An constructive proof for the Umemura polynomials for the third Painlev\'e equation

We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii--Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.Comment: 20 pages, 3 figure

The Possible J^{PC}=0^{--} Exotic State

In order to explore the possible existence of the exotic $0^{--}$ state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the $0^{+-}$ tetraquark operators without derivatives do not exist. The special Lorentz structure of the $0^{--}$ currents forbids the four-quark correction to the spectral density. Now the gluon condensate is the dominant power correction. Within the framework of the finite energy sum rule, none of the seven interpolating currents supports a resonant signal. Therefore we conclude that the exotic $0^{--}$ state does not exist below 2 GeV, which is consistent with the current experimental observations.Comment: 12 pages, 27 figure

Tracing and Predicting Collaboration for Junior Scholars

Academic publication is a key indicator for measuring scholars' scientific productivity and has a crucial impact on their future career. Previous work has identified the positive association between the number of collaborators and academic productivity, which motivates the problem of tracing and predicting potential collaborators for junior scholars. Nevertheless, the insufficient publication record makes current approaches less effective for junior scholars. In this paper, we present an exploratory study of predicting junior scholars' future co-authorship in three different network density. By combining features based on affiliation, geographic and content information, the proposed model significantly outperforms the baseline methods by 12% in terms of sensitivity. Furthermore, the experiment result shows the association between network density and feature selection strategy. Our study sheds light on the re-evaluation of existing approaches to connect scholars in the emerging worldwide Web of Scholars

N′-(3-Hy­droxy­benzyl­idene)-4-nitro­benzohydrazide

The title mol­ecule, C14H11N3O4, is approximately planar, with an inter­planar angle between the two benzene rings of 5.8 (2)°. In the crystal, four mol­ecules are linked by an R 4 4(12) motif with pairs of strong O—H⋯O and N—H⋯O hydrogen bonds. The motif is situated about the crystallographic centres of symmetry and it is composed of two pairs of parallel mol­ecules. This quadruplet of mol­ecules is further extended by symmetry-equivalent hydrogen bonds to form layers parallel to the (10) plane. In addition to the hydrogen bonds, there is also a weak π–π inter­action between the benzene rings

Motion State of Fuel within Shell in Projection Acceleration Process

The fuel-air explosive (FAE) warheads are charged with the liquid-solid mixture fuel. The fuel is different 'om conventional solid explosives in physical and mechanical properties. The mass centre of the charged fuel changes during projecting the projectile. In this study, a method to calculate the mass centre change of the charged fuel is suggested and the  influence of this change on the projectile motion state in the projection process is discussed. The results show that in projection, the fuel mass centre varies with the projection acceleration and the deformation characteristics of the mixture fuel. The higher is the acceleration, the larger is the displacement of the mass centre. This displacement also increases with the compressibility of the fuel. It constitutes an influence on the state of motion for the whole projectile in the projection process, whose calculation approach is also proposed. The result provides a theoretical basis for the design of the FAE weapons

N′-(4-Hy­droxy­benzyl­idene)-4-nitro­benzohydrazide

The title compound, C14H11N3O4, was prepared by the reaction of 4-nitro­benzohydrazide with 4-hy­droxy­benz­alde­hyde. The whole mol­ecule of the compound is approximately planar, with a mean deviation from the least-squares plane through all the non-H atoms of 0.050 (2) Å; the dihedral angle between the two benzene rings is 2.0 (2)°. In the crystal, the benzohydrazide mol­ecules are linked through inter­molecular O—H⋯O and N—H⋯O hydrogen bonds, forming layers in the bc plane

An algebraic proof for the Umemura polynomials for the third Painlevé equation

We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials

A new modified Newton iteration for computing nonnegative Z-eigenpairs of nonnegative tensors

We propose a new modification of Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. The method has local quadratic convergence to a nonnegative eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration

Control Design for Signal Transduction Networks

Signal transduction networks of biological systems are highly complex. How to mathematically describe a signal transduction network by systematic approaches to further develop an appropriate and effective control strategy is attractive to control engineers. In this paper, the synergism and saturation system (S-systems) representations are used to describe signal transduction networks and a control design idea is presented. For constructing mathematical models, a cascaded analysis model is first proposed. Dynamic analysis and controller design are simulated and verified