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A classical result of K. L. Chung and W. Feller deals with the partial sums S k S_k arising in a fair coin-tossing game. If N n N_n is the number of “positive” terms among S 1 S_1 , S 2 S_2 , …, S n S_n then the quantity P ( N 2 n = 2 r ) P(N_{2n} = 2r) takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for P ( N 2 n + 1 = r ) P(N_{2n+1} = r) , r = 0 r = 0 , 1 1 , 2 2 , …, 2 n + 1 2n+1 . We get to this ansatz by adaptating the Feynman–Kac methodology.

In this paper, we first generalize to any hyper-Kahler manifold X with $$b_3(X)\not =0$$ results proved by O’Grady for hyper-Kahler manifolds of generalized Kummer type. In the second part, we restrict to hyper-Kahler manifolds of generalized Kummer type and prove, using results of Markman, that their Kuga–Satake correspondence is algebraic.

“Real Normed Algebras Revisited,” the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their...

Rewinding machines are used in the paper converting industrial sector to unroll paper veils from large source reels and wind them around smaller rolls, for the production of paper logs to be used in household activities. Many different types of rewinding machine exist, and they are mostly based on stapling devices which automatically unroll a large coil of paper, roll it up around a new log, stop the veil allowing it to be torn off, unload the completed paper log, and reload a new paper core to be rolled up. Winding units generally include a primary and a secondary roller, supplying the desired rotational speed for winding, and a pressure unit consisting of a pressure roller in contact with the paper log being rolled up, which assures adequate containment and avoids the paper log to escape. All known systems have some mechanical limitations, mainly due to the contact of the pressure roller with the paper log, causing instabilities and vibrations, particularly when working with soft paper veils. This limits the maximum possible winding speed. The aim of this paper is it to present a detailed kinematic analysis of a novel pressure unit which overcomes the aforementioned limitation.

Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of $$p$$ -proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory.

The main result of this paper states that if $${\mathcal {F}}$$ is a subgroup-closed saturated formation of full characteristic, then the $${\mathcal {F}}$$ -residual of a K- $${\mathcal {F}}$$ -subnormal subgroup S of a finite group G is a large subgroup of G provided that the $${\mathcal {F}}$$ -hypercentre of every subgroup X of G containing S is contained in the $${\mathcal {F}}$$ -residual of X. This extends a recent result of Aivazidis, Safonova and Skiba.

Connectivity is the safety network for biodiversity conservation because connected habitats are more effective for saving the species and ecological functions. The nature of coupling for connectivity also plays an important role in the co-existence of species in cyclic-dominance. The rock-paper-scissors game is one of the paradigmatic mathematical model in evolutionary game theory to understand the mechanism of biodiversity in cyclic-dominance. In this paper, the metapopulation model for rock-paper-scissors with mutations is presented in which the total population is divided into patches and the patches form a network of complete graph. The migration among patches is allowed through simple random walk. The replicator-mutator equations are used with the migration term. When migration is allowed then the population of the patches will synchronized and attain stable state through Hopf bifurcation. Apart form this, two phases are observed when the strategies of one of the species mutate to other two species: co-existence of all the species phase and existence of one kind of species phase. The transition from one phase to another phase is taking place due to transcritical bifurcation. The dynamics of the population of species of rock, paper, scissors is studied in the environment of homogeneous and heterogeneous mutation. Numerical simulations have been performed when mutation is allowed in all the patches (homogeneous mutation) and some of the patches (heterogeneous mutation). It has been observed that when the number of patches is increased in the case of heterogeneous mutation then the population of any of the species will not extinct and all the species will co-exist.

In this short note, we show that Theorem 4.3 of Liu and Yu (Monatshefte Math 195:173–176, 2021) is a consequence of Lemma 2 of Ballester-Bolinches and Esteban-Romero (J Aust Math Soc 75:181–191, 2003).

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.

In this work, the effect of wheat flour and water replacement by pequi pulp and flour on the bread development and preparation enriched with this fruit was studied. Two experimental designs were used for two independent variables, the first evaluating the wheat flour partial replacement by pequi husk flour (x1) and pequi pulp flour (x2). The second design evaluated the wheat flour and water partial replacement by pequi husk flour (x1) and pequi pulp (x2), respectively. At the same time, a control test was conducted (without the addition of pequi flour and pulp) for comparison. The evaluated dependent variables of the bread quality characteristics were: dough volume; expansion rate; specific volume and density; texture profile and gluten content. It was possible to verify that only the gluten content was influenced by the replacement of wheat flour by pequi husk flour, whereas, only the specific volume was influenced by the replacement of water by pequi pulp. In general, the best replacement range was obtained with the formulation using between 0.75 to 2.5% pequi husk flour; up to 20% pequi pulp flour and between 5 and 35% of pequi pulp. In this work, the effect of wheat flour and water replacement by pequi pulp and flour on the bread development and preparation enriched with this fruit was studied. Two experimental designs were used for two independent variables, the first evaluating the wheat flour partial replacement by pequi husk flour (x1) and pequi pulp flour (x2). The second design evaluated the wheat flour and water partial replacement by pequi husk flour (x1) and pequi pulp (x2), respectively. At the same time, a control test was conducted (without the addition of pequi flour and pulp) for comparison. The evaluated dependent variables of the bread quality characteristics were: dough volume; expansion rate; specific volume and density; texture profile and gluten content. It was possible to verify that only the gluten content was influenced by the replacement of wheat flour by pequi husk flour, whereas, only the specific volume was influenced by the replacement of water by pequi pulp. In general, the best replacement range was obtained with the formulation using between 0.75 to 2.5% pequi husk flour; up to 20% pequi pulp flour and between 5 and 35% of pequi pulp.

Resident combustion of solid fuel has been widely acknowledged as a high potential for pollutant reduction. However, there is a marked asymmetry between more pollutant emission and less burned volatiles of biomass and coal in the combustion process. To study the solid fuel optimum combustion form in a household stove, both the pollution reduction and energy efficient utilization of crop straws and coals were investigated. Taking the molding pressure and clay addition ratio as variable process conditions, the research of bio-coal briquette (made from the mixture of anthracite and biomass) was implemented in the range of 15~35 MP and 5~15%, respectively. Biomass and coal work complementarily for each other’s combustion property development. In particular, the pyrolysis gas produced by biomass low-temperature devolatilization is featured with low ignition point and is distributed in the bio-coal briquette. Its own combustion provides energy for anthracite particle combustion. Consequently, a positive effect was identified when bio-coal briquettes were used as residential fuel, and further improvement manifested in reducing more than 90% of particle matter (PM) and achieving about twice the thermal efficiencies (TEs) compared with the mass-weighted average values of coal briquettes and biomass briquettes. 88.8 ± 11.8%, 136.7 ± 13.7% and 81.4 ± 17.7% more TEs were provided by wheat straw–coal briquettes, rice straw–coal briquettes and maize straw–coal briquettes. 93.3 ± 3.1% (wheat straw–coal), 97.6 ± 0.2% (rice straw–coal) and 90.4 ± 2.2% (maize straw–coal) in terms of PM2.5 emission factors (EFs) was reduced. For bio-coal briquette, a 25 MPa and 10% addition were determined as the optimum molding pressure and clay addition ratio. Bio-coal briquettes with higher TEs and lower PM EFs will bring about substantial benefits for air quality promotion, human health and energy saving.

This paper is devoted to the study of the qualitative properties of solutions to boundary-value problems for strongly elliptic differential-difference equations. Some results for these equations such as existence and smoothness of generalized solutions in certain subdomains of Q were obtained earlier. Nevertheless, the smoothness of generalized solutions of such problems can be violated near the boundary of these subdomains even for infinitely differentiable right-hand side. The subdomains are defined as connected components of the set that is obtained from the domain Q by throwing out all possible shifts of the boundary Q by vectors of a certain group generated by shifts occurring in the difference operators. For the one dimensional Neumann problem for differential-difference equations there were obtained conditions on the coefficients of difference operators, under which for any continuous right-hand side there is a classical solution of the problem that coincides with the generalized solution. 2 Also there was obtained the smoothness (in Sobolev spaces W k ) of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in subdomains excluding -neighborhoods of certain points. However, the smoothness (in Ho lder spaces) of generalized solutions of the second boundary-value problem for strongly elliptic differential-difference equations on the boundary of adjacent subdomains was not considered. In this paper, we study this question in Ho lder spaces. We establish necessary and sufficient conditions for the coefficients of difference operators that guarantee smoothness of the generalized solution on the boundary of adjacent subdomains for any right-hand side from the Ho lder space.

The converse of the Borel–Cantelli Lemma states that if { A i } i = 1 ∞ is a sequence of independent events such that ∑ P ( A i ) = ∞ , then almost surely infinitely many of these events will occur. Erdős and Renyi proved that it is sufficient to weaken the condition of independence to pairwise independence. Later, several other weakenings of the condition appeared in the literature. The aim of this paper is to provide a collection of conditions, all of which imply that almost surely infinitely many of the events occur, and determine the complete implicational relationship between them. Many of these results are known, or follow from known results, however, they are not widely known among non-specialists. Yet, the results can be extremely useful for areas outside of probability theory, as evidenced by the original motivation of this paper emerging from infinite combinatorics. Our proofs are aimed to be accessible to a general mathematical audience.

Part of the work was done while the authors were visiting the South China University of Science and Technology (SUSTech), Shenzhen, in 2018, and we are grateful (in particular to Professor Cai Heng Li) for the hospitality that we received.The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no.EP/R014604/1), where further work on this paper was undertaken. In particular we acknowledge a Simons Fellowship (Cameron) and a Kirk Distinguished Visiting Fellowship (Praeger) during this programme. Schneider thanks the Centre for the Mathematics of Symmetry and Computation of The University of Western Australia and Australian Research Council Discovery Grant DP160102323 for hosting his visit in 2017 and acknowledges the support of the CNPq projects Produtividade em Pesquisa (project no.: 308212/2019-3) and Universal (project no.:421624/2018-3). Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial structures such as affine spaces or Cartesian decompositions, but such structures for diagonal groups have not been studied in general. The main purpose of this paper is to describe and characterise such structures, which we call diagonal semilattices. Unlike the diagonal groups in the O'Nan-Scott theorem, which are defined over finite characteristically simple groups, our construction works over arbitrary groups, finite or infinite. A diagonal semilattice depends on a dimension m and a group T. For m=2, it is a Latin square, the Cayley table of T, though in fact any Latin square satisfies our combinatorial axioms. However, for m≥3, the group T emerges naturally and uniquely from the axioms. (The situation somewhat resembles projective geometry, where projective planes exist in great profusion but higher-dimensional structures are coordinatised by an algebraic object, a division ring.) A diagonal semilattice is contained in the partition lattice on a set Ω, and we provide an introduction to the calculus of partitions. Many of the concepts and constructions come from experimental design in statistics. We also determine when a diagonal group can be primitive, or quasiprimitive (these conditions turn out to be equivalent for diagonal groups). Associated with the diagonal semilattice is a graph, the diagonal graph, which has the same automorphism group as the diagonal semilattice except in four small cases with m

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras $\mathbf A$ there is a polynomial time algorithm that decides if an equation over $\mathbf A$ has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. The characterization results provided by the paper is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time., 50 pages

The intersection of two quadrics is called a biquadric. If we mark a non-singular quadric in the pencil of quadrics through a given biquadric, then the given biquadric is called a marked biquadric. In the classical papers of Plücker and Klein, a Kummer surface was canonically associated with every three-dimensional marked biquadric (that is, with a quadratic line complex provided that the Plücker–Klein quadric is marked). In Reid’s thesis, this correspondence was generalized to odd-dimensional marked biquadrics of arbitrary dimension . In this case, a Kummer variety of dimension corresponds to every biquadric of dimension . Reid only constructed the generalized Plücker–Klein correspondence. This map was not studied later. The present paper is devoted to a partial solution of the problem of creating the corresponding theory.

In the paper (Hill, 1973) from 1973 R.D. Hill studied linear matrix maps L : ℂ q × q → ℂ n × n which map Hermitian matrices to Hermitian matrices, or equivalently, preserve adjoints, i.e., L ( V ∗ ) = L ( V ) ∗ , via representations of the form L ( V ) = ∑ k , l = 1 m H k l A l V A k ∗ , V ∈ ℂ q × q , for matrices A 1 , … , A m ∈ ℂ n × q and continued his study of such representations in later work, sometimes with co-authors, to completely positive matrix maps and associated matrix reorderings. In this paper we expand the study of such representations, referred to as Hill representations here, in various directions. In particular, we describe which matrices A 1 , … , A m can appear in Hill representations (provided the number m is minimal) and determine the associated Hill matrix H = H k l explicitly. Also, we describe how different Hill representations of L (again with m minimal) are related and investigate further the implication of ∗ -linearity on the linear map L .

In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calder\'{o}n-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Fr\'echet--Kolmogorov criterion of compactness, whereas we avoid this by relying on "softer" tools, which might have an independent interest in view of further extensions of the method., Comment: v3: final version, incorporated referee comments, to appear in Indagationes Mathematicae, 27 pages

In this paper, we consider the propagation of waves in an open waveguide in ℝ$^{2}$ where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x$_{1}$ axis) and equal to one for |x$_{2}$| > h$_{0}$ for some h$_{0}$ > 0. Motivated by the limiting absorption principle (proven in an earlier paper by the author), we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part, we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.

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.

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.

The designed load of most quasi-zero stiffness (QZS) isolators is constant. The isolation performance will drop sharply once the load changes. A novel QZS isolator that can adapt to variable loads is proposed in this paper to improve the range of application of the isolator. The isolator is designed by paralleling the electromagnetic spring (ES), which provides negative stiffness, and the pneumatic spring (PS), which provides positive stiffness. The positive and negative stiffness can be adjusted by changing the pressure and coil current, which provides the possibility for the isolator to adapt to variable loads. This paper derived the conditions for the isolation system to obtain QZS characteristics, proposed the dynamic model of the isolation system, derived and verified the analytical expressions of the amplitude-frequency response and force transmissibility (FT), and discussed the change of FT and displacement transmissibility(DT) under different loads. Theoretical analysis shows that changing the pressure and coil current in the same proportion can maintain the superior low-frequency isolation performance when the load changes, thanks to the preservation of the QZS characteristics of the system after adjusting the pressure and coil current. Finally, the simulation results fg and isolation frequency band over the linear isolation system and PS isolation system. Furthermore, the proposed isolator can be adjusted online.

With the development of computer operation technology and algorithms, the lumped dynamic model is more practical, and the development and application are more comprehensive. Among them, the direct coal liquefaction residual oil pyrolysis and coking technology, as a coal-to-liquid process, can increase the oil yield of the coal liquefaction process and reduce environmental pollution. The purpose of this paper is to study the experiment and algorithm of coal direct liquefaction residual oil pyrolysis and coking technology based on lumped kinetic engineering. Starting from the lumped kinetic engineering, this paper takes the direct coal liquefaction residual oil pyrolysis and coking technology as the research object. Based on the experiment of small- and medium-sized equipment, the residual oil pyrolysis and coking experiment is carried out. This paper further analyzes the components of the experimental products and explores the factors that affect the yield of residual pyrolysis oil based on the five lumped kinetic model of coking. Experimental data shows that when the pyrolysis temperature is 450°C, the content of liquefied heavy oil HS in the pyrolysis oil is 47.87%, the content of asphaltene A is 44.28%, and the content of preasphaltene PA is 7.85%; the pyrolysis temperature is 500 °C. At this time, the content of liquefied heavy oil HS in the pyrolysis oil is 54.97%, the content of asphaltene A is 40.23%, and the content of preasphaltene PA is 4.8%. It can be seen that, with the increase of pyrolysis temperature, the content of liquefied heavy oil HS increases, and the content of asphaltene A and preasphaltene PA decreases.

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Game theory has become an important tool to study the competition between oligopolistic enterprises. After combing the existing literature, it is found that there is no research combining two-stage game and nonlinear dynamics to analyze the competition between enterprises for advertising. Therefore, this paper establishes a two-stage game model to discuss the effect of the degree of firms’ advertising input on their profits. And the complexity of the system is analyzed using nonlinear dynamics. This paper analyzes and studies the dynamic game for two types of application network models: data transmission model and transportation network model. Under the time-gap ALOHA protocol, the noncooperative behavior of the insiders in the dynamic data transmission stochastic game is examined as well as the cooperative behavior. In this paper, the existence of Nash equilibrium and its solution algorithm are proved in the noncooperative case, and the “subgame consistency” of the cooperative solution (Shapley value) is discussed in the cooperative case, and the cooperative solution satisfying the subgame consistency is obtained by constructing the “allocation compensation procedure.” The cooperative solution is obtained by constructing the “allocation compensation procedure” to satisfy the subgame consistency. In this paper, we propose to classify the packets transmitted by the source nodes, and by changing the strategy of the source nodes at the states with different kinds of packets, we find that the equilibrium payment of the insider increases in the noncooperative game with the addition of the “wait” strategy. In the transportation dynamic network model, the problem of passenger flow distribution and the selection of service parameters of transportation companies are also studied, and a two-stage game theoretical model is proposed to solve the equilibrium price and optimal parameters under Wardrop’s criterion.

In economic growth, the gradual increase in the effect of information technology makes the enterprise economic information management increasingly important for the survival and development of the enterprises. This paper designs an enterprise economic information management system for the complex internal economic information management business and process of enterprises. It provides daily office, information access, document preview, and transmission. The proposed design (i) copes with the inconsistency and irregularity of enterprise economic information data, (ii) quickly obtains valuable information from these massive high-frequency data, and (iii) improves the economic benefits of data assets and data management efficiency. The printing function systematizes the information management for departments such as enterprise economic information, personnel, and production. The main focus of this research includes the mode, framework, and function of the whole system software. Moreover, it also comprises of the use of Internet platform big data technology to realize the practicality, stability, and security of the system database algorithm, which has been practically used by enterprises to improve office efficiency and meet the needs of daily management of enterprises. Based on the analysis of the current status of enterprise big data application, this paper constructs an enterprise economic informational management system based on big data and also describes in detail the key technologies of enterprise economic informational data management from three aspects: NoSQL-based big data storage management, Hadoop-based economic informational big data informational and economic informational big data analysis, and mining algorithm. Provide theoretical basis and basic technical support for online decision analysis.

It is well known that the appearance of the delay in the fractional delay differential equation (FDDE) makes the convergence analysis very difficult. Dealing with the problem with the traditional reproducing kernel method (RKM) is very tricky. The feature of this paper is to gain a more credible approximate solution via fractional Taylor’s series (FTS). We use the FTS to deal with the delay for improving the accuracy of the approximate solutions. Compared with other methods, the five numerical examples demonstrate the accuracy and efficiency of the proposed method in this paper.

In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.

This paper discusses the study of asymptotic behavior of non-oscillatory solutions for high order differential equations of Poincaré type. We present two new and weaker hypotheses on the coefficients, which implies a well posedness result and a characterization of asymptotic behavior for the solution of the Poincaré equation. In our discussion, we use the scalar method: we define a change of variable to reduce the order of the Poincaré equation and thus demonstrate that a new variable can satisfies a nonlinear differential equation; we apply the method of variation of parameters and the Banach fixed-point theorem to obtain the well posedness and asymptotic behavior of the non-linear equation; and we establish the existence of a fundamental system of solutions and formulas for the asymptotic behavior of the Poincaré type equation by rewriting the results in terms of the original variable. Moreover we present an example to show that the results introduced in this paper can be used in class of functions where classical theorems fail to be applied.

The inconsistent or consistent general fuzzy matrix equation are studied in this paper. The aim of this paper is threefold. Firstly, general strong fuzzy matrix solutions of consistent general fuzzy matrix equation are derived, and an algorithm for obtaining general strong fuzzy solutions of general fuzzy matrix equation by Core-EP inverse is also established. Secondly, if inconsistent or consistent general fuzzy matrix equation satisfies $ X\in R(S^{k}) $, the unique solution or unique least squares solution of consistent or inconsistent general fuzzy matrix equation are given by Core-EP inverse. Thirdly, we present an algorithm for obtaining Core-EP inverse. Finally, we present some examples to illustrate the main results.

The Mackey–Zimmer theorem classifies ergodic group extensions X of a measure-preserving system Y by a compact group K, by showing that such extensions are isomorphic to a group skew-product X?Y??H for some closed subgroup H of K. An analogous theorem is also available for ergodic homogeneous extensions X of Y, namely that they are isomorphic to a homogeneous skew-product Y??H/M. These theorems have many uses in ergodic theory, for instance playing a key role in the Host–Kra structural theory of characteristic factors of measure-preserving systems.The existing proofs of the Mackey–Zimmer theorem require various “countability”, “separability”, or “metrizability” hypotheses on the group ? that acts on the system, the base space Y, and the group K used to perform the extension. In this paper we generalize the Mackey–Zimmer theorem to “uncountable” settings in which these hypotheses are omitted, at the cost of making the notion of a measure-preserving system and a group extension more abstract. However, this abstraction is partially counteracted by the use of a “canonical model” for abstract measure-preserving systems developed in a companion paper. In subsequent work we will apply this theorem to also obtain uncountable versions of the Host–Kra structural theory., AJ was supported by DFG-research fellowship JA 2512/3-1. TT was supported by a Simons Investigator grant, the James and Carol Collins Chair, the Mathematical Analysis & Application Research Fund Endowment, and by NSF grant DMS-1764034.

© 2022, University of Nis. All rights reserved.In this paper the authors gave an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms.The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given.

Partial balanced incomplete block designs have a wide range of applications in many areas. Such designs provide advantages over fully balanced incomplete block designs as they allow for designs with a low number of blocks and different associations. This paper introduces a class of partially balanced incomplete designs. We call it partially balanced network designs (PBNDs). The fundamentals and properties of PBNDs are studied. We are concerned with modeling PBNDs as graph designs. Some direct constructions of small PBNDs and generalized PBNDs are introduced. Besides that, we show that our modeling yields an effective utilization of PNBDs in constructing graph codes. Here, we are interested in constructing graph codes from bipartite graphs. We have proved that these codes have good characteristics for error detection and correction. In the end, the paper introduces a novel technique for generating new codes from already constructed codes. This technique results in increasing the ability to correct errors.

In recent years, deep learning has already been applied to English lip-reading. However, Chinese lip-reading starts late and lacks relevant dataset, and the recognition accuracy is not ideal. Therefore, this paper proposes a new hybrid neural network model to establish a Chinese lip-reading system. In this paper, we integrate the attention mechanism into both CNN and RNN. Specifically, we add the convolutional block attention module (CBAM) to the ResNet50 neural network, which enhances its ability to capture the small differences among the mouth patterns of similarly pronounced words in Chinese, improving the performance of feature extraction in the convolution process. We also add the time attention mechanism to the GRU neural network, which helps to extract the features among consecutive lip motion images. Considering the effects of the moments before and after on the current moment in the lip-reading process, we assign more weights to the key frames, which makes the features more representative. We further validate our model through experiments on our self-built dataset. Our experiments show that using convolutional block attention module (CBAM) in the Chinese lip-reading model can accurately recognize Chinese numbers 0–9 and some frequently used Chinese words. Compared with other lip-reading systems, our system has better performance and higher recognition accuracy.

Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. In numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing prior to numerical integration. Existing DAE solvers commonly adopt structural preprocessing methods based on combinatorial optimization. Unfortunately, the structural methods fail if the DAE has numerical or symbolic cancellations. For such DAEs, methods have been proposed to modify them to other DAEs to which the structural methods are applicable, based on the combinatorial relaxation technique. Existing modification methods, however, work only for a class of DAEs that are linear or close to linear. This paper presents two new modification methods for nonlinear DAEs: the substitution method and the augmentation method. Both methods are based on the combinatorial relaxation approach and are applicable to a large class of nonlinear DAEs. The substitution method symbolically solves equations for some derivatives based on the implicit function theorem and substitutes the solution back into the system. Instead of solving equations, the augmentation method modifies DAEs by appending new variables and equations. The augmentation method has advantages that the equation solving is not needed and the sparsity of DAEs is retained. It is shown in numerical experiments that both methods, especially the augmentation method, successfully modify high-index DAEs that the DAE solver in MATLAB cannot handle., Comment: A preliminary version of this paper is to appear in Proceedings of the 44th International Symposium on Symbolic and Algebraic Computation (ISSAC 2019), Beijing, China, July 2019

Big data has been developed for nearly a decade, and the information data on the network is exploding. Facing the complex and massive data, it is difficult for people to get the demanded information quickly, and the recommendation algorithm with its characteristics becomes one of the important methods to solve the massive data overload problem at this stage. In particular, the rise of the e-commerce industry has promoted the development of recommendation algorithms. Traditional, single recommendation algorithms often have problems such as cold start, data sparsity, and long-tail items. The hybrid recommendation algorithms at this stage can effectively avoid some of the drawbacks caused by a single algorithm. To address the current problems, this paper makes up for the shortcomings of a single collaborative model by proposing a hybrid recommendation algorithm based on deep learning IA-CN. The algorithm first uses an integrated strategy to fuse user-based and item-based collaborative filtering algorithms to generalize and classify the output results. Then deeper and more abstract nonlinear interactions between users and items are captured by improved deep learning techniques. Finally, we designed experiments to validate the algorithm. The experiments are compared with the benchmark algorithm on (Amazon item rating dataset), and the results show that the IA-CN algorithm proposed in this paper has better performance in rating prediction on the test dataset.

This paper uses big data technology to predict the employment rate of colleges and universities. In this paper, combined with the current rental price, daily life consumption, and college students’ personal interests and hobbies consumption and other indicators, the individual is simulated by big data, and the individual is associated by using the AI-driven edge fog computing service optimization algorithm to form a cluster, so as to realize the prediction from element to neural network cluster by using edge computing. In addition, this paper takes the employment data of colleges and universities in Hunan province from June 2020 to May 2021 as the research sample to test the prediction model and makes a comparative analysis with the CNN model and LSTM model. The edge fog computing model in this paper has more analytical indexes as tuples compared to the CNN model, so the results show that the prediction accuracy can reach 83.25%. In this case, there is little difference between the two models of data processing and predictive efficiency. Compared with the LSTM based classification prediction model, this model is edge computing, which greatly improves the data quality of model and data parameters, and the calculation efficiency can be increased by 45%–65%. Therefore, the use of big data technology can provide a reference for the research direction of higher education.

The interactive mechanism between college and university entrepreneurship education ecosystem and their students’ entrepreneurial performance needs to be further discussed, as college and university students are an important force in entrepreneurship. Since there is a lack of symbiotic mechanism analysis and interactive optimization research using ecological methods, this paper constructs the evaluation index system of entrepreneurship education ecosystem and entrepreneurship performance evaluation index system and uses the entropy weight method to determine the weight of various indicators in the index system more objectively. In this paper, Lotka–Volterra model in ecology is used to deeply study the mechanism between college and university entrepreneurship education ecosystem and entrepreneurship performance. Lotka–Volterra multichoice goal programming (MCGP) model is used to optimize the collaborative relationship between college and university entrepreneurship education ecosystem and entrepreneurship performance. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the research method. The results show that Lotka–Volterra multichoice goal programming (MCGP) method is effective in evaluating the synergy between college and university entrepreneurship education ecosystem and the students’ entrepreneurship performance.

The rapid development of artificial intelligence brings new development opportunities and challenges to English teaching university. This paper explores the concept of “smart education” and the path of building an ecological information-based teaching model of English college by interpreting the concepts of artificial intelligence, deep learning, ecological linguistics, and language education. Artificial intelligence, especially deep learning, will be promising in many aspects, such as the analysis of individual differences of language learners, customized learning content, diversified and three-dimensional teaching media, the role of teachers as smart classroom designers, and multidimensional and dynamic formative assessments. By relying on the data mining technology of deep learning to analyze learners’ characteristics, the smart classroom design, the promotion of language learners’ independent learning, and the establishment of dynamic and complete learner profiles, the language learning process is no longer a linear process but an evolving open loop, ultimately forming a harmonious development of various ecological niches in the language learning process. In this paper, we study and design a deep learning-based English informatics teaching system to develop a deep learning-based scoring prediction model. The model incorporates deep learning models based on word embedding and text convolutional networks, which can uncover the hidden interest features of academics for English. The experimental research results prove that the online e-learning service platform cannot only effectively meet the diverse and personalized English learning needs of university students, but also improve the learning efficiency of teachers and students.

The compatibility law of prescriptions is the core link of TCM theory of “theory, method, prescription and medicine,” which is of great significance for guiding clinical practice, new drug development and revealing the scientific connotation of TCM theory, and is also one of the hot spots and difficulties of TCM modernization research. How to efficiently analyze the frequency of drug use, core combination, and association rules between drugs in prescription is a basic core problem in the study of prescription compatibility law. In this paper, a systematic study was made on the compatibility rules of traditional Chinese antiviral classical prescriptions and the mechanism of traditional Chinese medicine molecules. FP-growth algorithm was used to analyze association rules of 961 classical prescriptions collected and to explore the compatibility rules of traditional Chinese antiviral classical prescriptions. In terms of compatibility law of traditional Chinese antiviral prescriptions, this paper studied the compatibility law of traditional Chinese antiviral prescriptions based on the FP-growth algorithm and made exploratory research on the compatibility law information of 961 traditional classical antiviral prescriptions. Firstly, FP tree was constructed based on the classic recipe data set. Then, frequent item set rules were established, and association rules contained in FP tree were extracted. Finally, the frequency and association rules of antiviral TCM prescriptions were analyzed according to dosage forms (decoction, pill, paste, and ingot). The results show that the FP-growth algorithm adopted in this paper has excellent algorithm performance and strong generalization and robustness in the screening and mining of large-scale prescription data sets, which can provide important processing tools and technical methods for the study of the compatibility rule of traditional Chinese medicine prescriptions.

A mathematical model of the dive phase is an important research content for improving the accuracy of terminal control in the small unmanned aerial vehicle. The acquisition of the diving model poses new challenges, such as the small installation space, ultra-low flying height of small suicide drones, short flight time, strong coupling, less observable measurement, and elastic deformation of the wings during the drone dive phase. Based on the autoregressive moving average method, a multi-input multioutput noise term topology mathematical model is proposed in this paper. Through an improved least squares identification method, the diving model in the flight test is analyzed and verified. The identification results of the diving model obtained by the proposed method are compared with the least squares method dive model. The results indicate that the mathematical model and identification method proposed in this paper can effectively obtain the parameters of the drone dive model.

This paper uses the partial least squares method to construct the investor sentiment index in Chinese stock market. The Shanghai Stock Exchange 180 Index and the Shenzhen Stock Exchange 100 Index are used as samples. From the perspectives of holistic sentiment and heterogeneous sentiment, this paper studies the impact of investor sentiment on stock price crash risk. The results show that investor sentiment can significantly affect stock price crash risk in Shanghai and Shenzhen A-share markets, especially in the Shenzhen A-share market no matter from which perspective. And investor pessimism has a greater impact on stock price crash risk in the Shenzhen A-share market from the perspective of heterogeneous sentiment. Compared with the available researches, this paper makes two contributions: (i) the comparative analysis is adopted to discuss the differences between Shanghai and Shenzhen A-share markets, abandoning the research approach that takes the two markets as a whole in existing literature, and (ii) this paper not only studies the impact of investor holistic sentiment on stock price crash risk from a macro perspective, but also adds a more micro heterogeneous sentiment and conducts a comparative analysis.

Euler path is one of the most interesting and widely discussed topics in graph theory. An Euler path (or Euler trail) is a path that visits every edge of a graph exactly once. Similarly, an Euler circuit (or Euler cycle) is an Euler trail that starts and ends on the same node of a graph. A graph having Euler path is called Euler graph. While tracing Euler graph, one may halt at arbitrary nodes while some of its edges left unvisited. In this paper, we have proposed some precautionary steps that should be considered in exploring a deadlock-free Euler path, i.e., without being halted at any node. Simulation results show that our proposed approach improves the process of exploring the Euler path in an undirected connected graph without interruption. Furthermore, our proposed algorithm is complete for all types of undirected Eulerian graphs. The paper concludes with the proofs of the correctness of proposed algorithm and its computation complexity.

In the process of global digital trade rules negotiation, game and cooperation coexist, and all parties are actively seeking cooperative relationship while negotiating game. Against this background, this paper provides a comprehensive overview of the negotiation process of global digital trade rules and analyzes the core issues of the negotiations and their implied political game. This paper firstly compares the core issues of global digital trade rules negotiations at multilateral and regional levels and quantitatively reflects the weighting relationship between core issues and keywords by means of a dynamic thematic model. In order to judge the potential partnership of each country, this paper constructs a theoretical model of partner selection for global digital trade rules negotiation from the perspective of political game and uses the data of 62 major digital trade countries for empirical testing. Compared with traditional trade agreements, the consensus reached in digital trade negotiations is less influenced by traditional economic geography factors and more influenced by the level of digital trade restrictions and political distance. When signing digital trade terms, a country tends to choose countries with similar levels of digital trade restrictions and high political similarity as partners. Financial restrictions and trade restrictions are the most important digital trade restriction factors that countries pay attention to when negotiating, and political stability is the most important political factor that countries pay attention to when negotiating. Compared with developed countries, developing countries pay more attention to market size, cultural differences, and digital infrastructure when negotiating. The formulation of global digital trade rules may follow a reconstructive path from bilateral to regional to multilateral, promoting regional digital trade rule systems at this stage and gradually expanding the scope of negotiations to the multilateral level.

The mission planning of active debris removal (ADR) of revolver mode on geosynchronous orbit (GEO) is studied in this paper. It is assumed that there are one service satellite, one space depot, and some pieces of space debris in the ADR mission. The service satellite firstly rendezvouses with the debris and then releases the thruster deorbit kits (TDKs), which are carried with the satellite, to push the debris to the graveyard orbit. Space depot will provide replenishment for the service satellite. The purpose of this mission planning is to optimize the ADR sequence of the service satellite, which represents the chronological order, in which the service satellite approaches different debris. In this paper, the mission cost will be stated firstly, and then a mathematical optimization model is proposed. ADR sequence and orbital transfer time are used as designed variables, whereas the fuel consumption in the whole mission is regarded as objective for optimizing, and a specific number of TDKs is also a new constraint. Then, two-level optimization is proposed to solve the mission planning problem, which is low-level for finding optimal transfer orbit using accelerated particle swarm optimization (APSO) algorithm and up-level for finding best mission sequence using immune genetic (IGA) algorithm. Numerical simulations are carried out to demonstrate the effectiveness of the model and the optimization method. Results show that TDK number influences the fuel consumption through impacting the replenishing frequency and TDK redundancy. To reduce fuel consumption, the TDK number should be optimized and designed with suitable replenishing frequency and minimum TDK redundancy.