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In this paper, we prove the global existence and asymptotic behavior, as time tends to infinity, of solutions in Hi (i=1, 2) to the initial boundary value problem of the compressible Navier–Stokes equations of one-dimensional motion of a viscous heat-conducting gas in a bounded region with a non-autonomous external force and a heat source. Some new ideas and more delicate estimates are used to prove these results. Copyright © 2008 John Wiley & Sons, Ltd.

The main required organ of the biological system is the Central Nervous System (CNS), which can influence the other basic organs in the human body. The basic elements of this important organ are neurons, synapses, and glias (such as astrocytes, which are the highest percentage of glias in the human brain). Investigating, modeling, simulation, and hardware implementation (realization) of different parts of the CNS are important in case of achieving a comprehensive neuronal system that is capable of emulating all aspects of the real nervous system. This paper uses a basic neuron model called the Izhikevich neuronal model to achieve a high copy of the primary nervous block, which is capable of regenerating the behaviors of the human brain. The proposed approach can regenerate all aspects of the Izhikevich neuron in high similarity degree and performances. The new model is based on Look-Up Table (LUT) modeling of the mathematical neuromorphic systems, which can be realized in a high degree of correlation with the original model. The proposed procedure is considered in three cases: 100 points LUT modeling, 1000 points LUT modeling, and 10,000 points LUT modeling. Indeed, by removing the high-cost functions in the original model, the presented model can be implemented in a low-error, high-speed, and low-area resources state in comparison with the original system. To test and validate the proposed final hardware, a digital FPGA board (Xilinx Virtex-II FPGA board) is used. Digital hardware synthesis illustrates that our presented approach can follow the Izhikevich neuron in a high-speed state (more than the original model), increase efficiency, and also reduce overhead costs. Implementation results show the overall saving of 84.30% in FPGA and also the higher frequency of the proposed model of about 264 MHz, which is significantly higher than the original model, 28 MHz.

In this paper, we give a short proof of the Lorentz estimates for gradients of very weak solutions to the linear parabolic equations with the Muckenhoupt class A q -weights u t − div ( A ( x , t ) ∇ u ) = div ( F ) , in a bounded domain Ω × ( 0 , T ) ⊂ R N + 1 , where A has a small mean oscillation, and Ω is a Lipchistz domain with a small Lipschitz constant.

In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order $\alpha$ for $\alpha > 1$. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, $2\pi$-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz., Comment: 22 pages. arXiv admin note: text overlap with arXiv:1810.00248 by other authors

This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results.

Intrusion detection in computer networks is of great importance because of its effects on the different communication and security domains. The detection of network intrusion is a challenge. Moreover, network intrusion detection remains a challenging task as a massive amount of data is required to train the state-of-the-art machine learning models to detect network intrusion threats. Many approaches have already been proposed recently on network intrusion detection. However, they face critical challenges owing to the continuous increase in new threats that current systems do not understand. This paper compares multiple techniques to develop a network intrusion detection system. Optimum features are selected from the dataset based on the correlation between the features. Furthermore, we propose an AdaBoost-based approach for network intrusion detection based on these selected features and present its detailed functionality and performance. Unlike most previous studies, which employ the KDD99 dataset, we used a recent and comprehensive UNSW-NB 15 dataset for network anomaly detection. This dataset is a collection of network packets exchanged between hosts. It comprises 49 attributes, including nine types of threats such as DoS, Fuzzers, Exploit, Worm, shellcode, reconnaissance, generic, and analysis Backdoor. In this study, we employ SVM and MLP for comparison. Finally, we propose AdaBoost based on the decision tree classifier to classify normal activity and possible threats. We monitored the network traffic and classified it into either threats or non-threats. The experimental findings showed that our proposed method effectively detects different forms of network intrusions on computer networks and achieves an accuracy of 99.3% on the UNSW-NB15 dataset. The proposed system will be helpful in network security applications and research domains.

The well-established Timoshenko system is characterized by a particular relation between shear stress and bending moment from its constitutive equations. Accordingly, a (thermal) dissipation added on the bending moment produces exponential stability if and only if the so called “equal wave speeds” condition is satisfied. This remarkable property extends to the case of non-homogeneous coefficients. In this paper, we consider a non-homogeneous thermoelastic system with dissipation restricted to the shear stress. To this new problem, by means of a delicate control observability analysis, we prove that a local version of the equal wave speeds condition is sufficient for the exponential stability of the system. Otherwise, we study the polynomial stability of the system with decay rate depending on the regularity of initial data.

This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic LU-approximately convex functions. Under geodesic LU-approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.

Secret image sharing is a hot issue in the research field of data hiding schemes for digital images. This paper proposes a general k,n threshold secret image sharing scheme, which distributes secret data into n meaningful image shadows based on a non-full rank linear model. The image shadows are indistinguishable from their corresponding distinct cover images. Any k combination of the n shares can perfectly restore the secret data. In the proposed scheme, the integer parameters k,n, with k≤n, can be set arbitrarily to meet the application requirement. The experimental results demonstrate the applicability of the proposed general scheme. The embedding capacity, the visual quality of image shadows, and the security level are satisfactory.

In this paper, a fuzzy (F) proportional (P)–integral (I)–derivative (D) (PID) (FPID) controller optimized with a water cycle algorithm is proposed for load frequency control of a multi-area multi-fuel (MAMF) power system. The MAMF system has the realistic feature of communication time delays (CTDs), in order to conduct an analysis nearer to realistic practice. Initially, the MAMF system is analyzed when subjected to a step load disturbance (SLD) of 10% on area 1. The superiority of the fuzzy PID controller is revealed upon comparing it with PID plus double derivative (DD) (PIDD) and PID controllers. The MAMF system is investigated with and without CTDs, to demonstrate their impact on system performance. Later, an additional HVDC line is incorporated in parallel with the existing AC line for further enhancement of the system performance. Finally, the MAMF system is targeted with random loading to validate the robustness of the presented control scheme.

The purpose of saliency detection is to detect significant regions in the image. Great progress on salient object detection has been made using from deep-learning frameworks. How to effectively extract and integrate multiscale information with different depths is an open problem for salient object detection. In this paper, we propose a processing mechanism based on a balanced attention module and interactive residual module. The mechanism addressed the acquisition of the multiscale features by capturing shallow and deep context information. For effective information fusion, a modified bi-directional propagation strategy was adopted. Finally, we used the fused multiscale information to predict saliency features, which were combined to generate the final saliency maps. The experimental results on five benchmark datasets show that the method is on a par with the state of the art for image saliency datasets, especially on the PASCAL-S datasets, where the MAE reaches 0.092, and on the DUT-OMROM datasets, where the F-measure reaches 0.763.

Economic development leads to the widespread use of energy, which results in carbon emissions. In order to determine the correlation between different urban carbon emissions and fiscal growth, a coupling and coordination model of urban carbon emissions and economic growth based on discrete Fourier transform (DFT) is constructed. According to the coupling and coordinated development characteristics of economic growth and carbon emissions, the evaluation index system of the regional economy and carbon emissions is constructed. This paper examines the proportion of primary energy consumption and the influencing factors of carbon emission in a city and constructs the economic growth computational intelligence model and urban carbon emission model. The coupling degree among economic growth, carbon emission, and energy consumption is studied; the coupling standard between economic growth and energy consumption carbon emission is determined; and the carbon emission factor under the method of DFT is introduced. The coupling coordination model between economic growth and carbon emission is constructed, and the interaction mechanism between carbon emission, economic development, and environmental protection is determined. The experimental findings demonstrate that when energy consumption intensity and carbon emission are relatively low, the model’s change in the trend of coupling coordination index is comparable with the real/actual condition and the model is more reliable.

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions. 2010Mathematics Subject Classification: 33E12, 33A17, 34A08. Resumen En este artículo, presentamos una función logarítmica de Mittag-Leffler y discutir algunas de sus propiedades. La aplicación de estas propiedades se vuelven útiles en la extensión de la integral de contorno de tipo de Pochhammer representaciones y fórmulas de Rodrigues de algunos conocidos hipergeométricos funciones. Desde el punto de vista de la aplicación, se discuten algunas relaciones que son útiles para interpretar el fenómeno de la propagación de infecciones enfermedades en términos de las múltiples funciones hipergeométricas de Lauricella.

The Jordan–Hölder theorem is proved by using Zassenhaus lemma which is a generalization of the Second Isomorphism Theorem for groups. Goursat’s lemma is a generalization of Zassenhaus lemma, it is an algebraic theorem for characterizing subgroups of the direct product of two groups G 1 × G 2 , and it involves isomorphisms between quotient groups of subgroups of G 1 and G 2 . In this paper, we first extend Goursat’s lemma to R -algebras, i.e., give the version of Goursat’s lemma for algebras, and then generalize Zassenhaus lemma to rings, R -modules, and R -algebras by using the corresponding Goursat’s lemma, i.e., give the versions of Zassenhaus lemma for rings, R -modules, and R -algebras, respectively.

Based on the theory of atmospheric refraction, combined with the atmospheric parameter data of NCEP (National Centers for environmental prediction), the Fourier interpolation fitting algorithm is used to model and analyze the parameters affecting atmospheric refraction on a global scale. The atmospheric temperature and density model with space-time variation is constructed. The spacecraft state equation and the measurement equation with the starlight apparent height as the observation quantity are established. Moreover, the Unscented Kalman filter is applied to the indirect sensitive horizon autonomous astronomical navigation of starlight refraction. The relative error of fitting the measured data with the spatiotemporal atmospheric temperature model established in this paper is less than 2%. The position estimation error of the navigation system is 94 m, and the velocity estimation error is 0.16 m/s. Compared with the traditional model, the navigation and positioning considering complex atmospheric changes are more accurate.

In this paper, we introduce a new slash distribution via the power normal distribution and uniform distribution. This new distribution, called the slash power normal distribution, models more appropriately the skewness and kurtosis of data than the power normal distribution. Moreover, the probability density function and the cumulative distribution function of the slash power normal distribution are derived and the density function curves with different parameters are given. We also study the basic properties of the moments, derive the maximum likelihood estimation of the parameters, and substantiate our arguments with numerical simulations. Finally, we model hourly measurements of sulphur dioxide concentrations of a station in Hong Kong by the slash power normal distribution, power normal distribution, and skew normal distribution and use the K-S test to evaluate the model fittings. The result demonstrates that the slash power normal distribution gives a better fit to the data.

The present investigation represents the first complete illustration of nanofluids flow. The effectiveness of wall slip and heat transfer on magnetohydrodynamic nanofluids flow over porous media in vertical stenotic artery with catheter has been analyzed. By considering the long-wavelength with low-Reynolds number approximation, a mathematical solution was derived to velocity, stream function, pressure difference, and temperature. The nanoparticle’s concentration, amplitude ratio, catheter size, and flow rate have been used to extract the pressure difference. This study analyzes the interaction effect of slip and thermal conditions on nanoparticles fluid suspension with a catheter in a vertical stenotic artery with/without the presence of magnetic field and porosity. The results are helpful for understanding the role of the engineering applications of nanofluids in biomedicine and some other applications. The results of this paper reveal that the nanoparticles concentration has little effect on the velocity, and the concentration, slipping, and porosity of the nanoparticles decreases the thermal energy.

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations.

This paper aims to develop a new training strategy to improve efficiency in estimation of weights and biases in a feedforward neural network (FNN). We propose a local linear approximation (LLA) algorithm, which approximates ReLU with a linear function at the neuron level and estimate the weights and biases of one-hidden-layer neural network iteratively. We further propose the layer-wise optimized adaptive neural network (LOAN), in which we use the LLA to estimate the weights and biases in the LOAN layer by layer adaptively. We compare the performance of the LLA with the commonly-used procedures in machine learning based on seven benchmark data sets. The numerical comparison implies that the proposed algorithm may outperform the existing procedures in terms of both training time and prediction accuracy.

Supply chain finance aims to coordinate multiple stakeholders to maximize the flow of cash and internal and external funding along the supply chain, as shown in prior research. From a regulatory standpoint, the goal of this paper is to maximize the profitability of an entire supply chain. As a result, a constrained finite time Linear Quadratic Regulation (LQR) approach is provided for determining an entity’s optimal profit state in a supply chain. The framework is represented by discrete-time linear dynamical equations for each entity in the supply chain network, taking state and input variables into account. The problem is formulated in terms of a convex quadratic programming optimization for which several numerically efficient algorithms are readily available. In order to validate the approach, it was tested on two topologies. The first topology is a fully connected supply chain with six nodes; the second is a simple topology based on the Iranian pharmaceutical supply chain. The results indicate that the proposed approach successfully planned production and financing decisions within the simulated supply chain and obtained globally optimal profit for all supply chain stakeholders.

An essential work in natural language processing is the Multi-Label Text Classification (MLTC). The purpose of the MLTC is to assign multiple labels to each document. Traditional text classification methods, such as machine learning usually involve data scattering and failure to discover relationships between data. With the development of deep learning algorithms, many authors have used deep learning in MLTC. In this paper, a novel model called Spotted Hyena Optimizer (SHO)-Long Short-Term Memory (SHO-LSTM) for MLTC based on LSTM network and SHO algorithm is proposed. In the LSTM network, the Skip-gram method is used to embed words into the vector space. The new model uses the SHO algorithm to optimize the initial weight of the LSTM network. Adjusting the weight matrix in LSTM is a major challenge. If the weight of the neurons to be accurate, then the accuracy of the output will be higher. The SHO algorithm is a population-based meta-heuristic algorithm that works based on the mass hunting behavior of spotted hyenas. In this algorithm, each solution of the problem is coded as a hyena. Then the hyenas are approached to the optimal answer by following the hyena of the leader. Four datasets are used (RCV1-v2, EUR-Lex, Reuters-21578, and Bookmarks) to evaluate the proposed model. The assessments demonstrate that the proposed model has a higher accuracy rate than LSTM, Genetic Algorithm-LSTM (GA-LSTM), Particle Swarm Optimization-LSTM (PSO-LSTM), Artificial Bee Colony-LSTM (ABC-LSTM), Harmony Algorithm Search-LSTM (HAS-LSTM), and Differential Evolution-LSTM (DE-LSTM). The improvement of SHO-LSTM model accuracy for four datasets compared to LSTM is 7.52%, 7.12%, 1.92%, and 4.90%, respectively.

Kinship verification aims to determine whether two given persons are blood relatives. This technique can be leveraged in many real-world scenarios, such as finding missing people, identification of kinship in forensic medicine, and certain types of interdisciplinary research. Most existing methods extract facial features directly from given images and examine the full set of features to verify kinship. However, most approaches are easily affected by the age gap among faces, with few methods taking age into account. This paper accordingly proposes an Age-Invariant Adversarial Feature learning module (AIAF), which is capable of factoring in full facial features to create two uncorrelated components, i.e., identity-related features and age-related features. More specifically, we harness a type of adversarial mechanism to make the correlation between these two components as small as possible. Moreover, to pay different attention to identity-related features, we present an Identity Feature Weighted module (IFW). Only purified identity features are fed into the IFW module, which can assign different weights to the features according to their importance in the kinship verification task. Experimental results on three public popular datasets demonstrate that our approach is able to capture useful age-invariant features, i.e., identity features, and achieve significant improvements compared with other state-of-the-art methods on both small-scale and large-scale datasets.

Complex networks with node attribute information are employed to represent complex relationships between objects. Research of attributed network embedding fuses the topology and the node attribute information of the attributed network in the common latent representation space, to encode the high-dimensional sparse network information to the low-dimensional dense vector representation, effectively improving the performance of the network analysis tasks. The current research on attributed network embedding is presently facing problems of high-dimensional sparsity of attribute eigenmatrix and underutilization of attribute information. In this paper, we propose a network embedding algorithm taking in a variational graph autoencoder (NEAT-VGA). This algorithm first pre-processes the attribute features, i.e., the attribute feature learning of the network nodes. Then, the feature learning matrix and the adjacency matrix of the network are fed into the variational graph autoencoder algorithm to obtain the Gaussian distribution of the potential vectors, which more easily generate high-quality node embedding representation vectors. Then, the embedding of the nodes obtained by sampling this Gaussian distribution is reconstructed with structural and attribute losses. The loss function is minimized by iterative training until the low-dimension vector representation, containing network structure information and attribute information of nodes, can be better obtained, and the performance of the algorithm is evaluated by link prediction experimental results.

In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly. This research is supported by the PDE-GIR project, which has received funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie SkodowskaCurie grant agreement No 778035. Andres Iglesias also thanks the project TIN2017-89275-R funded by MCIN/AEI/10.13039/501100011033/FEDER “Una manera de hacer Europa”.

Fa\`a di Bruno's formula gives an expression for the derivatives of the composition of two real-valued functions. In this paper we prove a multivariate and synthesized version of Fa\`a di Bruno's formula in higher dimensions, providing a combinatorial expression for the derivatives of chain compositions $F^{(1)} \circ \ldots \circ F^{(m)}$ of functions $F^{(l)} : \mathbb{R}^N \to \mathbb{R}^N$ in terms of sums over labelled trees. We give several applications of this formula, including a new involution formula for the inversion of multivariate power series. We use this framework to outline a combinatorial approach to studying the invertibility of polynomial mappings, giving a purely combinatorial restatement of the Jacobian conjecture. Our methods extend naturally to the non-commutative case, where we prove a free version of Fa\`a di Bruno's formula for multivariate power series in free indeterminates, and use this formula as a tool for obtaining a new inversion formula for free power series., Comment: 38 pages, 11 figures

Motivated by two identities published with Ramanujan's lost notebook and connected, respectively, with the Gauss circle problem and the Dirichlet divisor problem, in an earlier paper, three of the present authors derived representations for certain sums of products of trigonometric functions as double series of Bessel functions [8] . These series are generalized in the present paper by introducing the novel notion of balanced derivatives, leading to further theorems. As we will see below, the regions of convergence in the unbalanced case are entirely different than those in the balanced case. From this viewpoint, it is remarkable that Ramanujan had the intuition to formulate entries that are, in our new terminology, “balanced”. If x denotes the number of products of the trigonometric functions appearing in our sums, in addition to proving the identities mentioned above, theorems and conjectures for upper and lower bounds for the sums as x → ∞ are established.

The groups mentioned in the title are certain matrix groups of infinite size over a finite field $\mathbb F_q$. They are built from finite classical groups and at the same time they are similar to reductive $p$-adic Lie groups. In the present paper, we initiate the study of invariant measures for the coadjoint action of these infinite-dimensional groups. We examine first the group $\mathbb{GLB}$, a topological completion of the inductive limit group $\varinjlim GL(n, \mathbb F_q)$. As was shown by Gorin, Kerov, and Vershik [arXiv:1209.4945], the traceable factor representations of $\mathbb{GLB}$ admit a complete classification, achieved in terms of harmonic functions on the Young graph $\mathbb Y$. We show that there exists a parallel theory for ergodic coadjoint-invariant measures, which is linked with a deformed version of harmonic functions on $\mathbb Y$. Here the deformation means that the edges of $\mathbb Y$ are endowed with certain formal multiplicities coming from the simplest version of Pieri rule (multiplication by the first power sum $p_1$) for the Hall-Littlewood (HL) symmetric functions with parameter $t:=q^{-1}$. This fact serves as a prelude to our main results, which concern topological completions of two inductive limit groups built from finite unitary groups. We show that in this case, coadjoint-invariant measures are linked to some new branching graphs. The latter are still related to the HL functions, but the novelty is that now the formal edge multiplicities come from the multiplication by $p_2$ (not $p_1$) and the HL parameter $t$ turns out to be negative (as in Ennola's duality)., 46 pages; v2: minor modifications, shortened abstract, journal version, to appear in Adv. Math

In this paper we study the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. This is achieved by adapting the method of Brummelhuis to the non-analytic case. As an application we obtain a general form of uncertainty principle for measures on the complex sphere which subsumes certain classical results about pluriharmonic measures., Submitted

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program.

In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E1 , E2 , E3) of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the percentile estimator is the best in (E1, E2) but modification moment is the best in (E3) .

The main objective of this paper is to develop and validate flow injection method, a precise, accurate, simple, economic, low cost and specific turbidimetric method for the quantitative determination of mebeverine hydrochloride (MbH) in pharmaceutical preparations. A homemade NAG Dual & Solo (0-180º) analyser which contains two identical detections units (cell 1 and 2) was applied for turbidity measurements. The developed method was optimized for different chemical and physical parameters such as perception reagent concentrations, aqueous salts solutions, flow rate, the intensity of the sources light, sample volume, mixing coil and purge time. The correlation coefficients (r) of the developed method were 0.9980 and 0.9986 for cell 1 and 2 respectively and showed the linearity of response against concentration over the range of 1.0 to 6.5 and 0.7-6.5mmol/L for cell 1 & 2 respectively. The limit of detections (LOD) for cell 1 and cell 2 were 0.28 and 0.21 mmol/L respectively. The intra-day and inter-day precision for two serial estimations of 3.5 and 5.5 mmol/L of MBH exhibited a relative standard deviation of 0.46%, 0.28%, 0.23%, 0.26% and 0.39%, 0.79%, 0.14%, 0.05% for cell 1 & 2 respectively. The accuracy of the developed method has expressed a recovery percentage (Rec %) and error % which was between 99.22 to 101.13 and 99.39 to 101.17 for cell 1 and cell 2 respectively. The ICH guidelines were followed for method validation. The developed method was successfully applied for the determination of MbH in pure and pharmaceutical preparations and the method can be conveniently used for routine analysis in laboratory as a quality control method since the method permits quantitively determination of 60 samples/h.

Recently, the internet has made the users able to transmit the digital media in the easiest manner. In spite of this facility of the internet, this may lead to several threats that are concerned with confidentiality of transferred media contents such as media authentication and integrity verification. For these reasons, data hiding methods and cryptography are used to protect the contents of digital media. In this paper, an enhanced method of image steganography combined with visual cryptography has been proposed. A secret logo (binary image) of size (128x128) is encrypted by applying (2 out 2 share) visual cryptography on it to generate two secret share. During the embedding process, a cover red, green, and blue (RGB) image of size (512x512) is divided into three layers (red, green and blue). The blue layer is transformed using Discrete Shearlet Transform (DST) to obtain its coefficients. The first secret share is embedded at the coefficients of transformed blue layer to obtain a stego image. At extraction process, the first secret share is extracted from the coefficients of blue layer of the stego image and XORed with the second secret share to generate the original secret logo. According to the experimental results, the proposed method is achieved better imperceptibility for the stego image with the payload capacity equal to (1 bpp). In addition, the secret logo becomes more secured using (2 out 2 share) visual cryptography and the second secret share as a private key.

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

This paper introduces a relationship between the independence of polynomials associated with the links of the network, and the Jacobian determinant of these polynomials. Also, it presents a way to simplify a given communication network through an algorithm that splits the network into subnets and reintegrates them into a network that is a general representation or model of the studied network. This model is also represented through a combination of polynomial equations and uses Groebner bases to reach a new simplified network equivalent to the given network, which may make studying the ability to solve the problem of network coding less expensive and much easier.

Assume E is an imaginary quadratic field and O is its ring of integers. For each positive integer m, let I m be the free Hermitian lattice of rank m over O having an orthonormal basis. For each positive integer n, let S O ( n ) be the set of all Hermitian lattices of rank n over O that can be represented by some I m . Denote by g O ( n ) the smallest positive integer g such that each Hermitian lattice in S O ( n ) can be represented by I g . In this paper, we shall provide an explicit upper bound for g O ( n ) for all imaginary quadratic fields E and all positive integers n.

In this paper, we are mainly concerned with the following integral equations: (0.1) u ( x ) = C n ∫ R n ln ⁡ ( 1 | x − y | ) f ( y , u ( y ) ) d y + γ , x ∈ R n , where n ≥ 2 , γ ∈ R , u ∈ C ( R n ) and f ( x , u ) may change signs and satisfies some assumptions. By using the method of scaling spheres developed by Dai and Qin in [14] , we first derive nonexistence of positive solutions to the above IEs under some assumptions. Then, based on the equivalence between the above IEs and the following 2D PDEs: (0.2) − Δ u ( x ) = f ( x , u ) , x ∈ R 2 , we also obtain nonexistence of positive solutions to the 2D PDEs under some assumptions. One should note that there are no growth conditions on u and hence f ( x , u ) can grow exponentially (or even faster) on u.

This paper considers backward stochastic differential equations (BSDEs for short) on the infinite horizon under consistent nonlinear expectations which are dominated by consistent sublinear expectations. We derive the existence and uniqueness result by discretization and approximation method. Besides, we show the existence of the solution of Markovian ergodic BSDEs under G ˜ -expectations and state some applications.

This paper is devoted to the study of existence of solutions to some integro-differential problems. We establish the existence of solutions by employing a singular perturbations method as a natural tool. The perturbed problems are classical, nonlocal, non-linear, hyperbolic and the limits of the subsequences of their solutions, in weighted Sobolev type spaces, are solutions of the main problem. The existence of a solution to the nonlocal hyperbolic problem can be ensured using the Schauder fixed point theorem.

In this paper we study pseudo-differential operators with operator valued symbols on the Similitude group, SIM ( 2 ) . We characterize the unique infinite-dimensional, unitary, irreducible representations of SIM ( 2 ) and using that the Fourier inversion formula is given. The operator valued Wigner transform and the Weyl transform are also studied here. Furthermore we also obtain a necessary and sufficient condition on the symbols for which the pseudo-differential operators SIM ( 2 ) are Hilbert-Schmidt and trace class operators. Finally, we also give the trace formula for these operators.

The goal of this paper is to establish the relation between the notion of sets of finite perimeter and the theory of the Ornstein-Uhlenbeck semigroup in the setting of the Gauss space. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the Ornstein-Uhlenbeck semigroup and we also give a new characterization of BV functions in terms of a near-diagonal energy in this space.

In a recent paper [10], Peter A. Loeb showed how to convert non-standard measure spaces into standard ones and gave applications to probability theory. We apply these results to Brownian Motion and Ito integration. We first develop a number of new tools about Loeb spaces. We then show that Brownian Motion can be obtained as the Loeb process corresponding to a non-standard random walk obtained from a*-finite number of coin tosses. This permits a very constructive proof of a special case of Donsker's Theorem. The Ito integral with respect to this Brownian Motion is a non-standard Stieltjes integral with respect to the random walk. As a consequence, an easy proof of Ito’s Lemma is possible. The results in this paper were announced in [1].

This paper develops a mathematical model for condition-based maintenance optimization of multi-state systems. The majority of the existing literature on maintenance optimization assume that there is no additional cost incurred because of side effects of equipment degradation. Nevertheless, as the operating cost increases with equipment age and degradation, it is important to consider the degradation side effects in the maintenance decision-making process. An important feature of the proposed model lies in the fact that it incorporates side effect of degradation process into condition-based preventive maintenance optimization. We develop a continuous-time discrete-state Markov chain model describing the deterioration stochastic process of a single component. The component is modeled as a multi-state system, where each discrete state is characterized by a degradation level. Numerical examples show the importance of considering such side effect costs when optimizing the choice of maintenance policy. The proposed model is extended to deal with multi-state series systems. Using an example of a series system with two components, it is shown that preventive maintenance and side effect costs should not be optimized for each component individually, but from the perspective of the series system as a whole.

We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples where the new bound for the rate of convergence is the same as (resp. better than) the classical Markov–Dobrushin inequality.

In this paper, we study the long-time behavior of the solution for the linearized ideal MHD around sheared velocity and magnetic field under Stern stability condition. We prove that the velocity and magnetic field will converge to sheared velocity and magnetic field as time approaches infinity. Moreover a new depletion phenomenon is proved: the horizontal velocity and magnetic field at the critical points will decay to 0 as time approaches infinity.

The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by J. Lott, K.-T. Sturm and C. Villani, the noncompact case provides various surprising phenomena. Since the reversibility of noncompact irreversible spaces might be infinite, it is motivated to introduce a suitable nondecreasing function that bounds the reversibility of larger and larger balls. By this approach, we are able to prove satisfactory convergence/stability results in a suitable – reversibility depending – Gromov-Hausdorff topology. A wide class of irreversible spaces is provided by Finsler manifolds, which serve to construct various model examples by pointing out genuine differences between the reversible and irreversible settings. We conclude the paper by proving various geometric and functional inequalities (as Brunn-Minkowski, Bishop-Gromov, log-Sobolev and Lichnerowicz inequalities) on irreversible structures.

We show in this paper that the VC-dimension of the family of d-dimensional axis-parallel boxes and cubes on the d-dimensional torus are both asymptotically d log 2 ⁡ d . This is especially surprising as in most other examples the VC-dimension usually grows linearly with d in similar settings.

A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be useful for the design and optimization of small-scale devices exhibiting flexural behaviour.

While traffic speed data and travel time estimates are increasingly more available from commercial vendors, they are not sufficient for proper management and performance evaluation of transportation networks. Effective traffic control and demand management requires information about volumes, which is provided by fixed location sensors, such as loop detectors or cameras, and those are sparse. This paper proposes a method for estimating route choice using sparse flow measurements and estimated speed on the road network based on compressed sensing technology widely used in image processing, where from a handful of scattered pixels, a full image is recovered. What is known includes flows at origins and at selected links of the road network, where the detection is present; speed estimates are available for all network links. We find coefficients that split origin flows among routes starting at those origins. The advantage of the proposed methodology is that it does not rely on simulation that is prone to calibration errors but only on measured data. We also show how vehicle flows can be estimated at links with no detection, which enables computing performance measures for road networks lacking complete sensor coverage. Finally, we propose a method for selecting plausible routes between origins and destinations.

Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy measures, including, in particular, additive, probabilistic representations. In this paper, we discuss a couple of probability representations of a fuzzy measure: the Campos-Bolanos representation (CBR) and the Murofushi–Sugeno representation (MSR). The CBR is mainly represented by the Associated Probability Class (APC). The APC is well studied and the aspects of its use can be found in many interesting studies. This is especially true for the environment of interactive attributes in their identification and multi-attribute group decision-making (MAGDM) models, related to the attributes’ Shapley values and interaction indexes. The MSR is a less-used tool in practice today. The main motivation of the research presented here was to explore the connections between these two representations, which will help increase the usability of the MSR in practice in the future. In the MSR, we constructed the nonequivalent representation class (NERC) of a fuzzy measure. This probabilistic new representation is somewhat similar to the APC in the CBR environment. The proposition on the existence of the MSR induced by the CBR was proven. The presented formula of the APC by the NERC was obtained. The duality property of fuzzy measures for the CBR is well studied with respect to fuzzy measures—Choquet second-order dual capacities. Significant properties were proven for the representation of a monotone expectation (ME) under the NERC conditions: as is known, the necessary and sufficient conditions for the existence of the second-order Choquet dual capacities are proven in the terms of the APC of a CBR and ME. After establishing the links between the APC of a CBR and the NERC of a MSR, we proved the same in the case of the MSR. A recursive connection formula between the interaction indexes, Shapley values, and the probability distribution of the NERC of a two-order additive fuzzy measure was obtained in the environment of a general MAGDM. A new distance concept was introduced for all fuzzy measures’ classes defined in finite sets in terms of the NERC. The distance between two fuzzy measures was defined as the distance between their NERCs. This distance is equivalent to the distance defined on the same class under the conditions of the APC of a CBR. The correctness proposition on the extension of the distance between fuzzy measures for the NERC was preserved: distances between any two fuzzy measures and between their dual fuzzy measures also coincided in the CBR as the MSR. After parameterization, the calculation formula of the new distance was obtained. An illustrative example was considered in order to easily present the obtained results. The connection schemes between the CBR and MSR and the sequential scheme of key facts and results obtained are presented at the end of this work.

In this paper, we solve the problem of estimating the parameters of a system of ordinary differential equations from observations on a short interval of argument values. By analogy with linear regression analysis, a sufficiently large number of observations are selected on this segment and the values of the functions on the right side of the system and the values of the derivatives are estimated. According to the obtained estimates, unknown parameters are determined, using the differential equations system. The consistency of the estimates obtained in this way is proved with an increase in the number of observations over a short period of argument values. Here, an algorithm for estimating parameters acts as a system. The error of the obtained estimate is an indicator of its quality. A sequence of inaccurate measurements is a random process. The method of linear regression analysis applied to an almost linear regression function is used as an optimization procedure.