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Wide field application of curve number (CN) methodology in design flood estimation and forecasting studies is a well-accepted reality. The parameter CN is often regarded as a constant, but it is in fact a random variable, for it relies on a number of factors governing the process of rainfall-runoff. This paper suggests an alternative procedure to estimate design runoff (Q) using design storm (P) and design curve number (CN) values. To this end, design CN values for different durations and return periods have been derived from 25 years of daily annual maximum P-Q data of 10 Indian catchments. When compared, the computed design Q from design CN values was either very close to or slightly greater than the observed Q. The performance is also evaluated using coefficient of determination (R2), percentage of bias (PBIAS), and normalized Nash-Sutcliffe efficiency (NNSE). The magnitude of design CN is found to decrease for longer durations and smaller return periods, and vice versa, and such a behavior invoked the development of an empirical relation for estimation of design CN from given return period and duration for gauged as well as ungauged watersheds. The statistical analysis revealed the general extreme value (GEV) to fit best the P-CN series, whereas multiple probability distributions, viz., GEV, Gumbel max, log Pearson 3, and Gen Pareto fitted best the Q series. The 50-year, 100-year, and 200-year runoff estimated from the P-CN series exceeded only marginally those derived from the conventional Q series approach.

It is generally admitted that many financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management, for instance when risk is measured through the expected shortfall. This paper considers testing the existence of moments in the framework of GARCH processes. While the second-order stationarity condition does not depend on the distribution of the innovation, higher-order moment conditions involve moments of the independent innovation process. We propose tests for the existence of high moments of the returns process which are based on the joint asymptotic distribution of the Quasi-Maximum Likelihood (QML) estimator of the volatility parameters and empirical moments of the residuals. A bootstrap procedure is proposed to improve the finite-sample performance of our test. To achieve efficiency gains we consider non Gaussian QML estimators founded on reparameterizations of the GARCH model, and we discuss optimality issues. Monte Carlo experiments and an empirical study illustrate the asymptotic results.

In this paper, we propose an algorithm for the construction of substitution-box through a linear recurrence relation. S-box is considered as the building block of block ciphers; here we present a technique to construct Substitution-boxes by using linear recurrence relation to comply with the standards of good quality S-boxes. We have witnessed that the latest research relies more on improving already existing techniques, rather than developing wholly new methods. We use linear recurrence in an entirely new way. Real initial and obtained values are concealed by converting it into new numbers to avoid any pattern to follow. The obtained S-boxes are analyzed through performance tests to check the strength and quality of our S-boxes. Later we will encrypt an image and also perform encryption and decryption in noise channels to make it more applicable in low profile applications.

The solution of the grey model (GM(1,1) model) generally involves equal-precision observations, and the (co)variance matrix is established from the prior information. However, the data are generally available with unequal-precision measurements in reality. To deal with the errors of all observations for GM(1,1) model with errors-in-variables (EIV) structure, we exploit the total least-squares (TLS) algorithm to estimate the parameters of GM(1,1) model in this paper. Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation, we further present a nonlinear total least-squares variance component estimation approach for GM(1,1) model, which resorts to the minimum norm quadratic unbiased estimation (MINQUE). The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the p − q plane. The main goal of this paper is to find out sharp conditions of these moduli of continuity which classify between global (in time) existence of small data solutions and finite time blow-up of (even) small data solutions.

This paper is concerned with systems of linear functional differential equations of mixed type, that is, differential equations with delays and advances. In one of the sections, we obtain sufficient conditions under which the system has at least a nonoscillatory solution.These criteria, based on the form of the system matrices, are obtained via the analysis of the characteristic equation. In the other section we obtain criteria for the oscillatory behavior of the solutions. Some of these criteria are also obtained by studying the characteristic equation, while others use the definition of matrix measures. A set of examples illustrates the application of the theoretical results.

The Lyapunov–Floquet (L–F) theory, a powerful result of Floquet theory, is one of the main tools for the stability analysis and study of nonlinear periodic systems. In this paper, Lyapunov–Floquet and modal transformations of the nonlinear approximation model of spacecraft relative motion, containing periodic state dependent coefficients (SDC), are developed. The transformations, advantageously, retain the stability characteristics of the original nonlinear relative motion dynamics. To provide a form to which averaging method can be applied, the nonlinear approximated equation of motion is scaled using the chief’s eccentricity. Through the application of L–F transformation, the linear part with periodic coefficients is reduced to time-invariant form and the transformed periodic nonlinear part has coefficients with true anomaly as the independent variable. The modal transformation reduced LF transformed equation into a form containing Jordan canonical form. Afterward, the averaging method is applied to the L–F transformed equation to describe the evolution of the motion in terms of the average values of the dynamical variables. Both the LF and modal transformed relative motion equations and the averaged equations, with chief in elliptical orbit, present forms that are useful and applicable for spacecraft guidance, navigation and control, formation flying, rendezvous and proximity operations.

In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and L$ {\rm \acute{e}} $vy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.

For the main diesel engines of the fishing vessels, the pressure in the high-pressure pipelines (p hpp ) of the fuel injection system and the end-of-stroke compression pressure (p c ) directly affect the jet structure, leading to a change process forming combustion mixture and burning fuel. Decreasing the above parameters will cause the engine power to decline (N e ). In this study, the paper presents experimental results on the Yanmar 4CHE main diesel engines of the fishing vessels, when conducting the adjustment of p hpp , p c to evaluate their impact on N e , thereby diagnosing the decrease of p hpp and pc to a specific value, the diesel engine must be serviced repaired to avoid terrible damage. The research results show that when the p c decreased by 12% and the p hpp decreased by 16% compared to the first state then N e decreased by 19.85%. From experimental data, using Lagrange interpolation method, building a multivariate interpolation function expressing the influence of p hpp and p c to N e , as a basis for diagnosing the technical state of the main diesel engines of the fishing vessels.

Recorded electroencephalography (EEG) signals can be represented as square matrices, which have been extensively analyzed using mathematical methods to extract invaluable information concerning brain functions in terms of observed electrical potentials; such information is critical for diagnosing brain disorders. Several studies have revealed that certain such square matrices—in particular, those related to so-called “elementary EEG signals”—exhibit properties similar to those of prime numbers in which every square EEG matrix can be regarded as a composite of these signals. A new approach to ordering square matrices is pivotal to extending the idea of square matrices as composite numbers. In this paper, several ordering concepts are investigated and a new technique for ordering matrices is introduced. Finally, some properties of this matrix order are presented, and the potential applications of this technique to analyzing EEG signals are discussed.

This paper studies an interaction between one prey and one predator following Lotka-Volterra model with additive Allee effect in predator. The Atangana-Baleanu fractional-order derivative is used for the operator. Since the theoretical ways to investigate the model using this operator are limited, the dynamical behaviors are identified numerically. By simulations, the influence of the order of the derivative on the dynamical behaviors is given. The numerical results show that the order of the derivative may impact the convergence rate, the occurrence of Hopf bifurcation, and the evolution of the diameter of the limit-cycle.

In this paper, we first define the generalized (F, $ \varphi $, $ \alpha - \psi $)-contraction mappings. In the following, we consider the conditions in which these mappings have a $ \varphi $-fixed point and also we present examples and applications of these mappings in partial metric space and integral equations.

In Treschev (Proc Steklov Math Inst 310:262–290, 2020) we introduce the concept of a $$\mu $$ -norm for a bounded operator in a Hilbert space. The main motivation is the extension of the measure entropy to the case of quantum systems. In this paper we recall the basic results from Treschev (2020) and present further results on the $$\mu $$ -norm. More precisely, we specify three classes of unitary operators for which the $$\mu $$ -norm generates a bistochastic operator. We plan to use the latter in the construction of quantum entropy.

The minimization of automaton is important to reduce space and computational time. Reduction in number of states and transitions leads to equivalent automaton with less number of states and transitions. In this paper, state minimization of General Finite Fuzzy Automata (GFFA) is discussed. To obtain minimal equivalent GFFA we have removed redundant states and transitions using substitution property (SP) partition and quotient machine. The algorithm to find membership values of states of the GFFA is described and algorithm to associate states with quotient machine to obtain minimal machine with less number of states is discussed.

This paper proposed a chaotic system of N-level logistic cascaded homogenization mapping (N-LLCHM). The cascade structure of multiple one-dimensional logistic mappings results in an exponential increase in the number of fixed points in the mapping, which greatly increases the initial error divergence of the system during the iteration process, and ultimately increases the complexity of the system to generate time series. In the experiment, the homogenization adjustment function of the mapping is derived according to the maximum entropy theorem. The homogenization adjustment function and the N-level logistic cascade structure are cascaded again to construct a complete dynamics system. The analyses of indicators such as information entropy, Lyapunov exponent, spectral entropy and NIST SP800-22 randomness test reveal that the mapping generates a chaotic time series with good aperiodic and uniform distribution characteristics under the condition that N is greater than or equal to 4. Then, N-LLCHM is used as the core of pseudo-random number generator, and the color image encryption algorithm is constructed by using three steps of pixel bidirectional cross-coding, position scrambling and pixel diffusion as the main system. According to the evaluation of histogram, correlation, information entropy and anti-differential attack test, it is verified that this algorithm has better encryption effect and higher security than the present image encryption algorithms.

In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia.

In the paper, the comparison between the efficiency of using artificial intelligence methods and the efficiency of using classical methods in modelling the industrial processes is made, considering as a case study the separation process of the 18O isotope. Firstly, the behavior of the considered isotopic separation process is learned using neural networks. The comparison between the efficiency of these methods is highlighted by the simulations of the process model, using the mentioned modelling techniques. In this context, the final part of the paper presents the proposed model being simulated in different scenarios that can occur in practice, thus resulting in some interesting interpretations and conclusions. The paper proves the feasibility of using artificial intelligence methods for industrial processes modeling; the obtained models being intended for use in designing automatic control systems.

A plankton–herbivore state-dependent impulsive model with nonlinear impulsive functions and action threshold including population density and rate of change is proposed. Since the use of action threshold makes the model have complex phase set and pulse set, we adopt the Poincar $$\acute{\text{ e }}$$ map as a tool to study its complex dynamics. The Poincar $$\acute{\text{ e }}$$ map is defined on the phase set and its properties in different situations are analyzed. Furthermore, the periodic solution of model is discussed, including the existence and stability conditions of the order-1 periodic solution and the existence of the order-k ( $$k\ge 2$$ ) periodic solutions. Compared with the fixed threshold in the existing literature, our results show that the use of action threshold is more practical, which is conducive to the sustainable development of population and makes people obtain more economic benefits. The analysis method used in this paper can study the complex dynamics of the model more comprehensively and deeply.

This work presents some extensions and improvements of former results that allow proving asymptotic stability, uniform stability and global uniform asymptotic stability of zero solution to a class of non-linear Volterra integro-differential equations (VIDEs). Via the Lyapunov–Krasovskiĭ and the Lyapunov–Razumikhin methods, three new results are proved on the mentioned concepts. These results are proved using Lyapunov functional and quadratic Lyapunov function. The results of this paper improve and extend the known ones in the literature. Some examples are given to validate these results and the concepts introduced.

China is shifting from the stage of large-scale bridge construction to the stage of equal emphasis on the construction and maintenance of bridges. The problems of low efficiency and high cost in bridge inspection are becoming more and more prominent, which threaten people’s life safety. In this paper, the deterioration state prediction model of concrete beam bridge under Boosting DT C5.0 was established as the basis, and optimization suggestions were put forward in terms of bridge inspection standards and processes, which aims to perfect the bridge inspection mechanism, realize the fine management of the bridge and prolong the service life of the bridge. Research shows that: first, the bridge inspection standard with a single index should be improved into the bridge inspection standard with multiple indexes, so as to scientifically determine the bridges that need to be inspected and optimize the allocation of maintenance resources. Second, the bridge deterioration state prediction model is used to add a screening mechanism for the bridge in the inspection plan, which can effectively reduce the workload of bridge inspection and enhance the inspection efficiency. Third, the deterioration phenomenon of coexistence between adjacent traffic assets should be fully considered and the linkage inspection mechanism of adjacent traffic assets should be established to improve the effect of bridge inspection.

This paper gives explicit constructions of all irreducible representations of unipotent radicals $$N_{n_1,n_2,n_3}({\mathbb {F}}_q)$$ of the standard parabolic subgroups $$P_{n_1,n_2,n_3}({\mathbb {F}}_q)$$ of $${\mathrm {GL}}_n({\mathbb {F}}_q),$$ corresponding to the ordered partition $$ (n_1,\ n_2,\ n_3)$$ of n. The construction gives a bijection between coadjoint orbits of $$N_{n_1,n_2,n_3}({\mathbb {F}}_q)$$ and irreducible representations inducing from degree 1 characters in the sense of Boyarchenko’s construction. The result shows that the number of irreducible characters of $$N_{n_1,n_2,n_3}({\mathbb {F}}_q)$$ with a fixed degree is a polynomial in $$q-1$$ with nonnegative integer coefficients and verifies analogue conjectures of Higman, Lehrer, and Isaacs.

Let be a connected graph. Let be a subset of V with an order imposed on W. The k-vector is called the resolving vector of v with respect to W. The set W is called a resolving set if for any two distinct vertices In this paper we investigate the existence of independent resolving sets in Cartesian product and corona of graphs.

This paper proposes a fuzzy best-worst method (BWM), called the GITrF BWM, based on generalized interval-valued trapezoidal fuzzy (GITrF) numbers (GITrFNs) for multi-criteria decision-making (MCDM). The reference comparisons between criteria are represented by GITrFNs and the weights of criteria are also taken the form of GITrFNs. The concept of normalized GITrF weight vector is proposed and a new graded mean integration representation (GMIR) of GITrFN is given. A goal programming model is built to obtain the optimal normalized GITrF weights of criteria. Furthermore, the GITrF consistency index and the GITrF consistency ratio are proposed. The GMIR of the GITrF consistency ratio is calculated to measure the acceptable consistency of all the reference comparisons between criteria. For the unacceptable consistent reference comparisons, we propose an approach to improve the consistency of reference comparisons between criteria. Finally, a GITrF BWM is proposed for MCDM. Three real examples are analyzed to illustrate the proposed GITrF BWM. The comparison analyses show that the proposed GITrF BWM outperforms the existing methods for MCDM in GITrF environments.

The objective of this paper is to design an II phase algorithm employing median filters for enlightening the performance in removing impulse noise during the processing of the image. The cascaded filter section employs an Adaptive median filter in the first phase followed by a Recursive weighted median filter (RWM) in the second phase. The RWM filter weight is selected with the Median Controlled Algorithm. As a design parameter, the exponential weights of RWM filters are used in the feedback path. The projected algorithm can achieve suggestively improved quality of image when compared to fixed weight or the Center Weighted Median filters.

The concept of kurtosis is used to describe and compare theoretical and empirical distributions in a multitude of applications. In this connection, it is commonly applied to asymmetric distributions. However, there is no rigorous mathematical foundation establishing what is meant by kurtosis of an asymmetric distribution and what is required to measure it properly. All corresponding proposals in the literature centre the comparison with respect to kurtosis around some measure of central location. Since this either disregards critical amounts of information or is too restrictive, we instead revisit a canonical approach that has barely received any attention in the literature. It reveals the non-transitivity of kurtosis orderings due to an intrinsic entanglement of kurtosis and skewness as the underlying problem. This is circumvented by restricting attention to sets of distributions with equal skewness, on which the proposed kurtosis ordering is shown to be transitive. Moreover, we introduce a functional that preserves this order for arbitrary asymmetric distributions. As application, we examine the families of Weibull and sinh-arcsinh distributions and show that the latter family exhibits a skewness-invariant kurtosis behaviour.

Social media represent an important source of news for many users. They are, however, affected by misinformation and they might be playing a role in the growth of political polarization. In this paper, we create an agent based model to investigate how policing content and backlash on social media (i.e. conflict) can lead to an increase in polarization for both users and news sources. Our model is an advancement over previously proposed models because it allows us to study the polarization of both users and news sources, the evolution of the audience connections between users and sources, and it makes more realistic assumptions about the starting conditions of the system. We find that the tendency of users and sources to avoid policing, backlash and conflict in general can increase polarization online. Specifically polarization comes from the ease of sharing political posts, intolerance for opposing points of view causing backlash and policing, and volatility in changing one’s opinion when faced with new information. On the other hand, it seems that the integrity of a news source in trying to resist the backlash and policing has little effect.

In this paper, three different uniqueness data are investigated to reconstruct the potential function in the Sturm-Liouville boundary value problem in the normal form. Taking account of R\"{o}hrl's objective function, the steepest descent method is used in the computation of potential functions. To decrease the volume of computation, we propose a theorem to precalculate the minimization parameter that is required in the optimization. Further, we propose a novel time-saving algorithm in which the obligation of using the asymptotics of eigenvalues and eigenfunctions and the appropriateness of selected boundary conditions are also eliminated. As partial data, we take two spectra, the set of the $j$th elements of the infinite numbers of spectra obtained by changing boundary conditions in the problem, and one spectrum with the set of terminal velocities. In order to show the efficiency of the proposed method, numerical results are given for three test potentials which are smooth, nonsmooth continuous, and noncontinuous, respectively.

In the current paper, the concept of one-dimensional Shehu Transform have been generalized into three-dimensional Shehu Transform namely, Triple Shehu Transform (TRHT). Further, some main properties, several theorems and properties related to the TRHT have been established. Triple Shehu transform was used in solving fractional partial differential equations, with the fractional derivative described in Caputo sense. The proposed scheme finds the solution without any discretization, transformation or restrictive assumptions. Several examples are given to check the reliability and efficiency of the proposed technique. Key words: Caputo fractional derivative, exponential order, Triple Shehu transforms, partial derivative, uniqueness.

Based on the understanding and comparison of various main recommendation algorithms, this paper focuses on the collaborative filtering algorithm and proposes a collaborative filtering recommendation algorithm with improved user model. Firstly, the algorithm considers the score difference caused by different user scoring habits when expressing preferences and adopts the decoupling normalization method to normalize the user scoring data; secondly, considering the forgetting shift of user interest with time, the forgetting function is used to simulate the forgetting law of score, and the weight of time forgetting is introduced into user score to improve the accuracy of recommendation; finally, the similarity calculation is improved when calculating the nearest neighbor set. Based on the Pearson similarity calculation, the effective weight factor is introduced to obtain a more accurate and reliable nearest neighbor set. The algorithm establishes an offline user model, which makes the algorithm have better recommendation efficiency. Two groups of experiments were designed based on the mean absolute error (MAE). One group of experiments tested the parameters in the algorithm, and the other group of experiments compared the proposed algorithm with other algorithms. The experimental results show that the proposed method has better performance in recommendation accuracy and recommendation efficiency.

The concept of energy of a graph was first introduced by I. Gutman [5] in 1978. The energy E(G) of a simple graph G is defined to be the sum of the absolute values of the eigenvalues of G. The tree dendrimer d(n, k) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in d(n, k) is connected to $$(k-1)$$ . It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of d(2, k) and d(3, k) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of n and k is also given.

New technologies are advancing and emerging day by day to improve the safety of humans by making use of various autonomous technologies. The continuous utilization of autonomous vehicles/systems in search and rescue (SAR) operations is a challenging research area particularly for marine-based activities. A comprehensive systematic literature review (SLR) providing an overview of improvisations that have been done in the field of autonomous technologies for search and rescue operation over the last five years has been compiled in this paper. A methodology for using autonomous vehicles in water for SAR operations has been incorporated and demonstrated. The focus of this study is to look at the various techniques and address different challenges faced for human beings’ safety during rescue operation. The comparison of results achieved for various technologies and algorithms is highlighted in this paper. This literature survey proves to be a good source of information for fellow researchers to precisely analyze the study results.

The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group B n , FC ( B n ) , is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of FC ( B n ) into a disjoint union of two-sided Barbash–Vogan combinatorial cells, a type B extension of Rubey’s descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of FC ( B n ) with S n -cosets which yields a new decomposition of FC ( B n ) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier.

In this paper, we investigate $$L^{p}$$ estimates ( $$1\leq p\leq+\infty$$ ) and $$f$$ -Holder estimates for the Cauchy–Riemann equation in a class of convex domains of finite or infinite type with piecewise smooth boundary in $$\mathbb{C}^{2}$$ .

An updated parametric hysteretic model for steel tubular members, in which the member compressive buckling is considered, is proposed in this paper. The model can be used for simulating the complex inelastic force-displacement hysteresis behaviour of steel tubular members. Based on the general aspects of hysteretic behaviour and the traditional Marshall model, the modified Marshall model is developed to improve the simulation accuracy, whose control parameters are determined by batch parameter analysis results. For the applicability in multiple hysteresis loop process, the initial member curvature under compression-tension during hysteretic loop process is studied and the computation methods under compression and tension are given individually based on the finite element analysis results and theoretical derivation. On this foundation, the model control parameter correction and axial compression capacity redefined with large initial member curvature during hysteretic loop process are executed in the updated parametric hysteretic model proposed later in this paper. Finally, in addition to the comparison with the finite element results, the rationality and applicability of the proposed model are also verified by several experiments and the good agreement in loop curve trend and hysteretic energy consumption are found between the simulated and experimental results.

This paper investigates the stability analysis and stabilization of T‐S fuzzy systems with time‐varying delays. First, a new augmented Lyapunov–Krasovskii functional is constructed, delay‐dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership‐function‐dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time‐varying delays are presented under the imperfect premise‐matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.

In this paper, a stochastic eco-epidemiological system with patchy structure and transport-related infection is proposed and the stochastic dynamical behaviors are investigated. Firstly, by constructing suitable Lyapunov functions, it is revealed that there is a unique globally positive solution starting from the positive initial value. Secondly, it is proved that the presented system is stochastically ultimately bounded and the average in time of the second moment of solution is bounded. Thirdly, we prove that the large enough stochastic perturbations may lead the predator population and the diseases in the predator to be extinct while it is persistent in the deterministic system. Finally, some numerical simulations are given to test our theoretical results.

This paper studies the m-Steiner Traveling Salesman Problem with online edge blockages. Under the assumption that there might be some blockages on the roads which are non-recoverable in a short time, the goal of the Min-Max online m-Steiner Traveling Salesman problem (MinMax- m STSP online ) is to find m closed tours that visit each customer at least once such that the maximum cost of the m salesmen is as small as possible. We give an online algorithm and show that its competitive ratio is at most k − 1 m + 10 for m ≥ 2 and k + 2 for m = 1 , where k is the number of blockages. This ratio is asymptotically tight since a lower bound ⌈ k m ⌉ + 1 for this problem has been obtained in [16] .

Recently, Yu et al. presented an algorithm for a canonic DBC of a positive integer n by solving certain subproblems recursively and it requires O ( ( log n ) 2 log log n ) bit operations and O ( ( log n ) 2 ) bits of memory. This is currently the most efficient recoding type algorithm for canonic DBCs when balanced computing power and memory are available. In this paper, we present a memory efficient algorithm to compute a nearly DBC from the idea of Yu et al. We present a simple overview of Yu et al.’s algorithm focusing on canonic DBC and refine Yu et al.’s proof for range of the leading term of canonic DBCs. By using the refined range, we suggest how to improve the efficiency of Yu et al.’s algorithm computationally and present an algorithm for nearly canonic DBC with memory requirement O ( log n ) . We also present experimental comparison on the Hamming weights of Yu et al.’s algorithm, tree based algorithm, the classic greedy DBC algorithm, and our memory efficient algorithm.

The associated Legendre functions constituting the kernel function of spherical harmonics have a wide range of applications in geodesic and geophysical fields, such as calculating the Green’s functions for a spherical Earth model. The analytical expressions for the infinite series involving the associated Legendre functions are useful. In this paper, starting with the generating function, we present a set of analytical equations for an infinite series involving associated low-order $$\left( {m = 0,~1,~2} \right)$$ Legendre functions. After careful verification, the accuracy and effectiveness of the nearly sixty listed equations are confirmed. The open-source code written using the Wolfram language, GNU octave/MATLAB, and Fortran-90 are available through GitHub ( https://github.com/UCAStanghe2014/analytical_sums_associated_Legendre ).

In this paper we initiate an investigation into the class of meet semilattices endowed with an endomorphism. A consideration of the subdirectly irreducible algebras leads to a description of a subclass of those algebras (S;∧,k)(S;∧,k) in which (S;∧)(S;∧) is a meet semilattice and kk is an endomorphism on SS characterised by the property k⩾idSk⩾idS. We particularly show that such an algebra is subdirectly irreducible if and only if it is a chain with one of the following forms ⋯

This paper investigates the fuzzy normalization and stabilization issues of a class of singular fractional order nonlinear systems with order 0 < α < 1 based on a singular Takagi-Sugeno fuzzy model. First, we present the admissibility theorem of Takagi-Sugeno fuzzy singular fractional order systems. Next, benefited by that the fuzzy model and the state feedback controllers do not share the same membership functions, a proportional plus derivative state feedback controller is designed, which guarantees the closed-loop system normalized and admissible. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed method.

This paper is concerned with the event-triggered positive l 1 -gain non-fragile filter design of positive Markov jump systems. By using the upper and lower bounds of the error vector of system measurement outputs, the positive l 1 -gain filtering system to be designed is transformed into interval uncertain systems. Combining linear Lyapunov functions and linear programming, the positivity and stability of such systems can be obtained. Then, the proposed approach is developed to investigate positive l 1 -gain additive and multiplicative non-fragile filters, respectively. Furthermore, two classes of non-fragile positive filters are proposed for positive Markov jump systems with incomplete measurements and sensors saturation, respectively. Finally, two examples are provided to verify the effectiveness of the proposed design.

In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators $T_b^m$. Our results are new even for the first order commutator $T_b^1$. A new bump type necessary condition for the two-weighted boundedness of $T_b^m$ is obtained as well. We also provide some results related to a converse to Bloom's theorem., 39 pages

In this paper, we study $$\eta$$ η -Ricci solitons on almost cosymplectic $$(k,\mu )$$ ( k , μ ) -manifolds. As an application, it is proved that if an almost cosymplectic $$(k,\mu )$$ ( k , μ ) -metric with $$k k < 0 represents a Ricci soliton, then the potential vector field of the Ricci soliton is a strict infinitesimal contact transformation, and the corresponding almost cosymplectic manifold is locally isometric to a Lie group whose local structure is determined completely by $$k k < 0 . In addition, a concrete example is constructed to illustrate the above result.

A portfolio associated with a balanced signed graph that contains both positive and negative edges is more predictable and risk-averse, and is therefore likely to require less turnover. In this paper, we use a method based on spectral graph theory to determine whether a portfolio is balanced or not. Moreover, we combine this with spectral clustering to propose a strategy to build a balanced portfolio with hedging assets. This is applied to stocks listed on the Brazil Stock Exchange.

The controllability function method, introduced by V. I. Korobov in late 1970s, is known to be an efficient tool for control systems design. It is developed for both linear/nonlinear and finite/infinite dimensional systems. This paper bridges the method with the homogeneity theory popular today. The standard homogeneity known since 18th century is a symmetry of function with respect to uniform scaling of its argument. Some generalizations of the standard homogeneity were introduced in 20th century. This paper shows that the so-called homogeneous norm is a controllability function of the linear autonomous control system and the corresponding closed-loop system is homogeneous in the generalized sense. This immediately yields many useful properties known for homogeneous systems such as robustness (Input-to-State Stability) with respect to a rather large class of perturbations, in particular, with respect to bounded additive measurement noises and bounded additive exogenous disturbances. The main theorem presented in this paper slightly refines the design of the controllability function for a multiply-input linear autonomous control systems. The design procedure consists in solving subsequently a linear algebraic equation and a system of linear matrix inequalities. The homogeneity itself and the use of the canonical homogeneous norm essentially simplify the design of a controllability function and the analysis of the closed-loop system. Theoretical results are supported with examples. The further study of homogeneity-based design of controllability functions seems to be a promising direction for future research.

In this paper, the analysis of noise and sensitivity for different BP filter designs is observed. Calculation of the voltage noise spectral density, root mean square (RMS) value of the noise voltage, Schoeffler sensitivity and the multi-parameter sensitivity is done for the simply designed (SD) active RC, noise and sensitivity optimized (NO and SO) active RC, operational transconductance amplifiers (OTA-C) and switched capacitor (SC) filter designs. This is observed for the fourth-order Chebyshev band-pass filter, with central frequency fc = 4 kHz, bandwidth 1 kHz and pass-band ripple αmax = −0.1 dB. Cascade of two second-order sections is used for fulfilment realization of all four observing designs. Programming tools, such as MATLAB and SPICE (LTspice), are also used for the analyses. Highlights • We used three different designs and optimization (noise and sensitivity) procedure for design and optimize the fourth-order Chebyshev band-pass filter • Our results suggest which design is best to use for improving noise and sensitivity of this filter • MATLAB and SPICE software were used for calculations and simulations of different band-pass filter designs and analysis of noise and sensitivity

In this paper we formulate a general problem of extreme functional interpolation of real-valued functions of one variable (for finite differences, this is the Yanenko–Stechkin–Subbotin problem) in terms of divided differences. The least value of the -th derivative in , , needs to be calculated over the class of functions interpolating any given infinite sequence of real numbers on an arbitrary grid of nodes, infinite in both directions, on the number axis for the class of interpolated sequences for which the sequence of -th order divided differences belongs to . In the present paper this problem is solved in the case when . The indicated value is estimated from above and below using the greatest and the least step of the grid of nodes.

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

Estimating demand for large assortments of differentiated goods requires the specification of a demand system that is sufficiently flexible. However, flexible models are highly parameterized so estimation requires appropriate forms of regularization to avoid overfitting. In this paper, we study the specification of Bayesian shrinkage priors for pairwise product substitution parameters. We use a log-linear demand system as a leading example. Log-linear models are parameterized by own and cross-price elasticities, and the total number of elasticities grows quadratically in the number of goods. Traditional regularized estimators shrink regression coefficients towards zero which can be at odds with many economic properties of price effects. We propose a hierarchical extension of the class of global-local priors commonly used in regression modeling to allow the direction and rate of shrinkage to depend on a product classification tree. We use both simulated data and retail scanner data to show that, in the absence of a strong signal in the data, estimates of price elasticities and demand predictions can be improved by imposing shrinkage to higher-level group elasticities rather than zero.