Novel closed – form solutions in buckling of inhomogeneous columns under distributed variable loading

In this study we consider buckling of columns with variable stiffness, under axially distributed loading varying polynomially. The objective is to obtain closed – form solutions for the buckling load. The problem is posed in inverse setting: determine the column’s stiffness, so that it has the given, polynomial, buckling mode. Four sets of boundary conditions are investigated. Some perplexing results are obtained, namely, that irrespective of boundary conditions, the critical load of the column is the same; this occurs in conjunction with the fact that the obtained distribution for stiffness is different for each set of boundary conditions.     

Dynamic behaviors of the periodic predator–prey system with distributed time delays and impulsive effect

In this paper, a periodic predator–prey system with distributed time delays and impulsive effect is investigated. By using the Floquet theory of linear periodic impulsive equation, some conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are obtained. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We improve some results in Guo and Chen (2009) [1].     

Modeling and Analysis of Modal Switching in Networked Transport Systems

We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system.     

The Balassa–Samuelson effect in Romania – The role of regulated prices

Due to the Balassa–Samuelson effect, the candidate countries to the European Monetary Union face a possible conflict between the effects of tradable productivity increase on inflation and on the appreciation of the real exchange rate on one hand, and the Maastricht criteria regarding inflation and exchange rate stability on the other hand. A restrictive monetary policy could succeed in reaching inflation criteria, but only with the cost of slowing down real convergence. This paper deals with the Balassa–Samuelson effect in Romania. The main conclusion of the paper is that in the period 1998–2006 the average annual rate of inflation generated by the Balassa–Samuelson effect in Romania was on average 0.6% in the case of the classical model. Due to the existence of government-regulated prices (mostly non-tradable goods) accounting for as much as 21% of the CPI basket in Romania – the price of non-tradables has increased by less than in the case those prices were market prices. If we include these regulated prices in non-tradable, which is named by us extended model, the impact of Balassa–Samuelson on inflation could have been on average 2.46%. Therefore, the Balassa–Samuelson effect is expected to result into higher inflation with future price liberalization for non-tradables.     

Transient flow in natural gas pipeline – The effect of pipeline thermal model

One-dimensional, nonisothermal gas flow model was solved to simulate the slow and fast fluid transients, such as those typically found in high-pressure gas transmission pipelines. The results of the simulation were used to understand the effect of different pipeline thermal models on the flow rate, pressure and temperature in the pipeline. It was found that simplified flow model with steady-state heat transfer term overestimates the amplitude of the temperature fluctuations in the pipeline. This result indicated that unsteady heat transfer model with the effect of heat accumulation in the surroundings of the pipeline should be used to calculate the gas parameters at locations of interest within high-pressure gas transmission pipelines.     

The Lyapunov–Movchan method in problems of the stability of flows and deformation processes

The extension of Lyapunov's method to continuous mechanical systems are discussed. An annotated bibliography of papers is given in which, based on the Lyapunov–Movchan method, with the construction of corresponding functionals, a direct analysis is carried out of the stability of motion (deformation) of continuous mechanical systems. The material is divided into sections, devoted to the following: (a) the extension of the mathematical apparatus as a whole to continuous and dynamic systems, (b) the stability of elastic, elastoplastic and viscoelastic deformable solids, (c) stability in aeroelasticity and hydroelasticity theory, (d) the linearized theory of hydrodynamic stability, and (e) the stability with reference to perturbations of material functions in the theory of constitutive relations.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Dusty shock wave interaction – formation of fully dispersed waves and particle focusing effect

The problem of regular (symmetric and asymmetric) interaction of plane shock waves in a steady-state dusty gas flow is considered. For near-sonic flows with a fairly high particle mass loading, the possibility of the formation of wave structures is revealed, in which either all or only some of the incident or reflected waves degenerate into so-called fully dispersed waves, i.e. zones in which no discontinuities appear in the parameters of each phase. For stronger shock waves and low particle mass concentration, the effect of aerodynamic particle focusing and the formation of a narrow high-concentration beam of particles behind the point of the interaction of the waves are detected on the basis of parametric numerical calculations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of γ radiation on the distribution of stresses in polymers

Infrared spectroscopy has been used to study the effect of -radiation on the distribution of an applied stress over the individual polymer chains. It has been shown that, as the irradiation dose is increased, the maximum stress on the bonds which are ruptured is attained at a lower value for the mean stress applied to the sample.V. I. Lenin Tadzhik State University, Dushanbe. Translated from Mekhanika Polimerov, No. 2, pp. 214–217, March–April, 1975.     

Modeling and analysis of a prey–predator system with disease in the prey

A three dimensional ecoepidemiological model consisting of susceptible prey, infected prey and predator is proposed and analysed in the present work. The parameter delay is introduced in the model system for considering the time taken by a susceptible prey to become infected. Mathematically we analyze the dynamics of the system such as, boundedness of the solutions, existence of non-negative equilibria, local and global stability of interior equilibrium point. Next we choose delay as a bifurcation parameter to examine the existence of the Hopf bifurcation of the system around its interior equilibrium. Moreover we use the normal form method and center manifold theorem to investigate the direction of the Hopf bifurcation and stability of the bifurcating limit cycle. Some numerical simulations are carried out to support the analytical results.     

Spreading speed and traveling waves for a nonmonotone reaction–diffusion model with distributed delay and nonlocal effect

In this paper, spreading speed and traveling waves for reaction–diffusion model with distributed delay and nonlocal effect without monotonicity are investigated. It is shown that there exists the spreading speed c^∗ which coincides with the minimal wave speed, and its limiting integral equation has an unique traveling wave with speed c > c^∗, and no traveling wave with c < c^∗. Moreover, the dependence of the spreading speed on the delay and the nonlocal effect is considered.     

Kindergartners’ performance in length measurement and the effect of picture book reading

This paper addresses: firstly, kindergartners’ performance in length measurement, the components of their performance and its growth over time; secondly, the possibility to develop kindergartners’ performance in length measurement by reading to them from picture books. To answer the research questions, an experiment with a pretest–posttest experimental control group design was carried out involving nine experimental classes and nine control classes. The children in the experimental group participated in a 3-month picture book program that, among other things, spotlighted the measurement of length situated in meaningful contexts. Before and after the intervention, the children’s performance in length measurement was assessed in both groups. The responses of 308 kindergartners (4- to 6-year-olds) from two kindergarten years (K1 and K2) were analyzed. Analysis of the pretest data showed that the measurement tasks included in the test were not easy to solve. However, the children belonging to K2 did better than the younger children belonging to K1. Within children’s performance, three components could be identified: holistic visual recognition, ordering and unitizing. Finally, the effect of the intervention was investigated by comparing the performances of the experimental and control group in the pretest and the posttest. We found a weak but significant effect of reading picture books to children on their general measurement performance. However, this effect was only found for K1 children on the component of holistic visual recognition.     

Modeling nonlinear deformation of a plate with an elliptic inclusion by John’s harmonic material

The exact analytical solution of a nonlinear plane-strain problem has been obtained for a plate with an elastic elliptic inclusion with constant stresses given at infinity. The mechanical properties of the plate and inclusion are described with the model of John’s harmonic material. In this model, stresses and displacements are expressed in terms of two analytical functions of a complex variable that are determined from nonlinear boundary-value problems. Assuming the tensor of nominal stresses to be constant inside the inclusion has made it possible to reduce the problem to solving two simpler problems for a plate with an elliptic hole. The validity of the adopted hypothesis has been justified by the fact that the derived solution exactly satisfies all the equations and boundary conditions of the problem. The existence of critical plate-compression loads that lead to the loss of stability of the material has been established. Two special nonlinear problems for a plate with a free elliptic hole and a plate with a rigid inclusion have been solved.     

Dynamic Modeling and Tracking Control of 2-Joint Manipulators in Ocean Current Environment北大核心CSCD

The hydrodynamic performance of the underwater manipulator is greatly influenced by the current load. The underwater environment is assumed to be a still water environment and the current load is only considered as a simple random disturbance in the current control research, and the traditional control precision is usually rather low. Based on the Lagrange method and the Newton-Euler method, a dynamic model for 2-joint manipulators in the uniform ocean current environment was derived. In view of the relative motion of the ocean current and the manipulator, the Morison formula was introduced to calculate the water resistance and the inertia force of the ocean current on the manipulator. Based on this dynamic model, the sliding mode control strategy was used to achieve accurate tracking of the ideal trajectory of the manipulator. The simulation results show that, compared with the PD (proportional derivative) control, the sliding mode control strategy has better control effects. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

The effect of motion analysis activities in a video-based laboratory in students’ understanding of position,velocity and frames of reference

In this article, we present the results of a qualitative research project on the effect of motion analysis activities in a Video-Based Laboratory (VBL) on students’ understanding of position, velocity and frames of reference. The participants in our research were 48 pre-service teachers enrolled in Education Departments with no previous strong science or mathematics background. VBLs are presented in the context of a category of technology tools that allow the analysis of motion events for educational purposes followed by a review of literature regarding the use of VBL in science education. The qualitative methodology that we undertook is presented and justified and the results of our study are stated, escorted by selected and detailed dialogue extracts from our interviews with the participating students. The outcomes of our research are discussed and found to be positive and some implications for further research are stated.     

Spectral deformation and Bäcklund transformation of constrained Willmore surfaces

The class of constrained Willmore surfaces in space-forms forms a Möbius invariant class of surfaces with strong links to the theory of integrable systems. This paper is dedicated to an overview on the topic. We define a spectral deformation, by the action of a loop of flat metric connections, and Bäcklund transformations, by applying a dressing action. We establish a permutability between spectral deformation and Bäcklund transformation and verify that all these transformations corresponding to the zero multiplier preserve the class of Willmore surfaces. We show that, for special choices of parameters, both spectral deformation and Bäcklund transformation preserve the class of constrained Willmore surfaces admitting a conserved quantity, and, in particular, the class of constant mean curvature surfaces in 3-dimensional space-forms.     

Distributing inspections in space and time – Proposed solution of a difficult problem

There are several identical facilities in which precious or dangerous material is processed or stored. Since parts of this material may be diverted by some manager or employee of these facilities or since failures in the processing of the material may occur, an authorized organization inspects these facilities regularly at the beginning and at the end of some reference time interval. In order to shorten the time required for detecting such an illegal activity or failures, in addition some interim inspections are performed in these facilities during the reference time interval. The optimal distribution of these interim inspections in space and time poses considerable analytical problems since adversary strategies have to be taken into account. So far only special cases have been analysed successfully, but these results lead to a conjecture for the solution of the general case which is surprisingly simple in view of the complexity of this inspection problem.     

Modeling the Physiological Behavior of Arterial Walls – Comparative Study Regarding the Viscoelastic Response

This contribution deals with the modeling of the physiological behavior of arterial walls, in order to enable a reliable calculation of the transmural stress distribution including also the active response of arterial tissue. Therefore, a simple viscoelastic model, which only requires few material parameters, is considered. Furthermore, a comparative study, investigating the influence of viscoelasticity on the mechanical behavior of arterial walls, is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)