Random walks on a lattice

This paper discusses the mean-square displacement for a random walk on a two-dimensional lattice, whose transitions to nearest-neighbor sites are symmetric in the horizontal and vertical directions and depend on the column currently occupied. Under a uniform density condition for the step probabilities it is shown that the horizontal mean-square displacement aftern steps is asymptotically proportional ton, and independent of the particular column configuration. The model generalizes that of Seshadri, Lindenberg, and Shuler and the arguments are essentially probabilistic.     

Open quasi-free systems

We compute the time evolution of an infinitely extended, open, quasi-free system in the weak coupling limit followed by the thermodynamic limit, and we derive the Onsager relations and the properties of entropy production.On leave of absence from Istituto di Fisica dell'Università, Milan, Italy     

Correlation of acoustic and thermal anomalies in ferroelectric crystals

The Pippard-Janovec relations are derived for correlating the anomalous elastic coefficient and the anomalous specific heat near the phase transitions of ferroelectric crystals. These relations are verified in the case of ferroelectric triglycine selenate crystal.     

A note on the moments of order statistics from doubly truncated exponential distribution

Summary In a recent paper [2], the author has obtained some recurrence relations between the moments of order statitics from the exponential and right truncated exponential distributions. In this paper, similar relations are derived for a doubly truncated exponential distribution. It is shown that one can obtain all the moments by using these recurrence relations.     

Impurity effects on the critical behaviour of the electrical resistance of binary liquid mixtures

The electrical resistance of the binary liquid system cyclohexane + acetic anhydride is measured, in the critical region, both in the pure mixture and when the mixture is doped with small amounts (≈ 100 ppm) of H₂O/D₂O impurities.T _c was approached to aboutt=3×10⁻⁶ wheret=(T −T _c )/T _c . The critical exponentb ≈ 0.35 in the fit of the resistance data to the equationdR/dT ∼t ^−b does not seem to be affected appreciably by the impurities. There is a sign reversal ofdR/dt in the non-critical region. Binary liquid systems seem to violate the universality of the critical resistivity.     

中日关系、国民好感度及对旅游互动的影响

依据2005—2016年中日关系定量测定、国民好感度问卷调查、中日两国旅游互动数据,分析了中日关系、国民好感度及对旅游互动的影响。结果发现：在2005—2006年以及2010年“钓鱼岛事件”后中日关系恶化,导致两国国民对对方国家的好感度下降,给双边旅游互动造成不同程度的负面影响。日本国民好感度与中国大陆国民好感度均为完全中介效应,其值分别为0.040和0.143,即中日关系对双边旅游互动的影响通过国民好感度起作用。     

On Codes Identifying Sets of Vertices in Hamming Spaces

A code is called (t, 2)-identifying if for all the words x, y(x y) and the sets (B _t (x) B _t (y)) C and are nonempty and different. Constructions of such codes and a lower bound on the cardinality of these codes are given. The lower bound is shown to be sharp in some cases. We also discuss a more general notion of -identifying codes and introduce weakly identifying codes.     

Modeling of Structures in the Mechanics of Composites

One possible general statement of a quasi-static problem in the mechanics of composites is considered. It is assumed that a composite is characterized not only by the heterogeneity of a regular structure, but also by the presence of imperfections, impurities, cracks, and the roughness of surfaces, which are partly taken into account by introducing appropriate couple stresses. Two statements, in displacements and in stresses, are considered together with the statement of the same problems in the case where the constitutive relations are linear integral operators. The boundary-value problem remains nonlinear due to the nonlinearity of a scattering function which enters into the heat equation. The theory of effective moduli for a nonpolar medium is discussed in more detail. The equilibrium equations for a homogeneous medium with reduced characteristics and the equation of heat inflow, introduced in nonlinear (in an explicit form) and linear variants, are examined. For a simple laminated composite, all effective mechanical and thermophysical characteristics are found in an explicit form. The effective material functions for a transversely isotropic medium are constructed on the basis of a unique dimensionless relaxation kernel with the use of several Il'ushin kernels. Based on the known solution of the boundary-value problem for the reduced medium, the stress and strain concentration tensors, at any point of a simple laminated composite, are also constructed in an explicit form. In this case, the changes in the structure are taken into account.     

Simplicial Properties of the Set of Planar Binary Trees

Planar binary trees appear as the the main ingredient of a new homology theory related to dialgebras, cf.(J.-L. Loday, C.R. Acad. Sci. Paris 321 (1995), 141–146.) Here I investigate the simplicial properties of the set of these trees, which are independent of the dialgebra context though they are reflected in the dialgebra homology.The set of planar binary trees is endowed with a natural (almost) simplicial structure which gives rise to a chain complex. The main new idea consists in decomposing the set of trees into classes, by exploiting the orientation of their leaves. (This trick has subsequently found an application in quantum electrodynamics, c.f. (C. Brouder, On the Trees of Quantum Fields, Eur. Phys. J. C12, 535–549 (2000).) This decomposition yields a chain bicomplex whose total chain complex is that of binary trees. The main theorem of the paper concerns a further decomposition of this bicomplex. Each vertical complex is the direct sum of subcomplexes which are in bijection with the planar binary trees. This decomposition is used in the computation of dialgebra homology as a derived functor, cf. (A. Frabetti, Dialgebra (co) Homology with Coefficients, Springer L.N.M., to appear).