A major challenge in the clinical management of patients with mesial temporal lobe epilepsy (MTLE) is identifying those who do not respond to antiseizure medication (ASM), allowing for the timely pursuit of alternative treatments, such as epilepsy surgery. Here, we investigated changes in plasma metabolites as biomarkers of pharmacoresistance in patients with MTLE. Furthermore, we used the metabolomics data to gain insights into the mechanisms underlying MTLE and response to ASM. We performed an untargeted metabolomic method using magnetic resonance spectroscopy and multi- and univariate statistical analyses to compare data obtained from plasma samples of 28 patients with MTLE compared to 28 controls. The patients were further divided according to response to ASM: 20 patients were refractory to treatment, and eight were responsive to ASM. We only included patients using carbamazepine in combination with clobazam. We compared the group of patients with controls and found that the profiles of glucose (p = 0.01), saturated lipids (p = 0.0002), isoleucine (p = 0.0001), β-hydroxybutyrate (p = 0.0003), and proline (p = 0.02) were different in patients compared to controls (p < 0.05). In addition, lipoproteins (p = 0.05), lactate (p = 0.05), glucose (p = 0.05), unsaturated lipids (p = 0.05), isoleucine (p = 0.05), and proline (p = 0.05), could discriminate between the two groups of patients classified according to response to ASM. The identified metabolites were linked to different biological pathways related to cell energy metabolism, and pathways linked to inflammatory processes and the modulation of neurotransmitter release and activity in MTLE. In contrast, we found that pyruvate metabolism may be linked to resistance to ASM. In conclusion, in addition to insights into the mechanisms underlying MTLE and the response to treatment with ASM, our results suggest that plasma metabolites may be used as biomarkers of disease and response to ASM in patients with MTLE. These findings warrant further studies exploring the clinical use of metabolites to assist in decision-making when treating patients with MTLE.

This paper proposes a multifractal model, with the aim of providing a possible explanation for the locality phenomenon that appears in the estimation of the Hurst exponent in stationary second order temporal series representing self-similar traffic flows in current high-speed computer networks. It is shown analytically that this phenomenon occurs if the network flow consists of several components with different Hurst exponents.

Epilepsy is a neurological disorder that affects approximately 1% of the world's population. To diagnose and estimate the occurrence of epilepsy, the analysis of recorded brain activity is performed by a neurologist, which is not only time-consuming and tedious but also occasionally accompanied by human error. Therefore, in recent decades, researchers have aimed to unravel an approach for designing and building an automated method for diagnosing and estimating the occurrence of epilepsy. Accordingly, the present study proposed two new-fangled ways based on brain signals and a convolutional neural network (CNN). Moreover, this research implements a CNN with a sequential three-layer structure. Numerous experiments were performed, and the accuracy of estimating epilepsy using the developed methods was achieved at 95% without feedback and 97% with feedback. The proposed methods were proven to be more accurate than the previous techniques and can be employed as a physician's assistant once entering the field of operation.

We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.

It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly predicts what it is possible to observe (the emissions) it ignores the other half of natural phenomena, what cannot be observed (the absorptions), thereby violating the conservation laws. By describing only one-half of radiation processes conceptual difficulties such as wave function collapse, infinite paths, and inscrutable mathematics seem to be insoluble mysteries. The deficiencies are corrected by introducing Hamilton’s principle S = ∫ Ldt and applying the methods of quantum field theory to derive relativistic equations of motion. The calculus of variations is used to show that the wave function represents an incomplete equation of motion because it equals twice the allowable action minimum.

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.

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

This 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.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

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.

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.

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.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

In this paper, we develop the theory of the multiple q-analogue of the Heine’s binomial formula, chain rule and Leibnitz’s rule. We also derive many useful definitions and results involving multiple q-antiderivative and multiple q-Jackson’s integral. Finally, we list here multiple q-analogue of some elementary functions including trigonometric functions and hyperbolic functions. This may be a good consideration in developing the multiple q-calculus in combinatorics, number theory and other fields of mathematics.

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.

Background: Neuromuscular electrical stimulation (NMES) has beneficial effects on physical functions in Multiple Sclerosis (MS) patients. However, the neurophysiological mechanisms underlying these functional improvements are still unclear. This study aims at comparing acute responses in spinal excitability, as measured by soleus Hoffmann reflex (H-reflex), between MS patients and healthy individuals, following three experimental conditions involving the ankle planta flexor muscles: 1) passive NMES (pNMES); 2) NMES superimposed to isometric voluntary contraction (NMES+); and 3) isometric voluntary contraction (ISO). Methods: 20 MS patients (MSp) and 20 healthy individuals as control group (CG) took part in a single experimental session. During each condition, participants performed 15 repetitions of 6 seconds at 20% of maximal voluntary isometric contraction, with 6 seconds of recovery between repetitions. Before and after each condition, H-reflex amplitudes were recorded. Results: In MSp, H-reflex amplitude did not change following any experimental condition (ISO: p = 0.506; pNMES: p = 0.068; NMES+: p = 0.126). In CG, H-reflex amplitude significantly increased following NMES+ (p = 0.01), decreased after pNMES (p = 0.000) and was unaltered following ISO (p = 0.829). Conclusion: the different H-reflex responses between MS and CG might reflect a reduced ability of MS patients in modulating spinal excitability.

Using the h-index to assess individual researchers is not only unethical and unfair but also inaccurate and misleading. This index fails to offer a reliable measure of a researcher's impact based on their citation scores. Beyond statistical and conceptual considerations, authorship practices, especially in the case of multi-authored publications, give rise to significant problems that often go unnoticed. While some modifications of the h-index have been proposed to mitigate these weaknesses, the fundamental deficiencies persist. Most of these flaws have been effectively addressed by the c-score, a composite citation index. The c-score excludes self-citations, normalizes the number of citations by considering the number of authors in each paper, and takes into account first, single, and last authorship. This approach provides a more realistic measure of the impact of each individual researcher based on raw citations.

Individuals with Parkinson’s disease (PD) and freezing of gait (FOG) have a loss of presynaptic inhibition (PSI) during anticipatory postural adjustments (APAs) for step initiation. The mesencephalic locomotor region (MRL) has connections to the reticulospinal tract that mediates inhibitory interneurons responsible for modulating PSI and APAs. Here, we hypothesized that MLR activity during step initiation would explain the loss of PSI during APAs for step initiation in freezers. Thirty-four freezers were assessed in the ON-medication state. During a functional magnetic resonance imaging protocol of simulated APA task, we assessed beta of blood oxygenation level-dependent signal change of areas known to initiate and pace gait (e.g., MLR), in addition to PSI of the soleus muscle during APA for step initiation, and clinical (e.g., disease duration) and behavioral (e.g., FOG severity and APAs amplitude for step initiation) variables. A linear multiple regression model showed that MLR activity (R2=0.32, P=0.0006) and APA amplitude (R2=0.13, P=0.0097) explained together 45% of the loss of PSI during step initiation in freezers. Decreased MLR activity during a simulated APA task is related to a higher loss of PSI during APA for step initiation. Deficits in central and spinal inhibitions during APA may be related to FOG pathophysiology.

Helicobacter pylori, a gram-negative bacteria usually found in stomach and first part of small intestine, is known to cause infections and ulcers and may have association with cancer. Normally, the treatment options include combinations of antibiotics with proton pump inhibitors and antiinflammatory drugs. However, all of them have high systemic exposure, and hence, unfavourable side effects, whereas their exposure in stomach mucus, the predominant location of the bacteria, is very limited. We have attempted to develop a predominantly gut-restricted formulations of antibiotic + adjuvant combinations as a basis for potentially more safe and efficacious treatment of gastrointestinal tract infections. We have considered E. coli (as a model of H. pylori) and Lactobacilli to study the antibacterial activity of nanogel with combined drugs (classical antibiotics and individual components of essential oils). It has been shown that levofloxacin (LF) in combination with zephirol demonstrates synergy effect against E. coli (cell viability has decreased by about 50%) and weakens the effect against Lactobacilli. A number of other combinations of antibiotic + adjuvant is also shown to be effective. Using FTIR and UV spectroscopy, it has been proved that chitosan nanogels with the drug are well adsorbed on the mucosal model, thereby increasing the bioavailability of drugs. Using ABTS assay, the antioxidant properties of flavonoids and other drugs are shown, which is potentially necessary to minimize the harmful effects of toxins and radicals produced by pathogens. Thus, chitosan nanogels loaded with a combination of drugs can be considered as a new strategy for the treatment of infectious diseases of the gastrointestinal tract, and applicable to difficult-to-treat bacteria.

The increased emergence of multidrug-resistant Helicobacter pylori influences the prevention of stomach cancer. Zingiber officinale is a plant usually used in folk medicine to treat a variety of diseases involving infections, nausea, vomiting, peptic ulcer, dyspepsia, and inflammation. This study was conducted to evaluate the ability of Z. officinale extract to combat resistant H. pylori. The disc diffusion, microdilution, and microplate assays were performed to evaluate the susceptibility to antibiotics, and the antibacterial and antibiofilm activities of the Z. officinale extracts. Using the checkerboard method, the combined effects of the gentamicin and Z. officinale extract were investigated. In addition, anti-inflammatory activity and GC-MS analysis were determined by the modified protocol. According to the findings, H. pylori isolates exhibited resistance rates of 56.33, 50.0, and 45.85 for metronidazole, gentamicin, and tetracycline, respectively. The methanolic extract of Z. officinale had the strongest effectiveness against resistant H. pylori isolates with MIC of 20.0 to 50.0 µg/ml against both H. pylori isolates and the stranded strain NCTC 11637. Z. officinale extract suppress the biofilm formed by H. pylori isolates with a percentage of 92.96% at 50.0µg/ml, compared with 97.19% for gentamicin at the same concentration. According to FICI values, combination of methanolic Z. officinale extract to gentamicin increases bacterial sensitivity to such drugs. Moreover, the Z. officinale extract exhibits strong anti-inflammatory activity. The GC-MS analysis of Z. officinale extract exhibits 17 different chemical compounds. Conclusions: The Z. officinale extract contain the anti-inflammatory compound gingerol as the main constituent which inhibits the growth of H. pylori and its biofilm, are a promising natural therapeutic alternative or enhance antibiotics activity

Lead, known as a metal with high neurotoxicity to children, cadmium, which is a carcinogenic and bioaccumulative contaminant, and arsenic, a class 1 carcinogenic according to the International Agency for Research on Cancer, are toxic elements (TEs) whose relevant route of exposure may be diet. We determined the bio-accessible fraction of lead, cadmium, and arsenic from the diet of preschool children from two day care centers (DCC). A cross-sectional study was conducted with 64 one–four-year-old children from two DCCs where the 24-h duplicate diet samples were collected. The diet samples were analyzed by ICP-MS for lead, cadmium, and arsenic total concentrations (n = 64) and their bio-accessibility were analyzed for a subsample (n = 10). The dietary intake (DI) mean for lead, cadmium, and arsenic were 0.18 ± 0.11 µg kg⁻¹ bw, 0.08 ± 0.04 µg kg⁻¹ bw, and 0.61 ± 0.41 µg kg⁻¹ bw, respectively. All DI calculated for TEs, considering total intake, were found lower than the tolerable limits (TL) (European Union, or World Health Organization, WHO, when applicable) except for one child’s Pb intake. Bio-accessibilities ranged between 0% to 93%, 0% to 103%, and 0% to 69%, for lead, cadmium, and arsenic, respectively. Although DI for TEs has been found lower than TL, these reference values have been recently decreased or withdrawn since it was for lead and arsenic whose TL were withdrawn by WHO.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

Optical communications are described and analyzed by shaped beams; we challenge the ‎effects of parameters that impact the profile of a Flat Top Gaussian (FTG) beam. When ‎the laser beam propagates throughout the atmosphere, it can be influenced by different ‎optical phenomena including scattering, absorption, and turbulence due to changes in the ‎scintillation index and the forms of intensity that are displayed in the source and receiver ‎planes. In this project, the FTG laser beam that propagates through a weak turbulent ‎region is numerically investigated using open-source software. This simulation will be ‎performed according to a mathematical model based on the split-step beam propagation ‎method. Intensity distributions at the source plane and the received average intensity in ‎atmospheric turbulence are calculated, and additional contour is in the transducer plane. ‎The scintillation index, structure constant, source size, and other parameters, are applied ‎in the Rytov method to quantify the weak turbulent model. Moreover, these parameters ‎are analyzed in near-field propagation. Also, the effects of the beam’s scintillation and ‎beam wander are determined. All results simulated are discussed and compared with the ‎TEM00 Gaussian beam. Finally, these results are compared to measurements in the ‎experimental part of the work.

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.

We show succinctly a natural origin of the beautiful Gamma function in light of the WJ distribution, linking to quite distinct fields.

This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ&gt;0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

In this paper for every number field K generated by a root α of a trinomial x⁷ + ax + b ∈ Z[x] and for every prime integer p, we calculate ν_p(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.

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 theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action S_E « ħ. This is obtained through a Metropolis algorithm with weight exp(-β²S_E²) and β » ħ^-1. The squared action in the exponential allows to circumvene the problem of the non-positivity of S_E. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition S_E=0 exactly, or in certain cases even the stronger condition R(x)=0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's ''spacetime foam''.

In quantum gravity perturbation theory in Newton's constant $G$ is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge-Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of $G$ and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale $\xi$ in many ways analogous to the scaling violation parameter $\Lambda_{\bar MS} $ of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.

Any quantization maps linearly functions on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all ressources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. In this paper we emphasize the deep connection between Fourier transform and covariant integral quantization when the Weyl-Heisenberg and affine groups are involved. We show with our generalisations of the Wigner-Weyl transform that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

This research aims to deepen the understanding of the relationship between conductivity and morphology in polypyrrole (PPy) via a comparison of the bipolaron to polaron ratios with a focus on the C-H deformation area. PPy samples were synthesized with different surfactants: sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB), and tween 80 (TW). The study revealed that SDS significantly altered the bipolaron and polaron in C-H deformation region and showed higher conductivity than other surfactants. Notably, the morphological shifts to a sheet-like structure when using ammonium sulfate (APS) contrasted with the particle-like form observed with ferric chloride (FeCl3). These results showed that if the oxidant changed, the bi-polaron and polaron ratios in C-H deformation were unrelated to PPy morphology. However, this work showed a consistent relationship between SDS use, the bipolaron and polaron ratios in the C-H deformation, and the conductivity properties. Moreover, the natural positive charge of PPy and negatively charged SDS molecules may lead to an electrostatic interaction between PPy and SDS. This work assumes that this interaction might cause the transformation of polaron to bipolaron in the C-H deformation region, resulting in improved conductivity of PPy. This work offers more support for the future investigation of PPy characteristics.

Hepatitis B Virus (HBV) is a challenge for global health services, affecting millions and leading hundreds to end-stage liver disease each year. This comprehensive review explores the interactions between HBV and the host, examining their impact on clinical outcomes. HBV infection encompasses a spectrum of severity, ranging from acute hepatitis B to chronic hepatitis B, which can potentially progress to cirrhosis and hepatocellular carcinoma (HCC). Occult hepatitis B infection (OBI), characterized by low HBV DNA levels in hepatitis B surface antigen-negative individuals, can reactivate and cause acute hepatitis B. The identification of diverse HBV genotypes reveals distinct geographical distributions and associations with clinical outcomes. Moreover, single nucleotide polymorphisms (SNPs) within the host genome have been linked to several clinical outcomes, including cirrhosis, HCC, OBI, hepatitis B reactivation, and spontaneous clearance. The immune response plays a key role in controlling HBV infection by eliminating infected cells and neutralizing HBV in the bloodstream. Furthermore, HBV can modulate host metabolic pathways involved in glucose and lipid metabolism and bile acid absorption, further influencing disease progression. HBV clinical outcomes correlate with three levels of viral adaptation. In conclusion, the clinical outcomes of HBV infection could result from complex immune and metabolic interactions between the host and HBV. These outcomes can vary among populations and are influenced by HBV genotypes, host genetics, environmental factors, and lifestyle. Understanding the degrees of HBV adaptation is essential for developing region-specific control and prevention measures.

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the Internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link have fractal behavior when the Hurst exponent is in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between –0.5, 0. Based on these results, it is ideal to characterize both the singularities of the traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

Specifically this work is based on the concept of ‘dark energy’ as a phenomenal effect of expansion through which a theoretical value of Hubble’s constant has been introduced. It is a constant that is based on a postulate that the square root of ratio of the Siva’s constant ‘K’ and Hubble’s constant ‘H’ is exactly equal to the diameter of the neutral hydrogen atom. That is the, exact theoretical value of Hubble’s constant. This is always constant .However, space-time conversions and the changes in the velocity of light will affect the distance and velocity in Hubble’s equation. Deviation factors in velocity, distance and the Hubble’s constant have been calculated separately which are affected by change of velocity of light with expansion of space time. The observations are related to red shift. So the change factor in terms of Hubble’s constant has been calculated with respect to red shift. Thus a factor which affects the theoretical Hubble’s constant has been calculated to find the exact value of Hubble’s constant that satisfies the experimental results. The present theoretical value of Hubble’s constant has been calculated. The experimental results by plank, ACT (Atacama Cosmology Telescope), WMAP (Wilkinson Microwave Anisotropy Probe) etc. experiments are at par with the theoretical result. Thus the ontology of space time introduced in this theoretical work supposed to be correct and leads to a new theory of origin of universe for which a brief description has been provided.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

The current work addresses the control of two-input two-output (TITO) Wood and Berry model of a binary distillation column. The controller design problem is formulated in terms of multivariable H_∞ control synthesis. The controller structure takes the form of simplest static output feedback (SOF) control. The controller synthesis is performed using a hybrid approach of blending linear matrix inequalities (LMI) and genetic algorithm (GA). The performance of the static output feedback controller is compared with three other controllers designed for Wood and Berry model available in the literature. The first simulation study is performed for the case of tracking a unit step command in the presence of a step change in output disturbance. A second simulation study is performed for rejecting a change in sinusoidal output disturbance.

The mechanistic pathway of TEMPO/I₂-mediated oxidative cyclization of N,N-diaryl amino alcohols 1 is investigated in this study. Based on our direct empirical experiments, three key intermediates (the aminium radical cation 3, the α-aminoalkyl radical 4, and the iminium 5), four kind reactive species (radical TEMPO, cationic TEMPO, TEMPO-I and iodo radical) and three kind pathways (1. SET/PCET mechanism, 2. HAT/1,6-H transfer mechanism, 3. Ionic mechanism) were assumed. Under the assumption, nine free energy diagrams are acquired through DFT calculation. From the comparison of the solution phase free energy, some possibility can be excluded and then the chosen plausible mechanisms are concretized with the more stable intermediate 7.

Ship wave is of great interest for wave drag, coastal erosion and ship detection. In this paper, a highly-paralleled numerical scheme is proposed for simulating three-dimensional (3-D) nonlinear Kelvin ship waves effectively. First, a numerical model for nonlinear ship waves is established based on potential flow theory, boundary integral method and Jacobian-free Newton-Krylov (JFNK) method. In order to improve computational efficiency and reduce data storage of JFNK method, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU) based parallel computing framework is designed, and a GPU solver is developed by using Compute Unified Device Architecture (CUDA) language. Finally, numerical simulations of 3-D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

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

A quantitative description of the second law of thermodynamics in small scale systems and over short time scales comes from various fluctuation theorems. The applicability of the transient fluctuation theorem in particular to small scale systems perturbed from an initial equilibrium steady-state distribution has been demonstrated both theoretically and experimentally in several works over the past few decades. In addition, some experimental works in the past have also made successful attempts to demonstrate the applicability of the fluctuation theorem to small scale systems evolving from a certain nonequilibrium steady-state distribution over relatively long time scales. To this end, this paper seeks to demonstrate the transient fluctuation theorem for a Brownian particle confined within a power-law trapping potential by following the trajectory of the particle that itself is translating linearly along one dimension with constant acceleration in a viscous fluid. Considered herein is an idealized version of this model, in that it is assumed that the force of the trapping potential is only felt by the translating Brownian particle confined within the trap, and that this Brownian particle moves relative to the fluid molecules that are held stationary. The results presented herein show that the transient fluctuation theorem applies not only to equilibrium steady-state distributions but also to nonequilibrium steady-state distributions of an ideal colloidal system in an accelerated frame of reference in the asymptotic (long-time) limit.

Spatial planning holds a key role in preventing or mitigating the impacts of climate change on both cities and rural areas, taking a forward-thinking and holistic approach to urban and regional development. As such, spatial planning deals with challenges occurring at different scales and across sectors. The international literature points out the need for horizontal and vertical cooperation to tackle climate change impacts. While there is abundant knowledge regarding the challenges related to climate change at different spatial levels, procedural integration into planning frameworks and practice is currently under-researched. This paper presents a novel theoretical framework that integrates various steps towards a holistic, integrative and adaptive climate proofing process. An iterative process was used for conceptual development, based on literature review followed by external feedback meetings and two workshops with the core team of planning experts responsible for exchange across federal states. By specifically addressing the challenges relating to cross-regional and cross-sectoral planning, this novel framework attempts to (i) facilitate a hierarchy of measures, (ii) maximise co-benefits for various adaptation purposes and climate change mitigation and (iii) foster the long-term institutionalisation of integrative processes across sectors, planning areas and policy levels.

In this paper, the design of a low cost portable ventilator with performance analysis have been done to solve the scarcity of respiratory ventilators for COVID-19 patients. The materials used to build the system are: DC motor, rotating disc and pneumatic piston. The system input is the patient heart beat and the output is volume of air to the patient lung with adjusted breathing rate. This ventilator adjusts the breathing rate to the patient depending on his heart beat rate. The performance analysis of this system have been done using Proportional Integral Derivative (PID) and Full State Feedback H2 controllers. Comparison of the system with the proposed controllers have been done using a step change and a random change of the patient heart beat and a promising result have been analyzed successfully.

The Maastricht VI/Florence consensus recommends, as one of the measures to enhance the efficacy of Helicobacter pylori (H. pylori) infection eradication, a personalized treatment approach involving the selection of an antimicrobial agent based on the pre-determined resistance of H. pylori. To meet the need to develop test systems for personalized drug selection, we conducted a study of H. pylori molecular resistance in Moscow using a self-developed Sanger sequencing test platform. We validated our test system on 25 pure culture samples of H. pylori with known resistance. Sensitivity and specificity for detecting resistance to clarithromycin was 100%, and to levofloxacin - 93% and 92%, respectively. Then we tested our platform on 112 H. pylori -positive patients who had not previously received proton pump inhibitors (PPI) or antibacterial drugs. Mutations indicating resistance to clarithromycin were found in 27 (24%) samples, and to levofloxacin in 26 (23%) samples. Double resistance was observed in 16 (14%) samples. The most common mutations leading to clarithromycin resistance were 2143G and 2142G, to levofloxacin resistance – 261A and 271A in the gyrA gene, which account for 69% of all identified genetic determinants in levofloxacin-resistant bacteria. Thus, a personalized approach to the selection of H. pylori eradication therapy based on the detection of bacterial resistance before prescribing first-line therapy could help avoid the prescription of ineffective H. pylori eradication therapies and, overall, contribute to the control of antibiotic resistance of H. pylori.

Support effect is an important issue in heterogeneous catalysis while the explicit role of a catalytic support is often unclear for catalytic reactions. A systematic density functional theory computational study is reported in this paper to elucidate the effect of a model boron nitride (BN) support on the first N-H bond activation step of NH3 on Run (n =1, 2, 3) metal clusters. Geometry optimizations and energy calculations were carried out using density functional theory (DFT) calculation for intermediates and transition state from the starting materials undergoing the N-H activation process. The primary findings are summarized as follows. The involvement of the model BN support does not significantly alter the equilibrium structure of intermediates and transition state in the most favorable pathway (MFP). Moreover, the involvement of BN support decreases the free energy of activation, ΔG≠, thus improving the reaction rate constant. This improvement is more obvious at high temperatures like 673 K than low temperatures like 298 K. The BN support effect leading to the ΔG≠ decrease is most significant for the single Ru atom case among all three cases studied. Finally, the involvement of model BN may change the spin transition behavior of the reaction system during the N-H bond activation process. All these findings provide a deeper insight into the support effect on the N-H bond activation of NH3 for supported Ru catalyst in particular and for supported transition metal catalysts in general.

The role of DNA mismatch repair (MMR) tumor testing in colon and endometrial carcinomas is well-established, yet the universal application of this testing faces challenges due to limited data on its efficacy in diverse populations. This retrospective study at a community hospital in Northern Indiana examined MMR immunohistochemistry (IHC) results across 549 cases. Our analysis found intact MMR expression in 469 cases, while 80 demonstrated MMR deficiency, translating to MMR deficiency rates of 10% in colon cancers and 22% in uterine carcinomas. Notably, only 16 patients (2.9%) were categorized as high microsatellite instability (MSI-H), a rate significantly lower than the 3-5-fold higher incidences reported in other Midwestern populations, including Ohio. These findings suggest that the benefits of universal cascade methylation testing, particularly in MLH1/PMS2 IHC-negative tumors, may vary significantly based on regional demographics. Given the notably lower MSI-H incidence in this study, re-evaluating reflex testing protocols in low-resource settings could lead to more targeted, cost-effective approaches without compromising diagnostic accuracy. This study challenges the one-size-fits-all approach to MMR testing, highlighting the need for tailored strategies that consider regional variations in cancer genetics.

The removal of H2S from natural gas and other gases such as biogas, refinery gases, and coal gas is required because H2S is toxic and corrosive, even in traces. Zeolites are widely used in the removal of H2S from the above-mentioned gases. In this work, we prepared an Ag-exchanged 13X molecular sieve by using different concentrations of AgNO3 to increase its adsorption properties. XRD, SEM, and BET techniques were used to characterize samples. When compared to unmodified 13X, the adsorption capacity of AgII-13X increased by about 50 times. The results of this study suggest that the silver-modified 13X molecular sieve is highly effective at extracting H2S from natural gas.

Na⁺/H⁺ exchangers (NHEs) are known to be important regulators of pH in multiple intracellular compartments of eukaryotic cells. Sperm function is especially dependent on changes in pH and thus it has been postulated that NHEs play important roles in regulating the intracellular pH of these cells. For example, in order to achieve fertilization, mature sperm must maintain a basal pH in the male reproductive tract and then alkalize in response to specific signals in the female reproductive tract during the capacitation process. Eight NHE isoforms are expressed in mammalian testis/sperm: NHE1, NHE3, NHE5, NHE8, NHA1, NHA2, NHE10, and NHE11. These NHE isoforms are expressed at varying times during spermatogenesis and localize to different subcellular structures in developing and mature sperm where they contribute to multiple aspects of sperm physiology and male fertility including proper sperm development/morphogenesis, motility, capacitation, and the acrosome reaction. Previous work has provided evidence for NHE3, NHE8, NHA1, NHA2, and NHE10 being critical for male fertility in mice and NHE10 has recently been shown to be essential for male fertility in humans. In this article we review what is known about each NHE isoform expressed in mammalian sperm and discuss the physiological significance of each NHE isoform with respect to male fertility.

An extension of the models used to generate fractal traffic flows is presented by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated by the model, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

Ballasted railway tracks can be modelled using reduced/simplified models composed of several layers of discrete components. This paper deals with the two-layer model, which is very popular due to its computational efficiency. In order to provide some recommendations for track design, it is necessary to identify which set of parameters leads to some irregular/unexpected behavior. Such irregularity is investigated at three levels, such as: (i) critical velocity of moving constant force; (ii) instability of a single moving mass; (iii) instability of two moving masses. All results are presented in dimensionless form to cover a wide range of real parameters. Irregular cases are identified by sets of parameters leading to them and then general conclusions are drawn. Regarding the method, all results are obtained analytically or semianalytically, where “semi” refers to solving the roots of a given polynomial by predefined numerical procedures in symbolic software. No numerical integration is involved in all results presented. This means that the results are highly accurate and refer to exact values, so any kind of parametric or sensitivity analyses is readily possible.

Improper lifting measures of long-span spatial steel structures during construction process may delay the construction period and even cause safety accidents. Few studies on long-span spatial steel structures considered time-varying mechanical characteristic during construction process. In order to achieve safe and efficient installation in a long-span spatial steel structure, this research presents a time-varying mechanical analysis of the synchronous and asynchronous integral lifting and a single and interlaced point’s asynchronous integral lifting analysis method of a long-span spatial steel structure. The results showed that in the case of asynchronous lifting of single point, the displacement influence on other members is related to the distance. The closer the distance from the lifting point, the greater the influence. In asynchronous integral lifting, the lifting point with large lifting force is first installed to the specified position, and the lifting point with small lifting force is installed to the specified position.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

Polyhedral oligomeric silsesquioxane (POSS) is a suitable nanoscale reinforcement for thermosetting polymers, such as epoxy resin systems in order to modify its mechanical, thermal, and chemical properties. The inclusion of POSS in the epoxy resin at higher loading (greater than 1 wt.%), however, introduces the ductility during the fracture behavior of these nanocomposites. Consequently, the J-integral is used to quantify the fracture behavior of these materials and characterize the crack growth resistance curve against stable crack growth. A range of nanocomposites is prepared by adding 0.5, 1, 3, 5, and 8 wt.% of glycidyl POSS into DGEBF epoxy resin cured with an amine-based curing agent. From the fracture toughness experiment the load-displacement result confirms that when the POSS reinforcement is greater than 1 wt.%, the fracture behavior of the nanocomposite changes from brittle to ductile. For both brittle and ductile nanocomposites, the addition of POSS molecules improves the crack initiation toughness. The development of POSS–POSS compliant domains are reported previously, is attributed for this change in the failure behavior. The fractured images of POSS–epoxy nanocomposites, obtained using scanning electron microscopy, show that the increase in fracture resistance at higher values of POSS loading occurs due to the extensive shear yielding. Meanwhile, the increased fracture toughness at lower values of POSS loading occurs due to crack pinning and crack deflection.

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

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.

Heavy Ion Beam Probing (HIBP) diagnostic is a powerful tool for electric field studies in hot dense plasma of modern day toroidal magnetic confinement devices. On the TUMAN-3M to-kamak, the HIBP have been used in regimes with improved plasma confinement to clear up the role of radial electric field in the transition to good confinement regimes. Recently, a moderni-zation of the TUMAN-3M HIBP diagnostics was performed aiming to reconfigure it for a work with a reversed plasma current direction and improvement of overall stability of the diagnostic. The results of first measurements of plasma potential in co-NBI scenario are reported and dis-cussed.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

Arabidopsis contains eight different h-type thioredoxins (Trx) being distributed in different cell organelles. Although Trx h2 is deemed to be localized in mitochondria, its subcellular localization and function remains a matter of debate. Here, Trx h2 localization and function were investigated using cell fractionation studies and reverse genetics. Differential centrifugation and immunodetection showed the Trx h2 protein to be distributed to the microsomal fraction rather than to mitochondrial preparations. To analyze whether Trx h2 has different roles than mitochondrial Trxs, Arabidopsis mutants lacking Trx h2 were compared with mutants deficient in mitochondrial Trx o1 and double mutants with joint deficiencies in both Trxs. Under constant medium light, trxh2 grew as the wild type, while trxo1 and trxo1h2 mutants showed impaired growth. This was accompanied by differences in the metabolite profiles. The trxo1 and trxo1h2 mutants clustered differently from the wild type during the night, revealing a decrease in ascorbate and glutathione redox states. In fluctuating light intensities, genotypic differences in growth rates were attenuated. Compared to the wild type, the fluctuating-light induced decrease in the NADPH/NADP ratio was diminished in the mutants, with the trxo1h2 double mutant showing the strongest effect. This was accompanied by an increase in the photosynthetic efficiency of the trxo1h2 mutant, specifically in the high light phases of fluctuating light. Conclusively, these results support the view that Trxs o1 and h2 are localized in different subcellular compartments, and have different effects on ascorbate and glutathione redox states and growth in medium light, but cooperatively affect NADP(H) redox state and photosynthetic efficiency in fluctuating light.

Within an Internet of Multimedia Things, the risk of disclosing streamed video content, such as arising from video surveillance, is of heightened concern. This leads to the encryption of that content. To reduce the overhead and lack of flexibility arising from full encryption of the content, a good number of selective-encryption algorithms have been proposed in the last decade. Some of them have limitations, in terms of significant delay due to computational cost, or excess memory utilization, or, despite being energy efficient, do not provide a satisfactory level of confidentiality, due to their simplicity. To address such issues, this paper presents a lightweight selective encryption scheme, in which encoder syntax elements are encrypted with the innovative EXPer (EXtended Permutation with exclusive OR). The selected syntax elements are taken from the final stage of video encoding that is during entropy coding. As a diagnostic tool, the Encryption Space Ratio measures encoding complexity of the video relative to the level of encryption so as to judge the success of the encryption process, according to entropy coder. A detailed comparative analysis of EXPer with state-of-the-art algorithms confirms that the EXPer provides significant confidentiality with a small computational cost and negligible encryption bitrate overhead. Thus, the results demonstrate that the proposed security scheme is a suitable choice for constrained devices in an Internet of Multimedia Things environment.

Recently, the properties of bouncing oil droplets, also known as `walkers', have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behaviour. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie-Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie-Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well.

Rotavirus species H (RVH) has been detected in pigs, humans and bats. Moreover, porcine RVHs have been recently identified in several swine-producing countries. Despite their zoonotic impact, genome information of RVHs is still limited. This study aimed to establish a tentative complete genome-based genotyping system for RVHs, by appending genomic sequences from 12 porcine RVHs identified in Japan between 2013 and 2015 to those from human and other porcine RVHs reported in previous studies. Phylogenetic analysis of 11 RNA segments indicated that porcine RVHs could be classified into multiple genotypes. Consequently, the genotype classification for RVHs revealed the existence of genotypes 10G, 6P, 6I, 3R, 4C, 7M, 6A, 2N, 4T, 6E, 3H for the genes VP7, VP4, VP6, VP1, VP2, VP3, NSP1, NSP2, NSP3, NSP4 and NSP5, respectively. Surprisingly, two distinctive types in NSP1 and NSP3 genes were identified from among the twelve porcine RVHs. Our data suggest a potentially novel gene rearrangement event between porcine RVH and rotavirus species C in the NSP3 gene. These findings would provide a new insight in understanding for evolution of RV.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in all four operation modes: namely voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller performance under ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested, and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system.

Ensuring precise electric locomotive stopping is pivotal for achieving intelligent and unmanned auxiliary transportation systems. Currently, human drivers' expertise plays a central role in the stopping process, posing challenges for automation and cargo location accuracy, particularly in coal mining. This paper focuses on achieving accurate electric locomotive stopping under diverse conditions by utilizing permanent magnet synchronous motor-driven locomotives. This technique introduces a novel stopping control method that combines a fuzzy Proportional-Integral-Derivative (F-PID) controller and a vector control model for permanent magnet synchronous motors (PMSM). After this, we design the F-PID using the PMSM technique based on the new fuzzy rules for each sub-system. In the end, extensive simulations and real-world experiments are conducted on an electric locomotive stopping test bed, which demonstrate the effectiveness of the proposed control method. From the simulation results, it confirming that the ability to achieve precise stopping under various working conditions.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

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.

(S)-Atenolol ((S)-2-(4-(2-Hydroxy-3-(isopropylamino)propoxy)phenyl)acetamide) has been synthesized in >99% ee with use of Candida antarctica lipase B from Syncozymes (Shanghai, China), in a kinetic resolution of the corresponding racemic chlorohydrin. Deprotonation of the starting phenol building block was base catalyzed. The enantiopurity of the chlorohydrin building block remained unchanged upon subsequent amination. All four steps in the synthesis protocol have been optimized compared to previously reported methods, which makes this new protocol more sustainable and in accordance with green chemistry principles compared to previously reported protocols.

We report on the occurrence of natural Magnesium Alumina Silicate Hydrate (M-(A)-S-H) cement at Feragen and Leka in eastern and western Trøndelag Norway, respectively. Both occurrences are located in the sub-arctic climate zone and form in glacial till and moraine material deposited on ultramafic rock during the Weichselian glaciation. Weathering of serpentinized peridotite dissolve brucite and result in a relative high pH alkaline fluid that subsequently reacts with the felsic minerals of the till (quartz, plagioclase, K-feldspar) to form a cement consisting of an amorphous material or a mixture of nanocrystalline Mg-rich phyllosilicates, including illite. The presence of plagioclase in the till results in the enrichment of alumina in the cement, i.e., forms M-A-S-H instead of the M-S-H cement. Dissolution of quartz results in numerous etch-pits and negative quartz crystals filled with M-A-S-H cement. Where the quartz dissolution is faster that the cement precipitation, a honeycomb-like texture is formed. Compositionally the cemented till (tillite) contains more MgO and has a higher loss of ignition than the till, suggesting that the cement is formed by a MgO fluid that previously reacted with the peridotite. The M-(A)-S-H cemented till represent a new type of duricrust, coined magsilcrete. The study of natural Mg-cement provides information on peridotites as a Mg-source for Mg-cement and as a feedstock for CO2 sequestration.

Power converter technologies have become increasingly vital in various applications due to their efficient management of electrical energy. With the growing prominence of renewable energy sources like solar and wind, the high penetration of power electronic converters has been justified. However, ensuring power quality has emerged as a significant challenge for grid-connected power converters. The divergence from the ideal sinusoidal waveform in terms of magnitude and frequency impacts both grid-side currents and voltages. Several studies have proposed solutions to address power quality issues at the load side. The advancement of power converters has been fueled by the development of high-performance microprocessors and the emergence of high-speed switching devices, such as SiC-MOSFETs. This paper focuses on the design of voltage source converters, particularly those based on SiC-MOSFET semiconductor devices. The article presents the design of H-Bridge cells, discusses two-level voltage source converters based on cascade H-Bridge cells in parallel configuration with experimental fault analysis, addresses the seven-level voltage source converters topology, and explores the design and experimental results of the matrix converter. The findings underscore the importance of considering the entire converter design for improved performance at high switching frequencies. The article concludes by summarizing the main outcomes and implications of this research.

The construction of carbon-carbon bonds by direct involvement of two unactivated carbon-hydrogen bonds, without any directing group, ensures an high atom economy of the entire process. Here it is described a simple protocol for the Pd(II)/Cu(II)-promoted intermolecular cross-dehydrogenative coupling (CDC) of 5-arylimidazoles, benzimidazoles, benzoxazole and 4,5-diphenylimidazole at their C-2 position with functionalized styrenes. This specific CDC, known as Fujiwara-Moritani reaction or oxidative Heck coupling, allowed also the C-4 alkenylation of the imidazole nucleus when both 2 and 5 positions are occupied.

Body-centered cubic bismuth (Bi) is considered an enticing pressure marker, and therefore it is highly desirable to command its accurate equation of state (EOS). However, significant discrepancies are noted among the previous experimental EOSs. In the present work, the EOS up to 300 GPa is theoretically obtained by direct solving the partition function via a direct integral approach (DIA). The calculated results nearly reproduce the hydrostatic experimental measurements below 75 GPa, and the deviations from the measurements gradually get larger with increasing pressure. Based on the ensemble theory of equilibrium state, DIA works with high precision particularly in high-pressure conditions, so the hydrostatic EOS presented in this work is expected to be a reliable pressure standard.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

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

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.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

In this work, the problem is considered for eliminating a non-uniform rectilinear smearing of an image by mathematical and computer-based way, for example, a picture of several cars taken with a fixed camera and moving with different speeds. The problem is described by a set of 1-dimensional Fredholm integral equations (IEs) of the first kind of convolution type with a 1-dimensional point spread function (PSF) at uniform smearing and by a set of new 1-dimensional IEs of a general type (not convolution type) with a 2-dimensional PSF at non-uniform smearing. The problem is also described by one 2-dimensional IE of convolution type with a 2-dimensional PSF at uniform smearing and by a new 2-dimensional IE of a general type with a 4-dimensional PSF at non-uniform smearing. The problem for solving Fredholm IE of the first kind is ill-posed (unstable). Therefore, IEs of convolution type are solved by the Fourier transform (FT) method and Tikhonov's regularization (TR), and IEs of general type are solved by the quadrature/cubature and TR methods. Moreover, the magnitude of the image smear Δ is determined by the original “spectral method”, which increases the accuracy of image restoration. It is shown that the use of a set of 1-dimensional IEs is preferable to one 2-dimensional IE in the case of non-uniform smearing. In the inverse problem (image restoration), the Gibbs effect (the effect of false waves) in the image may occur. It can be edge or inner. The edge effect is well suppressed by the proposed technique “diffusing the edges". In the case of an inner effect, it is eliminated with difficulty, but the image smearing itself plays the role of diffusing and suppresses the inner Gibbs effect to a large extent. It is shown (in the presence of impulse noise in an image) that the well-known Tukey median filter can distort the image itself, and the Gonzalez adaptive filter also distorts the image (but to a lesser extent). We propose a modified adaptive filter. A software package was developed in MatLab and illustrative calculations are performed.

In this paper, we study the p-adic integral representation on Z_p of q-Bernoulli numbers arising from two variable q-Bernstein polynomials and investigate some properties for the q-Bernoulli numbers. In addition, we give some new identities of q-Bernoulli numbers.

The regulation of intracellular pH in yeast (Saccharomyces cerevisiae) cells is critical for cell function and viability. In yeast, protons (H+) can be excreted from cell by the plasma membrane ATPase Pma1 and pumped into vacuoles by the vacuolar H+-ATPase. Because Pma1 is critical to the survival of yeast cells, it is unknown whether other compensatory components are involved in the pH homeostasis in the absence of Pma1. To elucidate how intracellular pH is regulated independently of Pma1, we employed a screening approach by exposing the yeast haploid deletion mutant library (ver 4.0) to the selective plant plasma membrane H+-ATPase inhibitor PS-1, which we previously reported. After repeated screenings and verification, we identified two proteins, ALY1 and ALY2, that play a role in the regulation of intracellular pH when Pma1 is deficient. Our research uncovers a new perspective on the regulation of intracellular pH related to Pma1 and also preliminarily reveals a role for ALY1 and ALY2 in the regulation of intracellular pH.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

Protons are gaining increasing attention as neurotransmitters due to their extraordinary abilities to rapidly transfer electrical charge, mobilize cellular calcium and modulate ion channels. How all this is possible is currently the subject of in-depth studies and discussions concerning not only neurophysiology, but also biological materials for artificial intelligence. In this short review, some biochemical mechanisms are described by which protons, in combination with calcium, can initiate firing in sensory neurons and transmit impulse across synapses. Furthermore, mechanisms are put forward concerning how three neurotransmitters, glutamate, gamma-aminobutyric acid and acetylcholine, are able to generate protons. The results of the numerous experimental works taken into consideration indicate that protons can play a fundamental role both in the generation and in the transmission of the nerve impulse.

A methodology based on the concepts that arise from Density Functional Theory named Conceptual Density Functional Theory (CDFT) was chosen for the calculation of some global and local reactivity descriptors of the Discodermins A-H family of marine peptides through the consideration of the KID (Koopmans in DFT) technique that was successfully used in previous studies of this kind of molecular systems. The determination of active sites of the studied molecules for different kind of reactivities was achieved by resorting to some CDFT-based descriptors like the Fukui functions as well as the Parr functions derived from Molecular Electron Density Theory (MEDT). A few properties identified with their ability to behave as a drug and the bioactivity of the peptides considered in this examination were acquired by depending on a homology model by studying the correlation with the known bioactivity of related molecules in their interaction with various biological receptors. With the further object of analyzing their bioactivity some parameters of usefulness for future QSAR studies, their predicted biological targets and the the ADME (Absorption, Distribution, Metabolism, and Excretion) parameters related to the Discodermins A-H pharmacokinetics are also reported.

The details of antigen-antibody interactions and the identification of epitopes are critical for the development of monoclonal antibody drugs. Ab42 is a native human-derived anti-CFH monoclonal antibody. In this study, the interaction between antigen pCFH and antibody (Ab42) was theoretically demonstrated by molecular docking and MD simulation, combined with free energy calculation and computational alanine scanning (CAS), and key amino acids and epitopes were identified. Experimental alanine scanning (EAS) was then carried out to verify the results of the calculation, and our results indicated that Ab42 antibody forms hydrogen bonds and interacts hydrophobically with pCFH through the Tyr315, Ser100, Gly33, and Tyr53 residues on its CDR, while the main pCFH epitopes are located at the six sites of Pro441, Ile442, Asp443, Asn444, Ile447, and Thr448. In conclusion, this study has explored the mechanism of antigen-antibody interaction from both theoretical and experimental aspects, and our results have important theoretical significance for the design and development of relevant antibody drugs.

The Polyurethane (PU) mixture is a high−performance engineering material with different dynamic properties compared to a hot−mixed asphalt mixture (HMA). This paper analyzed whether the Kramers−Kronig (K−K) relation and thermo−rheological simple properties were applicable to the PU mixture. Based on the result discussion, the PU mixture exhibited thermo−rheological simple properties within the test conditions. The time−temperature superposition principle (TTSP) was applicable for the PU mixture to construct the dynamic modulus master curve using the standard logistic Sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak−Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The Core−Core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K−K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results. The phase angle of the PU mixture cannot be derived from the dynamic modulus data and currently needs to be derived from the laboratory measurement.

In the full load operating range, wind turbines typically use pitch control to maintain rotor speed and output power at their rated values to guarantee the whole system’s safety. Blade pitch actuators are subject to physical limitations and safety requirements, which imposes strict constraints on pitch angle’s amplitude and rate of change. These constraints will bring windup problem to the integral part of the pitch controller. It leads to deterioration of the pitch control system’s performance or even the instability problem, especially for large-scale turbines operating in extreme uncertain wind conditions or suffering from cyber attacks. This paper designs an anti-windup robust pitch angle control strategy to deal with pitch rate constraint issue to enhance the security of control system. First, to facilitate controller design, a filtered tracking error technique is employed to transform the nonaffine form into an affine one. Subsequently, a feedback robust controller based on UDE is developed to handle the model’s uncertainty and external disturbances. To address the issue of integral saturation in the pitch system and guarantee its safety, an elliptical bounded constraint is integrated into the designed UDE strategy. This bounded UDE controller can improve the stability of power generation quality, reduces the mechanical loads on components and enhance the whole system’s safety. Finally, the effectiveness of the proposed scheme is verified on the Wind Turbine Blockset platform in Matlab/Simulink. It can achieve better performance than the traditional method.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

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.

Hypotrochoidal profile contours have been produced in industrial applications in recent years using twin-spindle processes, and they are considered effective high-quality solutions for positive shaft–hub connections. This study mainly concerns analytical approaches to determine the bending stresses in hypotrochoidal profile shafts. The formulation was developed according to bending principles using the mathematical theory of elasticity and conformal mappings. The loading was further used to investigate the rotating bending behaviour. The stress factors for the classical calculation of maximum bending stresses were also determined for all those profiles presented and compiled in the German standard DIN3689-1 for practical applications. The results were also compared with the corresponding numerical and experimental results, and very good agreement was observed. Additionally, based on previous work, the stress factor was determined for the case of torsional loading to calculate the maximum torsional stresses in the standardised profiles, and the results are listed in a table. This study contributes to the further refinement of the current DIN3689 standard.

Although most people are infected with Epstein-Barr Virus (EBV) during their lifetime, only a minority of them develop an EBV-associated malignancy. EBV acts in both direct and indirect ways to transform infected cells into tumor cells. There are multiple ways in which the EBV, host, and tumor environment interact to promote malignant transformation. This paper focuses on some of the mechanisms that EBV uses to transform the tumor microenvironment (TME) of EBV-associated gastric cancer (EBVaGC) for its benefit, including overexpression of IDO1, synergism between H pylori and EBV coinfection, and M1 to M2 switch. In this review, we expand on different modalities and combinatorial approaches to therapeutically target this mechanism.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method based on the weakly singular boundary integral equation, the quadrature techniques, dedicated for the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take the full advantage of the multi-patch technique. The generated collo-cation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by the simple examples with analytical solutions. The feature of the present multi-patch WSIGABEM is investigated by the comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner and the arch bridge are verified to be effective.

High efficacy LED lamps combined with adaptive lighting control and greenhouse integrated photovoltaics (PV) could enable the concept of year-round cultivation and become a feasible option even in the harsh climate of the Nordic countries. Meteorological satellite data of this region was analyzed in a parametric study to evaluate the potential of these technologies. The generated maps showed monthly average temperatures fluctuating from -20°C to 20°C throughout the year. The natural photoperiod and light intensity also changed drastically, resulting in monthly average daily light integral (DLI) levels ranging from 45-50 mol·m-2·d-1 in summer and contrasting with 0-5 mol·m-2·d-1 during winter. To compensate, growth room cultivation independent from outdoor conditions could be used in winter. Depending on the efficacy of the lamps, the electricity required for sole-source lighting at 300 µmol·m-2·s-1 for 16 hours would be between 1.4 and 2.4 kWh·m-2·d-1. Greenhouses with supplementary lighting could help start the cultivation earlier in spring and extend it further into autumn. The energy required for lighting highly depends on several factors such as the natural light transmittance, the light threshold settings and the lighting control protocol, resulting in electric demands between 0.6 and 2.4 kWh·m-2·d-1. Integrating PV on the roof or wall structures of the greenhouse could offset some of this electricity, with specific energy yields ranging from 400 to 1120 kWh·kWp-2·yr-1 depending on the region and system design.

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

One of the rapidly developing research areas is the creation of systems. which are commonly referred to as cyberphysical complexes. In such systems, devices and complexes interact with a completely different physical nature. The role of a person in such systems usually consists in the formation of final tasks for “artificial intelligence” and executive mechanisms. The functioning of actuators is controlled by accurate information systems.