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Journal articles on the topic 'Real boundary conditions'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Котов and P. Kotov. "THE METHOD OF REAL BOUNDARY PROBLEMS DEVELOPING THE REAL BOUNDARY CONDITIONS." Modeling of systems and processes 9, no. 1 (September 23, 2016): 11–13. http://dx.doi.org/10.12737/21619.

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An efficient solution to the real equation of heat transfer with deterministic disturbance and informative method of the basic initial-boundary value problems for the unsteady heat propagation with measurable initial and boundary conditions.

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2

McDonald, Robb. "Geodesic Loewner paths with varying boundary conditions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (October 2020): 20200466. http://dx.doi.org/10.1098/rspa.2020.0466.

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Equations of the Loewner class subject to non-constant boundary conditions along the real axis are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian growth in which the slits represent thin fingers growing in a diffusion field. A single finger follows a curved path determined by the forcing function appearing in Loewner’s equation. This function is found by solving an ordinary differential equation whose terms depend on curvature properties of the streamlines of the diffusive field in the conformally mapped ‘mathematical’ plane. The effect of boundary conditions specifying either piecewise constant values of the field variable along the real axis, or a dipole placed on the real axis, reveal a range of behaviours for the growing slit. These include regions along the real axis from which no slit growth is possible, regions where paths grow to infinity, or regions where paths curve back toward the real axis terminating in finite time. Symmetric pairs of paths subject to the piecewise constant boundary condition along the real axis are also computed, demonstrating that paths which grow to infinity evolve asymptotically toward an angle of bifurcation of π /5.

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3

van Rees, Balt C. "Real-time gauge/gravity duality and ingoing boundary conditions." Nuclear Physics B - Proceedings Supplements 192-193 (July 2009): 193–96. http://dx.doi.org/10.1016/j.nuclphysbps.2009.07.078.

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4

Konin, A. "Boundary conditions in a real bipolar semiconductor-metal junction." Lithuanian Journal of Physics 46, no. 2 (2006): 233–35. http://dx.doi.org/10.3952/lithjphys.46214.

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5

Gnecco, Giorgio, Marco Gori, and Marcello Sanguineti. "Learning with Boundary Conditions." Neural Computation 25, no. 4 (April 2013): 1029–106. http://dx.doi.org/10.1162/neco_a_00417.

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Kernel machines traditionally arise from an elegant formulation based on measuring the smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space (RKHS) generated by the chosen kernel. It was pointed out that they can be formulated in a related functional framework, in which the Green’s function of suitable differential operators is thought of as a kernel. In this letter, our own picture of this intriguing connection is given by emphasizing some relevant distinctions between these different ways of measuring the smoothness of admissible solutions. In particular, we show that for some kernels, there is no associated differential operator. The crucial relevance of boundary conditions is especially emphasized, which is in fact the truly distinguishing feature of the approach based on differential operators. We provide a general solution to the problem of learning from data and boundary conditions and illustrate the significant role played by boundary conditions with examples. It turns out that the degree of freedom that arises in the traditional formulation of kernel machines is indeed a limitation, which is partly overcome when incorporating the boundary conditions. This likely holds true in many real-world applications in which there is prior knowledge about the expected behavior of classifiers and regressors on the boundary.

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6

WEHRHEIM, KATRIN. "BANACH SPACE VALUED CAUCHY–RIEMANN EQUATIONS WITH TOTALLY REAL BOUNDARY CONDITIONS." Communications in Contemporary Mathematics 06, no. 04 (August 2004): 601–35. http://dx.doi.org/10.1142/s0219199704001410.

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The main purpose of this paper is to give a general regularity result for Cauchy–Riemann equations in complex Banach spaces with totally real boundary conditions. The usual elliptic Lp-regularity results hold true under one crucial assumption: The Banach space is isomorphic to a closed subspace of an Lp-space. (Equivalently, the totally real submanifold is modelled on a closed subspace of an Lp-space.) Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural boundary conditions for the anti-self-duality equation on 4-manifolds with a boundary space-time splitting, leading towards the definition of a Floer homology for 3-manifolds with boundary, which is the first step in a program by Salamon for the proof of the Atiyah–Floer conjecture. The principal part of such a boundary value problem is an example of a Banach space valued Cauchy–Riemann equation with totally real boundary condition.

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7

Dallos Santos, Dionicio Pastor. "Problems with Mixed Boundary Conditions in Banach Spaces." Chinese Journal of Mathematics 2017 (March 15, 2017): 1–8. http://dx.doi.org/10.1155/2017/7838102.

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Using Leray-Schauder degree or degree for α-condensing maps we obtain the existence of at least one solution for the boundary value problem of the following type: φu′′=ft,u,u′, u(T)=0=u′(0), where φ:X→X is a homeomorphism with reverse Lipschitz constant such that φ(0)=0, f:0,T×X×X→X is a continuous function, T is a positive real number, and X is a real Banach space.

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8

Medková, Dagmar. "The transmission problem with boundary conditions given by real measures." Annales Polonici Mathematici 92, no. 3 (2007): 243–59. http://dx.doi.org/10.4064/ap92-3-4.

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9

Nogueira, José Alexandre, and Pedro Leite Barbieri. "Boundary conditions as mass generation mechanism for real scalar fields." Brazilian Journal of Physics 32, no. 3 (September 2002): 798–803. http://dx.doi.org/10.1590/s0103-97332002000400022.

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10

Frauenfelder, Urs, and Kai Zehmisch. "Gromov compactness for holomorphic discs with totally real boundary conditions." Journal of Fixed Point Theory and Applications 17, no. 3 (April 29, 2015): 521–40. http://dx.doi.org/10.1007/s11784-015-0229-0.

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11

Binding, Paul A., Patrick J. Browne, and Bruce A. Watson. "STURM–LIOUVILLE PROBLEMS WITH REDUCIBLE BOUNDARY CONDITIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (October 2006): 593–608. http://dx.doi.org/10.1017/s0013091505000131.

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AbstractThe regular Sturm–Liouville problem$$ \tau y:=-y''+qy=\lambda y\quad\text{on }[0,1],\ \lambda\in\CC, $$is studied subject to boundary conditions$$ P_j(\lambda)y'(j)=Q_j(\lambda)y(j),\quad j=0,1, $$where $q\in L^1(0,1)$ and $P_j$ and $Q_j$ are polynomials with real coefficients. A comparison is made between this problem and the corresponding ‘reduced’ one where all common factors are removed from the boundary conditions. Topics treated include Jordan chain structure, eigenvalue asymptotics and eigenfunction oscillation.

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12

Binding, P. A., and P. J. Browne. "Sturm–Liouville problems with non-separated eigenvalue dependent boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 2 (April 2000): 239–47. http://dx.doi.org/10.1017/s0308210500000135.

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Sturm–Liouville differential equations are studied under non-separated boundary conditions whose coefficients are first degree polynomials in the eigenparameter. Situations are examined where there are at most finitely many non-real eigenvalues and also where there are only finitely many real ones.

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13

Rousset, Frederic. "The residual boundary conditions coming from the real vanishing viscosity method." Discrete & Continuous Dynamical Systems - A 8, no. 3 (2002): 605–25. http://dx.doi.org/10.3934/dcds.2002.8.606.

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14

Chen, Jiangwei, and Huaixian Lu. "Generalized laws of reflection and refraction from real valued boundary conditions." Optics Communications 284, no. 16-17 (August 2011): 3802–7. http://dx.doi.org/10.1016/j.optcom.2011.04.022.

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15

Martín-Delgado, Miguel A., and Germán Sierra. "The role of boundary conditions in the real-space renormalization group." Physics Letters B 364, no. 1 (December 1995): 41–48. http://dx.doi.org/10.1016/0370-2693(95)01223-8.

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16

Katunský, Dušan, Marek Zozulák, Marián Vertaľ, and Jozef Šimiček. "Experimentally Measured Boundary and Initial Conditions for Simulations." Advanced Materials Research 1041 (October 2014): 293–96. http://dx.doi.org/10.4028/www.scientific.net/amr.1041.293.

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Real dynamic boundary conditions and initial condition has to be taken into an account when simulations need to be done. The most helpful are in situ measurement facilities with climate monitoring. Indoor environment operation modes with different air temperature and relative humidity made indoor boundary conditions. Measured weather data are used to create complete boundary conditions for the research locality. Initial condition of masonry water profile is set up. The initial and boundary conditions are considered for an individual locality simulation proposes.

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17

Stacey, P. J. "Regularity of simple nuclear real C*-algebras under tracial conditions." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (April 30, 2021): 139–47. http://dx.doi.org/10.1017/s0013091521000043.

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AbstractThe Toms–Winter conjecture is verified for those separable, unital, nuclear, infinite-dimensional real C*-algebras for which the complexification has a tracial state space with compact extreme boundary of finite covering dimension.

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18

DE TRAUBENBERG, M. RAUSCH, and C. A. SAVOY. "EQUIVALENT COMPLEX AND REAL FERMIONS IN HETEROTIC SUPERSTRING SOLUTIONS." International Journal of Modern Physics A 06, no. 08 (March 30, 1991): 1301–12. http://dx.doi.org/10.1142/s0217751x9100068x.

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As a first step towards a classification of the heterotic superstring solutions in the fermionic approach, we study a class of solutions characterized by complex fermions with ZN boundary conditions. The same solutions can be obtained by an equivalent modular invariant system of real fermions with Z2 boundary conditions. The proof is supplied by Riemann identities for Jacobi Θ-functions that we derive. The patterns of the gauge groups of the D-dimensional solutions are determined for 4≤D≤10, and their uniqueness in ten dimensions is checked for the different ZN boundary conditions. A construction of the E8×E8 supersymmetric solution based on nine complex fermions with Z3 periodicity is exhibited.

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19

Feng, Yaoqi, and Xianming Wang. "Matching Boundary Conditions for the Euler–Bernoulli Beam." Shock and Vibration 2021 (March 13, 2021): 1–12. http://dx.doi.org/10.1155/2021/6685852.

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Artificial boundary conditions play a crucial role in the dynamic simulation of infinite Euler–Bernoulli beams. In this paper, a class of artificial boundary conditions, matching boundary conditions (MBCs), is presented to provide effective absorption of incident waves in numerical simulations of the Euler–Bernoulli beam. First, matching boundary conditions are proposed based on the space central difference scheme of the Euler–Bernoulli beam, and then, the specific coefficients of MBCs are determined by matching the dispersion relation. Moreover, reflection coefficient study and numerical tests are carried out to analyze the effectiveness of the proposed MBCs, indicating a remarkable agreement. Taken together, the proposed boundary conditions herein can absorb dispersive waves efficiently and are more compact than previous artificial boundary conditions, particularly suitable for real-time simulation.

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20

Rahardjo, Harianto, Alfrendo Satyanaga Nio, Fakhrur Rozy Harnas, and Eng Choon Leong. "Comprehensive Instrumentation for Real Time Monitoring of Flux Boundary Conditions in Slope." Procedia Earth and Planetary Science 9 (2014): 23–43. http://dx.doi.org/10.1016/j.proeps.2014.06.015.

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21

Oh, Yong-Geun. "On the structure of pseudo-holomorphic discs with totally real boundary conditions." Journal of Geometric Analysis 7, no. 2 (June 1997): 305–27. http://dx.doi.org/10.1007/bf02921725.

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22

Okong'o, Nora, and Josette Bellan. "Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves." Journal of Computational Physics 176, no. 2 (March 2002): 330–44. http://dx.doi.org/10.1006/jcph.2002.6990.

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23

Nieminen, Tuukka, Jari Kangas, Saku Suuriniemi, and Lauri Kettunen. "Accuracy Improvement by Boundary Conditions for Inertial Navigation." International Journal of Navigation and Observation 2010 (June 30, 2010): 1–10. http://dx.doi.org/10.1155/2010/869127.

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The term inertial navigation is often automatically associated with the term initial value problem. However, there are many applications where it is possible to end up with a boundary value problem (BVP) as well. We show that in case of a BVP, the finite element method that incorporates boundary conditions can be efficiently used to compute position and velocity estimates not prone to accumulation of errors. For further accuracy enhancements, a method of combining inertial measurements with additional constraints is proposed. This way, we can model sensor errors, known to limit the accuracy of the system. The capabilities of the proposed methods are demonstrated with real-life examples.

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24

Marušić, Sanja. "A Note on Boundary Conditions for the LWR Model." PROMET - Traffic&Transportation 21, no. 6 (March 2, 2012): 379–86. http://dx.doi.org/10.7307/ptt.v21i6.253.

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The paper studies the boundary conditions for the standard LWR model describing the traffic flow. The notion of the BLN (Bardos, Leroux and Nédélec) condition is described. In the context of traffic flow the BLN conditions have some natural interpretation. The conditions on the density and on the flow and their meaning in real-life situations are discussed. KEY WORDS: LWR model, traffic flow, hyperbolic conservation law, boundary conditions

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25

Tam, Christopher K. W. "Advances in Numerical Boundary Conditions for Computational Aeroacoustics." Journal of Computational Acoustics 06, no. 04 (December 1998): 377–402. http://dx.doi.org/10.1142/s0218396x98000259.

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Advances in computational aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high-quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some of the much-needed research in numerical boundary conditions for CAA.

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26

Fucci, Guglielmo. "The Casimir effect for pistons with transmittal boundary conditions." International Journal of Modern Physics A 32, no. 31 (November 8, 2017): 1750182. http://dx.doi.org/10.1142/s0217751x17501822.

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This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type [Formula: see text] where [Formula: see text] is a closed interval of the real line and [Formula: see text] is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold [Formula: see text] is a [Formula: see text]-dimensional sphere.

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27

GEYER, B., G. L. KLIMCHITSKAYA, and V. M. MOSTEPANENKO. "CASIMIR FORCE UNDER THE INFLUENCE OF REAL CONDITIONS." International Journal of Modern Physics A 16, no. 19 (July 30, 2001): 3291–308. http://dx.doi.org/10.1142/s0217751x01004372.

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The Casimir force is calculated analytically for configurations of two parallel plates and a spherical lens (sphere) above a plate with an account of nonzero temperature, finite conductivity of the boundary metal and surface roughness. The permittivity of the metal is described by the plasma model. It is proved that in case of the plasma model the scattering formalism of quantum field theory in Matsubara formulation underlying Lifshitz formula is well defined and no modifications are needed concerning the zero-frequency contribution. The temperature correction to the Casimir force is found completely with respect to temperature and perturbatively (up to the second order in the relative penetration depth of electromagnetic zero-point oscillations into the metal) with respect to finite conductivity. The asymptotics of low and high temperatures are presented and contributions of longitudinal and perpendicular modes are determined separately. Serving as an example, aluminium test bodies are considered, showing good agreement between the obtained analytical results and previously performed numerical computations. The roughness correction is formally included and formulas are given permitting us to calculate the Casimir force under the influence of all relevant factors.

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28

Cabada, Alberto, and Nikolay D. Dimitrov. "Third-order differential equations with three-point boundary conditions." Open Mathematics 19, no. 1 (January 1, 2021): 11–31. http://dx.doi.org/10.1515/math-2021-0007.

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Abstract In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.

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29

Maros, Gábor, and Ferenc Izsák. "Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions." Fractal and Fractional 5, no. 3 (July 21, 2021): 75. http://dx.doi.org/10.3390/fractalfract5030075.

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The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian operator. The basis of the convergence analysis for a lower-order boundary element approximation is the theory for the corresponding continuous problem. In particular, we need continuity results for Riesz potentials and the fractional-order extension of the theory for boundary integral equations with the Laplacian operator. Accordingly, the convergence is stated in fractional-order Sobolev norms. The results were confirmed in a numerical experiment.

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30

Sovrano, Elisa, and Fabio Zanolin. "Ambrosetti–Prodi Periodic Problem Under Local Coercivity Conditions." Advanced Nonlinear Studies 18, no. 1 (February 1, 2018): 169–82. http://dx.doi.org/10.1515/ans-2017-6040.

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AbstractIn this paper we focus on the periodic boundary value problem associated with the Liénard differential equation{x^{\prime\prime}+f(x)x^{\prime}+g(t,x)=s}, wheresis a real parameter,fandgare continuous functions andgisT-periodic in the variablet. The classical framework of Fabry, Mawhin and Nkashama, related to the Ambrosetti–Prodi periodic problem, is modified to include conditions without uniformity, in order to achieve the same multiplicity result under local coercivity conditions ong. Analogous results are also obtained for Neumann boundary conditions.

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31

Szajewska, Marzena, and Agnieszka Maria Tereszkiewicz. "MULTIDIMENSIONAL HYBRID BOUNDARY VALUE PROBLEM." Acta Polytechnica 58, no. 6 (December 31, 2018): 402–13. http://dx.doi.org/10.14311/ap.2018.58.0402.

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The purpose of this paper is to discuss three types of boundary conditions for few families of special functions orthogonal on the fundamental region. Boundary value problems are considered on a simplex F in the real Euclidean space Rn of dimension n > 2.

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32

Zhang, Haiyan, Yaohong Li, and Jingbao Yang. "New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions." Journal of Function Spaces 2020 (April 27, 2020): 1–9. http://dx.doi.org/10.1155/2020/6821637.

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In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples.

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33

Faraci, Francesca, and Antonio Iannizzotto. "Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions." Abstract and Applied Analysis 2008 (2008): 1–13. http://dx.doi.org/10.1155/2008/756934.

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Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a functionu, and prove that the set of bifurcation points for the solutions of the system is notσ-compact. Then, we deal with a linear system depending on a real parameterλ>0and on a functionu, and prove that there existsλ∗such that the set of the functionsu, such that the system admits nontrivial solutions, contains an accumulation point.

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34

Pečiulytė, S., and A. Štikonas. "Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions." Nonlinear Analysis: Modelling and Control 11, no. 1 (February 27, 2006): 47–78. http://dx.doi.org/10.15388/na.2006.11.1.14764.

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The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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35

Kong, Q., H. Wu, and A. Zettl. "Geometric aspects of Sturm—Liouville problems I. Structures on spaces of boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 3 (June 2000): 561–89. http://dx.doi.org/10.1017/s0308210500000305.

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We consider some geometric aspects of regular Sturm—Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm—Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for separated boundary conditions and those for coupled boundary conditions, or the eigenvalues for self-adjoint boundary conditions and those for non-self-adjoint boundary conditions, are closely related under this structure. Then we give complete characterizations of several subsets of boundary conditions such as the set of self-adjoint boundary conditions that have a given real number as an eigenvalue, and determine their shapes. The shapes are shown to be independent of the differential equation in question. Moreover, we investigate the differentiability of continuous eigenvalue branches under this structure, and discuss the relationships between the algebraic and geometric multiplicities of an eigenvalue.

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36

Wang, Tao, Ji-jun Ao, and Mei-chun Yang. "A Classification of Fourth-Order Dissipative Differential Operators." Journal of Function Spaces 2020 (January 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/7510313.

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This paper is devoted to the classification of the fourth-order dissipative differential operators by the boundary conditions. Subject to certain conditions, we determine some nonself-adjoint boundary conditions that generate the fourth-order differential operators to be dissipative. And under certain conditions, we prove that these dissipative operators have no real eigenvalues.

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37

Bhattacharyya, Bhattacharyya T., and Mohandas J. P. Mohandas. "TWO-PARAMETER UNIFORMLY ELLIPTIC STURM–LIOUVILLE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS." Proceedings of the Edinburgh Mathematical Society 48, no. 3 (September 15, 2005): 531–47. http://dx.doi.org/10.1017/s0013091504000720.

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AbstractWe consider the two-parameter Sturm–Liouville system$$ -y_1''+q_1y_1=(\lambda r_{11}+\mu r_{12})y_1\quad\text{on }[0,1], $$with the boundary conditions$$ \frac{y_1'(0)}{y_1(0)}=\cot\alpha_1\quad\text{and}\quad\frac{y_1'(1)}{y_1(1)}=\frac{a_1\lambda+b_1}{c_1\lambda+d_1}, $$and$$ -y_2''+q_2y_2=(\lambda r_{21}+\mu r_{22})y_2\quad\text{on }[0,1], $$with the boundary conditions$$ \frac{y_2'(0)}{y_2(0)} =\cot\alpha_2\quad\text{and}\quad\frac{y_2'(1)}{y_2(1)}=\frac{a_2\mu+b_2}{c_2\mu+d_2}, $$subject to the uniform-left-definite and uniform-ellipticity conditions; where $q_{i}$ and $r_{ij}$ are continuous real valued functions on $[0,1]$, the angle $\alpha_{i}$ is in $[0,\pi)$ and $a_{i}$, $b_{i}$, $c_{i}$, $d_{i}$ are real numbers with $\delta_{i}=a_{i}d_{i}-b_{i}c_{i}>0$ and $c_{i}\neq0$ for $i,j=1,2$. Results are given on asymptotics, oscillation of eigenfunctions and location of eigenvalues.

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38

Shin, Kwang C. "The potential (iz)m generates real eigenvalues only, under symmetric rapid decay boundary conditions." Journal of Mathematical Physics 46, no. 8 (August 2005): 082110. http://dx.doi.org/10.1063/1.2009667.

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39

Börsing, Nele, Theodor S. Becker, Andrew Curtis, Dirk-Jan van Manen, Thomas Haag, Christoph Bärlocher, and Johan O. Robertsson. "Numerical simulations of acoustic cloaking in a real laboratory that deploys immersive boundary conditions." Journal of the Acoustical Society of America 144, no. 3 (September 2018): 1758. http://dx.doi.org/10.1121/1.5067783.

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40

Baleanu, Dumitru, Shahram Rezapour, Sina Etemad, and Ahmed Alsaedi. "On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/785738.

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The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.

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41

Ibrahim, Sobhy El-Sayed. "On the boundary conditions for products of Sturm-Liouville differential operators." Tamkang Journal of Mathematics 32, no. 3 (September 30, 2001): 187–99. http://dx.doi.org/10.5556/j.tkjm.32.2001.374.

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In this paper, the second-order symmetric Sturm-Liouville differential expressions $ \tau_1, \tau_2, \ldots, \tau_n $ with real coefficients are considered on the interval $ I = (a,b) $, $ - \infty \le a < b \le \infty $. It is shown that the characterization of singular self-adjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximan domain of the product operators, and is an exact parallel of the regular case. This characterization is an extension of those obtained in [6], [8], [11-12], [14] and [15].

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Bodisco, Timothy, and Ali Zare. "Practicalities and Driving Dynamics of a Real Driving Emissions (RDE) Euro 6 Regulation Homologation Test." Energies 12, no. 12 (June 17, 2019): 2306. http://dx.doi.org/10.3390/en12122306.

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One of the most important sources of air pollution, especially in urban areas, is the exhaust emissions from passenger cars. New European emissions regulations, to minimize the gap between manufacturer-reported emissions and those emitted on the road, require new vehicles to undergo emission testing on public roads during the certification process. Outlined in the new regulation are specific boundary conditions to which the route on which the vehicle is driven must comply during a legal test. These boundary conditions, as they relate to the design and subsequent driving of a compliant route, are discussed in detail. The practicality of designing a compliant route is discussed in the context of developing a route on the Gold Coast in Queensland, Australia, in a prescriptive manner. The route itself was driven 5 times and the results compared against regulation boundary conditions.

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Han, Guansheng, Fei Xiong, Yu Zhou, Leibo Song, and Xingkai Wang. "Research Progress on Shear Characteristics of Rock Joints under Constant Normal Stiffness Boundary Conditions." Shock and Vibration 2021 (September 1, 2021): 1–6. http://dx.doi.org/10.1155/2021/9670151.

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The constant normal stiffness (CNS) boundary condition is more representative for the underground engineering, in which the shear-induced dilation is restricted by surrounding rocks, resulting in an increase in the normal stress. Therefore, the use of CNS boundary conditions in the research of shear-slip failure of underground rock engineering is more in line with the actual situation. Taking the instability and failure of surrounding rock in underground engineering as the background, the present study introduces the engineering background of CNS boundary conditions and the research progress on shear characteristics of rock joints under CNS boundary conditions. Three key directions for future research are proposed based on the latest research results of shear characteristics of rock joint under CNS boundary conditions: ① developing a rock joint shear test system that can realize the function of “CNS boundary conditions + shear-seepage test + visualization”; ② carrying out the shear tests of real rock joints under CNS boundary conditions based on 3D scanning and 3D carving technology; and ③ carrying out the shear tests of rock joint network under CNS boundary conditions.

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Vojvodic, Biljana M., and Vladimir M. Vladicic. "Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions." Journal of Inverse and Ill-posed Problems 28, no. 2 (April 1, 2020): 237–41. http://dx.doi.org/10.1515/jiip-2019-0074.

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AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

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Everitt, W. N., M. Möller, and A. Zettl. "Sturm—Liouville problems and discontinuous eigenvalues." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 707–16. http://dx.doi.org/10.1017/s0308210500013093.

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If a Sturm—Liouville problem is given in an open interval of the real line, then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues are not, in general, continuous functionsof the end-points and boundary conditions. The paper shows the surprising form of these discontinuities. The results have applications to the approximations of singular Sturm—Liouville problems by regular problems, and to the theoretical aspects of the Sleign2 Computer program.

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Klimek, Malgorzata. "Homogeneous robin boundary conditions and discrete spectrum of fractional eigenvalue problem." Fractional Calculus and Applied Analysis 22, no. 1 (February 25, 2019): 78–94. http://dx.doi.org/10.1515/fca-2019-0005.

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Abstract We discuss a fractional eigenvalue problem with the fractional Sturm-Liouville operator mixing the left and right derivatives of order in the range (1/2, 1], subject to a variant of Robin boundary conditions. The considered differential fractional Sturm-Liouville problem (FSLP) is equivalent to an integral eigenvalue problem on the respective subspace of continuous functions. By applying the properties of the explicitly calculated integral Hilbert-Schmidt operator, we prove the existence of a purely atomic real spectrum for both eigenvalue problems. The orthogonal eigenfunctions’ systems coincide and constitute a basis in the corresponding weighted Hilbert space. An analogous result is obtained for the reflected fractional Sturm-Liouville problem.

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Pavelcová, Veronika, Tereza Poklopová, Tomáš Janda, and Michal Šejnoha. "THE INFLUENCE OF BOUNDARY CONDITIONS ON THE RESPONSE OF UNDERGROUND STRUCTURES SUBJECTED TO EARTHQUAKE." Acta Polytechnica CTU Proceedings 15 (December 31, 2018): 74–80. http://dx.doi.org/10.14311/app.2018.15.0074.

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The paper deals with the prediction of the response of a real underground structure subjected to earthquake. A fully dynamic analysis is carried out in the GEO5 FEM program using the Finite Element Method. Limiting our attention to a two-dimensional analysis we focus on the implementation of special boundary conditions along the vertical edges of the computational model. A simple study is carried out first to show that incorrectly applied boundary conditions may significantly influence the actual design of underground structures loaded by vertically propagating shear waves. This study promotes the combination of so called free-field and static boundary conditions as demonstrated on a simple example.

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Park, Ill Woo, Baek Kyu Cho, and Jung Yup Kim. "A Real-Time Center of Gravity Trajectory Generation of a Biped Humanoid under Variable Reference ZMP Trajectory." Applied Mechanics and Materials 284-287 (January 2013): 1734–38. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.1734.

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This paper describes a method for generating a center of gravity trajectory of a biped humanoid robot under variable reference ZMP trajectory. A simple inverted pendulum model (SIPM) is used to calculate a center of gravity (CoG) trajectory from a reference zero moment point (ZMP) trajectory with an analytic form, which is based on the Fourier series. Fundamentally, we used a time segmentation based approach. For each segment, we defined its duration and boundary conditions, which are the key parameters of ZMP trajectory design. After designing the ZMP trajectory in each segment, we can automatically calculate the CoG trajectory by matching the boundary conditions and by calculating the coefficients between the time segments. The reference ZMP trajectory can be changed by updating the boundary conditions during walking. We successfully verified the proposed method through full-body dynamic simulations with variable step length.

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Boresch, Stefan, and Othmar Steinhauser. "Presumed versus real artifacts of the Ewald summation technique: The importance of dielectric boundary conditions." Berichte der Bunsengesellschaft für physikalische Chemie 101, no. 7 (July 1997): 1019–29. http://dx.doi.org/10.1002/bbpc.19971010706.

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Garay-Martinez, Roberto, Bejay Jayan, and Beñat Arregi. "Design of a Calorimetric Test Facility to Replicate Real Boundary Conditions in the Gulf Countries." E3S Web of Conferences 172 (2020): 11007. http://dx.doi.org/10.1051/e3sconf/202017211007.

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The design and modelling of a calorimetric test infrastructure for building envelopes is performed for the side-by-side assessment of different building envelope systems. The infrastructure is designed for representing transient weather conditions in Middle east. It consists of 3 “cold” experimental chambers and a larger “hot” experimental chamber. All three cold chambers have one equally sized envelope element exposed to the larger chamber. The test facility is designed to allow testing on walls and roofs, where different envelope insulation systems will be installed over a common substrate. Heating and cooling loads of all experimental chambers are calculated, and systematic load differences assessed. Heat flow across test samples and other surfaces in the test are calculated. Insulation levels of envelope surfaces in experimental chambers are specified to provide a good match between heat transfer across test samples and heat input to experimental chambers.

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