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1
Carpinelli, G. "Generalised convertor models for iterative harmonic analysis in power systems". IEE Proceedings - Generation, Transmission and Distribution 141, nr 5 (1994): 445. http://dx.doi.org/10.1049/ip-gtd:19941212.
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Lehar, S. "Generalised Model of Illusory Grouping Accounts for Collinear, Orthogonal, and Vertex Grouping Percepts". Perception 25, nr 1_suppl (sierpień 1996): 91. http://dx.doi.org/10.1068/v96l0704.
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A number of illusory phenomena, for example the Kanizsa illusion, exhibit boundary completion by collinearity between visible inducing edges. These phenomena have been addressed by models such as Grossberg's boundary contour system (BCS) (1985 Psychological Review92 173 – 211), which incorporates collinearity cells with receptive fields specialised to detect and enhance collinearity. Other illusory phenomena like the Ehrenstein illusion exhibit boundary completion orthogonal to the oriented inducers. The BCS model explains such orthogonal grouping by disinhibition, due to competition between collinearity cells of orthogonal orientations. There are many illusory grouping phenomena, however, which exhibit boundary completion through sharp corners in a variety of configurations, producing illusory ‘V’ or ‘Y’ vertices. Examples are seen in the diamond percept of the four-line Ehrenstein illusion, the triangular grouping percept of three dots arranged in a triangular configuration, as well as in the hexagonal percept of a grid of dots in a honeycomb pattern. These completions cannot be explained by models based on collinearity. Lehar's orientational harmonic model (1994, PhD thesis, Boston University) offers a single generalised grouping mechanism capable of collinear, orthogonal, and sharp vertex grouping. The proposed mechanism is a harmonic resonance, or pattern of standing waves in the orientational representation which promotes orientational periodicity. Computer simulations show that the model can account for a large number of diverse illusory phenomena using a single simple mechanism, and predicts the specific conditions under which a grouping of one type yields to a different grouping type.
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PALUMBO, P., i L. PIRODDI. "HARMONIC ANALYSIS OF NON-LINEAR STRUCTURES BY MEANS OF GENERALISED FREQUENCY RESPONSE FUNCTIONS COUPLED WITH NARX MODELS". Mechanical Systems and Signal Processing 14, nr 2 (marzec 2000): 243–65. http://dx.doi.org/10.1006/mssp.1999.1264.
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Loo, Tee-How, Avik De, Sanjay Mandal i P. K. Sahoo. "How a projectively flat geometry regulates F(R)-gravity theory?" Physica Scripta 96, nr 12 (1.12.2021): 125034. http://dx.doi.org/10.1088/1402-4896/ac3a51.
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Abstract In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.
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Yao, Yuan, i Longyun Kang. "The Virtual Harmonic Power Droop Strategy to Mitigate the Output Harmonic Voltage of the Inverter". Energies 11, nr 9 (22.08.2018): 2196. http://dx.doi.org/10.3390/en11092196.
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The harmonic voltage issue becomes a challenge for a distributed generation system. Considering that droop control is the most common control algorithm used in the distributed system, a virtual harmonic power droop strategy which aims to mitigate the harmonic voltage is proposed in this paper. First, the conventional droop control is analyzed. Based on that concept, the virtual power algorithm is introduced. Second, the output harmonic voltage issue and the mathematical model of the inverter are presented. In addition, the second-order generalized integrator is briefly discussed. Third, taking into consideration the algorithms and models presented, a virtual harmonic power droop strategy is proposed to implement the harmonic voltage mitigation. In this algorithm, signals in fundamental frequency and harmonic frequency are separated with the help of second-order generalized integrators. Unlike the conventional voltage–current dual loop structure which is used to mitigate system harmonics, this method only needs the virtual power feedback to mitigate the harmonic voltage. Based on these features, the system’s control structure is simplified. Simulation and experimental results verified the harmonic voltage mitigation ability of the proposed strategy.
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Mahadik, Mujeeb Khan Habib, Hassan Bahrami, Mofazzal Hossain i Tsar Mitchel. "Production decline analysis and forecasting in tight-gas reservoirs". APPEA Journal 52, nr 1 (2012): 573. http://dx.doi.org/10.1071/aj11045.
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Exponential decline curve analysis is widely used to estimate recoverable reserves due to its simplicity. In most cases, however, an exponential model cannot provide a satisfactory match of overall production history. The generalised form of a hyperbolic decline model is more powerful in matching production history than the other decline models, but it is difficult to apply in practical production data analysis since it requires predicting two unknowns as decline constants. Although a hyperbolic model may provide a good fit to early-time production decline data; it may overestimate the late-time production, especially for hydraulic fractured wells in a tight-gas reservoir. In fact, the exponential decline model might be more reliable for forecasting the late-time production. This paper presents a practical approach to production decline analysis for non-fractured and fractured wells in a tight-gas reservoir using numerical simulation. Some production rate functions and type curves are introduced to obtain the best matching values of hyperbolic, exponential and harmonic production decline constants. The simulated production rate decline data for various well and reservoir parameters are used to indicate the optimum time duration of use of each decline model and to show the time when the production decline starts following the exponential model. The proposed approach is applied in production data analysis and forecasting for a tight-gas field in WA. The results showed good agreement with the production forecast obtained from a reservoir simulation.
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XIE, GUANGLONG, i BUHAN ZHANG. "PROBABILISTIC HARMONIC ANALYSIS OF WIND GENERATORS BASED ON GENERALIZED GAMMA MIXTURE MODELS". Modern Physics Letters B 27, nr 03 (13.12.2012): 1350020. http://dx.doi.org/10.1142/s0217984913500206.
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Grid-connected wind generators pose the power quality problems such as harmonic propagation and summation, and these problems are hard to solve by deterministic harmonic analysis due to the random harmonic current emissions. In this paper, probabilistic harmonic analysis is utilized to approximate harmonic currents of wind generators. Generalized gamma mixture models based on Gaussian mixture models, phasor clustering and generalized gamma models, are proposed to approximate the probability density functions of harmonic propagation and summation. And the simulation network built on PSCAD/EMTDC is utilized to verify the proposed models and method.
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Ray, A., T. K. Dey i S. K. Ghatak. "Low Field Second Harmonic Response and AC Susceptibility of (Bi,Pb)-2223 Pellet in a Generalized Critical State Model". International Journal of Modern Physics B 17, nr 21 (20.08.2003): 3831–46. http://dx.doi.org/10.1142/s0217979203021848.
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The AC susceptibility and second harmonic response of bulk high Tc superconductor (Bi,Pb) -2223 is measured in presence of small AC field excitation and DC magnetic field superimposed on it. This response increases with the increase in DC field whereas decreases at a higher excitation amplitude. Critical state models are used to explain the nonlinear magnetic response in HTSCs. With a generalized field dependence of critical current Jc : Jc(B) = J0/(1 + B/B0)n, the fundamental AC susceptibility and low field second harmonics response are calculated for different n values. It is found that the theoretical consideration adopted here explains the observed AC susceptibility and low field second harmonic response qualitatively reasonably well within the Anderson–Kim regime (n = 1).
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Sitepu, Husin. "Texture and structural refinement using neutron diffraction data from molybdite (MoO3) and calcite (CaCO3) powders and a Ni-rich Ni50.7Ti49.30 alloy". Powder Diffraction 24, nr 4 (grudzień 2009): 315–26. http://dx.doi.org/10.1154/1.3257906.
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Preferred orientation or texture is a common feature of experimental powder patterns. The mathematics of two commonly used models for preferred orientation—the March-Dollase and the generalized spherical-harmonic models—is reviewed. Both models were applied individually to neutron powder data from uniaxially pressed molybdite (MoO3) and calcite (CaCO3) powders in Rietveld analyses, as well as the as-received powders. The structural refinement results are compared to single-crystal structures. The results indicate that reasonable refinement of crystal structures can be obtained using either the March model or generalized spherical-harmonic description. However, the generalized spherical-harmonic description provided better Rietveld fits than the March model for the molybdite and calcite. Therefore, the generalized spherical-harmonic description is recommended for correction of preferred orientation in neutron diffraction analysis for both crystal structure refinement and phase composition analysis. Subsequently, the generalized spherical-harmonic description is extended to crystal structure refinement of annealed and the aged polycrystalline Ni-rich Ni50.7Ti49.30 shape memory alloys.
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Van Nimmen, Katrien, Benedicte Vanwanseele i Peter Van den Broeck. "Reconstruction of the Vertical Dynamic Running Load from the Registered Body Motion". Vibration 5, nr 3 (25.07.2022): 464–82. http://dx.doi.org/10.3390/vibration5030026.
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In view of in-field applications, this paper introduces a methodology that uses the registered body motion to reconstruct the vertical dynamic running load. The principle of the reconstruction methodology is to use the time-variant pacing rate that is identified from the body motion together with a generalized single-step load model available in the literature. The methodology is reasonably robust against measurement noise. The performance of the methodology is evaluated by application to an experimental dataset where the running load and the body motion were registered simultaneously. The results show that a very good fit is found with the measured forces, with coefficients of determination of 95% in the time domain and 98% for the amplitude spectrum. Considering a 90% confidence interval, the fundamental harmonic is shown to be reconstructed with a maximum error of 12%. With nearly 90% of the energy concentrated around the fundamental harmonic, this harmonic is the dominant component of the running load. Due to the large inter-person variability in the single-step load pattern, a generalized single-step load model does not arrive at a good fit for the higher harmonics: the reproduction errors easily exceed 50% for a 90% confidence interval. Finally, the methodology is applied to reproduce the dynamic running load induced during full-scale tests on a flexible footbridge. The tests are designed such that the structural response is governed by the (near-)resonant contribution of the fundamental harmonic of the running load. The results show that even when a 12% uncertainty bound is taken into account, the structural response is significantly over-estimated by the numerical simulations (up to 50%). These results suggest a non-negligible impact of other phenomena, such as human–structure interaction, that are not accounted for in current load models.
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Wang, Jian, LingLing Shen, LeSheng Jin i Gang Qian. "Age Sequence Recursive Models for Long Time Evaluation Problems". International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, nr 02 (kwiecień 2018): 299–325. http://dx.doi.org/10.1142/s0218488518500162.
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The evaluation models for long time historical data is important in many applications. In this study, based on Age measure defined by Yager, we propose the definitions of Age Sequence and Age Series. Then, we provide a Generalized Recursive Smoothing method. Some classical smoothing models in evaluation problems can be seen as special cases of Generalized Recursive Smoothing method. In order to obtain more reasonable and effective aggregation results of the historical data, we propose some different Age Sequences, e.g., the Generalized Harmonic Age Sequence and p Age Sequence, which theoretically can provide infinite more recursive smoothing methods satisfying different preferences of decision makers.
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Sitepu, Husin, Brian H. O'Connor i Deyu Li. "Comparative evaluation of the March and generalized spherical harmonic preferred orientation models using X-ray diffraction data for molybdite and calcite powders". Journal of Applied Crystallography 38, nr 1 (19.01.2005): 158–67. http://dx.doi.org/10.1107/s0021889804031231.
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Preferred crystallographic orientation,i.e.texture in crystalline materials powder diffraction data, can cause serious systematic errors in phase composition analysis and also in crystal structure determination. The March model [Dollase (1986).J. Appl. Cryst.19, 267–272] has been used widely in Rietveld refinement for correcting powder diffraction intensities with respect to the effects of preferred orientation. In the present study, a comparative evaluation of the March model and the generalized spherical harmonic [Von Dreele (1997).J. Appl. Cryst.30, 517–525] description for preferred orientation was performed with X-ray powder diffraction data for molybdite (MoO3) and calcite (CaCO3) powders uniaxially pressed at five different pressures. Additional molybdite and calcite powders, to which 50% by weight silica gel had been added, were prepared to extend the range of preferred orientations considered. The patterns were analyzed initially assuming random orientation of the crystallites and subsequently the March model was used to correct the preferred orientation. The refinement results were compared with parallel refinements conducted with the generalized spherical harmonic [Sitepu (2002).J. Appl. Cryst.35,274–277]. The results obtained show that the generalized spherical harmonic description generally provided superior figures-of-merit compared with the March model results.
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Popa, Nicolae C. "Spherical harmonics analysis based on the Reuss model in elastic macro strain and stress determination by powder diffraction". Journal of Applied Crystallography 50, nr 6 (14.11.2017): 1735–43. http://dx.doi.org/10.1107/s1600576717014431.
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In this paper a new approach to macro strain/stress analysis by generalized spherical harmonics is presented. It consists of expanding the stress tensor weighted by texture in a series of generalized spherical harmonics with the ground state of expansion specific to the classical Reuss model of an isotropic polycrystal. Like previously reported models having a ground state of hydrostatic type [Popa & Balzar (2001).J Appl Cryst.34, 187–195] and of Voigt type [Popaet al.(2014).J Appl Cryst.34, 154–159], the actual model is appropriate for use with Rietveld refinement.
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SHOJAEI, M. R., i A. A. RAJABI. "THREE-BODY FORCE MODELS OF NONHYPERCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN THREE-DIMENSIONAL POTENTIALS". Modern Physics Letters A 23, nr 40 (28.12.2008): 3411–17. http://dx.doi.org/10.1142/s0217732308027291.
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We present a theoretical approach to the internal motion of a system based on three-body forces among particles in a special case, using three-body potentials. The three-body force models are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of the Jacobian relative coordinates ρ, λ and R. The problems related to three-body nonhypercentral potentials in three dimensions are investigated. While the difficulties that arise in the study of nonhypercentral potentials are explicitly shown, we discuss some results obtained using nonhypercentral harmonic and anharmonic and some inverse power terms; however the potential can be easily generalized in order to allow a systematic analysis, which presents an exact solution to the wave function. The method is also applied to some other types of potentials.
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Alhulaimi, B., R. J. van den Hoogen i A. A. Coley. "Spatially homogeneous Einstein-aether cosmological models: scalar fields with a generalized harmonic potential". Journal of Cosmology and Astroparticle Physics 2017, nr 12 (28.12.2017): 045. http://dx.doi.org/10.1088/1475-7516/2017/12/045.
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Safaryan, V. S. "STUDY OF TRANSIENT AND STATIONARY OPERATION MODES OF SYNCHRONOUS SYSTEM CONSISTING IN TWO MACHINES". ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations 60, nr 3 (17.05.2017): 228–36. http://dx.doi.org/10.21122/1029-7448-2017-60-3-228-236.
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The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes. During the functioning of electric power system in asynchronous regime, besides the main frequencies, the currents and voltages include harmonic components, the frequencies of which are multiple of the difference of main frequencies. At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors. Also, in the article varieties of mathematical models of EPS transient regimes (trivial, simple, complete) are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings. When there are two excitation windings on the rotor (dual system of excitation), the mathematical model of electromagnetic transient processes of a synchronous machine is represented in a complex form, i.e. in coordinate system d, q, the current of rotor being represented by a generalized vector. In asynchronous operation of a synchronous two-machine system with two excitation windings on the rotor the current and voltage systems include only harmonics of two frequencies. The mathematical model of synchronous steady-state process of a two-machine system is also provided, and the steady-state regimes with different structures of initial information are considered.
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Addazi, Andrea, i Homa Shababi. "Aspects of nonperturbative GUP models". International Journal of Modern Physics A 35, nr 32 (2.11.2020): 2042002. http://dx.doi.org/10.1142/s0217751x20420026.
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We review on further new developments of Generalized Uncertainty Principle (GUP) and implications for the cosmological vacuum energy. First, we introduce basic aspects of GUP as well as several possible different and viable formulation of it. Second, we move on discussing two recent new types of higher D-dimensional nonperturbative GUP models; which we dub D-Type-I and D-Type-II GUPs. The D-Type-I and D-Type-II GUPs are both related to the existence of a critical conspiracy between a minimal uncertainty length and a maximal observable momentum. Finally, we show direct implications of D-Type-I and D-Type-II on the cosmological vacuum energy obtained in quantum mechanical systems such as the typical quantum harmonic oscillator. Such a computation goes through investigations of the density of states for D-dimensional coordinate systems in the momentum space. We will also comment on several possible connections with fundamental issues of quantum gravity such as black hole physics and gravitational radiative aspects.
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Biedermann, Stefanie, i David C. Woods. "Optimal designs for generalized non-linear models with application to second-harmonic generation experiments". Journal of the Royal Statistical Society: Series C (Applied Statistics) 60, nr 2 (13.01.2011): 281–99. http://dx.doi.org/10.1111/j.1467-9876.2010.00749.x.
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MATOS, TONATIUH, i ALFREDO MACÍAS. "BLACK HOLES FROM GENERALIZED CHATTERJEE SOLUTIONS IN DILATON GRAVITY". Modern Physics Letters A 09, nr 40 (28.12.1994): 3707–12. http://dx.doi.org/10.1142/s0217732394003555.
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In the framework of the dilaton gravity theory, we consider the Papapetrou metric together with the harmonic maps ansatz in order to find exact solutions for the field equations of the theory. By this means a generalized four-dimensional solution is obtained which for definite values of the dilaton coupling constant (α) reduces to solutions of the four-dimensional Einstein-Dilaton theory, low energy strings models and Kaluza-Klein theories. In particular, for the last case it contains the four-dimensional version of the well-known Chatterjee solution.
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Raisanen, Ville, Saku Suuriniemi i Lauri Kettunen. "Generalized Slip Transformations and Air-Gap Harmonics in Field Models of Electrical Machines". IEEE Transactions on Magnetics 52, nr 9 (wrzesień 2016): 1–8. http://dx.doi.org/10.1109/tmag.2016.2561907.
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Garcia, R. D. M., i C. E. Siewert. "A generalized spherical harmonics solution for radiative transfer models that include polarization effects". Journal of Quantitative Spectroscopy and Radiative Transfer 36, nr 5 (listopad 1986): 401–23. http://dx.doi.org/10.1016/0022-4073(86)90097-x.
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Zrazhevsky, G. M., i V. F. Zrazhevska. "Usage of generalized functions formalism in modeling of defects by point singularity". Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, nr 1 (2019): 58–61. http://dx.doi.org/10.17721/1812-5409.2019/1.12.
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The paper proposes a new approach to the construction of point defect models, based on the solution of boundary value problems with non smooth coefficients. Heterogeneity is included in the determining equation of the boundary problem. This approach allows us to formalize defects at the stage of use of state equations, and thus automatically reconciles the defect with the hypotheses of diminution of dimension and does not break the energy closed. The solution is sought in the form of weakly convergent series of generalized functions. The proposed approach simplifies the mechanical interpretation of defect parameters and is demonstrated in several examples. In the first example, the Green function for harmonic oscillations of an elastic beam with a point defect is constructed. The defect model is a limiting state of elastic inclusion with weakening or strengthening. The second example considers the inclusion of an elliptical shape in the problem of harmonic oscillations of the elastic plate. The first approximation of the equivalent volumetric force is constructed and the path to the following approximations is indicated. In the third example, a model of a brittle crack with a known displacement jump is constructed for a static two-dimensional problem of elasticity theory.
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GRUNDLAND, A. M., i İ. YURDUŞEN. "SURFACES OBTAINED FROM ℂPN-1 SIGMA MODELS". International Journal of Modern Physics A 23, nr 32 (30.12.2008): 5137–57. http://dx.doi.org/10.1142/s0217751x08042699.
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In this paper, the Weierstrass technique for harmonic maps S2 → ℂPN-1 is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the ℂPN-1 model equations are defined on the sphere S2 and the associated action functional of this model is finite, then the generalized Weierstrass formula for immersion describes conformally parametrized surfaces in the su (N) algebra. In particular, for any holomorphic or antiholomorphic solution of this model the associated surface can be expressed in terms of an orthogonal projector of rank (N - 1). The implementation of this method is presented for two-dimensional conformally parametrized surfaces immersed in the su (3) algebra. The usefulness of the proposed approach is illustrated with examples, including the dilation-invariant meron-type solutions and the Veronese solutions for the ℂP2 model. Depending on the location of the critical points (zeros and poles) of the first fundamental form associated with the meron solution, it is shown that the associated surfaces are semiinfinite cylinders. It is also demonstrated that surfaces related to holomorphic and mixed Veronese solutions are immersed in ℝ8 and ℝ3, respectively.
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EL-NABULSI, AHMAD RAMI. "THE FRACTIONAL CALCULUS OF VARIATIONS FROM EXTENDED ERDÉLYI-KOBER OPERATOR". International Journal of Modern Physics B 23, nr 16 (30.06.2009): 3349–61. http://dx.doi.org/10.1142/s0217979209052923.
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Fractional calculus of variations (FCV) has recently attracted considerable attention as it is deeply related to the fractional quantization procedure. In this work, the FCV from extended Erdélyi-Kober fractional integral is constructed. Our main goal is to exhibit a general treatment for dissipative systems, in particular the harmonic oscillator (HO) that has time-dependent mass and time-dependent frequency. The general linear equation of damped Erdélyi-Kober harmonic oscillator is constructed from which a time-dependent mass generalized law was derived exhibiting different types of behavior. This relatively new time-dependent mass law permits us to point out several possible cases simultaneously in contrast to many models discussed in the literature and without making use of any types of fractional derivatives. Some results on Hamiltonian part, namely Hamilton equations for the damped HO were obtained and discussed in detail.
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Bhagat, Kaushik Y., Baibhab Bose, Sayantan Choudhury, Satyaki Chowdhury, Rathindra N. Das, Saptarshhi G. Dastider, Nitin Gupta, Archana Maji, Gabriel D. Pasquino i Swaraj Paul. "The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions". Symmetry 13, nr 1 (30.12.2020): 44. http://dx.doi.org/10.3390/sym13010044.
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The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional Potential Well problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.
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Fitzpatrick, R. "Multi-harmonic Rutherford island theory". Physics of Plasmas 29, nr 9 (wrzesień 2022): 092501. http://dx.doi.org/10.1063/5.0099489.
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Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans [Phys. Rev. Lett. 126, 085003 (2021)] recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.
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BANDOS, IGOR A., i WOLFGANG KUMMER. "p-BRANES, POISSON-SIGMA MODELS AND EMBEDDING APPROACH TO (p+1)-DIMENSIONAL GRAVITY". International Journal of Modern Physics A 14, nr 31 (20.12.1999): 4881–914. http://dx.doi.org/10.1142/s0217751x99002311.
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A generalization of the embedding approach for d-dimensional gravity based upon p-brane theories is proposed. We prove that the D-dimensional p-brane coupled to an antisymmetric tensor field of rank (p+1) provides the dynamical basis for the description of d=(p+1)-dimensional gravity in the isometric embedding formalism. By that we mean that the equations of motion following from this action describe any (p+1)-dimensional space–time (at least locally) once the antisymmetric tensor field is chosen appropriately. "Physical" matter appears in such an approach as a manifestation of a D-dimensional antisymmetric tensor (generalized Kalb–Ramond) background. For the simplest case, the Lorentz harmonic formulation of the bosonic string in a Kalb–Ramond background and its relation to a first order Einstein–Cartan approach for (d=2)-dimensional gravity is analyzed in some detail. We show that a general Poisson-sigma model structure emerges in this case. For the minimal choice of a free D=3 string an interesting "dual" formulation is found which has the structure of a Jackiw–Teitelboim theory, coupled minimally to a massive scalar field. Our approach is intended to serve as a preparation for the study of d-dimensional supergravity theory, either starting from the generalized action of free supersymmetric (d-1)-branes or D(d-1)-branes, or from the corresponding geometric equations ("rheotropic" conditions).
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Zenkour, Ashraf M. "TWO-DIMENSIONAL COUPLED SOLUTION FOR THERMOELASTIC BEAMS VIA GENERALIZED DUAL-PHASE-LAGS MODEL". Mathematical Modelling and Analysis 21, nr 3 (19.05.2016): 319–35. http://dx.doi.org/10.3846/13926292.2016.1157835.
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The generalized thermoelastic problem of a thick-walled simply-supported beam subjected to different applied heat source and mechanical loads at its surfaces is studied. The thermoelastic coupling differential equations of motion of the beam are established. The generalized thermoelasticity based on the dual-phase-lags (DPLs) theory is considered to treat this problem. An exact 2-D coupled solution is presented to deduce analytical expressions for the temperature, displacements and stresses. The time-harmonic motion behavior as well as the thermal and mechanical conditions at the bounded faces of the beam is used for this purpose. The effect of the DPLs on the field quantities against the axial and normal directions of the beam under thermomechanical loads is discussed. Final investigations to various thermoelastic models are made.
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Tenzer, Robert. "Mathematical models of the Earth’s density structure and their applications in gravimetric forward modeling". Contributions to Geophysics and Geodesy 45, nr 2 (1.06.2015): 67–92. http://dx.doi.org/10.1515/congeo-2015-0014.
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Abstract A generalized mathematical model of the Earth’s density structure is presented in this study. This model is defined based on applying the spectral expressions for a 3-D density distribution within the arbitrary volumetric mass layers. The 3-D density model is then converted into a form which describes the Earth’s density structure by means of the density-contrast interfaces between the volumetric mass layers while additional correction terms are applied to account for radial density changes. The applied numerical schemes utilize methods for a spherical harmonic analysis and synthesis of the global density structure models. The developed the Earth’s density models are then defined in terms of the spherical density and density-contrast functions. We also demonstrate how these Earth’s density models can be applied in the gravimetric forward modeling and discuss some practical aspects of representing mathematically density structures within particular components of the Earth’s interior.
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Abo-Dahab, S. M., Mohamed S. Mohamed i T. A. Nofal. "A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation". Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/614874.
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The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.
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Bakoban, Rana Ali, i Ashwaq Mohammad Al-Shehri. "A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications". Symmetry 13, nr 4 (18.04.2021): 711. http://dx.doi.org/10.3390/sym13040711.
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In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.
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Wang, Dan, Ahmed H. Tewfik, Yingchun Zhang i Yunhe Shen. "Sparse Representation of Deformable 3D Organs with Spherical Harmonics and Structured Dictionary". International Journal of Biomedical Imaging 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/658930.
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This paper proposed a novel algorithm to sparsely represent a deformable surface (SRDS) with low dimensionality based on spherical harmonic decomposition (SHD) and orthogonal subspace pursuit (OSP). The key idea in SRDS method is to identify the subspaces from a training data set in the transformed spherical harmonic domain and then cluster each deformation into the best-fit subspace for fast and accurate representation. This algorithm is also generalized into applications of organs with both interior and exterior surfaces. To test the feasibility, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques and then both ex vivo and in vivo experiments are conducted using 3D magnetic resonance imaging (MRI) scans for verification in practical settings. All results demonstrated that the proposed algorithm features sparse representation of deformable surfaces with low dimensionality and high accuracy. Specifically, the precision evaluated as maximum error distance between the reconstructed surface and the MRI ground truth is better than 3 mm in real MRI experiments.
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Xu, Yuchao, Jason Hou i Kostadin Ivanov. "Methodology for Discontinuity Factors Generation for Simplified P3 Solver Based on Nodal Expansion Formulation". Energies 14, nr 20 (10.10.2021): 6478. http://dx.doi.org/10.3390/en14206478.
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The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport-corrected interface and boundary conditions in an NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to minimize the error introduced by pin-wise homogenization. Moreover, several colorset models with varying sizes and configurations are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport-corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or with only the zeroth moment DF. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size colorset models show a slightly reduced prediction error than that using smaller colorset models in the whole-core calculations.
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Krishna, S., A. Shukla i R. P. Malik. "Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models". Canadian Journal of Physics 92, nr 12 (grudzień 2014): 1623–31. http://dx.doi.org/10.1139/cjp-2014-0047.
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We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the [Formula: see text] = 2 SUSY quantum mechanical model of a (0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY-invariant restrictions on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and [Formula: see text] with [Formula: see text]). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of the SUSY conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other [Formula: see text] = 2 SUSY quantum mechanical systems with physically interesting potential functions. To corroborate the preceding assertion, we apply our method to derive the [Formula: see text] = 2 continuous and nilpotent SUSY transformations for one of the simplest interacting SUSY systems of a 1D harmonic oscillator.
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Pheh, Kai-Shuen, Chee-Seng Tan, Kai Wei Lee, Kok-Wai Tay, Hooi Tin Ong i Sook Fan Yap. "Factorial structure, reliability, and construct validity of the Generalized Anxiety Disorder 7-item (GAD-7): Evidence from Malaysia". PLOS ONE 18, nr 5 (11.05.2023): e0285435. http://dx.doi.org/10.1371/journal.pone.0285435.
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Generalized anxiety disorder (GAD) is one of the most common mental disorders in Malaysia. Psychometrically sound measurements are urgently needed to assess anxiety symptoms. The extensively used Generalized Anxiety Disorder 7-item (GAD-7) is a promising candidate. However, studies on its factorial validity show mixed findings. While the one-factor solution has been replicated in different cultural contexts, some studies found different factorial structures instead. This study aimed to clarify the factorial validity of the English version of the GAD-7 in the Malaysian context. The responses collected from 1272 emerging to older adults in Malaysia were randomly divided into two halves and submitted to exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) respectively. Four acceptable models were explored in EFA ranging from unidimensional factor with 7 items to 3-factor models with 6 items. The four models revealed in EFA and the other competing models found in past studies were then examined and compared using CFA. The 6-item second-order model with a general factor of anxiety and three first-order factors with two items respectively (i.e., GAD-6) showed a more harmonic result and hence, is preferable. Moreover, the GAD-6 and its three subscales also showed satisfactory internal consistency and construct validity. This study uncovers a new and unique factorial structure of the GAD screening tool that fits in the Malaysian context. The scale may reveal GAD symptomatic dimensions that guide clinical interventions.
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Grabova, Ulyana, i Svetlana Salnikova. "GENERALIZED POISSON INTEGRAL AND ITS APPLIED ASPECTS". Journal of Automation and Information sciences 2 (1.03.2021): 102–11. http://dx.doi.org/10.34229/1028-0979-2021-2-9.
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Mathematical methods based on statistics have been used in sociology for a long time. The functioning of socio-economic and socio-politic systems is a complex process, which is caused by a number of various factors. Thus, the construction of models of socio-economic and socio-politic processes requires solving problems of both the decomposition of structures and processes, and their integration into a single system model, taking into account the changing conditions of the external environment. Mathematical modeling of such problems can be carried out by methods of network analysis or game theory, which allows finding optimal strategies for the behavior of competitive parties. Asymptotic formulations have a central role in game theory, since, due to the complex strategic nature, explicit solutions can be found only in very rare cases. A large number of models created to study complex social processes that occur in society are dynamical systems, or non-autonomous differential equations, or difference equations with a large number of parameters in any cases. In this situation, it is important to choose an appropriate tool for studying the behavior of such systems. In this paper, generalized Poisson delta operators are considered as approximating aggregates, since periodic processes, which are subdivided into harmonic and polyharmonic, provide the internal integrity of complex systems and their dynamic functioning. Questions of the asymptotic behavior of the exact upper bounds for approximations by generalized Poisson delta operators on classes of periodic functions that satisfy the Lipschitz condition are also studied. The received formulas provide a solution to the Kolmogorov-Nikol’ski problem for generalized Poisson delta operators and Lipschitz classes. The proof is based on the use of formulas that give integral representations of the deviations of linear methods generated by linear processes of summation of Fourier series on sets of periodic functions in the uniform metric obtained in the works of L.I. Bausov. The results can be an effective tool for modeling the processes of social dynamics.
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Walther, Jürgen, Pablo D. Dans, Alexandra Balaceanu, Adam Hospital, Genís Bayarri i Modesto Orozco. "A multi-modal coarse grained model of DNA flexibility mappable to the atomistic level". Nucleic Acids Research 48, nr 5 (20.01.2020): e29-e29. http://dx.doi.org/10.1093/nar/gkaa015.
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Abstract We present a new coarse grained method for the simulation of duplex DNA. The algorithm uses a generalized multi-harmonic model that can represent any multi-normal distribution of helical parameters, thus avoiding caveats of current mesoscopic models for DNA simulation and representing a breakthrough in the field. The method has been parameterized from accurate parmbsc1 atomistic molecular dynamics simulations of all unique tetranucleotide sequences of DNA embedded in long duplexes and takes advantage of the correlation between helical states and backbone configurations to derive atomistic representations of DNA. The algorithm, which is implemented in a simple web interface and in a standalone package reproduces with high computational efficiency the structural landscape of long segments of DNA untreatable by atomistic molecular dynamics simulations.
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Popa, Nicolae C., Davor Balzar i Sven C. Vogel. "Elastic macro strain and stress determination by powder diffraction: spherical harmonics analysis starting from the Voigt model". Journal of Applied Crystallography 47, nr 1 (25.12.2013): 154–59. http://dx.doi.org/10.1107/s1600576713029208.
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A new approach for the determination of the elastic macro strain and stress in textured polycrystals by diffraction is presented. It consists of expanding the strain tensor weighted by texture in a series of generalized spherical harmonics where the ground state is defined by the strain/stress state in an isotropic sample in the Voigt model. In contrast to similar expansions already reported by other authors, this new approach provides expressions valid for any sample and crystal symmetries and can easily be implemented in whole powder pattern fitting, including Rietveld refinement. An earlier article [Popa & Balzar (2001).J. Appl. Cryst.34, 187–195] reported a similar model, but with a spherical harmonics expansion around the hydrostatic strain/stress state of the isotropic polycrystal. The availability of several different models is beneficial in order to allow one to select the representation in which the ground state is the closest to the actual stress state in the sample.
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Wickert, J. A., i C. D. Mote. "Response and Discretization Methods for Axially Moving Materials". Applied Mechanics Reviews 44, nr 11S (1.11.1991): S279—S284. http://dx.doi.org/10.1115/1.3121365.
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Through a convective acceleration component, the equations of motion for axially-moving materials are skew-symmetric in the state space formulation, so that the response problem is best analyzed within the broader context of continuous gyroscopic systems. With particular application to the prototypical traveling string and beam models, a modal analysis that associates degrees of freedom with the complex state eigenfunctions and their conjugates is presented. This procedure is well-suited for harmonic excitation sources, and in some instances, it is more convenient than previous methods which decompose the modal coordinates, eigenfunctions, and generalized forces into real and imaginary components. Also from the state space perspective, Rayleigh’s quotient for gyroscopic systems provides a variational method for determining the eigensolutions of axially-moving materials. Ritz discretization of the quotient can make effective use of the speed-adapting modes of the traveling string and beam models as they are rich in phase, as well as amplitude, content.
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Wang, F., i A. K. Bajaj. "Model reduction for discrete and elastic structures with inertial quadratic non-linearities". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, nr 10 (10.08.2011): 2422–35. http://dx.doi.org/10.1177/0954406211413658.
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This work discusses model reduction for non-linear structural systems under harmonic excitations. Model reduction can be achieved by different techniques, one of the recent techniques being the non-linear normal modes (NNMs) of the system. The dimension reduction achievable depends on the possibilities of internal resonances. A master–slave separation of degrees of freedom is used, and a non-linear relation between the slave and master coordinates is constructed based on the method of multiple timescales. More specifically, three cases involving external resonance of a mode without any internal resonance, and subharmonic as well as superharmonic resonances for systems with 1:2 internal resonances are considered. Reduced-order models based on the ‘ Conservative NNMs’ as well as ‘ Damped NNMs’ are constructed. The steady-state periodic responses of the reduced models determined by the method of multiple timescales are compared to exact solutions of the system models computed by the bifurcation analysis and parameter continuation software AUTO. The analysis is specifically applied to a spring-mass-pendulum system with external excitation, and to an elastic three-beam-tip-mass structure, which is first reduced to a high-fidelity non-linear discretized model through a Galerkin approximation. Both systems exhibit essential quadratic non-linearities and couplings between the various generalized coordinates. The NNMs of the two systems are used to perform model reductions when excited by harmonic excitations. It is seen that for systems with essential inertial quadratic non-linearities, the technique for model-order reduction through multiple timescales approximation based on NNMs over-predicts the softening non-linear response in each of the cases studied.
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Wang, Linjie, Pengtu Zhang, Yali Geng, Zaisheng Zhu i Shiling Yuan. "Harmonic Vibrational Frequency Simulation of Pharmaceutical Molecules via a Novel Multi-Molecular Fragment Interception Method". Molecules 28, nr 12 (8.06.2023): 4638. http://dx.doi.org/10.3390/molecules28124638.
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By means of a computational method based on Density Functional Theory (DFT), using commercially available software, a novel method for simulating equilibrium geometry harmonic vibrational frequencies is proposed. Finasteride, Lamivudine, and Repaglinide were selected as model molecules to study the adaptability of the new method. Three molecular models, namely the single-molecular, central-molecular, and multi-molecular fragment models, were constructed and calculated by Generalized Gradient Approximations (GGAs) with the PBE functional via the Material Studio 8.0 program. Theoretical vibrational frequencies were assigned and compared to the corresponding experimental data. The results indicated that the traditional single-molecular calculation and scaled spectra with scale factor exhibited the worst similarity for all three pharmaceutical molecules among the three models. Furthermore, the central-molecular model with a configuration closer to the empirical structure resulted in a reduction of mean absolute error (MAE) and root mean squared error (RMSE) in all three pharmaceutics, including the hydrogen-bonded functional groups. However, the improvement in computational accuracy for different drug molecules using the central-molecular model for vibrational frequency calculation was unstable. Whereas, the new multi-molecular fragment interception method showed the best agreement with experimental results, exhibiting MAE and RMSE values of 8.21 cm−1 and 18.35 cm−1 for Finasteride, 15.95 cm−1 and 26.46 cm−1 for Lamivudine, and 12.10 cm−1 and 25.82 cm−1 for Repaglinide. Additionally, this work provides comprehensive vibrational frequency calculations and assignments for Finasteride, Lamivudine, and Repaglinide, which have never been thoroughly investigated in previous research.
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Holzapfel, Gerhard A., Ray W. Ogden i Selda Sherifova. "On fibre dispersion modelling of soft biological tissues: a review". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, nr 2224 (kwiecień 2019): 20180736. http://dx.doi.org/10.1098/rspa.2018.0736.
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Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.
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COLOMO, F., i L. LUSANNA. "WIGNER THEORY OF THE NAMBU STRING: (I) THE OPEN STRING". International Journal of Modern Physics A 07, nr 08 (30.03.1992): 1705–54. http://dx.doi.org/10.1142/s0217751x92000740.
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A set of relative variables for the open string with P2>0 is found, which has Wigner covariance properties. It allows one to obtain global Lorentz-invariant abelianizations of the constraints, and then to find global Lorentz-invariant canonically conjugated gauge variables. By means of the multitemporal approach a noncanonical redundant set of Dirac observables is defined; these transform as spin-1 Wigner vectors and satisfy constraints of the type of σ models. The generalized Virasoro algebra, except for L0, lives entirely in the gauge sector of the theory. The original canonical variables are expressed by means of the resulting generalized harmonic analysis in terms of these observables, and of the noncovariant center-of-mass ones. Quantization is not done, because a canonical basis of observables is still lacking, but the program to find them is expounded: instead of making a reduction from O (D–1)(P) to O (D–2), which would give a nonlinear realization of the Poincaré group like in the noncovariant approach, one has to find a Thomas-spin-adapted basis of observables which are Lorentz-invariant (except for three of them).
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Xi, Hui, Hu Jiang, Jiachun An, Zemin Wang, Xueyong Xu, Houxuan Yan i Can Feng. "Spatial and Temporal Variations of Polar Ionospheric Total Electron Content over Nearly Thirteen Years". Sensors 20, nr 2 (19.01.2020): 540. http://dx.doi.org/10.3390/s20020540.
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It is of great significance for the global navigation satellite system (GNSS) service to detect the polar ionospheric total electron content (TEC) and its variations, particularly under disturbed ionosphere conditions, including different phases of solar activity, the polar day and night alternation, the Weddell Sea anomaly (WSA) as well as geomagnetic storms. In this paper, four different models are utilized to map the ionospheric TEC over the Arctic and Antarctic for about one solar cycle: the polynomial (POLY) model, the generalized trigonometric series function (GTSF) model, the spherical harmonic (SH) model, and the spherical cap harmonic (SCH) model. Compared to other models, the SCH model has the best performance with ±0.8 TECU of residual mean value and 1.5–3.5 TECU of root mean square error. The spatiotemporal distributions and variations of the polar ionospheric TEC are investigated and compared under different ionosphere conditions in the Arctic and Antarctic. The results show that the solar activity significantly affects the TEC variations. During polar days, the ionospheric TEC is more active than it is during polar nights. In polar days over the Antarctic, the maximum value of TEC always appears at night in the Antarctic Peninsula and Weddell Sea area affected by the WSA. In the same year, the ionospheric TEC of the Antarctic has a larger amplitude of annual variation than that of the TEC in the Arctic. In addition, the evolution of the ionization patch during a geomagnetic storm over the Antarctic can be clearly tracked employing the SCH model, which appears to be adequate for mapping the polar TEC, and provides a sound basis for further automatic identification of ionization patches.
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Nguyen, Hoai-Minh, i Linh Viet Nguyen. "Generalized impedance boundary conditions for strongly absorbing obstacle: The full wave equation". Mathematical Models and Methods in Applied Sciences 25, nr 10 (22.06.2015): 1927–60. http://dx.doi.org/10.1142/s0218202515500499.
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This paper is devoted to the study of the generalized impedance boundary conditions (GIBCs) for a strongly absorbing obstacle in the time regime in two and three dimensions. The GIBCs in the time domain are heuristically derived from the corresponding conditions in the time harmonic regime. The latter is frequency-dependent except the one of order 0; hence the formers are non-local in time in general. The error estimates in the time regime can be derived from the ones in the time harmonic regime when the frequency dependence is well controlled. This idea is originally due to Nguyen and Vogelius [Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807] for the cloaking context. In this paper, we present the analysis to the GIBCs of orders 0 and 1. To implement the ideas in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807], we revise and extend the work of Haddar, Joly, and Nguyen, [Generalized impedance boundary condition for scattering by strongly absorbing obstacles: the scalar case, Math. Models Methods Appl. Sci.15 (2005) 1273–1300], where the GIBCs were investigated for a fixed frequency in three dimensions. Even though we heavily follow the strategy in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807], our analysis on the stability contains new ingredients and ideas. First, instead of considering the difference between solutions of the exact model and the approximate model, we consider the difference between their derivatives in time. This simple idea helps us to avoid the machinery used in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807] concerning the integrability with respect to frequency in the low frequency regime. Second, in the high frequency regime, the Morawetz multiplier technique used in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variable, SIAM J. Math. Anal.44 (2012) 769–807] does not fit directly in our setting. Our proof makes use of a result by Hörmander in [Lp estimates for (pluri-) subharmonic functions, Math. Scand.20 (1967) 65–78]. Another important part of the analysis in this paper is the well-posedness in the time domain for the approximate problems imposed with GIBCs on the boundary of the obstacle, which are non-local in time.
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Abouelregal, Ahmed E., Hijaz Ahmad, Taher A. Nofal i Hanaa Abu-Zinadah. "Thermo-viscoelastic fractional model of rotating nanobeams with variable thermal conductivity due to mechanical and thermal loads". Modern Physics Letters B 35, nr 18 (22.04.2021): 2150297. http://dx.doi.org/10.1142/s0217984921502973.
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This paper analyzes the thermoelastic dynamic behavior of simply supported viscoelastic nanobeams of fractional derivative type due to a dynamic strength load. The viscoelastic Kelvin–Voigt model with fractional derivative with Bernoulli–Euler beam theory is introduced. The generalized thermoelastic heat conduction model with a two-phase lag is also used. It is assumed that the beam is rotating at a uniform angular velocity and that the thermal conductivity varies linearly depending on the temperature. Due to a variable harmonic heat and retreating time-dependent load, the nanobeam is excited. The Laplace integral transformation technique is used as the solution method. The thermodynamic temperature, deflection function, bending moment, and displacement are numerically calculated. Results of fractional and integer viscoelastic material models are compared. In the studied system, the effect of the nonlocal parameter, viscosity and varying load on the solutions is shown, and the temperature-dependence of the thermal conductivity is analyzed.
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Mahmoud, Rehab, i Salah M. Mohamed. "New Mathematical Properties For Rayleigh distribution". Jurnal Matematika, Statistika dan Komputasi 19, nr 1 (7.09.2022): 223–34. http://dx.doi.org/10.20956/j.v19i1.21946.
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Regression analysis is one of the most commonly statistical techniques used for analyzing data in different fields. And used to fit the relation between the dependent variable and the independent variables require strong assumption to be met in the model. Generalized linear models (GLMs) allow the extension of linear modeling ideas to a wider class of response types, such as count data or binary responses. Many statistical methods exist for such data types, but the advantage of the GLM approach is that it unites a seemingly disparate collection of response types under a common modeling methodology. So, the problem of the current research is to try to provide a new mathematical property for Exponentiated Rayleigh distribution, and it was one of the most important properties that was studied is to determine Harmonic Mean, as well as calculating the Quantile function, Moments of Residual life (MRL), Reversed Residual Life, Mean of Residual life. The study also presented the probability density function (pdf) and cumulative distribution function according to linear representations.
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Karl, Robert M., Giulia F. Mancini, Joshua L. Knobloch, Travis D. Frazer, Jorge N. Hernandez-Charpak, Begoña Abad, Dennis F. Gardner i in. "Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams". Science Advances 4, nr 10 (październik 2018): eaau4295. http://dx.doi.org/10.1126/sciadv.aau4295.
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Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved—sub–100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution—represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.
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Wang, Ai Ying, i Li Dong Zhu. "2-D DOA Estimation of Coherent Wide-Band Sources for Arbitrary Array Plane Geometry". Applied Mechanics and Materials 427-429 (wrzesień 2013): 1826–31. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.1826.
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Direction of Arrival (DOA) estimation is of big importance in Sonar, Radar and satellite systems. In this work, we estimated the 2-D DOA (two-dimensional DOA) of coherent wide-band sources by using a broadband focusing method, which was based on the separation of angle and frequency of the array manifold matrix. At first, we transform the element position of the plane array into the spherical coordinates. Then we adopted a generalized Fourier series expansion based on the spherical harmonics and the first kind of spherical Bessel functions to get the arbitrary plane array steering vector. In this vector, the angle and frequency of array manifold matrix was separated, so we could get the matrix of focusing transformation. Finally, we used the traditional narrow-band algorithm to estimate the 2-D DOA. The design is suitable for arbitrary array geometry models of coherent broadband signals, and avoids the angle pre-estimation in traditional methods. Simulation results demonstrate its validity and better performance.
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Kushch, Volodymyr I., Igor Sevostianov i Albert Giraud. "Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, nr 2207 (listopad 2017): 20170472. http://dx.doi.org/10.1098/rspa.2017.0472.
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An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.