), PMC vs PMO (Pr = 0.592), and PMR vs PMO (Pr = 0.625). This study provides new models that can motivate and support the design and implementation of intelligent irrigation in the state considered “the breadbasket of Mexico.”

Previous control methods developed by our research team cannot satisfy the high-accuracy requirements of unmanned surface vessel (USV) path-tracking during bathymetric mapping because of the excessive overshoot and slow convergence speed. For this reason, this study developed an adaptive fuzzy integral-derivative line-of-sight (AFIDLOS) guidance law for USV path-tracking control. Integral and derivative terms were added to counteract the effect of the sideslip angle, with which the USV could be quickly guided to converge to the planned path for bathymetric mapping. To obtain a high-accuracy of the look-ahead distance, a fuzzy control method was proposed. The proposed method was verified using simulations and outdoor experiments. The results demonstrate that the AFIDLOS guidance law can reduce the overshoot by 79.85%, shorten the settling time by 55.32% in simulation experiments, and reduce the average cross-track error by 10.91%, and can ensure a 30% overlap of neighboring strips of bathymetric LiDAR outdoor mapping when compared with the traditional method.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

Monogenity is a classical area of algebraic number theory that is very actively researched even today. This paper is a collection of the results obtained during the last few years in this area. Several of these results were presented at the series of online conferences "Monogenity and power integral bases".

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

This article proposes a novel formulation of quantization, which considers the Koopman-von Neumann formulation (KvN) and ordinary non-relativistic quantum mechanics (OQM) as unitarily inequivalent representations of the same underlying structure. The approach is grounded in the notion that contextuality, rather than occurrence if Plank's constant, is the fundamental aspect of quantum mechanics. The motivation for this novel view arises from the limitations of traditional approaches to quantization, combined with previous research demonstrating contextuality in KvN. Using a representation-theoretic approach, both KvN and OQM are regarded as valid quantum theories, separated by a superselection rule.

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

Gaze tracking of high-speed moving targets is a novel application mode for low Earth orbit microsatellites. In this mode, small satellites are equipped with high-resolution narrow-field-of-view video cameras for stable gaze-tracking imaging of high-speed moving targets. This paper proposes a high-precision attitude adaptive integral sliding mode control method with a feedforward compensation disturbance observer to enhance the capability of a microsatellite attitude control system for gaze tracking of high-speed moving targets. Specifically, first, we present the attitude control system model for microsatellites and the calculation method for the desired attitude of target tracking based on image feedback. Then, an adaptive integral sliding mode attitude control algorithm with a feedforward compensation disturbance observer, which meets the requirements of high-precision tracking control, is designed. The developed algorithm utilizes the disturbance observer to observe the friction torque of the flywheel and compensates for it through feedforward control. It also employs the adaptive integral sliding mode control algorithm to reduce the impact of uncertain disturbances, decrease the steady-state error of the system, and enhance the attitude control precision. Simulation experiments demonstrated that the designed disturbance observer can successfully observe the frictional disturbance torque of the flywheel. The attitude Euler angle control precision for high-speed moving target tracking reached 0.009°, and the angular velocity control precision reached 0.005°/s, validating the effectiveness of the proposed approach.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

The goal was to model the irrigated (IBY) and rainfed (RBY) bean yields, as a function of essential climatic variables (ECVs), in the center (Culiacán) and south (Rosario) from Sinaloa. In Sinaloa, and for the period 1982–2013 (October–March), the following were calculated: a) temperatures. b) average degree days for the bean, c) cumulative potential evapotranspiration and d) cumulative effective precipitation. For ECVs, from the European Space Agency, e) daily soil moisture. f) IBY and RBY, from the Agrifood and Fisheries Information Service. Multiple linear regressions were applied, which modeled IBY–RBY (dependent variables), as a function of ECVs (independent variables). Then, to establish each Pearson correlation (PC) as significantly different from zero, a hypothesis test was applied: PC vs Pearson's critical correlation (CPC). The four models obtained were significantly predictive: IBY–Culiacán (PC = 0.590 > CPC = |0.349|), RBY–Culiacán (PC = 0.734 > CPC = |0.349|), IBY–Rosario (PC = 0.621 > CPC = |0.355|) and RBY–Rosario (PC = 0.532 > CPC = |0.349|). This study is the first in Sinaloa to predict IBY and RBY based on ECVs, contributing to the production of sustainable food.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

Prosthechea karwinskii is an orchid endemic to Mexico, threatened by the destruction of its habitat and the extraction of specimens to meet its demand for ornamental and religious use. Most of its populations, and the most locally abundant ones, are found in Oaxaca state. Variations in some floral traits have been observed in these populations. We implemented a morphometric analysis to assess their floral variation and identify the most significant characters in the morphological patterns of this orchid. Floral samples were collected from 17 populations of P. karwinskii in Oaxaca, as well as from specimens used as ornaments during Easter in a Oaxacan community (Zaachila), whose origin is unknown. Sampling of natural populations covered the environmental, geographic and morphological variation of the species. We performed an analysis of variance (ANOVA), principal component analysis (PCA), and canonical variate analysis (CVA), and cluster analysis including 185 individuals and 45 variables (13 of them were discarded in the multivariate analyzes due to high correlation). Characters of the column, lateral sepal, and labellum were most informative about the observed morphological patterns. Albarradas showed the greatest morphological differentiation, mainly due to the column. In general, individuals from the same locality tended to overlap more, especially the populations of Jaltianguis and Yahuiche, which were different from the geographically close population of Etla. Teposcolula presented the highest values in perianth characters, unlike Sola_Rancho Viejo. The specimens recovered from religious ornaments were morphologically more similar to those from the Mixtec region and surroundings of Etla. Our work encourages working on collaborative conservation strategies to ensure the long-term permanence of both the species and its traditional uses.

Artificial intelligence technologies based on deep convolutional neural networks and large lan-guage models have made significant breakthroughs in many tasks such as image recognition, target detection, semantic segmentation and natural language processing, but also face the problem of contradiction between the high computational capacity of the algorithms and the limited deployment resources. Quantization, which converts floating-point neural networks into low-bit-width integer networks, is an important and essential technique for efficient deploy-ment and cost reduction in edge computing. This paper analyze various existing quantization methods, showcase the deployment accuracy of advanced techniques, and discuss the future challenges and trends in this domain.

In industry 4.0 era, video applications such as surveillance visual systems, video conferencing, or video broadcasting have been playing a vital role. In these applications, for manipulating and tracking objects in decoded video, the quality of decoded video should be consistent because it largely affects to the performance of the machine analysis. To cope with this problem, we propose a novel perceptual video coding (PVC) solution in which a full reference quality metric named Video Multimethod Assessment Fusion (VMAF) is employed together with a deep convolutional neural network (CNN) to obtain the consistent quality while still achieving the high compression performance. First of all, to achieve the consistent quality requirement, we propose a CNN model with an expected VMAF as input to adaptively adjust the quantization parameters (QP) for each coding block. Afterwards, to increase the compression performance, a Lagrange coefficient of Rate-Distortion optimization (RDO) mechanism is adaptively computed under Rate-QP and Quality-QP models. Experimental results show that the proposed PVC has achieved two targets simultaneously: the quality of video sequence is kept consistently with an expected quality level and the bit rate saving of the proposed method is higher than traditional video coding standards and relevant benchmark, notably with around 10% bitrate saving in average.

We apply Rosen’s approach to the quantization of the gravitational collapse in the simple case of a pressureless “star of dust” and we find the gravitational potential, the Schroedinger equation and the solution for the collapse’s energy levels without any approximation. By applying the constrains for a black hole (BH), we found the analogous quantum quantities and the BH mass spectrum, again without any approximation. Remarkably, such a mass spectrum is the same which was found by Beken- stein in 1974. Finally, our approach permits to find the exact quantum representation of the Schwarzschild BH ground state at the Planck scale.

Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity.

A half-harmonic oscillator, which gets its name because the coordinate is strictly positive, has been quantized and determined that it was a physically correct quantization. This positive result was found using affine quantization (AQ). The main purpose of this paper is to compare results of this new quantization procedure with those of canonical quantization (CQ). Using Ashtekar-like classical variables and CQ, we quantize the same toy model. While these two quantizations lead to different results, they both would reduce to the same classical Hamiltonian if $\hbar\rightarrow0$. Since these two quantizations have differing results, only one of the quantizations can be physically correct. Two brief sections illustrate how AQ can correctly help quantum gravity and the quantization of most field theory problems.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

In this note we prove that the Riemann hypothesis is false. The proof is by contradiction based on a criterion of Hu.

Science seeks to explicate truths about our reality. But what is truth? How do we know things? Given our ignorance, and our fallibility, why should scientists be trusted? A theory of knowledge that addresses these human questions is sketched, in conversation with recent advances in thermodynamics which underline the seminal importance of unity by demonstrating (i) a definite physical meaning of the idea of “unitary entity”, (ii) the commensurability of the local and the non-local (resolving the Loschmidt Paradox), and (iii) the applicability of this entropic physics to entities at all scales, whether small (“quantum mechanical”) or large (subject to “general relativity”). Similarly, integrity is indispensable to the scientific enterprise, whether at the level of the mathematico-physical, the practising scientist, the scientific community, or the public. As a human activity aimed at touching reality, it is fundamental that the scientific enterprise necessarily also has an irreducibly poetic component. Although in principle it cannot be completely specified, this enterprise is a cluster of procedures designed to increase our understanding of the natural world. Our apprehension of knowledge is irreducibly personal, depending both on our own individual integrity as well as on the integrity of the scientific community. Believing that “reality” exists and can be grasped (however incompletely), scientists look for coherence and value unified accounts. Strictly speaking, although reality can be known truly (if only in part) the idea of “objective” knowledge is an oxymoron, even if such an idea is often a useful approximation. Knowledge is necessarily personal.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Novel approaches under the extreme conditions of ultra-high gravity of a super massive black hole allow us to assume that the spacetime degrades into the single dimension of time. A unique interpretation of the non-relativistic Schrödinger equation together with the relativistic Klein-Gordon and Dirac equations is presented by swapping the three dimensional space derivatives with the singular time derivative in the D’Alembertian operator. This apparatus reveals a unique time dependent wave equation that results in some implications such as possible time quantization with the intervals of around 3.36 × 10−21 ? which is in the order of uncertainty in time, ∆? = 1.3 × 10−21 ?, calculated from the energy-time version of the Heisenberg uncertainty principle for electrons. As a result of this, an antisymmetric wave function around the edge of the event-horizon zone appears and indicates that the virtual particle-antiparticle pairs of the electron field split into two real components with the spin-up and down states, reconfirming the Hawking radiation. Energy eigenvalues calculated from the application of the Dirac equation satisfies the preservation of energy and charge. The wave equation invoked in this study reduces into the time dependent Dirac equation within the neighborhood of zero-point, ? = 0, insuring the relevance of the evaluations.

Abstract: Individualized nursing care allows a systematic assessment and intervention, considers the patient's preferences, values, and context, and contributes to a positive care trajectory. However, its operationalization has proven to be challenging. This research aims to determine which items of nursing care individualization are most integrated into nurses' clinical practice, and those that are less included. A cross-sectional study was conducted on 122 eligible and registered nurses at a Hospital Center, in Ophthalmology (operating room and inpatient ward), Cardiology Service, Internal Medicine, and Medical Emergency Unit, in Portugal. The Indi-vidualized Care Scale nursing version (ICS-Nurse) was used for the assessment, including three sub-dimensions: clinical situation, personal life situation, and decisional control over care-related decisions. Analyses were performed using Cronbach's Alpha and Principal Component Analysis to confirm the relationships between the variables, suggested by the literature and previous studies. In the results, no statistically significant differences were identified between the sociodemographic profile and the sub-dimensions of individualization. Nurses overall have a good perception of the importance of individualized care (4.06 ± 0.46 ICS-A-NURSE), but face difficulties in its implementation during the last shift worked (3.97 ± 0.49 ICS-B-NURSE). The sub-dimensions more integrated into the care environment were clinical situations and decisional control, and the less integrated were the personal lives of patients. This study identifies key aspects of the individualization of nursing care in acute and perioperative settings, as its omission represents a failure to address the multidimensional health needs of patients, families, and caregivers. We suggest the development of training programs that promote a holistic approach, as well as future studies that consider patient outcomes related to the individualization of nursing care.

Fatigue performance and self-repairing activity of asphalt binders are two properties that highly influence the fatigue cracking response of asphalt pavement. There are still numerous gaps of knowledge to fill linked with these two characteristics. For instance, current parameters fail to fully accommodate these two bitumen phenomena. This study aims to propose a new procedure to address this issue utilizing the linear amplitude sweep (LAS) test, LAS with rest period (RP) (LASH) test, and simplified viscoelastic continuum damage (S-VECD) model. This research work used four different types of asphalt binders: neat asphalt (NA), self-healing thermoplastic polyurethane (STPU)-modified bitumen (STPB), self-healing poly (dimethyl siloxane) crosslinked with urea bond (IPA1w)-modified bitumen (IPAB), and styrene–butadiene–styrene (SBS)-modified bitumen (SBSB). Before the testing process, all the materials were subjected to short-term and long-term aging. The new procedure showed a superior capacity to analyze and accommodate all bitumen fatigue performances and self-repairing activities compared to the current method. Another finding proved that asphalt binders with higher self-restoration behavior failed to show better fatigue performance. A breakthrough finding demonstrated that asphalt binder fatigue response augmented when the RP was applied at a higher damage intensity (S) value. STPBs and IPABs reached their highest increments of fatigue response, containing 1.0% of STPU and 0.5% of IPA1w, respectively. Those augmentations were 207.54% and 232.64%, respectively.

The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ. The meaning of variable ħ is seen to be related to the rate of time passage along each path increment. The changes resulting in the Euler-Lagrange equation, Newton’s first and second laws, Newtonian gravity, Friedmann equation with a Cosmological Constant, and the impact on gravitational radiation for the dominant path are shown and discussed.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

When it comes to financial transactions and counterfeit detection systems, banknote classification is crucial. In this paper, we propose an approach for the classification of Kazakhstan banknote images integrating Learning Vector Quantization (LVQ) with Statistical Texture Feature Extraction using the Gray Level Co-occurrence matrix (GLCM). Our methodology demonstrates effectiveness in accurately classifying banknote images, as evidenced by experimental results. The comprehensive testing scenarios show promising outcomes, with the combination of GLCM and Color Histogram under the LVQ algorithm achieving a high accuracy of 94.87 percent at distance 1 and 90°. These findings indicate the robustness and practical viability of the proposed method for authenticating banknotes.

Post-training quantization is pivotal in deploying convolutional neural networks for mobile applications. Block-wise reconstruction with adaptive rounding, as employed in prior works like BrecQ and Qdrop, facilitates acceptable 4-bit quantization accuracy. However, adaptive rounding is time-intensive, and its constraint on weight optimization space curtails the potential for quantization performance. The optimality of block-wise reconstruction hinges on the quantization status of subsequent network blocks. In this investigation, we delve into the theoretical underpinnings of the limitations inherent in adaptive rounding and block-wise reconstruction. Our exploration leads to the development of a post-training quantization methodology, designated as AE-Qdrop. This algorithm operates in two distinct phases: block-wise reconstruction and global fine-tuning. The block-wise reconstruction phase introduces a progressive optimization strategy, superseding adaptive rounding, which not only augments quantization precision but also significantly improves quantization efficiency. To mitigate the risk of overfitting, we introduce a random weighted quantized activation mechanism. During the global fine-tuning phase, we account for interdependencies among quantized network blocks. The weight of each network block will be corrected with logit matching and feature matching. Extensive experiments validate that AE-Qdrop achieves high-precision and efficient quantization. For instance, in the case of 2-bit MobileNetV2, AE-Qdrop outperforms Qdrop by achieving a 6.26% enhancement in quantization accuracy and quintupling the quantization efficiency.

If "quantization is an art" then it can be greatly rened by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we can demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.

Cosmic inflation has presented solutions for a number of important cosmological problems, yet left some unanswered. In this paper, we present a cosmological model based on the quantization of the zero-point field which is consistent with empirical data, requires fewer assumptions, and presents answers to some of those unanswered questions. A comparison between standard cosmology and the theory presented in this paper is given below. Vacuum energy density: Standard inflationary model needs both Hubble’s constant and Matter density to estimate it. But, new cosmological model needs only Hubble’s constant. Non-vacuum energy density: Standard model can’t predict it. But, the new model can predict using only Hubble’s constant. Ratio of vacuum energy to total energy: Standard model can’t predict it. But, new model can predict it, that too without using Hubble’s constant. Energy conservation: In standard model, total energy is not conserved before inflation. But, in the new model, energy is conserved right from beginning of the universe whose net energy (including gravitational potential energy) is always zero. Flatness and homogeneity: Standard model needs Inflaton field with a specific potential energy distribution to explain it. But, new model doesn’t need any such hypothetical field, just the zero-point field is sufficient. Based on the new cosmological model, in the conclusion, realistic possibility for existence of multiverse and a mechanism for end of universe are discussed.

We prove through path integral Monte Carlo computer experiments that the affine quantization of the $\varphi_4^4$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum limit of the one- and two-point-function. Affine quantization leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, $\hbar^2/\varphi^2$ which arises only in the quantum aspects.

In this paper, we prove some common fixed point theorems on complex partial metric space. The presented results gener- alize and expand some of the literature well-known results. We also explore some of the application of our key results.

In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

Background: Functional Movement Screening (FMS) allows for rapid assessment of an individual’s physical activity level and timely detection of sports injury risk. However, traditional functional movement screening often requires on-site assessment by experts, which is time-consuming and prone to subjective bias. Therefore, the study of automated functional movement screening has become increasingly important. Methods: In this study, we propose an automated assessment method for FMS based on the improved Gaussian Mixture Model (GMM). First, the oversampling of minority samples is conducted, the movement features are manually extracted from the FMS dataset collected with two Azure Kinect depth sensors, then we train the Gaussian mixture model with different scores (1 point, 2 points, 3 points) of feature data separately, finally, we conducted FMS assessment by the Maximum Likelihood estimation. Results: The improved GMM has a higher scoring accuracy (Improved GMM:0.8) compared to other models (Traditional GMM=0.38, Adaboost.M1=0.7, Naïve-Bayes=0.75), and the scoring results of improved GMM have a high level of agreement with the expert scoring (kappa=0.67). Conclusions: The results show that the proposed method based on the improved Gaussian mixture model can effectively perform the FMS assessment task and it is potentially feasible to use depth cameras for FMS assessment.

The Pearl River Delta (PRD) has undergone complex geological development within a multi-island faulted basin, shaped by the interplay of regional tectonic movements, Quaternary sea-level fluctuations, and fluvial-marine interactions. Despite a great number of studies on the Holocene sedimentary sequences and spatial difference of lithofacies and environments, scant attention has been paid to the overarching human influence on deltaic evolution and coastline modifications since the Neolithic epoch. To further elucidate the spatial variation in Holocene sedimentation and its underlying basement topography shaped during the Last Glacial Maximum (LGM), we compiled a comprehensive dataset incorporating borehole data from over 2,800 cores within the PRD. Subsequently, high-resolution isobath maps of Quaternary deltaic deposits were generated, offering unprecedented insights into sediment distribution. This dataset facilitated a nuanced reconstruction of pre-Holocene topography, revealing a zone characterized by elongated, deep-incised valleys governed by NW-SE fault orientations. Further, we delineated coastline shifts since the period of maximum marine transgression (~7000 years BP), contributing to an enhanced understanding of the formation and evolutionary patterns of the delta and the river network oscillations. Our findings illuminate increasing anthropogenic impact on the rate of fluvial sedimentation and land growth, particularly accentuated over the last two millennia, favoring deltaic accretion. The current study has considerable implications for understanding the dynamic interplay between land-sea interactions and anthropogenic activities in shaping the delta, and stands to significantly inform land and resource management strategies, as well as future urban planning within the delta's bay areas.

Uterine fibroid (UF) is a tumour in some parts of the uterus, which introduces health challenges or death due to failed surgery among women globally. This study was designed to ascertain the involvement of micro-nutrients, inflammation, and antioxidant enzymes in the UF development to gain further insights and provide a strategy for managing the disease. One hundred ninety reproductive-aged women were recruited and classified equally into case and control subjects. The supernatant obtained from excised tissues from the fibroid and the normal samples from the adjacent myometrium were assessed for the selected biochemical parameters with standard methods. The levels of vitamin A and sodium between 26-35 years; vitamins D, E, zinc, and selenium between 46-55 years; and vitamin E at 56 years and above significantly decreased (p<0.05). Interleukin-2 (IL-2) level significantly increased (P < 0.05) among the case between 36-45 years. An increase in the activity of glutathione-s-transferase and the reduction in glutathione peroxidase activity and vitamin A level in the uterus between 26-45 years were the most pronounced significant findings (p<0.05) recorded. Prolonged vitamin A deficiency coupled with excess sodium salts facilitating inflammation induced by IL-2 are critical factors for UF development.

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.

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, zero-point energy calculation with an unexpected “length’ added to the ‘width’ of a graviton wavefunction just prior to the entrance of ‘gravitons’ to a small region of space-time prior to a nonsingular start to the universe. We compare this to a solution worked out using Klauder Enhanced quantization, for the same given problem. The solution of the first Cosmological Constant problem relies upon the geometry of the multiverse generalization of CCC cosmology which is explained in this paper. The second solution, used involves Klauder enhanced quantization. We look at energy given by our methods and compare and contrast it with the negative energy of the Rosen model for a mini sub universe and estimate GW frequencies

In this work, an improved collocation method based on the Bernoulli polynomials is presented to solve the Volterra integral equation (VIE) of the second kind. The main idea of the proposed method is to improve the results of the classic Bernoulli collocation method (BCM) by dividing the interval into some sub-intervals and considering the collocation points on each of them. Here, the zeros of the shifted Chebyshev polynomials (SCPs) are considered as collocation points. Then, BCM is applied step by step from the first sub-interval to the last one. By this process, a system of algebraic equations is attained for each sub-interval that could be easily solved. Convergence of the scheme is analyzed. For the purpose of demonstrating the validity, applicability, and efficiency of the suggested scheme several numerical examples are provided. Numerical results illustrate that the accuracy of the improved Bernoulli collocation method (IBCM) is more than BCM.

Pectin extracted via hydrodynamic cavitation in water only from waste lemon peel and further isolated via freeze drying displays significant antibacterial activity against Staphylococcus aureus, a Gram positive pathogen which easily contaminates food. The antibacterial effect of the new IntegroPectin is largely superior to that of commercial citrus pectin, opening the way to advanced applications of a new bioproduct now obtainable in large amounts and at low cost from citrus juice industry’s waste.

This paper showed that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We showed the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding, the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

In this paper we establish some generalizations of Opial’s inequal- ities for Riemann-Stieltjes integral and for two functions. Applications related to trapezoid and Grüss’ ’type inequalities are also given.

The biophenol integral extraction protocol from vegetation water developed in the early 2000s for the three-phase olive mill was adapted to a large two-phase mill operating in Sicily during the 2016/2017 season. The new set-up allows extensive recovery of olive phenolics, transforming previous waste into a source of revenues for the milling company and of valued bioproducts for its bioeconomy partner, while eliminating a source of potential pollution altogether.

The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied ac electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear dc current as it is second-order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of nonzero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On examining the effect of short-ranged Hubbard interactions upto first-order corrections, we find that this quantization is destroyed. This implies that unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in topological semimetals is not protected.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

The precise determination of the State-of-Health (SOH) of lithium-ion batteries is critical in the domain of battery management systems. The proposed model in this research paper emulates any deep learning or machine learning model by utilizing a Look Up Table (LUT) memory to store all activation inputs and their corresponding outputs. The operation that follows the completion of training is referred to as the LUT memory preparation procedure. The lookup operation performed on this method simply substitutes for the inference process. This is achieved by discretizing the input data and features before binarizing them. The term for the aforementioned operation is the LUT inference method. The procedure was evaluated in this study using two distinct neural network architectures: a bidirectional long short-term memory (LSTM) architecture and a standard fully connected neural network (FCNN). It is anticipated that considerably greater efficiency and velocity will be achieved during the inference procedure when the pre-trained deep neural network architecture is inferred directly. The principal aim of this research is to construct a lookup table that effectively establishes correlations between the SOH of lithium-ion batteries and ensures a degree of imprecision that is tolerable. According to the results obtained from the NASA PCoE lithium-ion battery dataset, the proposed methodology exhibits performance that is largely comparable to that of the initial machine learning models. Utilising the error assessment metrics RMSE, MAE, and (MAPE), the accuracy of SOH prediction has been quantitatively evaluated. The indicators mentioned above demonstrate a significant degree of accuracy when predicting SOH.

Particle acceleration, and the thermalisation of energetic particles, are fundamental processes across the universe. Whilst the Sun is an excellent object to study this phenomenon, since it is the most energetic particle accelerator in the Solar System, this phenomenon arises in many other astrophysical objects, such as active galactic nuclei, black holes, neutron stars, gamma ray bursts, solar and stellar coronae, accretion disks and planetary magnetospheres. Observations in the Extreme Ultraviolet (EUV) are essential for these studies but can only be made from space. Current spectrographs operating in the EUV use an entrance slit and cover the required field of view using a scanning mechanism. This results in a relatively slow image cadence on the order of minutes to capture inherently rapid and transient processes, and/or in the spectrograph slit `missing the action'. The application of image slicers for EUV integral field spectrographs is therefore revolutionary. The development of this technology will enable observations of EUV spectra from an entire 2D field of view in seconds, over two orders of magnitude faster than what is currently possible. The Spectral Imaging of the Solar Atmosphere (SISA) instrument is the first integral field spectrograph proposed for observations at 180A combining the image slicer technology and curved diffraction gratings in a highly efficient and compact layout, while providing important spectroscopic diagnostics for characterization of solar coronal and flare plasmas. SISA's characteristics, main challenges and the on-going activities to enable the image slicer technology for EUV applications are presented in this paper.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods.

Assume that $f:C\rightarrow \mathbb{R}$ is subadditive (superadditive) and hemi-Lebesgue integrable on $C,$ a cone in the linear space $X$ with $0\in C. $ Then for all $x,$ $y\in C$ and a symmetric Lebesgue integrable and nonnegative function $p:\left[ 0,1\right] \rightarrow \lbrack 0,\infty ),$ \begin{align*} \frac{1}{2}f\left( x+y\right) \int_{0}^{1}p\left( t\right) dt& \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( \left( 1-t\right) x+ty\right) dt \\ & \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( tx\right) dt+\int_{0}^{1}p\left( t\right) f\left( ty\right) dt. \end{align*} In particular, for $p\equiv 1,$ we have \begin{equation*} \frac{1}{2}f\left( x+y\right) \leq \left( \geq \right) \int_{0}^{1}f\left( \left( 1-t\right) x+ty\right) dt\leq \left( \geq \right) \int_{0}^{1}f\left( tx\right) dt+\int_{0}^{1}f\left( ty\right) dt. \end{equation*} Some particular inequalities related to Jensen's dicrete inequality for convex functions are also given.

Waste orange peel represents a heavy burden for the orange juice industry, estimated in several million tons per year worldwide; nevertheless, this by-product is endowed with valuable bioactive compounds, such as pectin, polyphenols and terpenes. The potential value of the waste orange peel has stimulated the search for extraction processes, alternative or complementary to landfilling or to the integral energy conversion. This study introduces controlled hydrodynamic cavitation processes, as a new route to the integral valorization of this by-product, based on simple equipment, speed, effectiveness and efficiency, scalability, and compliance with green extraction principles. Waste orange peel, in batches of several kg, was processed in more than 100 L of water, absent any other raw materials, in a device comprising a Venturi-shaped cavitation reactor. The extractions of pectin, endowed with a very low degree of esterification, polyphenols (flavanones and hydroxycinnamic acid derivatives), and terpenes (mainly d-limonene) were effective and fast (high yield, few min of process time), as well as the biomethane generation potential of the process residues was effectively exploited. The achieved results proved the viability of the proposed route to the integral valorization of waste orange peel, though wide margins exist for further improvements.

Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.

In this study, the complex interactions between the well-known Mittag-Leffler functions with two, three, and four parameters are explored. We first study the integral forms of the Mittag-Leffler function $\mathsf{E}_{\alpha, \beta}^{\rho,\kappa}(z)$ with the goal of clarifying its mathematical behaviours and features. Moreover, we create relations between these functions and generalised hypergeometric functions and Fox-Wright functions, expanding the range of their use and comprehension. We explore a number of unique situations by in-depth examination, providing insight into the subtle characteristics of these functions. This investigation advances our theoretical knowledge and opens up possibilities for future applications in a number of scientific fields. As such, this study adds to the current conversation in mathematical analysis and is an important tool for both practitioners and researchers.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

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.

The efficient recognition and classification of personal protective equipment are essential for en-suring the safety of personnel in complex industrial settings. Using the existing methods, manually performing macro-level classification and identification of personnel in intricate spheres is tedious, time-consuming, and inefficient. The availability of several artificial intelligence models in recent times presents a new paradigm shift in object classification and tracking in complex settings. In this study, several compact and efficient deep learning model architectures are explored, and a new efficient model is constructed by fusing the learning capabilities of the individual, efficient models for better object feature learning and optimal inferencing. The new model construct follows the contributory learning theory whereby each fussed model brings its learned features, which are then combined to obtain a more accurate and rapid model using normalized quantization-aware learning. During the investigation, a separable convolutional driven model was constructed as a base model, and then the various efficient architectures combined for the rapid identification and classification of the various hardhat classes used in complex industrial settings. A remarkable rapid classification and accuracy were recorded with the new resultant model.

Biosensors based on an oxygen electrode, a mediator electrode and a mediator microbial biofuel cell (MFC) using on the bacteria Gluconobacter oxydans B-1280 have been formed and tested to determine the integral toxicity. G. oxydans bacteria exhibit high sensitivity to the toxic effects of phenol, 2,4-dinitrophenol, salicylic and trichloroacetic acid and a number of heavy metal ions. The system “G. oxydans bacteria – ferrocene – graphite-paste electrode” is superior in sensitivity to biosensors formed using an oxygen electrode and MFC, in particular regarding heavy metal ions (EC50 of chromium (II), manganese (II) and cadmium (II) was 0.8 mg/dm3, 0.3 mg/dm3 and 1.6 mg/dm3, respectively). It has been determined that the period of stable functioning of electrochemical systems during measurements is reduced by half due (from 30 to 15 days) due to changes in the enzyme system of microbial cells when exposed to toxicants. Samples of products made from polymeric materials were analyzed using developed biosensor systems and standard biotesting methods based on inhibiting the growth of duckweed L. minor, reducing the motility of bull sperm and quenching the luminescence of the commercial test system "Ecolum". The developed bioelectrocatalytic systems are comparable in sensitivity to commercial biosensors, which made it possible to correlate the results and identify by all methods a highly toxic sample containing diphenylmethane-4,4'-diisocyanate according to GC-MS data.

We obtain some generalised Minkowski-type integral formulas for compact Riemannian (resp. spacelike) hypersurfaces in Riemannian (resp. Lorentzian) manifolds admitting an arbitrary vector field that we assume to be timelike in the case where the ambient space is Lorentzian. Some of these formulas generalize existing formulas in the case of conformal and Killing vector fields. We apply these integral formulas to obtain interesting results concerning the characterization of such hypersurfaces in some particular cases such as when the ambient space is Einstein admitting an arbitrary (in particular, conformal or Killing) vector field, and when the hypersurface has constant mean curvature.

Genetic and environmental factors including lifestyle are thought to play an important role in the pathophysiology of rheumatoid arthritis (RA). There is evidence that diet can enhance the inflammatory response in genetically predisposed individuals. On the other hand, certain types of diets are thought to alleviate RA symptoms due to their anti-inflammatory and antioxidant activities. Also, natural compounds with potential effectiveness in RA management belong to different chemical classes such as flavonoids, polyphenols, carotenoids, and alkaloids with their antioxidant characteristics. In this paper, the nutritional approaches to prevent or extenuate the disease progress were examined in the light of current literature. Mediterranean and vegan diets equally have been shown to exhibit positive effects on RA as the consumption of dietary fiber, antioxidants and anti-inflammatory compounds from fruits, vegetables, grains, nuts, and seeds are high. Whereas Mediterranean diet additionally includes beneficial nutrients of animal origin such as omega-3 polyunsaturated fatty acids from fish and seafood, patients on vegan diet need to be monitored closely for intake of all critical nutrients. Certain calorie restrictions and intermittent fasting diets have been shown to benefit RA patients although there is an obvious need for further studies to establish solid evidence-based recommendations and guidelines. The research data available strongly suggest that dietary approaches may help delay the onset of RA and/or improve symptoms and thus nutrition should be routinely addressed to facilitate management of the disease.

This paper investigates the path following control problem for a unmanned surface vehicle (USV) in the presence of unknown disturbances and system uncertainties. The simulation study combines two different types of sliding mode surface based control approaches due to its precise tracking and robustness against disturbances and uncertainty. Firstly, an adaptive linear sliding mode surface algorithm is applied, to keep the yaw error within the desired boundaries and then an adaptive integral non-linear sliding mode surface is explored to keep an account of the sliding mode condition. Additionally, a method to reconfigure the input parameters in order to keep settling time, yaw rate restriction and desired precision within boundary conditions is presented. The main strengths of proposed approach is simplicity, robustness with respect to external disturbances and high adaptability to static and dynamics reference courses without the need of parameter reconfiguration.

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.

Lemon pectin extracted along with water-soluble flavonoids and other phytochemicals from citrus industry’s waste lemon peel via hydrodynamic cavitation in water, directly at pre-industrial scale and further isolated via freeze drying, shows exceptionally high antioxidant and non-cytotoxic activity. Preliminary investigation indicates also significant antimicrobial activity. These findings open the route to the development of new nutraceutical and healthcare application of a versatile biopolymer endowed with new functionality, rapidly and conveniently obtained from an abundant by-product of the agrofood industry.

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.

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

This paper analyzes the theoretical and pragmatic implications, for international relations and world politics, of the new holistic approach to climate change articulated by Pope Francis in the Encyclical Laudato si’, particularly through the notion “integral ecology”. Far for being just a new chapter in the unfolding process of the “greening” of religions, the document raises in radical terms the issue of the sustainability of the present world system. I contend that the perspective of the Encyclical calls for a radical transformation of international relations, since it puts emphasis on the deep implications of environmental issues on the entire spectrum of security, development, economic and ethical challenges of contemporary world politics. Against this backdrop, I connect the main tenets of the Encyclical to the environmental turn in International Relations Theory and to the new epistemological challenges related to paradigm shift induced by the new planetary condition of the Anthropocene and the questions arising for a justice encompassing the humanity-earth system. Practicing sustainable international relations means exiting the logic of power or hegemony, operationalizing the concept of care.

In the article, the authors presented the problem of the transition effect in bridge engineering, its causes, negative consequences, and suggested a solution involving the use of integral bridges with the embankment through a spatial bars structure using reinforced composite polymer material. Integral bridges are designed to collaborate with road or railway embankments in bearing loads. Additionally, their application minimizes maintenance and construction costs while enhancing durability. Current solutions in bridge engineering were described. It is predicted that the presented concept will reduce the amount of plastic waste and contribute to the long-term use of materials. The article emphasized the importance of sustainable development, recycling, and the potential application of substitute materials.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.