Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations

AbstractIn this paper we consider the Cauchy problem of multidimensional generalized double dispersion equations utt−Δu−Δutt+Δ2u=Δf(u), where f(u)=a|u|p. By potential well method we prove the existence and nonexistence of global weak solution without establishing the local existence theory. And we derive some sharp conditions for global existence and lack of global existence solution

Measurement and Analysis of the Scientific and Technological Contribution Rate of Chongqing City Tobacco Agriculture

The tobacco agriculture has an important economic and social significance in Chongqing. By relying on technological innovation, accelerating the development of modern tobacco agriculture has become an inevitable choice. This paper selects 1996-2012 year’s Chongqing flue-cured tobacco input and output data, builds C-D functions, measures the flexibility and annual contribution of scientific and technological progress, capital, labor and land, and proposes the corresponding improvement measures and countermeasures, in order to enhance the scientific and technological efficiency and benefit of Chongqing tobacco agriculture

A Concept Knowledge Graph for User Next Intent Prediction at Alipay

This paper illustrates the technologies of user next intent prediction with a concept knowledge graph. The system has been deployed on the Web at Alipay, serving more than 100 million daily active users. To explicitly characterize user intent, we propose AlipayKG, which is an offline concept knowledge graph in the Life-Service domain modeling the historical behaviors of users, the rich content interacted by users and the relations between them. We further introduce a Transformer-based model which integrates expert rules from the knowledge graph to infer the online user's next intent. Experimental results demonstrate that the proposed system can effectively enhance the performance of the downstream tasks while retaining explainability.Comment: Accepted by WWW 2023 poste

Instability and stability properties of traveling waves for the double dispersion equation

In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms $u_{xxxx}$ and $u_{xxtt}$. We obtain an explicit condition in terms of $a$, $b$ and $p$ on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up. In the special case of the Boussinesq equation ($b=0$), our condition reduces to the one given in the literature. For the double dispersion equation, we also investigate orbital stability of traveling waves by considering the convexity of a scalar function. We provide both analytical and numerical results on the variation of the stability region of wave velocities with $a$, $b$ and $p$ and then state explicitly the conditions under which the traveling waves are orbitally stable.Comment: 16 pages, 4 figure

Analysis on the MinRank Attack using Kipnis-Shamir Method Against Rainbow

Minrank problem is investigated as a problem related to a rank attack in multivariate cryptography and decoding of a rank code in coding theory. Recently, the Kipnis-Shamir method for solving this problem has been made significant progress due to Verbel et al. As this method reduces the problem to the MQ problem that asks for a solution of a system of quadratic equations, its complexity depends on the solving degree of a quadratic system deduced from the method. A theoretical value introduced by Verbel et al. approximates the minimal solving degree of the quadratic systems in the method although their value is defined under a certain limit for a considering system. A quadratic system outside their limitation often has the larger solving degree, but its solving complexity is not necessary larger since it has a smaller number of variables and equations. Thus, in order to discuss the best complexity of the Kipnis-Shamir method, we need a theoretical value approximating the solving degree of each deduced quadratic system. A quadratic system deduced from the Kipnis-Shamir method has a multi-degree always, and its solving complexity is influenced by this property. In this paper, we introduce a theoretical value defined by such a multi-degree and show it approximates the solving degree of each quadratic system. Thus we are able to compare the systems in the method and to discuss the best complexity. As its application, in the Minrank problem from the rank attack using the Kipnis-Shamir method against Rainbow, we show a case that a quadratic system outside Verbel et al.\u27s limitation is the best. Consequently, by using our estimation, the complexities of the attack against Rainbow parameter sets Ia, IIIc and Vc are improved as $2^{160.6}, 2^{327.9}$ and $2^{437.0}$, respectively

New Complexity Estimation on the Rainbow-Band-Separation Attack

Multivariate public key cryptography is a candidate for post-quantum cryptography, and it allows generating particularly short signatures and fast verification. The Rainbow signature scheme proposed by J. Ding and D. Schmidt is such a multivariate cryptosystem and is considered secure against all known attacks. The Rainbow-Band-Separation attack recovers a secret key of Rainbow by solving certain systems of quadratic equations, and its complexity is estimated by the well-known indicator called the degree of regularity. However, the degree of regularity generally is larger than the solving degree in experiments, and an accurate estimation cannot be obtained. In this paper, we propose a new indicator for the complexity of the Rainbow-Band-Separation attack using the $F_4$ algorithm, which gives a more precise estimation compared to one using the degree of regularity. This indicator is deduced by the two-variable power series $$\frac{\prod _{i=1}^m(1-t_1^{d_{i1}}t_2^{d_{i2}})}{(1-t_1)^{n_1}(1-t_2)^{n_2}},$$ which coincides with the one-variable power series at $t_1=t_2$ deriving the degree of regularity. Moreover, we show a relation between the Rainbow-Band-Separation attack using the hybrid approach and the HighRank attack. By considering this relation and our indicator, we obtain a new complexity estimation for the Rainbow-Band-Separation attack. Consequently, we are able to understand the precise security of Rainbow against the Rainbow-Band-Separation attack using the $F_4$ algorithm

GRB 211211A-like Events and How Gravitational Waves May Tell Their Origin

GRB 211211A is a rare burst with a genuinely long duration, yet its prominent kilonova association provides compelling evidence that this peculiar burst was the result of a compact binary merger. However, the exact nature of the merging objects, whether they were neutron star pairs, neutron star-black hole systems, or neutron star-white dwarf systems, remains unsettled. This Letter delves into the rarity of this event and the possibility of using current and next-generation gravitational wave detectors to distinguish between the various types of binary systems. Our research reveals an event rate density of $\gtrsim 5.67^{+13.04}_{-4.69} \times 10^{-3}\ \rm Gpc^{-3} yr^{-1}$ for GRB 211211A-like GRBs, which is significantly smaller than that of typical long and short GRB populations. We further calculated that if the origin of GRB 211211A is a result of a neutron star-black hole merger, it would be detectable with a significant signal-to-noise ratio, given the LIGO-Virgo-KAGRA designed sensitivity. On the other hand, a neutron star-white dwarf binary would also produce a considerable signal-to-noise ratio during the inspiral phase at decihertz and is detectable by next-generation space-borne detectors DECIGO and BBO. However, to detect this type of system with millihertz space-borne detectors like LISA, Taiji, and TianQin, the event must be very close, approximately 3 Mpc in distance or smaller.Comment: 8 pages, 3 figures, 1 tabl