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Molecular dynamics simulations of reactions in Al/Ni layered systems have been carried out under isothermal conditions for a wide range of temperatures and several system sizes. An embedded atom method potential, known to reasonably reproduce the phase behavior of Al/Ni, was employed. Simulations revealed reaction mechanisms involving an initial fast process and much slower more complex longer-time reactions. The initial reaction process consists of diffusion of Ni from the pure solid Ni phase into the molten Al phase, resulting in the formation of an Al-rich Al/Ni liquid. The initial reaction ends when the Al/Ni liquid becomes saturated in Ni and solid Al/Ni phases begin to form at the interfaces between the pure solid Ni phase and the Al/Ni liquid. The growth of these solid phases is intrinsically slow compared to the formation of the liquid and is further slowed by the need for Ni to diffuse through the growing interfacial Al/Ni solid phases. Analysis of the initial Al/Ni liquid forming process indicates Fickian behavior with the Ni diffusion coefficient exhibiting Arrhenius temperature dependence. The longer-time slow reaction process(es) resulting in the growth of Al/Ni solid phases do not lend themselves to detailed numerical analysis because of the complex dependence of the Ni transport on the detailed nature of the interfacial layers. [ABSTRACT FROM AUTHOR]

The paper presents the results of 5 case studies on complex site effects selected within the project for the level 3 seismic microzonation of several municipalities of Central Italy damaged by the 2016 seismic sequence. The case studies are characterized by different geological and morphological configurations: Monte San Martino is located along a hill slope, Montedinove and Arquata del Tronto villages are located at ridge top whereas Capitignano and Norcia lie in correspondence of sediment-filled valleys. Peculiarities of the sites are constituted by the presence of weathered/jointed rock mass, fault zone, shear wave velocity inversion, complex surface and buried morphologies. These factors make the definition of the subsoil model and the evaluation of the local response particularly complex and difficult to ascertain. For each site, after the discussion of the subsoil model, the results of site response numerical analyses are presented in terms of amplification factors and acceleration response spectra in selected points. The physical phenomena governing the site response have also been investigated at each site by comparing 1D and 2D numerical analyses. Implications are deduced for seismic microzonation studies in similar geological and morphological conditions. [ABSTRACT FROM AUTHOR]

In order to deal with the problem of low precision and ignoring the influence of some factors on the growth system of cyanobacteria, this paper considers the effects of light, water temperature and other influencing factors to analyze cyanobacteria growth system. The time stochastic differential equation of cyanobacteria growth with double nutrient cycling is established. The numerical analysis and the intelligent evolutionary algorithm are used to optimize the steady parameters in the time stochastic differential equation of cyanobacteria growth. The light, water temperature and other factors is used to build time series modeling. The time stochastic parameters and the prediction of cyanobacteria biomass is realized. The bifurcation theory and the central manifold theory were used to analyze the nonlinear dynamics of cyanobacteria growth with double nutrient cycling system, so that the conditions of cyanobacteria bloom and prediction of cyanobacteria blooms are achieved. Compared with the existing research, the method proposed in this paper not only determines the conditions of cyanobacteria bloom, but also improves the accuracy of water bloom prediction, and provides an effective reference for environmental protection departments. [ABSTRACT FROM AUTHOR]

Bursting phenomena are found in a wide variety of fast–slow systems. In this article, we consider the Hindmarsh–Rose neuron model, where, as it is known in the literature, there are homoclinic bifurcations involved in the bursting dynamics. However, the global homoclinic structure is far from being fully understood. Working in a three-parameter space, the results of our numerical analysis show a complex atlas of bifurcations, which extends from the singular limit to regions where a fast–slow perspective no longer applies. Based on this information, we propose a global theoretical description. Surfaces of codimension-one homoclinic bifurcations are exponentially close to each other in the fast–slow regime. Remarkably, explained by the specific properties of these surfaces, we show how the Hindmarsh–Rose model exhibits isolas of homoclinic bifurcations when appropriate two-dimensional slices are considered in the three-parameter space. On the other hand, these homoclinic bifurcation surfaces contain curves corresponding to parameter values where additional degeneracies are exhibited. These codimension-two bifurcation curves organize the bifurcations associated with the spike-adding process and they behave like the "spines-of-a-book," gathering "pages" of bifurcations of periodic orbits. Depending on how the parameter space is explored, homoclinic phenomena may be absent or far away, but their organizing role in the bursting dynamics is beyond doubt, since the involved bifurcations are generated in them. This is shown in the global analysis and in the proposed theoretical scheme. [ABSTRACT FROM AUTHOR]

The article focuses on the bending problem for a cantilever beam with a straight through-thickness crack, perpendicular to its axis under bending by concentrated force. Depending on the crack location in relation to the axis, crack faces may be in three states: perfect contact, particular contact, or noncontact. Using the theory of functions of complex variable and complex potentials, the considered problem was reduced to a linear conjunction one. An analytical solution of the problem was obtained. In the case of particular contact, the length of the contact area and stress intensity factors were determined. The ultimate force that causes beam destruction was determined. Numerical analyses of the problem were also performed. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an analytical solution for determining the dynamic characteristics of axially loaded piles embedded in elastic‐poroelastic layered soil of finite thickness. The interface between the elastic and poroelastic soil coincides with the groundwater table level, which is explicitly taken into account in the solution. The pile is modelled as elastic one‐dimensional rod to account for the effect of its dynamic characteristics on the response of the soil‐pile system. The solution is based on Biot's poroelastodynamic theory and the classical elastodynamic theory, which we use to establish the governing equations of the soil and pile. Accordingly, the pile base resistance, shaft reaction, and the complex impedance of soil‐pile system are obtained using the method of Hankel integral transformation. Following the validation of the derived solution, we identify the main parameters affecting the vertical dynamic impedance of the pile via a parametric study. The presented method poses as an efficient alternative for quickly estimating the dynamic characteristics of axially loaded piles, without having to resort to complex numerical analyses. [ABSTRACT FROM AUTHOR]

The subject of the work was the assessment of the possibility of using Cadmould 3D-F® software based on numerical analysis to design complex injection moulding cavities with plasticised polymer feed channels on the example of an element requiring special dimensional accuracy. The overarching goal of the design process was to create the most advantageous geometry of the injection moulding cavity model and the dedicated material supply channels, which will minimize the effect of problems occurring during injection moulding process, such as processing shrinkage, surface collapse, warpage and mouldings deformation. As an additional criterion, the smallest possible degree of complexity of the designed system was adopted for economical reasons and elimination of subsequent production problems resulting from the complex geometry of the designed mould. [ABSTRACT FROM AUTHOR]

Radiant cooling systems (wall and ceiling) are low exergy systems which can help in solving efficiently the comfort needs of occupants. However, a complex energy and exergy analysis should be done in the design phase of such cooling systems in order to choose the most appropriate solution. This paper attempts to present a mathematical model and methodology of such a complex analysis and illustrates through a case study the energy and exergy comparison of cooling systems with mechanical compression and absorption cooling systems. Simple relations were developed in order to evaluate rapidly the energy and exergy efficiency of these types of cooling systems taking into account the avoidance of surface condensation. It was proven that, besides the coefficient of performances of installed chillers, the temperatures in the generator and absorber, respectively the supply and return temperatures are the main influencing factors of the exergy efficiencies of such types cooling systems. Based on the developed mathematical method a numerical analysis was done assuming different operational parameters of the cooling system used in practice. • The maximal heat load, neutralizable with radiant cooling, was determined. • The relations for exergy content calculation of the "cold energy" were presented. • Three new evaluation indices were introduced for radiant cooling systems. • The energy and exergy efficiencies of the whole cooling systems were analysed. [ABSTRACT FROM AUTHOR]

• The purpose of the study was the multifaceted and complex analysis of the impact behaviour of hybrid titanium glass fibres laminates (HTGL) based on the experiment method. Moreover the appropriate model to prediction of impact damage resistance was proposed. Different quantitative and qualitative criteria were used to measure and compare the impact behaviour of HTGL. • Based on impact parameters and damage analysis of HTGL after impact, FEM model was proposed to predict the impact resistance of HTGL. • Based on the obtained results of experimental studies it was proven that fibre metal laminates based on titanium and glass-epoxy composite are characterised by high resistance to low-velocity impact. • Greater resistance of these laminates to damage propagation and perforation was noted for the impact with a spherical indenter in comparison to the previously used GLARE laminates. • Three aspects of mechanical response of FMLs, such as metal properties, composite properties and metal-composite interphase were used in the FEM simulation. Results of numerical analyses indicate the correctness of the adopted calculation assumptions and the study procedure itself. Fibre metal laminates (FML) constitute a group of hybrid materials made of alternating layers of metal and fibre polymer composite. One of the more prospective materials of the next FML generation is a laminate based on titanium and glass or carbon fibres. The use of titanium increases laminate stiffness in comparison to laminates based on aluminium alloys and significantly increases the corrosion resistance and impact properties. The purpose of the study was a multifaceted and complex analysis of the impact behaviour of hybrid titanium glass fibres laminates (HTGL) based on the experiment and modelling methods. Based on the obtained results of experimental studies it was proven that fibre metal laminates based on titanium and glass-epoxy composite are characterised by high resistance to low-velocity impact within the range of energy of 2.5–30 J at least, expressed by the criteria of maximum force, deformations, work performed by the indenter, impact energy absorption capacity, and the parameters describing the extent of damage after impact. The obtained results of numerical analyses indicate the correctness of the adopted calculation assumptions and the study procedure itself. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of an iterative method based on the Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. As it was proven in "A new family of iterative methods widening areas of convergence, Appl. Math. Comput.", this family has the property of getting good estimations of the solution when Newton's method fails. Moreover, the set of converging starting points for several non-polynomial test functions was plotted and they showed to be wider in the case of proposed methods than in Newton's case, for small values of the parameter. Now, we make a complex dynamical analysis of this parametric class in order to justify the stability properties of this family. [ABSTRACT FROM AUTHOR]

The classification of a new item may be viewed as a matter of associating it with the class where it is the least at odds w.r.t. the elements already in the class. An oddness measure of an item with respect to a multiset, applicable to Boolean features as well as to numerical ones, has been recently proposed. It has been shown that cumulating this measure over pairs or triples (rather than larger subsets) of elements in a class could provide an accurate estimate of the global oddness of an item with respect to a class. This idea is confirmed and refined in the present paper. Rather than considering all the pairs in a class, one can only deal with the pairs whose an element is one of the nearest neighbors of the item, in the target class. The oddness evaluation computed on this basis still leads to good results in terms of accuracy. One can take a step further and choose the second element in the pair also as another nearest neighbor in the class. Although the method relies on the notion of neighbors, the resulting algorithm is far from being a variant of the classical k‐nearest neighbors approach. The oddness with respect to a class computed only on the basis of pairs made of two nearest neighbors leads to a low complexity algorithm. Experiments on a set of UCI benchmarks show that the classifier obtained can compete with other well‐known approaches. [ABSTRACT FROM AUTHOR]

We study the spectrum of the spin-boson model with two photons in Rd for arbitrary coupling α>0. It is shown that the discrete spectrum is finite and the essential spectrum consists of a half-line, the bottom of which is a unique zero of a simple Nevanlinna function. Besides the simplicity and more abstract nature of our approach, the main novelty is the achievement of these results under minimal regularity conditions on the photon dispersion and the coupling function. [ABSTRACT FROM AUTHOR]

Abstract: We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface is given by a fixed topological contribution, independent of the temperature or details of the entangling region. We offer a definition and interpretation of subregion complexity in the context of tensor networks, and show numerically that it reproduces the qualitative features of the holographic computation in the case of a random tensor network using its relation to the Ising model. Finally, we give a prescription for computing subregion complexity directly in CFT using the kinematic space formalism, and use it to reproduce some of our explicit gravity results obtained at zero temperature. We thus obtain a concrete matching of results for subregion complexity between the gravity and tensor network approaches, as well as a CFT prescription. [ABSTRACT FROM AUTHOR]

The form of the general solution of the steady-state Euler-Helmholtz equation (reducible to the Joyce-Montgomery one) in arbitrary domains on the plane is considered. This equation describes the dynamics of vortex hydrodynamic structures. [ABSTRACT FROM AUTHOR]

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations. [ABSTRACT FROM AUTHOR]

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the value distribution of complex partial q-difference polynomials of meromorphic functions of zero order, and also investigate the existence of meromorphic solutions of some types of systems of complex partial q-difference equations in Cn. Some existing results are improved and generalized, and some new results are obtained. Examples show that our results are precise. [ABSTRACT FROM AUTHOR]

The dynamical system governing the motion of a curved rigid two-dimensional circular-arc fiber in simple shear is derived in analytical form. This is achieved by finding the solution for the associated low-Reynolds-number flow around such a fiber using the methods of complex analysis. Solutions of the dynamical system display the "flipping" and "scooping" recently observed in computational studies of three-dimensional fibers using linked rigid rod and bead-shell models [J. Wang et al., "Flipping, scooping, and spinning: Drift of rigid curved nonchiral fibers in simple shear flows," Phys. Fluids 24, 123304 (2012)]. To complete the Jeffery-type equations for a curved fiber in a linear flow field we also derive its evolution equations in an extensional flow. It is expected that the equations derived here also govern the motion of slender, curved, three-dimensional rigid fibers when they evolve purely in the plane of shear or strain. [ABSTRACT FROM AUTHOR]

Warner (1965) introduced a Randomized Response Technique (RRT) to minimize bias due to nonresponse or false response. Thereafter, several researchers have made significant contribution in the development and modification of different Randomized Response Models. We have modified a few onestage Simple Randomized Response Models to two-stage randomized response models in complex surveys and found that our developed models are more efficient. [ABSTRACT FROM AUTHOR]

Letandbe elements of a complex unital Banach algebra. The numerical range submultiplicityis investigated. As a consequence of the inclusions established, we confirm a conjecture that ifandare self-adjoint operators such thatis positive then the productis self-adjoint whenever it is normal. [ABSTRACT FROM PUBLISHER]

We develop the theory of coverings of complexes of groups. For ϕ : G ′ ⟶ G a covering of complexes of groups we prove that G is developable if and only if G ′ is developable. [ABSTRACT FROM AUTHOR]

We investigate the hyper-order of solutions of two class of complex linear differential equations. We investigate the growth of solutions of higher order and certain second order linear differential equations, and we obtain some results which improve and extend some previous results in complex oscillations. [ABSTRACT FROM AUTHOR]

Grafting is a syntactic device developed and defended by van Riemsdijk (2000 and subsequent work) by which two independent input trees are connected via external remerger of internal elements, thus sharing a constituent. Grafting clearly violates standard assumptions about phrase structure. Still, several structures found in natural language are best analyzed in terms of grafting. The present paper discusses one such construction: complex numerals. It shows that the characteristic multidominance of grafting explains the word order, case assignment, plural, paucal, and singular distribution associated with complex numeral combinations better than a coordination approach and is more compatible with more number (or counting) systems found in the world's languages. [ABSTRACT FROM AUTHOR]

The fractional-order total variation(TV) image denoising model has been proved to be able to avoid the “blocky effect”. However, it is difficult to be solved due to the non-differentiability of the fractional-order TV regularization term. In this paper, the proximity algorithm is used to solve the fractional-order TV optimization problem, which provides an effective tool for the study of the fractional-order TV denoising model. In this method, the complex fractional-order TV optimization problem is solved by using a sequence of simpler proximity operators, and therefore it is effective to deal with the problem of algorithm implementation. The final numerical procedure is given for image denoising, and the experimental results verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

A diameter graph in ℝ is a graph in which vertices are points of a finite subset of ℝ and two vertices are joined by an edge if the distance between them is equal to the diameter of the vertex set. This paper is devoted to Schur's conjecture, which asserts that any diameter graph on n vertices in ℝ contains at most n complete subgraphs of size d. It is known that Schur's conjecture is true in dimensions d ≤ 3. We prove this conjecture for d = 4 and give a simple proof for d = 3. [ABSTRACT FROM AUTHOR]

We propose a numerical-analytic method for the investigation of parametric vibrations of the plates under the action of static and periodic loads applied in the middle plane. The method is used for the equations of motion of plates obtained within the framework of the classical theory. The developed approach is based on the application of the theory of R-functions and variational methods, which enables us to study plates of arbitrary geometric shapes with various boundary conditions. According to the proposed approach, we first find the subcritical state of the plate if it is not homogeneous. To construct the zones of dynamic instability, we use the method proposed by Bolotin. The results obtained with the help of the developed approach are compared with the available data. We solve a number of new problems for multilayer plates of complex geometric shapes with holes. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study zeros and poles of the forward differences Δ f( z), where f( z) is a finite order meromorphic function with two Borel exceptional values. [ABSTRACT FROM AUTHOR]

Abstract: Using a new fixed point relation, the interval methods for the simultaneous inclusion of complex multiple zeros in circular complex arithmetic are constructed. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Schröder’s and Halley-like corrections under computationally verifiable initial conditions. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Two numerical examples are given to demonstrate convergence characteristics of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the positive definite solutions of the nonlinear matrix equation (NME) where A is a given complex matrix. We show that such an NME has a positive definite solution if and only if an auxiliary standard NME in the form of has. Furthermore, the relationship regarding the maximal positive definite solution and the minimal positive definite solution between these two NMEs are established. Three iterative algorithms are proposed to solve the considered NME. The first method is directly related to the considered original equation but involves matrix inversion; the second method avoids the computation of matrix inversion; while the third method is an accelerated version of the first one. Convergence performances of these three kinds of algorithms are analyzed in detail. Numerical examples are worked out to validate the effectiveness of the proposed algorithms. [Copyright &y& Elsevier]

Complex regulatory networks often have to be further expanded and improved with regard to the unknown effects of additional parameters and factors that can emit a disturbing influence on the key variables under consideration. The concept of target-environment (TE) networks provides a holistic framework for the analysis of such parameter-dependent multi-modal systems. In this study, we consider time-discrete TE regulatory systems with spline entries. We introduce a new regression model for these particular two-modal systems that allows us to determine the unknown system parameters by applying the multivariate adaptive regression spline (MARS) technique and the newly developed conic multivariate adaptive regression spline (CMARS) method. We obtain a relaxation by means of continuous optimization, especially, conic quadratic programming (CQP) that could be conducted by interior point methods. Finally, a numerical example demonstrates the efficiency of the spline-based approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the qualitative behavior of following discrete-time population model: xn+1 = α + βxn + γxn-1e-yn,yn-1 = δ+ εyn + ζyn-1e-xn, where parameters α,β,γ,δ,ε,ζ and initial conditions x0, x-1, y0,y-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the stability of Runge–Kutta methods applied to the complex linear system . The condition under which the numerical solution is asymptotically stable is presented, which is stronger than A-stability and weaker than -stability. Furthermore, in the case of 2-norm and L being a real symmetric matrix, by using Pad approximation and order star theory, it is proved that for A-stable Runge–Kutta methods, suppose whose stability function is given by the -Pad approximation to , the numerical solution is asymptotically stable if and only if r is even. [Copyright &y& Elsevier]

Abstract: The simulation of complex systems is important in many fields of science and in real-world applications. Such systems are composed of many interacting subsystems. There might exist different software packages for simulating the individual subsystems and co-simulation refers to the simultaneous execution of multiple interacting subsystem simulators. Simulation or co-simulation, if not designed properly, can return misleading numerical solutions (unstable numerical solutions for what is in fact a stable system or vice versa). To understand the cause of these numerical artifacts, we first propose a simple mathematical model for co-simulation, and then construct stability charts. These charts shed light on transitions between stable and unstable behavior in co-simulation. Our goal is to understand the stability properties of the simulated and co-simulated representation of the continuous system. We will achieve this goal by expressing the trace and determinant of the discretized system in terms of the trace and determinant of the continuous system to establish stability criteria. [Copyright &y& Elsevier]

By means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related results of Barsegian et al. (2002). We also give some examples to show that our results occur in some special cases. [ABSTRACT FROM AUTHOR]

We consider the nonlinear pseudoparabolic equation with a memory term ut - Δu - Δut + ∫0t λ (t - τ) Δu (τ) dτ = div (|∇u|p-2u) + u1+α, x ∈ Ω, t > 0, with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions on p, α, and the relaxation function λ(t), we prove a finite-time blow-up result by using the concavity method. [ABSTRACT FROM AUTHOR]

Abstract: We investigate applications of the method of fundamental solutions (MFS) for the numerical solution of two-dimensional boundary value problems in complex geometries, governed by the Laplace equation and subject to Dirichlet boundary conditions which are not harmonic. Such problems can be very challenging because of the appearance of boundary singularities. We consider several ways of choosing the boundary collocation points as well as the source points in the MFS. We show that with an appropriate such choice the MFS yields highly accurate results. [Copyright &y& Elsevier]

Abstract: In the present paper we obtain a list of algebras, up to isomorphism, such that the closure of any complex finite-dimensional algebra contains one of the algebras of the given list. [Copyright &y& Elsevier]

We study the restricted projective dimension of complexes and give some new characterizations of the restricted projective dimension. In particular, it is shown that the restricted projective dimension can be computed in terms of the so-called restricted projective resolutions. As applications, we get some results on the behavior of the restricted projective dimension under the change of rings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex dynamical behaviors of a biological network that is derived from innate immune responses and that couples positive and negative feedback loops. The stability conditions of the non-negative equilibrium points (EPs) of the system are obtained, using the theory of dynamical systems, and we deduce that no more than three stable EPs exist in this system. Through bifurcation analysis and numerical simulations, we find that the system presents rich dynamical behaviors, such as monostability, bistability and oscillations. These results reveal how positive and negative feedback cooperatively regulate the dynamical behavior of the system. [ABSTRACT FROM AUTHOR]

In a previous paper the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The method applies in particular to complex cones and stratified Morse functions in the sense of the theory developed by Goresky and MacPherson. It is well-known from stratified Morse theory that the singular points of the complex cone contribute to the stratified Morse inequalities in middle degree only. In this paper, an analytic proof of this fact is given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study numerically quantized vortex dynamics and their interaction in the two-dimensional complex Ginzburg–Landau equation (CGLE) with a dimensionless parameter on bounded domains under either Dirichlet or homogeneous Neumann boundary condition. We begin with a review of the reduced dynamical laws (RDLs) for time evolution of quantized vortex centers in CGLE and show how to solve these nonlinear ordinary differential equations numerically. Then we present efficient and accurate numerical methods for solving the CGLE on either a rectangular or a disk domain under either Dirichlet or homogeneous Neumann boundary condition. Based on these efficient and accurate numerical methods for CGLE and the RDLs, we explore rich and complicated quantized vortex dynamics and interaction of CGLE with different ε and under different initial physical setups, including single vortex, vortex pair, vortex dipole and vortex lattice, compare them with those obtained from the corresponding RDLs, and identify the cases where the RDLs agree qualitatively and/or quantitatively as well as fail to agree with those from CGLE on vortex interaction. Finally, we also obtain numerically different patterns of the steady states for quantized vortex lattices in the CGLE dynamics on bounded domains. [Copyright &y& Elsevier]

Abstract: This paper examined the spectral properties of quadruple symmetric real functions. Theorem is formulated, under which the complex spectra of such symmetric functions are conjugated. The properties of the trigonometric functions are used in the proof of the theorem. Numerical results are presented for illustrating of the proven theorem. [Copyright &y& Elsevier]

Highlights: [•] Vibration analysis is achieved by the least cost of analysis and high accuracy of results. [•] The stability and accuracy of results have been evaluated, numerically. [•] We have examined a broad-frequency-content excitation governing on a MDOF structure. [•] We have examined efficiency of the proposed scheme on a large-scaled MDOF structure. [•] A complex and a simple wavelet functions have been considered, comparatively. [ABSTRACT FROM AUTHOR]

The sequence space BVć was introduced and studied by Mursaleen [9]. In this paper we extend BVć to BVć(M, p, q, r) on a seminormed complex linear space by using orlicz function. We give various properties and some inclusion relations on this space. [ABSTRACT FROM AUTHOR]

Abstract: We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations. [Copyright &y& Elsevier]

Abstract: The complex potential theory of two-dimensional decagonal quasicrystals is constructed and the complex variable method of Muskhelishvili is developed. Based on the complex representation of stresses and displacements, the arbitrariness and restrictions on the complex potentials are discussed. As an illustration of the complex potential theory, a decagonal quasicrystals plate with an elliptic notch under the action of stretch is considered. Some special cases of the results are also observed, which are helpful to check the correctness of the complex potential theory. [Copyright &y& Elsevier]

We prove the Gol’dberg conjecture, which states that the frequency of distinct poles of a meromorphic function f in the complex plane is governed by the frequency of zeros of the second derivative f″. As a consequence, we prove Mues’ conjecture concerning the defect relation for the derivatives of meromorphic functions in the complex plane. [ABSTRACT FROM PUBLISHER]