Abstract:
The problem of the M5 brane anomaly cancellation is addressed. We reformulate FHMM construction making explicit the relation with the M5 brane SUGRA solution. We suggest another solution to the magnetic coupling equation which doesn't need anomalous SO(5) variation of the 3-form potential and coincides with the SUGRA solution outside smoothed out core of the magnetic source. Chern-Simons term evaluated on this solution generates the same anomaly inflow as achieved by FHMM.

Abstract:
In this letter we address the problem of inducing boundary degrees of freedom from a bulk theory whose action contains higher-derivative corrections. As a model example we consider a topological theory with an action that has only a ``higher-derivative'' term. By choosing specific coupling of the brane to the bulk we show that the boundary action contains gravity action along with some higher-derivative corrections. The co-dimension of the brane is more than one. In this sense the boundary is singular.

Abstract:
We provide strong $L_p$-rates of approximation of nonsmooth integral-type functionals of Markov processes by integral sums. Our approach is, in a sense, process insensitive and is based on a modification of some well-developed estimates from the theory of continuous additive functionals of Markov processes.

Abstract:
The aim of this paper was to evaluate persistency of several grass and legume species in meadow sward on peat-muck soil. The studies were carried out in 1996-2007 at the Didactic-Research Station in Sosnowica on peat-muck soil (Mt II). In 1996, Poa pratensis was a predominant species in the sward of this complex. The research, tested mixtures with different species composition. The basic species estimated in this studies were Lolium perenne, Festuca arundinacea, Phleum pratense, Dactylis glomerata, Trifolium repens and Trifolium pratense. In the studies, there was applied control fertilization N - 40 kg ha-1, P - 35 kg ha-1 i K - 100 kg ha-1. During 12-years' studies, meadow sward considerably varied. It was caused by a varied ground water level, total of precipitations and temperatures in the growing season in particular years of the studies. Lolium perenne, Festuca arundinacea and Dactylis glomerata were characterized by the largest persistency and share stability, considerably limiting simplification of species composition as well as the domination of Poa pratensis in meadow sward. However, legumes (Trifolium pratense and Trifolium repens) as well as Phleum pratense were very short-lived species in the tested habitat.

Abstract:
To our knowledge, this study applied for the first time a recently developed combination of atomic force microscopy (AFM) and nanoindentation on trabecular and compact bone tissue. The major aim was to check the advantage of the available AFM-mode over the conventionally used optical microscope. First, we investigated if removal of the water content helped to prevent enzymatic degradation of the bone tissue and preserve its mechanical properties during a week. After the positive issue of this test, we quantified the intrinsic mechanical properties of single bone structural units (BSU). Bone specimens were obtained from the femoral neck of an 86 year old female. Four BSU were randomly selected and tested each with 24 indents of 5 mN maximum force. The available AFM mode proved to be a very useful tool for surface characterization and precise selection of the indentation area. The elastic modulus ranged from 18 ± 1.7 GPa for a BSU of compact bone to 22.5 ± 3.1 GPa for a BSU of trabecular bone. Hardness showed values between 0.6 ± 0.11 GPa for compact bone and 1.1 ± 0.17 GPa for trabecular bone. The results suggest that the micromechanics of bone tissue may also be described as an assembly of distinct structural units with rather homogeneous material properties.

Abstract:
We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum $\hbar c/e$ as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to $F_3$ centers in alkali halides) with one trapped electron in one spin projection state.

Abstract:
We examine a generic three state mechanism which realizes all fundamental single and double qubit quantum logic gates operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. At the instant of time that the gate operations are defined the third level is unoccupied which, in a certain sense, derives analogy with the recently suggested dissipation free qubit subspaces. The physical implementation of the mechanism is tentatively suggested in a form of the Aharonov-Bohm persistent current loop in crossed electric and magnetic fields, with the output of the loop read out by a (quantum) Hall effect aided mechanism.

Abstract:
By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation dX_t=a_\theta(X_t)dt + dZ_t with a tempered \alpha-stable process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved.

Abstract:
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and the derivative has an integrable upper bound of a certain type, we derive the accuracy rates for strong and weak approximations of the functionals by Riemannian sums. Some examples are provided.

Abstract:
We consider the Fisher-Snedecor diffusion; that is, the Kolmogorov-Pearson diffusion with the Fisher-Snedecor invariant distribution. In the nonstationary setting, we give explicit quantitative rates for the convergence rate of respective finite-dimensional distributions to that of the stationary Fisher-Snedecor diffusion, and for the $\beta$-mixing coefficient of this diffusion. As an application, we prove the law of large numbers and the central limit theorem for additive functionals of the Fisher-Snedecor diffusion and construct $P$-consistent and asymptotically normal estimators for the parameters of this diffusion given its nonstationary observation.