Well-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditions

This work is devoted to the study of a phase-field transition system of Caginalp type endowed with a general polynomial nonlinearity and a general class of nonlinear and nonhomogeneous dynamic boundary conditions (in both unknown functions). The existence, uniqueness and regularity of solutions are established. Here we extend several results proved by some authors, including the already studied boundary conditions, which makes the present mathematical model capable of revealing the complexity of a wide class of physical phenomena (for instance, phase change in Ω at the boundary of Ω).     

On whistling of pipes with a corrugated segment: Experiment and theory

Corrugated pipes are commonly used because of their local rigidity combined with global flexibility. The flow through such a pipe can induce strong whistling tones, which is an environmental nuisance and can be a threat to the mechanical integrity of the system. This paper considers the use of a composite pipe: a shorter corrugated pipe segment embedded between smooth pipe segments. Such a pipe retains some flexibility, while the acoustical damping in the smooth pipe reduces whistling tones. Whistling is the result of coherent vortex shedding at the cavities in the wall. This vortex shedding is synchronized by longitudinal acoustic waves traveling along the pipe. The acoustic waves trigger the vortex shedding, which reinforces the acoustic field for a critical range of the Strouhal number values. A linear theory for plane wave propagation and the sound production is proposed, which allows a prediction of the Mach number at the threshold of whistling in such pipes. A semi-empirical approach is chosen to determine the sound source in this model. This source corresponds to a fluctuating force acting on the fluid as a consequence of the vortex shedding. The functional form of the Strouhal number dependency of the dimensionless sound source amplitude is based on numerical simulations. The magnitude of the source and the Strouhal number range in which it can drive whistling are determined by matching the model to results for a specific corrugated pipe segment length. This semi-empirical source model is then applied to composite pipes with different corrugated segment lengths. In addition, the effect of inlet acoustical convective losses due to flow separation is considered. The Mach number at the threshold of whistling is predicted within a factor 2.     

On co-ordinated quasi-convex functions

A function f: I → ?, where I ? ? is an interval, is said to be a convex function on I if $$f(tx + (1 - t)y) \le tf(x) + (1 - t)f(y)$$ holds for all x, y ∈ I and t ∈ [0, 1]. There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensenconvex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions on the coordinates. We also prove some inequalities of Hadamard-type as Dragomir’s results in Theorem 5, but now for Jensen-quasi-convex and Wright-quasi-convex functions. Finally, we give some inclusions which clarify the relationship between these new classes of functions.     

From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

Assessing the subsequent effect of nitrogen released from tobacco-waste on maize crop using a 15N isotope technique

The investigation of the residual effect of nitrogen (N) released from tobacco-waste (TW) using isotope techniques will provide valuable data for sustainable organic farming. For this aim, a pot experiment was conducted using the ¹⁵N isotope technique. The experiment was based on a completely randomised design with four replications and was conducted on a calcareous ustochrepts soil. TW at levels of 0, 10, 20, 30 and 40 t ha^?1 and N fertiliser as (NH₄)₂SO₄ at levels of 0, 20, 40, 60 and 80 kg N ha^?1 were used for the Bezostaja-1 wheat variety. Concerning mineral N fertilisation with 20 and 80 kg N ha^?1, additional treatments with ¹⁵N-labelled (NH₄)₂SO₂ (10 at.% exc.) have been applied. Following harvesting wheat plants, the Pioneer 3377 maize variety was used to see the residual effect of TW. After harvesting, dry matter yields were recorded and total N concentrations were determined. ¹⁵N determinations and calculations were also made for ¹⁵N treatments separately. TW had a significant residual effect on the growth of corn plant under the pot condition. Increasing rates of TW significantly increased the dry matter yield of corn plant following wheat from 3.31 t ha^?1 (at control) to 7.89 t ha^?1 (at the TW treatment of 40 t ha^?1). The ¹⁵N values derived from the ¹⁵N fertiliser decreased with increasing TW application. The average values of N derived from N fertiliser (Ndff) varied from 2.14 to 3.09% at the rates of 20 and 80 kg N ha^?1, respectively. However, N derived from TW (Ndftw) significantly increased from 16.93 to 24.59% (at 20 kg N ha^?1), and it also increased from 23.06 to 28.15% (at 80 kg N ha^?1) with increasing TW applications from 20 to 40 t ha^?1, respectively.     

On Approximation Properties of Generalized q-Bernstein Operators

In this study, we identify a generalization of q-Bernstein type operators and investigate approximation properties of a sequence of these operators . We estimate rate of approximation by modulus of continuity. We prove Voronovskaya type theorem for these operators.     

Generalized Bosbach states: part I

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics.