从特列季亚科夫看“列夫”的悲剧

特列季亚科夫是俄罗斯著名的政论家、剧作家和诗人。他最有影响的作品《怒吼吧,中国!》几乎演遍全球。他于1937年被捕后被枪决。1956年得到平反。本文的意图是透过特列季亚科夫本人的悲剧,看看他所在的左派文艺团体"列夫",以及20世纪二三十年代苏联左派文艺团体的悲剧是怎样造成的。布尔什维克党曾经利用"同路人"的力量,可是当最迫切的任务已经转变为创造一种为工农大众服务、为千百万人理解的艺术形式,"列夫"就开始跟不上形势的需要。斯大林的文艺路线与"左"的话语实质上并无共同之处,也和"左"的思想没有共同之处。它更像是一个修复古代艺术品所需要的行动方案,宁可让艺术存活在某种经过审批的形式中。

some Results on Embedding Spaces of Sobolev Type into Lorentz Spaces

Lorentz spaces L^(s,l) provide a deeper insight into integrable functions than L^s spaces do. Various results of the embedding of the following anisotropic spaces B_(p,).~ _p^and Ⅳ_p~ in- to L^(s,l) together with a counterexample are obtained.

Position detection of component aperture based on integral imaging technology

Aiming at the problem that it is difficult to locate all the aperture positions of the large size component using Houghcircle detection method,this article presents a non-contact measurement method combining the integral imaging technology withHough circle detection algorithm.Firstly,a set of integral imaging information acquisition algorithms were proposed accordingto the classical imaging theory.Secondly,the camera array experiment device was built by using two-dimensional translationstage and charge coupled device(CCD)camera.When the system is operating,element image array captured with the camera isused to achieve the positioning of the component aperture using Hough circle detection and coordinate acquisition algorithm.Based on the above theory,a verification experiment was carried out.The results show that the detection error of the componentaperture position is within0.3mm,which provides effective theoretical support for the application of integral imagingtechnology in high precision detection

The Gagliardo-Nirenberg-Sobolev Inequality for Non-lsotropic Riesz Potentials

In this study, the inequality of Gagliardo-Nirenberg-Sobolev type are established for non-isotropic Generalized Riesz Potential depending on 2-distance.

An efficient priority service model with two-level-polling scheme

This paper considers an efficient priority service model with two-level-polling scheme which the message packets conform to the discrete-time Geom/G/1 queue with multiple vacations and bulk arrival. By the embedded Markov chain theory and the probability generating function method, we set up the mathematics functions and give closed form expressions for obtaining the mean cyclic period （MCP）, the mean queue length （MQL） and the mean waiting time （MWT） characteristics, the analytical results are also verified through extensive computer simulations. The performance analysis reveals that this priority polling scheme can gives better efficiency as well as impartiality in terms of system characteristics, and it can be used for differentiating priority service to guarantee better QoS and system stability in design and improvement of MAC protocol.

Rearrangement Inequality and Chebyshev＇s Sum Inequality on Positive Tensor Products of Orlicz Sequence Space with Banach Lattice

Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.

Probabilistic model for remain passenger queues at subway station platform

The remain passenger problem at subway station platform was defined initially,and the period variation of remain passenger queues at platform was investigated through arriving and boarding analyses.Taking remain passenger queues at platform as dynamic stochastic process,a new probabilistic queuing method was developed based on probabilistic theory and discrete time Markov chain theory.This model can calculate remain passenger queues while considering different directions.Considering the stable or variable train arriving period and different platform crossing types,a series of model deformation research was carried out.The probabilistic approach allows to capture the cyclic behavior of queues,measures the uncertainty of a queue state prediction by computing the evolution of its probability in time,and gives any temporal distribution of the arrivals.Compared with the actual data,the deviation of experimental results is less than 20%,which shows the efficiency of probabilistic approach clearly.

Toeplitz operators on Fock-Sobolev spaces with positive measure symbols

We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.

Hardy-Sobolev spaces and their multipliers

In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces. In addition,the spectrum theorem is obtained for some special multiplier.

Strichartz estimates for parabolic equations with higher order differential operators

The present paper first obtains Strichartz estimates for parabolic equations with nonnegative elliptic operators of order 2m by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-LittlewoodSobolev inequality. Some conclusions can be viewed as the improvements of the previously known ones. Furthermore, an endpoint homogeneous Strichartz estimates on BMOx(Rn) and a parabolic homogeneous Strichartz estimate are proved. Meanwhile, the Strichartz estimates to the Sobolev spaces and Besov spaces are generalized. Secondly, the local well-posedness and small global well-posedness of the Cauchy problem for the semilinear parabolic equations with elliptic operators of order 2m, which has a potential V(t, x) satisfying appropriate integrable conditions, are established. Finally, the local and global existence and uniqueness of regular solutions in spatial variables for the higher order elliptic Navier-Stokes system with initial data in Lr(Rn) is proved.

Fractional Sobolev-Poincar Inequalities in Irregular Domains

This paper is devoted to the study of fractional(q, p)-Sobolev-Poincar′e inequalities in irregular domains. In particular, the author establishes(essentially) sharp fractional(q, p)-Sobolev-Poincar′e inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional(q, p)-Sobolev-Poincar′e inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P.,Sobolev-Poincar′e implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out.

A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).

An integration by parts formula on path space over manifolds carrying geometric flow

We establish an integration by parts formula on the path space with reference measure P, the law of the(reflecting) diffusion process on manifolds with possible boundary carrying geometric flow, which leads to the standard log-Sobolev inequality for the associated Dirichlet form. To this end, we first modify Hsu's multiplicative functionals to define the damp gradient operator, which links to quasi-invariant flows; and then establish the derivative formula for the associated inhomogeneous diffusion semigroup.

Carleman Estimates for the Schrdinger Equation and Applications to an Inverse Problem and an Observability Inequality

The authors prove Carleman estimates for spaces of negative orders, and use these estimates to problem of determining L^p-potentials. An L^2-1evel continuation results for the SchrSdinger equation are the Schrodinger equation in Sobolev prove the uniqueness in the inverse observability inequality and unique also obtained.

Remainder terms for several inequalities on some groups of Heisenberg-type

We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev(FS) and Hardy-Littlewood-Sobolev(HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri(BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev(Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al.(2013) and Dolbeault and Jankowiak(2014) onto some groups of Heisenberg-type. We worked for "almost"all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case.

On Regularity of Incompressible Fluid with Shear Dependent Viscosity

The authors consider a non-Newtonian fluid governed by equations with p-structure in a cubic domain.A fluid is said to be shear thinning(or pseudo-plastic) if 1 < p < 2,and shear thickening(or dilatant) if p > 2.The case p > 2 is considered in this paper.To improve the regularity results obtained by Crispo,it is shown that the secondorder derivatives of the velocity and the first-order derivative of the pressure belong to suitable spaces,by appealing to anisotropic Sobolev embeddings.

Periodic tables of diatomic and triatomic molecules

The Mendeleev periodic table of atoms is one of the most important principles in natural science. However, there is shortage of analog for molecules. Here we propose two periodic tables, one for diatomic molecules and one for triatomic molecules. The form of the molecular periodic tables is analogous to that of Mendeleev periodic table of atoms. In the table, molecules are classified and arranged by their group number G, which is the number of valence electrons, and the periodic number P, which represents the size of the molecules. The basic molecular properties, including bond length, binding energy, force constant, ionization potential, spin multiplicity, chemical reactivity, and bond angle, change periodically within the tables. The periodicities of diatomic and triatomic molecules are thus revealed. We also demonstrate that the periodicity originates from the shell-like electronic configurations of the molecules. The periodic tables not only contain free molecules, but also the "virtual" molecules present in polyatomic molecules. The periodic tables can be used to classify molecules, to predict unknown molecular properties, to understand the role of virtual molecules in polyatomic molecules, and to initiate new research fields, such as the periodicities of aromatic species, clusters, or nanoparticles. The tables should be of interest not only to scientists in a variety of disciplines, but also to undergraduates studying natural sciences.

Implicit Sampling,with Application to Data Assimilation

There are many computational tasks, in which it is necessary to sample a given probability density function （or pdf for short）, i.e., to use a computer to construct a sequence of independent random vectors x~ （i ---- 1, 2, ~ ~ ~ ）, whose histogram converges to the given pdf. This can be difficult because the sample space can be huge, and more importantly, because the portion of the space, where the density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markov- chain Monte Carlo, the most widely used sampling scheme, can be thought of as a search algorithm, where one starts at an arbitrary point and one advances step-by-step towards the high probability region of the space. This can be expensive, in particular because one is typically interested in independent samples, while the chain has a memory. The authors present an alternative, in which samples are found by solving an algebraic equation with a random right-hand side rather than by following a chain; each sample is independent of the previous samples. The construction in the context of numerical integration is explained, and then it is applied to data assimilation.

Stochastic Systems Arising from Markov Modulated Empirical Measures

This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.

Continuous-Time Independent Edge-Markovian Random Graph Process

In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence of the number of isolated nodes and the probability of having no isolated nodes when the initial distribution of the random graph process is stationary distribution, derive the lower limit of the probability in which two arbitrary nodes are connected and the random graph is also connected, and prove that the random graph is almost everywhere connected when the number of nodes is sufficiently large.