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Highlights • A 2-DOF vibro-imapct system with dry friction is given. • The analytical switching conditions for motion on the discontinuous boundaries caused by friction and impact are obtained. • Switching sets and basic mappings are adopted to describe different periodic motions. • The numerical simulations are gievn to illustrate the analytical results. Abstract In this paper, the discontinuous dynamics in a 2-DOF (two-degree-of-freedom) vibro-impact system with dry friction is investigated by using the flow switchability theory for discontinuous dynamical systems. Multiple domains and discontinuous boundaries are defined according to friction and impact discontinuity. Based on above domains and boundaries, the onset and disappearance conditions of sliding-stick motion are developed and the analytical conditions of side-stick motion and grazing motion are obtained mathematically. The switching sets and mapping structures are adopted to describe the complex motions in such discontinuous system. The numerical simulations are also given to illustrate the analytical results of motion switching on different boundaries. This investigation can help us understand the motion switching mechanism in non-stick, sliding-stick or side-stick motions of the oscillator with friction and impact. [ABSTRACT FROM AUTHOR]

Abstract: We give a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. Some examples are given to illustrate our obtained result. [Copyright &y& Elsevier]

Abstract: Two-dimensional recurrence resolvents for an inhomogeneous thin body (plates of variable thickness and shells) are derived by an asymptotic method based on the three-dimensional equations of the coupled dynamic problem of the thermoelasticity of an anisotropic body, which are solved in the case of anisotropy, having, at each point, one plane of symmetry perpendicular to the transverse axis. Recurrence formulae are derived in a general formulation for determining the components of the stress tensor, the strain vector and the function of the change in the temperature field, when different boundary conditions of dynamic problems of the theory of coupled thermoelasticity and thermal conductivity are given on the end surfaces of a thin body. An algorithm for determining the analytical and numerical (necessary) solutions of these boundary-value problems with an arbitrarily specified accuracy is developed. [Copyright &y& Elsevier]

Abstract: Residues of partial sums in a class of dependent random variables, including functionals of uniformly recurrent Markov chains, are in the domain of attraction of the uniform distribution. These types of limit theorems arise for example in the multiplication of floating-point numbers. [Copyright &y& Elsevier]

Abstract: We propose a new method for the numerical evaluation of the spherical Bessel transform. A formula is derived for the transform by using an integral representation of the spherical Bessel function and by changing the integration variable. The resultant algorithm consists of a set of the Fourier transforms and numerical integrations over a linearly spaced grid of variable k in Fourier space. Because the k-dependence appears in the upper limit of the integration range, the integrations can be performed effectively in a recurrence formula. Several types of atomic orbital functions are transformed with the proposed method to illustrate its accuracy and efficiency, demonstrating its applicability for transforms of general order with high accuracy. [Copyright &y& Elsevier]

Abstract: The algebra of truth values of type-2 fuzzy sets consists of all mappings of the unit interval to itself, with type-2 operations that are convolutions of ordinary max and min operations. This paper is concerned with a special subalgebra of this truth value algebra, namely the set of nonzero functions with values in the two-element set {0,1}. This algebra can be identified with the set of all non-empty subsets of the unit interval, but the operations are not the usual union and intersection. We give simplified descriptions of the operations and derive the basic algebraic properties of this algebra, including the identification of its automorphism group. We also discuss some subalgebras and homomorphisms between them and look briefly at t-norms on this algebra of sets. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an unsupervised context-sensitive technique for change-detection in multitemporal remote sensing images. Here a modified self-organizing feature map neural network is used. Each spatial position of the input image corresponds to a neuron in the output layer and the number of neurons in the input layer is equal to the number of features of the input patterns. The network is updated depending on some threshold value and when the network converges, status of output neurons depict a change-detection map. To select a suitable threshold of the network, a correlation based and an energy based criteria are suggested. The proposed change-detection technique is unsupervised and distribution free. Experimental results, carried out on two multispectral and multitemporal remote sensing images, confirm the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: A rational approximant of third order, which is applied to a three-time level recurrence relation, is used to transform the two-dimensional sine-Gordon (SG) equation into a second-order initial-value problem. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is solved by an appropriate predictor–corrector (P–C) scheme, in which the predictor is an explicit one of second order. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behavior of the proposed P–C/MPC schemes is tested numerically on the line and ring solitons known from the bibliography, regarding SG equation and conclusions for both the mentioned schemes regarding the undamped and the damped problem are derived. [Copyright &y& Elsevier]

Using Recurrence Quantification Analysis it was possible to detect singularities in non-stationary lung sounds recorded on both right and left apexes. This result indicates that respiratory dynamics is controlled by a discrete non-deterministic dynamics based on violation of Lipschitz conditions. [Copyright &y& Elsevier]

We present a practical scheme for the evaluation of nonstandard two-electron integrals including the factors r12kexp(−γr122) which have been appeared recently, where k⩾−1 is an integer. The method used throughout this paper is based on the highly efficient Head-Gordon and Pople (HGP) approach of evaluation of electron repulsion integrals (ERI). Thus only straightforward modifications of existing codes that employ HGP or HGP-PRISM scheme are necessary to implement our approach. [Copyright &y& Elsevier]

Demonstrates that many of the properties of the Fibonacci numbers can be stated and proved for much more general tools for studying recurrent equations. Famous Fibonacci properties; Analysis of two-term recurrences; Difference operators; Binet formulas; Matrix formulation; Pythagorean triples; Common divisor.

Details recurrence relations evaluating Fresnel and exponential integrals. Comparison between the recurrences and the asymptotic series; Advantages of the recurrences; Derivation of rational approximations from the asymptotic series.

Abstract: A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. [Copyright &y& Elsevier]

Argues that the backward recurrence relation method is both pedagogically more natural for students and more efficient for hand computations. Application in extending Euclid's algorithm; Backward recurrence relation; Forward recurrence relations.

The article focuses on the genomic analysis that reveals the origins of European places. According to the author, genetic analysis can locate Europeans' geographic origins within a few hundred kilometers through mathematically mapping the differences between people's genomes into a two dimensional grid, and its result looked much like a map of Europe. Moreover, it cites the implication of the study to a disease by looking for genetic variations shared by people who suffered from it.