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The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated. [ABSTRACT FROM AUTHOR]

This article proposes a novel approach that leverages graph theory, machine learning, and graph embedding to evaluate research groups comprehensively. Assessing the performance and impact of research groups is crucial for funding agencies and research institutions, but many traditional methods often fail to capture the complex relationships between the evaluated elements. In this sense, our methodology transforms publication data into graph structures, allowing the visualization and quantification of relationships between researchers, publications, and institutions. By incorporating symmetry properties, we offer a more in-depth evaluation of research groups cohesiveness and structure over time. This temporal evaluation methodology bridges the gap between unstructured scientometrics networks and the evaluation process, making it a valuable tool for decision-making procedures. A case study is defined to demonstrate the potential to provide valuable insights into the dynamics and limitations of research groups, which ultimately reinforces the feasibility of the proposed approach when supporting decision making for funding agencies and research institutions. [ABSTRACT FROM AUTHOR]

The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated.

The symmetry properties of vibronic Hamiltonian of the linear G 3 / 2 , g × (t 2 g + e g) relativistic John-Teller system are investigated and the separation of angular and radial variables is achieved. Transformation to radial adiabatic representation allows us to obtain four biradial adiabatic potential energy surfaces. Two upper surfaces include potential wells and contain quasi discrete resonances. In this work we found the positions of low-lying resonances. [ABSTRACT FROM AUTHOR]

We give a detailed discussion of a nonlocal derivative nonlinear Schrödinger (NL-DNLS) equation with zero boundary conditions at infinity in terms of the inverse scattering transform. The direct scattering problem involves discussions of the analyticity, symmetries, and asymptotic behavior of the Jost solutions and scattering coefficients, and the distribution of the discrete spectrum points. Because of the symmetries of the NL-DNLS equation, the discrete spectrum is different from those for DNLS-type equations. The inverse scattering problem is solved by the method of a matrix Riemann–Hilbert problem. The reconstruction formula, the trace formula, and explicit solutions are presented. The soliton solutions with special parameters for the NL-DNLS equation with a reflectionless potential are obtained, which may have singularities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain all magic squares of size four, by using an Optimization Model where, in addition to the traditional restrictions (sums for rows, columns and diagonals), other restrictions related to four 2 x 2 submatrices, into which the square can be divided, are taken into account. It is shown that these additional restrictions are included in the traditional ones; therefore, all squares of size four could be classified as supermagic. The problem is represented by means of a Linear Programming Model in Integers with multiple solutions; which, when solved with the help of LINGO software, allowed to find the 880 squares that meet such restrictions. The way squares are presented makes it easy to locate them from characteristics referred to the position of number one. The different combinations for number one in any row for which these squares do not exist, are ordered.

This article proposes a novel approach that leverages graph theory, machine learning, and graph embedding to evaluate research groups comprehensively. Assessing the performance and impact of research groups is crucial for funding agencies and research institutions, but many traditional methods often fail to capture the complex relationships between the evaluated elements. In this sense, our methodology transforms publication data into graph structures, allowing the visualization and quantification of relationships between researchers, publications, and institutions. By incorporating symmetry properties, we offer a more in-depth evaluation of research groups cohesiveness and structure over time. This temporal evaluation methodology bridges the gap between unstructured scientometrics networks and the evaluation process, making it a valuable tool for decision-making procedures. A case study is defined to demonstrate the potential to provide valuable insights into the dynamics and limitations of research groups, which ultimately reinforces the feasibility of the proposed approach when supporting decision making for funding agencies and research institutions.

A new reading of westward intensification is put forward by decomposing the transport stream function in the sum of a couple of symmetric and anti-symmetric terms, relatively to the mirror reflection with respect to the central longitude of a reference basin, rectangular in shape and included into a certain beta plane. The consequence of the decomposition is twofold: first, the anti-symmetric term turns out to be a strict consequence of the latitudinal dependence of Coriolis acceleration, in the sense that it disappears in a hypothetical f-plane; second, whatever the wind forcing may be, the symmetric and anti-symmetric components of the meridional transport are always parallel in the western region of the basin and anti parallel in the eastern one. As a consequence of their superposition, the meridional transport is more energetic into the western region and it gives rise to the phenomenon of westward intensification. On the other hand, the components of the meridional transport tend to compensate each other in the eastern region in accordance with the Sverdrup balance. [ABSTRACT FROM AUTHOR]

This paper describes a digital application designed for learning Space Groups of Symmetry (SGS). It teaches how to recognize the operations performed by the symmetry elements, both point (or 2D) operators (proper and improper rotations, including mirroring, inversion, and other rotoinversions), and space (or 3D) operators (screw axes and glide planes), as well as their combinations with the translations of the lattice. The software applies a 3D space vision to identify the elements of symmetry compatible with the proposed structural models. The symbols of internationally accepted representation are used. The system, class, and space group of the crystal that agree with the proposed model are solved. Two settings are taken into account in the Monoclinic system. The application self-evaluates and assesses the knowledge acquired, allowing each exercise to be re-done until it is correctly completed with the appropriate recommendations. This application constitutes a useful and easy-to-use tool for SGS learning. It is aimed at beginner students of crystallography, with elementary knowledge about elements of symmetry, Bravais lattices, crystal classes, and wallpaper groups.

We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimensions 2 and 3. More precisely, we prove that stable solutions in dimension 2 and minimizers and monotone solutions in dimension 3 depend on only one Euclidean variable. Monotone solutions in the 2-dimensional case without weights were studied in de la Llave and Valdinoci (Math Res Lett 16(5):909–918, 2009). In our paper, a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument. [ABSTRACT FROM AUTHOR]

New classification of particles is proposed. This classification is based on U(Nf,g) ×SU(3c)×SU(4, fs)×O(3) -group, where U(Nf,g) corresponds to the particle generations, SU(3,c) - to the color, SU(4,fs) - to the flavor and the spin (instead of known SU(6,fs) -group), and O(3) - to the orbital excitation with the L -momentum. The Nf -number equals the quantity of fermion generations. From the convergence of the integrals corresponding to the Green functions for generalized Dirac equations and the continuity of these functions it follows that the minimal quantity of the Nf -number equals six. The homogeneous solutions of derived equations are sums of fields, corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the particle generations. For example, the electronic kind (e1 = e, e2 = μ, e3 =τ , e4, e5, e6, ), the kind of up-quarks (U1 = u, U2 = c, U3 = t, U4, U5, U6, ⋅⋅ ), and the kind of down-quarks (D1 = d, D2 = s, D4 = b, D4, D5, D6, ⋅⋅ ) can exist. Massless neutrino can be one only. The photonic and the gluonic kinds must include massive particles in addition to usual the photon and the gluon. At NF = 6 the nucleons and Δ(1232) belong to the 56×1×20×1 - representation. Lagrangians for the generalized Dirac equations of arbitrary order are derived.

We consider two-parameter real-valued parabolic diffraction-free beams. An analytical expression for the complex amplitude of the beam is obtained using the superposition of the Bessel functions. Symmetry properties of beams are analyzed and numerically demonstrated for different cases. The variety of the formed pictures increases significantly in comparison with earlier regarded parabolic beams. Particularly interesting properties exhibit beams with half-integer indices, they have symmetry properties different from the symmetry of beams with integer indices. For an arbitrary fractional index, the beams have a more complex distribution and do not have any symmetry. This fact facilitates the solution of the inverse problem when it is necessary to form similar structures, since just small changes in two parameters of the analytical expression are needed. This is much simpler than the implementation of iterative procedures, which, as a rule, provide essentially non-smooth solutions that are complex in optical implementation. Experimental generation of the fractional two-parameter parabolic beams is implemented for the first time by a spatial light modulator using phase coding of the calculated complex amplitudes. The different types of experimentally generated parabolic beams are in a good agreement with the modeling results. [ABSTRACT FROM AUTHOR]

The concept of sub-symmetry of a differential system was introduced in [ 40 ], where it was shown that a sub-symmetry is a considerably more powerful tool than a regular symmetry with regard to deformation of conservation laws. In this paper, we study the nature of a correspondence between sub-symmetries and conservation laws of a differential system. We show that for a large class of non-Lagrangian systems, there is a natural association between sub-symmetries and local conservation laws based on the Noether operator identity, and we prove an analogue of the first Noether theorem for sub-symmetries. We also demonstrate that a similar association can be established for infinite sub-symmetries of the system. We discuss the role of sub-symmetries in generation of infinite series of conservation laws for the constrained Maxwell system and the incompressible Euler equations of fluid dynamics. Despite the fact that infinite symmetries (with arbitrary functions of dependent variables) are not known for the Euler equations, we find infinite sub-symmetries for the two- and three-dimensional Euler equations with certain constraints. We show that these sub-symmetries generate known series of infinite conservation laws, and obtain new classes of infinite conservation laws. [ABSTRACT FROM AUTHOR]

Digital forensics practitioners encounter numerous new terminologies during time-intensive digital investigation processes because of the explosive growth of the web, an immense amount of data, and rapid changes in technology. In such a scenario, the time needed to find and interpret the cause of the potential digital incident can be affected by the complexity involved in understanding the meaning of newly encountered terminologies. Although various approaches have been designed to assist digital practitioners in understanding the newly encountered terminologies during the investigation of the accident, none of them is capable of supporting investigators to interpret new terminologies. Our work focuses on reconstructing and analyzing the timeline of events and artifacts backed by the abstraction concept to help practitioners in reasoning about the perceived meaning of different digital forensics terminologies that are encountered during the investigation. This paper introduces an ontological approach based on the abstraction concept to reconstruct the timeline provided by command-based digital forensic tools, i.e., Log2timeline and Psort in the L2TCSV format, and assist in resolving the meaning of new encountered concepts. The performed experiments show that the novel methodology is capable of enhancing the timeline and assisting practitioners in determining the significance of encountered terminologies or concepts.

This paper reviews the recent progress in the analysis and applications of the symmetry-related electromagnetic properties of transmission lines loaded with symmetric configurations of resonant elements. It will be shown that the transmission characteristics of these reactively loaded lines can be controlled by the relative orientation between the line and the resonant elements. Two main types of loaded lines are considered: (i) resonance-based structures; and (ii) frequency-splitting structures. In resonance-based transmission lines, a line is loaded with a single resonant (and symmetric) element. For a perfectly symmetric structure, the line is transparent if the line and resonator exhibit symmetry planes of different electromagnetic nature (electric or magnetic wall), whereas the line exhibits a notch (resonance) in the transmission coefficient if the symmetry planes behave as either electric or magnetic walls (symmetric configuration), or if symmetry is broken. In frequency-splitting lines, paired resonators are typically loaded to the transmission line; the structure exhibits a single notch for the symmetric configuration, whereas generally two split notches appear when symmetry is disrupted. Applications of these structures include microwave sensors (e.g., contactless sensors of spatial variables), selective mode suppressors (of application in common-mode suppressed differential lines, for instance) and spectral signature barcodes, among others.

• Group classification performed with the new method of indeterminates. • Soliton solutions and other solutions found by four different methods. • General results derived on properties of four order Lagrange equations. We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed method for group classification, termed the method of indeterminates. A model equation from the classified family of fourth order Lagrange equations is singled out. Travelling wave solutions of the latter are found through a similarity reduction by variational symmetry operators, followed by a double order reduction into a second order ordinary differential equation. Multi-soliton solutions and other exact solutions are also found by various methods including Lie group and Hirota methods. The most general action of the full symmetry group on any given solution is provided. Some remarkable facts on Lagrange equations emerging from the whole study are outlined. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the second eigenfunctions of the p- Laplacian, p > 1, are not radial on the unit ball in RN, for any N ⩾ 2. Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs {τn,ψn} such that ψn is nonradial and has exactly 2n nodal domains. A few related open problems are also stated. [ABSTRACT FROM AUTHOR]

The nonlinear generalized NLS equation in the sense of the Riemann-Liouville derivatives is considered. The symmetry properties of nonlinear generalized NLS equation is investigated by using the Lie group analysis method. By right of the obtained Lie point symmetries, it is shown that this equation could transform into a nonlinear ordinary differential equation of fractional order with the new independent variable. The derivative is an Erdélyi-Kober derivative depending on a parameter $$ \alpha $$ . [ABSTRACT FROM AUTHOR]

This paper reviews the recent progress in the analysis and applications of the symmetry-related electromagnetic properties of transmission lines loaded with symmetric configurations of resonant elements. It will be shown that the transmission characteristics of these reactively loaded lines can be controlled by the relative orientation between the line and the resonant elements. Two main types of loaded lines are considered: (i) resonance-based structures; and (ii) frequency-splitting structures. In resonance-based transmission lines, a line is loaded with a single resonant (and symmetric) element. For a perfectly symmetric structure, the line is transparent if the line and resonator exhibit symmetry planes of different electromagnetic nature (electric or magnetic wall), whereas the line exhibits a notch (resonance) in the transmission coefficient if the symmetry planes behave as either electric or magnetic walls (symmetric configuration), or if symmetry is broken. In frequency-splitting lines, paired resonators are typically loaded to the transmission line; the structure exhibits a single notch for the symmetric configuration, whereas generally two split notches appear when symmetry is disrupted. Applications of these structures include microwave sensors (e.g., contactless sensors of spatial variables), selective mode suppressors (of application in common-mode suppressed differential lines, for instance) and spectral signature barcodes, among others. [ABSTRACT FROM AUTHOR]

We study the nonlinear fractional equation $$(-\Delta )^su=f(u)$$ in $$\mathbb R ^n,$$ for all fractions $$0

Based on recent theoretical developments (Cremaschini and Tessarotto, 2011-2013), in this paper the issue is addressed of the first-principle construction of the nonlocal relativistic radiation-reaction (RR) equation for classical spherical-shell, finite-size particles and antiparticles. This is achieved invoking the axioms of Classical Electrodynamics by means of the Hamilton variational principle. In connection with this, the Lagrangian conservation laws, together with the possible existence of adiabatic invariants, and the transformation laws of the RR equation with respect to CPT and time-reversal transformations are investigated. The latter properties make possible the parametrization of the RR equations, holding respectively for particles and antiparticles of this type, in terms of the same coordinate time t and the investigation of the qualitative properties of their solutions. In particular, in both cases the RR self-force is found to have the same signature, which implies that the dynamics of classical finite-size antiparticles is equivalent to that of classical extended particles of opposite charge. Therefore, in the framework of Classical Mechanics, a distinction between particles and antiparticles cannot be made based solely on the electromagnetic interactions associated with electromagnetic RR phenomena. As a basic application of the theory, the Lagrangian conservation laws and symmetry properties for the Hamiltonian asymptotic approximations of the exact RR equation are also addressed. [ABSTRACT FROM AUTHOR]

The paper focuses on Bayesian confirmation measures used for evaluation of rules induced from data. To distinguish between many confirmation measures, their properties are analyzed. The article considers a group of symmetry properties. We demonstrate that the symmetry properties proposed in the literature focus on extreme cases corresponding to entailment or refutation of the rule's conclusion by its premise, forgetting intermediate cases. We conduct a thorough analysis of the symmetries regarding that the confirmation should express how much more probable the rule's hypothesis is when the premise is present rather than when the negation of the premise is present. As a result we point out which symmetries are desired for Bayesian confirmation measures. Next, we analyze a set of popular confirmation measures with respect to the symmetry properties and other valuable properties, being monotonicity M, Ex1 and weak Ex1, logicality L and weak L. Our work points out two measures to be the most meaningful ones regarding the considered properties. [ABSTRACT FROM AUTHOR]

We prove a version of the Titchmarsh convolution theorem for distributions on the circle. We show that a certain 'naïve' form of the Titchmarsh theorem can be violated, but only for the convolution of distributions with certain symmetry properties. [ABSTRACT FROM AUTHOR]

We consider the semilinear electromagnetic Schrödinger equation $${(-i{\nabla} + \mathcal{A}(x))^{2}u + V (x)u = |u|^{{2}^{\ast}-2}u, u\, {\in}\, D_{\mathcal{A},0}^{1,2}{(\Omega,\mathbb{C})}}$$, where $${\Omega = (\mathbb{R}^{m}\;{\backslash}\;\{0\}) {\times} {\mathbb{R}^{N-m}}}$$ with 2 ≤ m ≤ N, N ≥ 3, 2* : = 2 N/( N - 2) is the critical Sobolev exponent, V is a Hardy term and $${\mathcal{A}}$$ is a singular magnetic potential of a particular form which includes the Aharonov- Bohm potentials. Under some symmetry assumptions on $${\mathcal{A}}$$ we obtain multiplicity of solutions satisfying certain symmetry properties. [ABSTRACT FROM AUTHOR]

Within the National Environmental Satellite, Data, and Information Service, National Oceanic and Atmospheric Administration, multiplatform synthetic aperture radar (SAR) imagery is being used to aid post hurricane and postaccident response efforts in the Gulf of Mexico, such as in the case of the recent Deepwater Horizon oil spill. The main areas of interest related to such disasters are the following: (1) to identify oil pipeline leaks and other oil spills at sea and (2) to detect man-made metallic targets over the sea. Within the context of disaster monitoring and response, an innovative processing chain is proposed to observe oil fields (i.e., oil spills and man-made metallic targets) using both Land C-band full-resolution and fully polarimetric SAR data. The processing chain consists of two steps. The first one, based on the standard deviation of the phase difference between the copolarized channels, allows oil monitoring. The second one, based on the different symmetry properties that characterize man made metallic targets and natural distributed ones, allows man made metallic target observation. Experiments, accomplished over single-look complex L-band Advanced Land Observing Satellite (ALOS) Phased Array type L-band Synthetic Aperture Radar (PALSAR) and C-band RADARSAT-2 fully polarimetric SAR data gathered in the Gulf of Mexico and related to the Deepwater Horizon accident, show the effectiveness of the proposed approach. Furthermore, the proposed approach, being able to process both Land C-band fully polarimetric and full resolution SAR measurements, can take full benefit of both the ALOS PALSAR and RADARSAT-2 missions, and therefore, it allows enhancing the revisit time and coverage which are very critical issues in oil field observation. [ABSTRACT FROM PUBLISHER]

We consider the magnetic nonlinear Schrödinger equations in $${\Omega=\mathcal{O}\times \mathbb{R}}$$, where $${\mathcal{O}}$$ is an open subset of $${\mathbb{R}^{2}{\smallsetminus}\{0\}, s\in\mathbb{R}}$$, and $${A:\Omega\rightarrow\mathbb{R}^{3}}$$ is the Aharonov–Bohm magnetic potential We prove multiplicity results and describe the symmetry properties of the solutions obtained. [ABSTRACT FROM AUTHOR]

Spatiochromatic information of colour images is analysed in sequency domain using CIE La*b* colour space. RGB image is processed in transform domain using spatiochromatic‐conjugate symmetric sequency ordered complex Hadamard transform (SC‐CS‐SCHT). Spatiochromatic vectors (a*, b* and a*b*) are considered as real, imaginary and complex inputs to the SC‐CS‐SCHT. This transform has symmetry properties that are similar to the discrete Fourier transform. Resultant phasor paths are observed with respect to different input signals along the unit complex plane. In sequency domain opponent colour paths are discussed and applied on two‐dimensional signals. Peak signal‐to‐noise ratio is measured for ideal lowpass filter. [ABSTRACT FROM AUTHOR]

Abstract: We introduce the class of bivariate copulas with piecewise linear horizontal sections whose graph is composed, at most, of two segments. It is a wide class of copulas which contains some known copulas. We study several properties of the copulas in the new class concerning absolute continuity, singular components, measures of association, concordance ordering, dependence concepts and symmetry. Finally, we provide several examples. [Copyright &y& Elsevier]

This paper describes a digital application designed for learning Space Groups of Symmetry (SGS). It teaches how to recognize the operations performed by the symmetry elements, both point (or 2D) operators (proper and improper rotations, including mirroring, inversion, and other rotoinversions), and space (or 3D) operators (screw axes and glide planes), as well as their combinations with the translations of the lattice. The software applies a 3D space vision to identify the elements of symmetry compatible with the proposed structural models. The symbols of internationally accepted representation are used. The system, class, and space group of the crystal that agree with the proposed model are solved. Two settings are taken into account in the Monoclinic system. The application self-evaluates and assesses the knowledge acquired, allowing each exercise to be re-done until it is correctly completed with the appropriate recommendations. This application constitutes a useful and easy-to-use tool for SGS learning. It is aimed at beginner students of crystallography, with elementary knowledge about elements of symmetry, Bravais lattices, crystal classes, and wallpaper groups. [ABSTRACT FROM AUTHOR]

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for non-linear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband. [ABSTRACT FROM AUTHOR]

A structural phase transition from space-group symmetry P21/ c to C2/ c is reported for NaTaOGeO4 (NTGO). The critical temperature has been located at Tc = 116 K, based on the appearance of sharp diffraction maxima at positions h + k = 2 n + 1 of reciprocal space on cooling below this temperature. Strongly anisotropic diffuse scattering in sheets normal to [001] is observable for T > Tc and persists up to ambient temperature. Similarities to phase transitions observed in other compounds of the titanite structure type are discussed. The symmetry properties of these phase transitions are reassessed on the basis of the structural data available. The primary order parameter is identified with the displacement of the transition metal cation M ( M = Ta in NTGO) away from the centre of symmetry that it nominally occupies in the paraphase. The order parameter transforms as the Y representation. The anisotropic diffuse scattering is attributed to the one-dimensional correlation of local M displacements parallel to the direction of chains of trans-corner-sharing MO6 octahedra. The critical temperatures of the isomorphous phase transitions in various titanite-type compounds depend linearly on the squared transition-metal displacement measured in the ordered P21/ c phase. [ABSTRACT FROM AUTHOR]

Abstract: The Fučík spectrum for systems of second order ordinary differential equations with Dirichlet or Neumann boundary values is considered: it is proved that the Fučík spectrum consists of global surfaces, and that through each eigenvalue of the linear system pass exactly two of these surfaces. Further qualitative, asymptotic and symmetry properties of these spectral surfaces are given. Finally, related problems with nonlinearities which cross asymptotically some eigenvalues, as well as linear–superlinear systems are studied. [Copyright &y& Elsevier]

A new class of copulas, depending on a univariate function, is studied and its properties (dependence, ordering, measures of association, symmetry) are investigated. [ABSTRACT FROM AUTHOR]

Abstract: Eigenstates and associated eigenvalues of a quantum-mechanical particle confined to a three-dimensional arbitrarily curved nanowire structure are determined. Special emphasis is given to the influence of nanowire geometry and curvature effects which are expected to play important roles for the physical properties of several nanowire structures recently grown in laboratories. Use of differential-geometry arguments allows separation of the three-dimensional Schrödinger equation into either (i) two partial differential equations plus one ordinary differential equation in the general nanowire cross-section case or [for simple cross-sectional nanowire shapes] (ii) three ordinary differential equations (ODEs) in appropriate curved coordinates for the case where the cross-sectional area is constant along the nanowire axis. Problems corresponding to item (ii) with three ODEs can be solved either completely analytically or by use of a simple one-dimensional finite-difference scheme. Three case studies are finally analyzed in details: the rectangular cross-sectional-shaped nanowire with a (a) straight-line axis, (b) a circular-shaped axis, and (c) the sinusoidal-shaped nanowire axis including discussion of symmetry properties. [Copyright &y& Elsevier]

The entanglement of formation as well as the conditional entropy can be used to define leaves in the state space, given by the linear superposition of their extremal points. Examples, where these leaves can be found and can be used to calculate the entanglement respectively the conditional entropy are presented. The definition of entanglement is generalized to infinite systems and allows again to find a leaf structure. Finally we remark on the additivity property of both expressions, offering a counter example to the additivity of the conditional entropy. [ABSTRACT FROM AUTHOR]

Summary form only given. We describe the use of symmetry for verification of transistor-level circuits by symbolic trajectory evaluation (STE). We present a new formulation of STE which allows a succinct description of symmetry properties in circuits. Symmetries in circuits are classified as structural symmetries, arising from similarities in circuit structure, data symmetries, arising from similarities in the handling of data values, and mixed structural-data symmetries. We use graph isomorphism testing and symbolic simulation to verify the symmetries in the original circuit. Using conservative approximations, we partition a circuit to expose the symmetries in its components, and construct reduced system models which can be verified efficiently. Introducing X-drivers into switch-level circuits simplifies the task of creating conservative approximations of switch-level circuits. Our empirical results show that exploiting symmetry with conservative approximations can allow one to verify systems several orders of magnitude larger than otherwise possible. We present results of verifying Static Random Access Memory (SRAM) circuits with up to 1.5 million transistors [ABSTRACT FROM PUBLISHER]