Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.     

Invariant measures ofC 2-diffeomorphisms of Markov type inR d

A class of uniformly expanding, piecewiseC ²-diffeomorphisms from domainsIR ^d (bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix (P )={gG:Pg=g} whereP is the Frobenius-Perron operator associated with andG={gL ¹: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence {P ^j g} is convergent inL ¹ for anygG, and in the topology of uniform convergence for anygG(1). The limit is a linear projectionR inL ¹ (defined by (3.1)) which mapsG onto Fix (P ) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On stationary flow of asymmetric fluids with diffusion

We prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ?³. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.     

Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.     

Lottery and Auction on Quantum Blockchain

This paper proposes a protocol for lottery and a protocol for auction on quantum Blockchain. Our protocol of lottery satisfies randomness, unpredictability, unforgeability, verifiability, decentralization and unconditional security. Our protocol of auction satisfies bid privacy, posterior privacy, bids’ binding, decentralization and unconditional security. Except quantum Blockchain, the main technique involved in both protocols is quantum bit commitment.     

Synthesis and characterization of LSMO manganite-based biocomposite

In this paper we study the structural, morphological and magnetic properties of La_0.67Sr_0.33MnO₃ (LSMO) manganite nanoparticles (NPs) and its biocomposite, obtained by mixing NPs of hydroxyapatite (HA). From the studies of X-ray diffraction and Fourier transmission of infrared spectroscopy it is evident that in the biocomposite sample both the individual phases are distinguishable from each other. The measurements of direct current (DC) magnetization and hysteresis loops reveal that the basic magnetic behaviour of LSMO–HA is similar to that of LSMO; however, the admixture of HA makes the sample magnetically softer. From the investigation of transmission electron microscopy it is observed that such a biocomposite is composed of the NPs of LSMO surrounded by HA particles, which can be found suitable for biomedical applications.     

Theoretical analysis of trends in hydrogen bonding involving halogen acceptors (F−At) covalently bonded to a group 14 atom (C−Pb)

In this work, extensive quantum-chemical calculations have been carried out to identify and elucidate trends in the hydrogen-bonding (HB) interaction involving halogen acceptors covalently bonded to a group 14 atom. A series of 25 heterodimers composed of MH₃X (where M = C?Pb and X = F?At) and HNC molecules have been selected as model complexes stabilised by the HB interaction occurring between the X atom of MH₃X and the H atom of HNC. The interaction energy (E_int) between MH₃X and HNC in the MH₃X···HNC complexes falls in the range from ?2.7 to ?10.8 kcal/mol, indicating weak or medium strength of HB in these complexes. The strength of HB in the complexes remains consistent with the well-known HB weakening as X gets heavier. Regarding the effect of M on E_int, the gradual strengthening of HB is observed while descending group 14, but only from M = Si to M = Pb. The trends in E_int are compared with various HB-related parameters obtained from vibrational analysis, the natural bond orbital (NBO) method, the symmetry-adapted perturbation theory (SAPT) and the quantum theory of atoms in molecules (QTAIM). The parameters that present clear (possibly linear) relationships with E_int have been selected to characterise the effect of M and X on the HB interaction.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Free Radicals, Salicylic Acid and Mycotoxins in Asparagus After Inoculation with Fusarium proliferatum and F. oxysporum

Electron paramagnetic resonance was used to monitor free radicals and paramagnetic species like Fe, Mn, Cu generation, stability and status in Asparagus officinalis infected by common pathogens Fusarium proliferatum and F. oxysporum. Occurrence of F. proliferatum and F. oxysporum, level of free radicals and other paramagnetic species, as well as salicylic acid and mycotoxins content in roots and stems of seedlings were estimated on the second and fourth week after inoculation. In the first term free and total salicylic acid contents were related to free radicals level in stem (P?=?0.010 and P?=?0.033, respectively). Concentration of Fe(3+) ions in porphyrin complexes (g?=?2.3, g?=?2.9) was related to the species of pathogen. There was no significant difference between Mn(2+) concentrations in stem samples; however, the level of free radicals in samples inoculated with F. proliferatum was significantly higher when compared to F. oxysporum.