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Journal articles on the topic 'Multiple integral contours'
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1
Mihic, Ljubica, Aleksandar Pejcev, and Miodrag Spalevic. "Error bounds for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind." Filomat 30, no. 1 (2016): 231–39. http://dx.doi.org/10.2298/fil1601231m.
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For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -+1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.]
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Gupta, Preetam, and Srinivas G. "Aerodynamic Performance Enhancement of a Sports Vehicle Using Numerical Techniques." IOP Conference Series: Earth and Environmental Science 1100, no. 1 (2022): 012012. http://dx.doi.org/10.1088/1755-1315/1100/1/012012.
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Abstract Evaluation of vehicle aerodynamics is an integral part of automotive engineering. The aerodynamic performance of automobile has great influence on the power performance, economy, handling stability and ride comfort of the vehicle. In this context, the present work focuses on improving the aerodynamic performance of a modelled sports vehicle using numerical techniques. Baseline analysis of a research paper was conducted for validation of the results obtained in numerical simulations. Multiple turbulence models, flow boundary conditions, and inlet parameters were explored using Ansys Fluent Computational Fluid Dynamics software. The validation of the baseline data was proved using convergence, numerical and theoretical validation. Solution convergence parameters were Absolute Residual criteria and Mass Flow Rate. Grid Independency, Inlet Velocity and Flow Turbulence Model checks were employed to further refine the accuracy of simulations. This research studied and presented the effects of a two-flap spoiler on the aerodynamic performance of the vehicle using pressure, velocity, and eddy viscosity contours using simulations of incompressible air flow over the modelled car body. Improved flow contours exhibited a reduction of Coefficient of Drag and Lift parameters. Using Coefficient of Pressure (Cp) as a baseline parameter, multiple configurations of flow boundary conditions were explored. The literature consists of theoretical, experimental, and numerical aspects of the research papers and journals that were studied for this research. The objectives were to model, mesh and simulate a sports car to better understand the flow vortices and validate the aerodynamic flow parameters with the studied literature.
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LI, SHUAI, SHI-PING WANG, and A.-MAN ZHANG. "CHARACTERISTICS OF THE JET IMPACT DURING THE INTERACTION BETWEEN A BUBBLE AND A WALL." International Journal of Modern Physics: Conference Series 42 (January 2016): 1660157. http://dx.doi.org/10.1142/s2010194516601575.
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The dynamics of a toroidal bubble splitting near a rigid wall in an inviscid incompressible fluid is studied in this paper. The boundary integral method is adopted to simulate the bubble motion. After the jet impact, the vortex ring model is used to handle the discontinued potential of the toroidal bubble. When the toroidal bubble is splitting, topology changes are made tear the bubble apart. Then, the vortex ring model is extended to multiple vortex rings to simulate the interaction between two toroidal bubbles. A typical case is discussed in this study. Besides, the velocity fields and pressure contours surrounding the bubble are used to illustrate the numerical results. An annular high pressure region is generated at the splitting location, and the maximum pressure may be much higher than the jet impact. More splits may happen after the first split.
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Frédéric, Ayant, Kumar Prvindra, and Singh Harendra. "On unified infinite integral involving product of multivariable Gimel-function and others special functions." APPLIED SCIENCE PERIODICAL XXIII, no. 3, August 2021 (2021): 1–16. https://doi.org/10.5281/zenodo.6796914.
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The multivariable Gimel function [2] is an unified special function, it’s an extension of the multivariable Aleph-function defined by Ayant [1], the multivariable I-function defined by Prasad [9], the multivariable I-function defined by Prathima et al. [11] at a time, of course this function is a generalization of the multivariable H-function. To define this function, we use the multiple Mellin-Barnes integrals contour.
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Bobkov, V. A., M. A. Morozov, and A. A. Shupikova. "Algorithm for Recognizing an Underwater Pipeline from Stereo Images." Informacionnye Tehnologii 29, no. 12 (2023): 639–49. http://dx.doi.org/10.17587/it.29.639-649.
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The problem of recognition of an underwater pipeline (UP) from stereo images using an autonomous underwater robot (AUV) is considered in relation to the initial position of tracking the UP, or to situations where the previous section of the UP is hidden by interference (submerged in the ground, hidden by algae, etc.). The final result of the identification of the UP section, visible by the stereo camera, is the calculation of its center line and the detection of the relative position of the AUV and UP in the camera coordinate system. The article proposes a recognition method based on the selection of visible UP boundaries (contours) on vectorized images of a stereopair. At the stage of vectorization, noise is eliminated, illumination is equalized, and the image is processed using the Canny method to obtain a binary image. The construction of UP contours is performed using the algorithm proposed by the authors, which is a modification of the Hough method. The main feature of the proposed algorithm is a relatively high performance due to a multiple reduction in the amount of information being processed. Reducing the volume of processed data is done by pre-sorting the line segments in the vectorized image, and by optimizing the computational scheme in the algorithm. The experiments also showed that the algorithm can detect the visible boundaries of the UP on blurry, non-contrasting images. The algorithmic basis of the method is described in detail, including: — search and construction of the most reliable UP boundaries using the method of the integral contribution of the line segments to the line formation; generation and selection of point features belonging to the surface of the UP (due to the constructed contours); calculation of the 3D direction of the center line; calculation of the center line of the visible section of UP; —calculation of the AUV position parameters relative to the UP required for the AUV control system. The centerline calculation is performed using the least squares method using point features belonging to the surface of the UP. The performed computational experiments on virtual scenes using the real texture of the seabed confirm the operability of the implemented approach and the possibility of its application for the inspection of underwater infrastructure.
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Shao, Zijia, Shuohao Wang, and Hetian Yu. "Application of the Residue Theorem to Euler Integral, Gaussian Integral, and Beyond." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 311–16. http://dx.doi.org/10.54097/hset.v38i.5821.
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The paper is divided into three different parts, which use the residue theorem to solve several different integrals, namely, the Euler integral, the Gaussian integral, the Fresnel integral, and so forth. The process of using the resiude theorem to determine these integrals is to first turn the integrals into convenient forms of complex integrals, and then find integral perimeters so that any integral on one of the curves is the required integral, through the drawing observation of the contour to write the original integral into the form of multiple integral. By studying the resiude theorem to solve the problem of complex integrals, it is demonstrated that the resiude theorem is actually a process that makes the calculation easier. These solved integrals have a wide range of applications including the study of the refraction of light, analytics, probability theory, combinatorial mathematics, and unification of the continuous Fourier transform.
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Kravchenko, S. A. "Sociology on the move: The demand for the humanistic digital turn." RUDN Journal of Sociology 19, no. 3 (2019): 397–405. http://dx.doi.org/10.22363/2313-2272-2019-19-3-397-405.
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Digitalization of society has ambivalent consequences: there are new benefits (‘smart’ technologies, artificial intellect, multiple knowledge), but at the same time digital risks and metamorphoses that traumatize the behavior and thinking of people, alienate them from social ties and life-worlds. These processes have become a challenge for sociology and other social sciences that strive to develop new approaches, among which the digital and humanistic turns are the most relevant. The author aims at (a) analyzing the impact of digitalization on the production of metamorphoses and side effects on society and man, which are related to new complex risks and manifest challenges to sociology; (b) developing the contours of the conception of ‘the digital turn in sociology’ and identifying its essence in comparison with other, previous turns in sociology - linguistic, risk, cultural, etc.; (c) proposing the means that allow to overcome or minimize the side effects of the existing type of digitalization - the author argues for the demand to move sociology in the direction of the integral use of the instruments of the digital and humanistic turns. The article considers new challenges to mankind and scientific knowledge as determined not so much by the very process of digitalization, but by its existing type based on principles of formal rationality, pragmatism, and mercantilism neglecting, in fact, life-worlds of people. This type of digitalization is not ‘universal’ and can be changed by an alternative humanistic trend of digitalization. In order to begin establishing the humanistic trend of digitalization scientists should integrate the theoretical instruments of the proposed digital turn with other interdisciplinary turns and especially with the humanistic turn.
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Xu, Guang Shen, Ya Ning Wang, and Kuang Kuang Jin. "Research of Mask Image’s Generation Based on STL Model for Integral Stereolithography System." Applied Mechanics and Materials 540 (April 2014): 468–71. http://dx.doi.org/10.4028/www.scientific.net/amm.540.468.
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To solve the problem that generation of mask image based on STL model for integral Stereolithography System, a novel method that can generate mask image based on STL model for integral Stereolithography System is proposed. Firstly, contour data is obtained with STL model slicing software; then properties of contour loop’s internal and external are determined; and then the order of contour loop’s filling is determined; Lastly, the contour loop is filled with the order, and mask image based on STL model can be produced. Generation of mask image is implemented with VC++6.0. The verification result indicates that this method can fill multiple nested contour loops correctly and generate correct mask image for integral Stereolithography System.
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Chang, JH, and LW Guo. "Evaluation of surface energy for formation of multiple edge cracks using Medg-integral." International Journal of Damage Mechanics 29, no. 9 (2020): 1445–64. http://dx.doi.org/10.1177/1056789520922281.
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A novel contour integral approach termed Medg is introduced for computation of the surface energy required for the formation of multiple edge cracks. The method is developed by reinterpretation of the conventional M-integral with deliberate delimitation of integration contour and selection of coordinate origin. Due to path independence, this method is efficient, easy to implement by using finite elements, and does not require a complicated mesh around the crack tips for good accuracy. Attention is also addressed to discussion of the size effects on proper interpretation of its physical meaning. The adequacy of the numerical results computed for the finite size corrections has been validated by using some of the available empirical formulations. It is observed that the size effect can be neglected when the crack size remains under one-tenth of the structure size. The results of a specific multi-cracked geotechnical structure suggest that, the damage state such as degradation of the structural stiffness due to the presence of edge cracks can be properly inspected by using Medg.
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Lenells, Jonatan, and Fredrik Viklund. "Asymptotic Analysis of Dotsenko–Fateev Integrals." Annales Henri Poincaré 20, no. 11 (2019): 3799–848. http://dx.doi.org/10.1007/s00023-019-00849-5.
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Abstract We develop a method for evaluating asymptotics of certain contour integrals that appear in conformal field theory under the name of Dotsenko–Fateev integrals and that are natural generalizations of the classical hypergeometric functions.We illustrate the method by establishing a number of estimates that are useful in the context of martingale observables for multiple Schramm–Loewner evolution processes.
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Lakhno, Valerii, Volodimir Maliukov, Larysa Komarova, Dmytro Kasatkin, Tetiana Osypova, and Yehor Chasnovskyi. "OPTIMIZATION OF PLACEMENT OF INFORMATION PROTECTION MEANS BASED ON THE APPLICATION OF A GENETIC ALGORITHM." Cybersecurity: Education, Science, Technique 1, no. 17 (2022): 6–20. http://dx.doi.org/10.28925/2663-4023.2022.17.620.
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the article considers the possibilities of modifying the genetic algorithm (GA) for solving the problem of selecting and optimizing the configurations of information protection means (IPR) for security circuits of information and communication systems (ICS). The scientific novelty of the work lies in the fact that in GA, as criteria for optimizing the composition of IPR, it is proposed to use the total value of risks from loss of information, as well as the integral indicator of IPR and cost indicators for each class of IPR. The genetic algorithm in the task of optimizing the selection of the composition of the IPR for ICS is considered as a variation of the problem associated with multiple selection. In such a statement, the optimization of the placement of IPR along the contours of ICS protection is considered as a modification of the combinatorial problem about the backpack. The GA used in the computing core of the decision support system (DSS) differs from the standard GA. As part of the GA modification, chromosomes are presented in the form of matrices, the elements of which are numbers that correspond to the numbers of the IPR in the ICS nodes. In the process of GA modification, k-point crossover was applied. The fitness function is represented as the sum of efficiency coefficients. At the same time, in addition to the traditional absolute indicators of the effectiveness of IPR, the total value of risks from loss of information, as well as cost indicators for each class of IPR are taken into account. The practical value of the research lies in the implementation of the DSS based on the proposed modification of the GA. Computational experiments on the selection of a rational software algorithm for the implementation of the model were performed. It is shown that the implementation of GA in DSS allows to speed up the search for optimal options for the placement of cyber security means (CS) for ICS by more than 25 times. This advantage allows not only to perform a quick review of various options of hardware and software IPR and their combinations for ICS, but also to further combine the proposed algorithm with existing models and algorithms for optimizing the composition of ICS cyber security circuits. Potentially, such a combination of models and algorithms will provide an opportunity to quickly rebuild ICS protection, adjusting its profiles in accordance with new threats and classes of cyberattacks.
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Judt, Paul O., and Andreas Ricoeur. "Crack growth simulation of multiple cracks systems applying remote contour interaction integrals." Theoretical and Applied Fracture Mechanics 75 (February 2015): 78–88. http://dx.doi.org/10.1016/j.tafmec.2014.11.001.
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Yang, Ouyang, Zhang, Zhang, Hu, and Liu. "Receptance-Based Dominant Eigenvalues Computation of Controlled Vibrating Systems with Multiple Time-Delays Using a Contour Integral Method." Applied Sciences 9, no. 23 (2019): 5263. http://dx.doi.org/10.3390/app9235263.
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The computation of dominant eigenvalues of second-order linear control systems with multiple time-delays is tackled by using a contour integral method. The proposed approach depends on a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on the reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system, and has the same eigenvalues as those of the original. Then, the eigenvalues computation is equivalent to solve a nonlinear eigenvalue problem of the associated characteristic matrix by using a contour integral method. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
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Buschman, R. G., and H. M. Srivastava†. "Convergence regions for some multiple Mellin‐Barnes contour integrals representing generalized hypergeometric functions." International Journal of Mathematical Education in Science and Technology 17, no. 5 (1986): 605–9. http://dx.doi.org/10.1080/0020739860170509.
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VALVI, F. N., and V. S. GEROYANNIS. "COUNTING AND COMPUTING THE EIGENVALUES OF A COMPLEX TRIDIAGONAL MATRIX, LYING IN A GIVEN REGION OF THE COMPLEX PLANE." International Journal of Modern Physics C 24, no. 02 (2013): 1350008. http://dx.doi.org/10.1142/s0129183113500083.
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We present a numerical technique for counting and computing the eigenvalues of a complex tridiagonal matrix, lying in a given region of the complex plane. First, we evaluate the integral of the logarithmic derivative p′(λ)/p(λ), where p(λ) is the characteristic polynomial of the tridiagonal matrix, on a simple closed contour, being the closure of that region. The problem of evaluating this integral is transformed into the equivalent problem of numerically solving a complex initial value problem defined on an ordinary first-order differential equation, integrated along this contour, and solved by the Fortran package dcrkf54.f95 (developed recently by the authors). In accordance with the "argument principle," the value of the contour integral, divided by 2πi, counts the eigenvalues lying in the region. Second, a Newton–Raphson (NR) method, fed by random guesses lying in the region, computes the roots one by one. If, however, NR signals that |p′(λ)| converges to zero, i.e. a multiple root probably exists at the current value λ, then counting the roots within an elementary square centered at λ reveals the multiplicity of this root.
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Aktulga, Hasan Metin, Lin Lin, Christopher Haine, Esmond G. Ng, and Chao Yang. "Parallel eigenvalue calculation based on multiple shift–invert Lanczos and contour integral based spectral projection method." Parallel Computing 40, no. 7 (2014): 195–212. http://dx.doi.org/10.1016/j.parco.2014.03.002.
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Veldhuis, J. D., and M. L. Johnson. "A novel general biophysical model for simulating episodic endocrine gland signaling." American Journal of Physiology-Endocrinology and Metabolism 255, no. 6 (1988): E749—E759. http://dx.doi.org/10.1152/ajpendo.1988.255.6.e749.
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A multiple-parameter convolution integral is used to define and generate waveforms that quantitatively and qualitatively resemble the experimentally observed behavior of episodic endocrine signals. Our formulation of the convolution integral in terms of multiple distinct parameters with statistically bounded values allows investigators to quantitatively model variations in the duration, amplitude, frequency, and/or contour of the hormone secretory pulse, as well as alterations in rates of endogenous hormone clearance. Here we demonstrate the applicability of this new concept of endocrine gland signaling to experimentally observed (physiological) endocrine data, parameter sensitivity analysis, the evaluation of statistical errors in hormone peak detection, and the estimation of random-pulse coincidence rates between two independent endocrine series.
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Chen, Xiao-Ping, and Hao Liu. "A Novel Method to Determine the Local Stability of the n-Species Lotka-Volterra System with Multiple Delays." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7920482.
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The n-species Lotka-Volterra system with discrete delays is considered. The local asymptotic stability of positive equilibrium is investigated based on a contour integral method. The main purpose of this paper is to propose a new and general algorithm to study the local asymptotic stability of the positive equilibrium for then-dimensional Lotka-Volterra system. Some numerical experiments are carried out to show the effectiveness of the proposed method.
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Adhikari, Ganesh Prasad. "EXPANDING THE LAURENT SERIES WITH ITS APPLICATIONS." JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 10, no. 01 (2022): 173–84. http://dx.doi.org/10.56827/jrsmms.2022.1001.15.
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In Nepal, there are many mathematics subjects taught at university level. Among them, complex analysis is the most powerful. In complex analysis, the Laurent series expansion is a well-known subject because it may be used to find the residues of complex functions around their singularities. It turns out that computing the Laurent series of a function around its singularities is an effective way to calculate the integral of the function along any closed contour around the singularities as well as the residue of the function. Learning the Laurent series concepts can be difficult, and many students struggle to develop adequate understanding, reasoning, and problem-solving skills. Therefore, this article presents multiple practical examples where the Laurent series of a function is found and then utilized to compute the integral of the function over any closed contour around the singularities of the function, based on the theory of the Laurent series.
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Zhao, Yani, and Franco Ferrari. "A study of polymer knots using a simple knot invariant consisting of multiple contour integrals." Journal of Statistical Mechanics: Theory and Experiment 2013, no. 10 (2013): P10010. http://dx.doi.org/10.1088/1742-5468/2013/10/p10010.
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Ouyang, P. R., T. Dam, and V. Pano. "Cross-coupled PID control in position domain for contour tracking." Robotica 33, no. 6 (2014): 1351–74. http://dx.doi.org/10.1017/s0263574714000769.
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SUMMARYAccurate contour tracking is one of the main tasks in modern manufacturing processes. By considering coupling effects among multiple axes, this paper proposes a cross-coupled proportional-integral-derivative (PID) control developed in position domain, and the controller is applied to a multi-axis computer numerical control (CNC) machine for contour tracking performance improvement. Stability analysis is conducted for the developed position domain cross-coupled PID control using the Lyapunov method, and guidelines for the selection of control gains are provided. The contour tracking performance are improved compared to an equivalent time domain controller, since the reference axis in position domain control does not contribute any error to the overall contouring error of the system. Simulation results demonstrate the effectiveness of cross-coupled PID position domain control for both linear and circular contour tracking, and prove the robustness of the controller to deal with random disturbances. It also shows that position domain cross-coupled PID control provides better contour tracking performance over position domain PID control and the equivalent time domain PID control.
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Hai, N. T., and H. M. Srivastava. "The convergence problem of certain multiple Mellin-Barnes contour integrals representing H-functions in several variables." Computers & Mathematics with Applications 29, no. 6 (1995): 17–25. http://dx.doi.org/10.1016/0898-1221(95)00003-h.
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Batool, Tahira, Aly R. Seadawy, and Syed T. R. Rizvi. "Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields." Nonlinear Analysis: Modelling and Control 28 (February 22, 2023): 1–24. http://dx.doi.org/10.15388/namc.2023.28.31449.
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In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions.
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Tatarina, Alena V., Svetlana N. Dubrovskikh, and Elmira A. Gumerova. "Ultrasound diagnostics in the assessment of traumatic peripheral nerve damage in combat trauma." Digital Diagnostics 4, no. 1S (2023): 129–32. http://dx.doi.org/10.17816/dd430369.
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BACKGROUND: Traumatic peripheral nerve damage is a significant clinical and social problem, which is characterized by a high level of disability in young patients.
 AIM: To assess the diagnostic efficiency of ultrasound in the diagnosis of peripheral nerve damage in combat trauma.
 METHODS: A total of 163 patients (362 peripheral nerves) were examined. The duration of traumatic nerve damage was 2273 days. All patients were men aged 2048 years. Ultrasound was performed with 717 MHz linear transducers on an ACUSSON S2000 device using standard technique in B-mode, in longitudinal and transverse scanning planes, with the use of Doppler techniques. Statistical analysis was conducted to assess diagnostic efficiency. Calculation of operational (sensitivity and specificity) and integral (accuracy) characteristics was performed by the qualitative assessment of the reference method (surgical intervention) and the method under study (ultrasound).
 RESULTS: Peripheral nerve damage resulted from combat trauma. In 120 (73.6%) cases, injuries of the limbs were accompanied by injuries of the osteoarticular apparatus and vessels. A total of 274 (75.7%) nerves had signs of traumatic damage. Multiple nerve injuries were observed in 95 (58.3%) people. Nerves of the upper extremities were damaged more frequently (185 [67.5%]) compared to nerves of the lower extremities (89 [32.5%]). Contusional structural changes were observed in 181 (66%) nerves. Impairment of anatomical integrity was diagnosed in 46 (16.8%) nerves, while complete impairment was found in 29 (10.6%) cases with the presence of diastasis between the nerve ends. Early after injury, a wound canal and hematomas were visualized near the nerve. In 4 cases, a foreign body of metallic density was visualized in the nerve sheath. After 3 weeks from the moment of injury, terminal neuromas were observed. The neuroma sizes for the proximal and distal ends were 0.50.3 to 1.60.6 cm and 0.40.2 to 1.30.6 cm (avascular), respectively. Adjacent sections of the nerve over 35 cm were thickened and characterized by echo structure, however, with thickening of all fasciculi and blood flow observed along the periphery of the nerve. Marginal nerve damage was observed in 17 (6.2%) people. In case of marginal neuroma, a significant nerve thickening of 1.43.2 times over a short distance (from 0.4 cm to 1.5 cm) with loss of bundle differentiation of the part of the nerve, pronounced decrease in echogenicity, and absence of Doppler signal was detected. Nerve compression in 47 cases (17.1%) was accompanied by 1.22.3 times thickening of nerve trunks, indistinct contours, decreased echogenicity, and significant changes in the nerve structure. Compression was due to cicatricial changes, hematomas, foreign bodies, bone fragments, and in 2 cases spokes from external fixation devices. A total of 106 patients underwent surgery.
 CONCLUSIONS: The ultrasound sensitivity and specificity were 96% and 67%, respectively. The peculiarities of the examination included extensive soft tissue defects and external fixation devices, which significantly complicated the examination. The diagnostic accuracy was 91%. A pronounced cicatricial process (70%) was the main cause of false-positive (6.6%) and false-negative (2.8%) results.
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Chang, J. H., and J. S. Lin. "Surface Energy for Creation of Multiple Curved Cracks in Rubbery Materials." Journal of Applied Mechanics 74, no. 3 (2006): 488–96. http://dx.doi.org/10.1115/1.2338058.
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A fracture parameter Mc is proposed for evaluation of the surface energy associated with the creation of multiple curved cracks in 2D rubbery solids under the action of large deformation. Based on the concept of the M-integral, the parameter is developed by performing the integration along a closed contour enclosing all the cracks and with respect to a reference coordinate system originated at the geometric center of all the crack tips. The integration is shown to be path-independent so that the complicated singular stress field in the near-tip areas need not be involved in the calculation. It is thus suggested that Mc be possibly used as a fracture parameter for describing the degradation of material and∕or structural integrity caused by irreversible evolution of multiple curved cracks in a rubbery media.
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Frédéric, Ayant, Kumar Prvindra, and Singh Harendra. "Multidimensional Laguerre Transform and Modified of generalized multivariable A-function." APPLIED SCIENCE PERIODICAL XXIII, no. 2, May 2021 (2021): 14–28. https://doi.org/10.5281/zenodo.6796596.
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<em> The object of this paper is to use the multidimensional Laguerre transforms involving the modified of </em> <em>generalized multivariable A-function. In the end, we shall see several corollaries and remarks.</em>
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Zhang, Jianming, Wensheng Yang, Jun Chen, and Rui Xu. "Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method." Applied Sciences 11, no. 17 (2021): 8111. http://dx.doi.org/10.3390/app11178111.
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Stress intensity factor (SIF) is one of three important parameters in classical linear elastic fracture mechanics (LEFM). The evaluation of SIFs is of great significance in the field of engineering structural and material damage assessment, such as aerospace engineering and automobile industry, etc. In this paper, the SIFs of a central straight crack plate, a slanted single-edge cracked plate under end shearing, the offset double-edge cracks rectangular plate, a branched crack in an infinite plate and a crucifix crack in a square plate under bi-axial tension are extracted by using the p-version finite element method (P-FEM) and contour integral method (CIM). The above single- and multiple-crack problems were investigated, numerical results were compared and analyzed with results using other numerical methods in the literature such as the numerical manifold method (NMM), improved approach using the finite element method, particular weight function method and exponential matrix method (EMM). The effectiveness and accuracy of the present method are verified.
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Dimitrov, Evgeni. "Six-vertex Models and the GUE-corners Process." International Mathematics Research Notices 2020, no. 6 (2018): 1794–881. http://dx.doi.org/10.1093/imrn/rny072.
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Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.
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Haasjes, R., and A. P. Berkhoff. "A solution method for active suppression of reflections in anechoic chambers." Journal of the Acoustical Society of America 157, no. 1 (2025): 569–78. https://doi.org/10.1121/10.0034881.
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A solution method to improve an anechoic chamber at low frequencies with the use of active noise control is presented. The approach uses the Kirchhoff-Helmholtz integral to compute the reflected sound field resulting from the primary sources together with an algorithm to compute the filter coefficients of a controller driving secondary sources on the walls of the enclosure using reference signals as inputs, which are measured on a contour enclosing the primary sources. A causal frequency domain method with conjugate gradient iterations is derived to determine the controller. The method is sufficiently efficient to allow computation of a causal time-domain controller with hundreds of secondary sources and hundreds of reference sensors in two- (2D) or three-dimensional configurations using a fully coupled multiple-input multiple-output system. The paper shows the results of a simulation with 200 secondary sources, 200 reference sensors, and 225 performance sensors based on a 2D finite element simulation. The method is verified in real-time in an experiment with the objective to suppress the reflections from the walls in a smaller 2D setup. Measurements with verification microphones show that the reverberation time is effectively reduced in the real-time experiment.
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Liu, T., S. Kitipornchai, K. M. Liew, and G. Wang. "Analysis of Acousto-Ultrasonic Characteristics for Contact-Type Transducers Coupled to an Orthotropic Composite Plate." Journal of Vibration and Acoustics 121, no. 4 (1999): 460–67. http://dx.doi.org/10.1115/1.2894003.
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Acousto-ultrasonic input-output characteristics for contact-type transmitting and receiving transducers coupled to a thin orthotropic composite plate are analyzed in this paper. By introducing the point source/point receiver assumption, the governing equations of the problem, which relates to wave generation, wave propagation and wave reception, are first established. Using the multiple integral transform method, contour integration technique and some complex function theories, a spectral analysis method which is completely different from the present wave path tracing method for this problem is developed. From this approach, the spectral response of the normal contact force between the receiving transducer and the plate, due to an arbitrary input interrogation pulse excited by the transmitting transducer, is expressed in explicit form. Based on this, some physical properties involved with the output of the receiver are examined in the frequency domain. Finally, combining the fast Fourier transform (FFT) technique, some time domain numerical results are calculated to show the input-output characteristics of the AU system considered.
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Akemann, Gernot, Eugene Strahov, and Tim R. Würfel. "Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles." Annales Henri Poincaré 21, no. 12 (2020): 3973–4002. http://dx.doi.org/10.1007/s00023-020-00963-9.
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Abstract Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic polynomials in general polynomial ensembles. Using Schur polynomials, we show that polynomial ensembles constitute Giambelli compatible point processes, leading to a determinant formula for such ratios as in classical ensembles of random matrices. In the second part, we introduce invertible polynomial ensembles given, e.g. by random matrices with an external field. Expectation values of arbitrary ratios of characteristic polynomials are expressed in terms of multiple contour integrals. This generalises previous findings by Fyodorov, Grela, and Strahov. for a single ratio in the context of eigenvector statistics in the complex Ginibre ensemble.
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Amnuanpol, S., and S. Kongkarat. "Free surface from convective flow in a vibrated granular medium." Europhysics Letters 150, no. 3 (2025): 37001. https://doi.org/10.1209/0295-5075/adb44f.
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Abstract Vertical vibration of a granular medium with greater acceleration than g creates a pair of convection rolls with opposite rotation propagating along its edges. For 2D monodisperse disks, the top free surface bends downward for inclined walls with angles with respect to the horizontal axis. It remains flat for , identical to rotational invariance of the hexagonal close packing, and bends upward for . Grain boundaries of alternating 5- and 7-fold disclinations emerge at the center of a container to separate two hexagonal lattices, on the left and right halves of a container, with different orientation. When the opening angle of inclined walls is equal to an integral multiple of , namely and , such grain boundaries disappear. For 2D bidisperse disks, the top free surface is still smooth but is less deformed from a flat profile. Hexagonal close packing exists only locally in small plaquettes without grain boundaries for all angles θ. In hydrodynamic description the monodisperse free surface is well described by a contour of the constant pressure calculated from the Navier-Stokes equation.
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Mikishanina, E. A. "Boundary value problems for systems of inhomogeneous polyharmonic equations with applications in the theory of thin shells and plates." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 136–44. http://dx.doi.org/10.15593/perm.mech/2019.4.13.
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A number of problems in the theory of elasticity, the theory of heterogeneous media, the theory of thin shells and plates is reduced to solving boundary value problems for systems of inhomogeneous polyharmonic equations. The paper proposes a numerical algorithm for solving systems of polyharmonic equations of the form in single-connected and multi-connected areas with a piecewise smooth contour with specified boundary conditions. Two cases are considered when the function is a known polyharmonic function and when the function is also the desired polyharmonic function. The boundary conditions can have the form similar to Dirichlet conditions, Neiman conditions, and can have a mixed form when on one part of the boundary conditions of the Dirichlet type are given, and on the other - hand, the conditions of the Neiman type. On the basis of multiple applications of the Laplace operator and the boundary element method, which is based on the green integral identity, the given system is reduced to a system of integral identities. After approximating the boundary by an inscribed n-gon and discretizing the system of integral identities, the latter is reduced to a system of linear algebraic equations, which is conveniently represented as a system of matrix equations. The existence and uniqueness of the solution follows from the existence of a unique solution of a system of linear algebraic equations. Special attention is paid to the application of the algorithm to the solution of problems on the bending of thin plates, and the bending load can be a known function, and can be an unknown polyharmonic function of an arbitrary order with given boundary conditions. The problem of bending a thin plate of elliptic shape with a known load on the surface is solved, as well as the problem of bending a thin square plate with an unknown load, which is the solution of a harmonic equation with given boundary conditions. The level lines are constructed and the forms of curved plates are given.
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EL BHILAT, Hanan, MABCHOUR Hassan, SALMI Houda, HACHIM Abdelilah, and EL HAD Khalid. "EXPERIMENTAL INVESTIGATION OF THE INFLUENCE OF MULTI-RECYCLING ON THE FRACTURE BEHAVIOR OF POST CONSUMER HIGH IMPACT POLYSTYRENE FROM DISPOSABLE CUPS EVALUATED BY THE J-INTEGRAL APPROACH." IIUM Engineering Journal 23, no. 1 (2022): 268–81. http://dx.doi.org/10.31436/iiumej.v23i1.1693.
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The aim of the present paper is to study the effect of multi-recycling on the fracture behavior of high impact polystyrene from disposable cups. After collecting and washing the material, it was subjected to six cycles of recycling. After each cycle, it was subjected to tensile tests to determine the R-curves. The theory of the J-integral contour has been used for the development of a characterization method of the fracture strength appropriate to the case of this non-linear elastoplastic polymer material. To this end, the method of multiple specimens (Single edge notch tension SENT) of thin thickness was used, by introducing cracks of the same lengths to several identical test pieces. The results suggested a slight decrease in crack resistance of recycled high impact polystyrene, especially during the first cycle, demonstrated by a comparison of JIC values related to initiation of crack propagation. The fracture energy absorbed as a function of the cycles suggested a weakening within the material. ABSTRAK: Tujuan kajian ini adalah bagi mengkaji kesan tindak balas pada pelbagai peringkat-kitar semula ke atas kerapuhan polisterin berimpak tinggi pada cawan pakai buang. Selepas mengumpul dan membasuh cawan ini, terdapat enam peringkat kitar semula. Pada setiap peringkat, ianya akan melalui ujian tegangan bagi mendapatkan lengkung-R. Teori kamiran-J kontur telah digunakan bagi mencipta kaedah khas bagi mengkaji kekuatan retakan bersesuaian bagi kes bahan polimer elastoplastik yang tidak-linear. Sehingga kini, kaedah Regangan Tepi Takuk Tunggal (SENT) telah digunakan pada spesimen berketebalan rendah, dengan menghasilkan keretakan sama panjang di permulaan kajian di buat pada pelbagai bahan uji yang serupa. Dapatan kajian menunjukkan rintangan pada retakan telah berkurang sedikit pada polisterin kitar semula berimpak tinggi, terutama pada kitaran pertama, yang ditunjukkan pada nilai JIC pada permukaan rambatan retakan awal. Tenaga kerapuhan yang meresap pada setiap kitaran menunjukkan bahan telah melemah dari dalam.
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Khanal and Weijermars. "Modeling Flow and Pressure Fields in Porous Media with High Conductivity Flow Channels and Smart Placement of Branch Cuts for Variant and Invariant Complex Potentials." Fluids 4, no. 3 (2019): 154. http://dx.doi.org/10.3390/fluids4030154.
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A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still describe the same type of physical flow (but only rotated by π/2). Such invariants can be formulated with Euler’s formula to depict the same flow for any arbitrary orientation with respect to the coordinate system used. In contrast, variant complex potentials, when swapping their real and imaginary parts, will result in two fundamentally different physical flows. Next, we show that the contour integrals of the real and imaginary part of simple variant and invariant complex potentials generally do not generate any discernable branch cut problems. However, complex potentials due to the multiple superpositions of simple flows, even when invariant, may involve many options for selecting the branch cut locations. Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced permeability flow channels. After a discussion of the branch cut solutions, applications to a series of synthetic and field examples with enhanced permeability flow channels are given with examples of the streamline and pressure field solutions.
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Plante, Mathieu, Jean-François Lemieux, L. Bruno Tremblay, et al. "A sea ice deformation and rotation rate dataset (2017–2023) from the Environment and Climate Change Canada automated sea ice tracking system (ECCC-ASITS)." Earth System Science Data 17, no. 2 (2025): 423–34. https://doi.org/10.5194/essd-17-423-2025.
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Abstract. Sea ice forms a thin but horizontally extensive boundary between the ocean and the atmosphere and has complex, crust-like dynamics characterized by intermittent sea ice deformations. The heterogeneity and localization of these sea ice deformations are important characteristics of the sea ice cover that can be used to evaluate the performance of dynamical sea ice models against observations across multiple spatial and temporal scales. Here, we present a new pan-Arctic sea ice deformation and rotation rate (SIDRR; https://doi.org/10.5281/zenodo.13936609, Plante et al., 2024a) dataset derived from the RADARSAT Constellation Mission (RCM) and Sentinel-1 (S1) synthetic aperture radar (SAR) imagery from 1 September 2017 to 31 August 2023. The SIDRR estimates are derived from contour integrals of triangulated ice motion data, obtained from the Environment and Climate Change Canada automated sea ice tracking system (ECCC-ASITS). The SIDRR dataset is not regularized and consists of stacked data from multiple SAR images computed on a range of spatial (4–10 km) and temporal (0.5–6 d) scales. It covers the entire Arctic Ocean and all peripheral seas except the Okhotsk Sea. Uncertainties associated with the propagation of tracking errors on the deformation values are included. We show that rectangular patterns of deformation features are visible when the sampled deformation rates are lower than the propagation error. This limits the meaningful information that can be extracted in areas with low SIDRR values but allows for the study of linear kinematic features with a high SIDRR signal-to-noise ratio. The spatial coverage and range of resolutions of the SIDRR dataset provide an interesting opportunity to investigate regional and seasonal variability in sea ice deformation statistics across scales, and these data can also be used to determine metrics for model evaluation.
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SILVA, Rogério Mariotto Bitetti da, Fernando A. M. HERBELLA, and Daniel GUALBERTO. "NORMATIVE VALUES FOR A NEW WATER-PERFUSED HIGH RESOLUTION MANOMETRY SYSTEM." Arquivos de Gastroenterologia 55, suppl 1 (2018): 30–34. http://dx.doi.org/10.1590/s0004-2803.201800000-40.
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ABSTRACT BACKGROUND: Esophageal manometry is the most reliable method to evaluate esophageal motility. High resolution manometry (HRM) provides topographic contour colored plots (Clouse Plots) with simultaneous analysis from the pharynx to the stomach. Both solid state and water-perfused systems are available. OBJECTIVE: This study aims to determinate the normative data for a new water-perfused HRM. METHODS: HRM was made in 32 healthy volunteers after 8 hours fasting. HRM system used consisted of a 24-channel water-perfused catheter (Multiplex, Alacer Biomedica, São Paulo, Brazil). The reusable catheter is made of polyvinyl chloride (PVC) with 4.7 mm of diameter. Side holes connected to pressure transducers are spaced 2 cm for the analysis from the pharynx to the lower esophageal sphincter (LES). Holes are spaced 5 mm and 120° in a spiral disposition in the LES area. The sensors encompass 34 cm in total. Upper esophageal sphincter (UES) parameters studied were basal and relaxation pressures. Esophageal body parameters were distal contractile integral (DCI), distal latency (DL) and break. LES parameters studied were basal pressure, integrated residual pressure (IRP), total and abdominal length. Variables are expressed as mean ± standard deviation, median (interquartile range) and percentiles 5-95th. RESULTS: All volunteers (17 males, aged 22-62 years) completed the study and tolerated the HRM procedure well. Percentiles 5-95th range were calculated: Upper Esophageal Sphincter (UES) basal pressure 16.7-184.37 (mmHg), DL: 6.2-9.1 (s), DCI: 82.72-3836.61 (mmHg.s.cm), break: <7.19 (cm), LES basal pressure: 4.89-37.16 (mmHg), IRP: 0.55-15.45 (mmHg). CONCLUSION: The performance and normative values obtained for this low-cost water-perfused HRM seems to be adequate for clinical use.
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Squire, Shane, Sharon Langston, and James Donley. "probGRV: a workflow for geostatistical depth conversion and probabilistic assessment of gross rock volume." APPEA Journal 54, no. 1 (2014): 91. http://dx.doi.org/10.1071/aj13012.
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Understanding and estimating the probability of geological success (Pg) and original hydrocarbon-in-place (OHIP) are an integral part of the geoscientist’s role from exploration though to development. This paper presents a workflow developed at Santos for the systematic assessment of two key elements in this process: the probability of structural closure (Pcl); and, the estimation of the uncertainty of gross rock volume (GRV). There are two distinct parts to the workflow. Firstly, Kriging and sequential Gaussian simulation (SGS) are used in map-based, seismic time-to-depth conversion to generate multiple equi-probable depth maps (in the order of 1,000+ realisations). Numerous depth conversion methods are considered where appropriate. Secondly, every depth map realisation is validated for structural closure around a target location (e.g. a proposed or existing well). Primary outputs from the workflow include estimates of Pcl, and probability distributions of GRV and pool area for valid maps, which may then be used directly in estimating geological risk and OHIP. Secondary outputs from the workflow include basic statistics associated with depth conversion uncertainty, such as target depth prognosis and the distribution of the depth to lowest closing contour. The ultimate objective is to provide the interpreter with a greater appreciation of the range of possible outcomes given the uncertainty in structural geometry. This workflow, named probGRV, has been designed and developed within Santos using commercially available geophysical software and in-house proprietary software. During the past few years, the workflow has been implemented on key assets at various stages of the prospect/field life cycle and in both pre- and post-drilling campaigns for audit purposes. Case studies from the Cook Field in the onshore Eromanga Basin and the Finucane South Field in the offshore Carnarvon Basin are shown to illustrate the methods and results.
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Lam Kai, Shun. "A Verification of Riemann Non-Trivial Zeros by Complex Analysis by Matlab™ Computation." European Journal of Statistics and Probability 11, no. 1 (2023): 69–83. http://dx.doi.org/10.37745/ejsp.2013/vol11n16983.
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With my most recent paper, I tried to prove the Riemann Hypothesis by catching out those contradictory parts of the non-trivial zeros. In the present paper, I will try to verify these known values of Riemann nontrivial zeros by first using U.S.A. Matlab coding with a list of well-organized complex analysis theories. At the same time, as the major core of my verification is just a mono-direction one (i.e. there may be a possibility of the missing non-trivial zeros although the residue value is zero), hence this author try to solve such problem by assuming that there are some other zeros existing between the two known zeros but the contradiction arises – as singularity implies the residue has a value with a multiple of 2πi. In addition, this author also apply the ingenious design (or a hybrid skill) with Feynman technique and Integration by parts to solve a special zeta function integral. Next, this author finds that one may consider those non-trivial zeros as a Fourier transform (or an impulse) between other normal complex numbers. The result is consistent with my previous papers in quantum physics [23], [25] for the electron jumps or reverse. Hence, we may get the (dirac) delta equation for Riemann Zeta. Then we may formulate our quantum circuit & computer. Finally, this author concludes all findings with an algorithm for searching, finer and checking the non-trivial zeros like below: Step 1: Use the computer software with some suitable program codes for an elementary search of feasible non-trivial zeta values among the closed real-complex plane interval – Method Matlab Simulation for searching zeta zeros; Step 2: Substitute back the values laying in the contour interval for zeta as found in Step 1 into the limit of ln(zeta(z))/((zeta'(z)) ) in order to adjust the answer in a finer and accurate way (just like the case of Newton’s method etc) with more decimal digitals – Method Ingenious Design for finer the zeta zero’s values; Step 3: Employ the Cauchy Residue Theorem for a check and hence confirm the previous found non-trivial zeta roots’ uniqueness without any zeta zeros laying in between the two consecutive zeta roots – Method Cauchy’s Residue for checking those already found zeta zeros.
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Bressloff, Paul C., Jack D. Cowan, Martin Golubitsky, Peter J. Thomas, and Matthew C. Wiener. "Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 356, no. 1407 (2001): 299–330. http://dx.doi.org/10.1098/rstb.2000.0769.
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This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants comprising (i) gratings, lattices, fretworks, filigrees, honeycombs and chequer–boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv) spirals. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex (henceforth referred to as V1)—the retinocortical map—and of neuronal circuits in V1, both local and lateral, determine their geometry. In the first part of the paper we show that form constants, when viewed in V1 coordinates, essentially correspond to combinations of plane waves, the wavelengths of which are integral multiples of the width of a human Hubel–Wiesel hypercolumn, ca . 1.33–2 mm. We next introduce a mathematical description of the large–scale dynamics of V1 in terms of the continuum limit of a lattice of interconnected hypercolumns, each of which itself comprises a number of interconnected iso–orientation columns. We then show that the patterns of interconnection in V1 exhibit a very interesting symmetry, i.e. they are invariant under the action of the planar Euclidean group E(2)—the group of rigid motions in the plane—rotations, reflections and translations. What is novel is that the lateral connectivity of V1 is such that a new group action is needed to represent its properties: by virtue of its anisotropy it is invariant with respect to certain shifts and twists of the plane. It is this shift–twist invariance that generates new representations of E(2). Assuming that the strength of lateral connections is weak compared with that of local connections, we next calculate the eigenvalues and eigenfunctions of the cortical dynamics, using Rayleigh–Schrödinger perturbation theory. The result is that in the absence of lateral connections, the eigenfunctions are degenerate, comprising both even and odd combinations of sinusoids in ϕ, the cortical label for orientation preference, and plane waves in r , the cortical position coordinate. 'switching–on' the lateral interactions breaks the degeneracy and either even or else odd eigenfunctions are selected. These results can be shown to follow directly from the Euclidean symmetry we have imposed. In the second part of the paper we study the nature of various even and odd combinations of eigenfunctions or planforms, the symmetries of which are such that they remain invariant under the particular action of E(2) we have imposed. These symmetries correspond to certain subgroups of E(2), the so–called axial subgroups. Axial subgroups are important in that the equivariant branching lemma indicates that when a symmetrical dynamical system becomes unstable, new solutions emerge which have symmetries corresponding to the axial subgroups of the underlying symmetry group. This is precisely the case studied in this paper. Thus we study the various planforms that emerge when our model V1 dynamics become unstable under the presumed action of hallucinogens or flickering lights. We show that the planforms correspond to the axial subgroups of E(2), under the shift–twist action. We then compute what such planforms would look like in the visual field, given an extension of the retinocortical map to include its action on local edges and contours. What is most interesting is that, given our interpretation of the correspondence between V1 planforms and perceived patterns, the set of planforms generates representatives of all the form constants. It is also noteworthy that the planforms derived from our continuum model naturally divide V1 into what are called linear regions, in which the pattern has a near constant orientation, reminiscent of the iso–orientation patches constructed via optical imaging. The boundaries of such regions form fractures whose points of intersection correspond to the well–known ‘pinwheels’. To complete the study we then investigate the stability of the planforms, using methods of nonlinear stability analysis, including Liapunov–Schmidt reduction and Poincaré–Lindstedt perturbation theory. We find a close correspondence between stable planforms and form constants. The results are sensitive to the detailed specification of the lateral connectivity and suggest an interesting possibility, that the cortical mechanisms by which geometric visual hallucinations are generated, if sited mainly in V1, are closely related to those involved in the processing of edges and contours.
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Yu, N. Y., Q. Li, and Y. H. Chen. "Experimental Evaluation of the M-Integral in an Elastic-Plastic Material Containing Multiple Defects." Journal of Applied Mechanics 80, no. 1 (2012). http://dx.doi.org/10.1115/1.4007083.
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An experimental technique for evaluation of the M-integral in an elastic-plastic material containing multiple defects is proposed by using digital image correlation (DIC). This technique makes direct use of the definition of M by experimentally evaluating the integrand of M at various points along a square contour and determining the integral by numerical integration. The nonlinear Ramberg–Osgood model is used to capture the elastic-plastic behavior such as the elastic-plastic stress and the total strain energy density in terms of the measured displacements by DIC used in an ARAMIS 4M instrument. Compared with the previous experimental method proposed by King and Herrmann (King and Herrmann, 1981, “Nondestructive Evaluation of the J and M Integrals,” ASME J. Appl. Mech., 48, pp. 83–87), the present technique could be suitable to measure the M-integral for the various complicated damages, specimen geometries, loading conditions, and material behaviors. The path-independence or path-dependence of the M-integral is investigated under small-scale and large-scale yielding conditions, respectively. It is found that the values of M are path independent when the contours entirely enclose the nonlinear plastic region near the multiple defects. In contrast, the path-dependence is concluded for an elastic-plastic solid under large-scale yielding condition when the contours have to pass through the plastic zone. This interesting path-dependence of the M-integral is consistent with numerical prediction via the finite element method and theoretical analysis developed in this paper.
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Niccoli, Giuliano, Hao Pei, and Véronique Terras. "Correlation functions by separation of variables: the XXX spin chain." SciPost Physics 10, no. 1 (2021). http://dx.doi.org/10.21468/scipostphys.10.1.006.
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We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.
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Widya Nugrohowati, Christina, Wignyo Hadriyanto, and Tunjung Nugraheni. "Direct Composite Resin Restoration of Anterior Maxillary Teeth and Esthetic Smile Design: A Case Report and Esthetic Smile Design: A Case Report." Journal of Dentistry Indonesia 27, no. 2 (2020). http://dx.doi.org/10.14693/jdi.v27i2.1131.
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Dental esthetic complex involves more than one caries with malformed shape and malposition. Dental trauma most commonly affects maxillary anterior teeth, and subsequently affects the esthetics, functions, and psychological well-being of the individual. Composite resins have become an integral part of contemporary restorative and minimally invasive dentistry. Objective: To summarize the successful use of direct composite resin restoration in the management of a 29-year old male patient. Case Report: A 29-year old male patient presenting with multiple secondary caries and crown fractures in the anterior maxillary teeth, resulting in an unaesthetic smile. Comprehensive esthetic dental treatment was carried out. The patient was highly satisfied with the results even after eleven months of follow-up. Conclusion: restorative success with composite resins, the dental treatment plan should be carefully executed with attention to factors such as dental convexities and contours, re‑establishment of function, and esthetics. Smile design should always be a multifactorial decision-making process that allows the clinician to treat patients with an individualized and interdisciplinary approach.
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Rayarao, Geetha, Robert W. Biederman, Diane V. Thompson, et al. "Abstract 12587: An Improved Approach to Cardiac Volumetrics: A Cardiac MRI Technique to Further Augment Accuracy." Circulation 130, suppl_2 (2014). http://dx.doi.org/10.1161/circ.130.suppl_2.12587.
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Introduction: In cardiac MRI (CMR), heart volumes are traditionally measured using contouring methods applied to contiguous image data. Herein, we introduce a new approach, Automatic Threshold and Manual Trimming (ATMT), which is applied to the same contiguous data set. Potentially, the ATMT method can be applied by seed/region-growing algorithms with minimal user supervision. We sought to establish its clinical validity. Hypothesis: We hypothesize that the ATMT approach is more accurate as compared to conventional 'gold standard', cardiac contouring. Methods: Hearts from two populations (N=74) were evaluated: explanted heart transplant (Tx) and a clinical validation cohort ( in vivo ). The transplanted hearts were imaged ex vivo using CMR and then weighed on a high-fidelity scale. Cardiac volume/mass was compared (N=54) to the patient cohort (N=20) and measured non-invasively with stroke volume, independently measured via CMR phase velocity technique. Bland-Altman was applied in a 3-way manner for each group. Results: Bland-Altman analysis for Standard Deviation (SD), Bias and Correlation (R) are summarized in Table 1. When compared with independent measurements (weight/flow), ATMT has lower Bias (close to zero) and SD. Further, any comparison involving cardiac contours has a substantially larger bias term and a higher SD. From the table below, ATMT has consistently higher correlations with the independent measurement than does the contour method. Conclusions: Based on multiple comparison metrics with independent measures, the ATMT approach is more accurate and reproducible for quantification of cardiac volume (integral for EF determination) as compared to standard contouring. Furthermore, ATMT accommodates trabeculae and papillary structures more intuitively than the contouring method. This intrinsic accuracy coupled with the potential for more rapid analysis gives a valid impetus to further develop the ATMT approach further increasing CMR accuracy.
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Banik, Sumit, and Samuel Friot. "Multiple Mellin-Barnes integrals with straight contours." Physical Review D 107, no. 1 (2023). http://dx.doi.org/10.1103/physrevd.107.016007.
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Omercic, Jasmin. "Bridging Islamic and Conventional Finance through Integration of Knowledge (IoK): The Potential of the Third Sector." International Journal of Islamic Economics and Finance (IJIEF) 6, no. 1 (2023). http://dx.doi.org/10.18196/ijief.v6i1.14712.
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Finance is integral to civilizational prosperity yet has impacted the global development of recent centuries, proved inherently inconsistent, and created multiple issues, i.e., inequalities. In this regard, Islamic finance (IF) offers solutions. Moreover, contemporary appraisals of the Integration of Knowledge (IoK) methodology represent a novel alternative to extant challenges and issues. The paper’s objectives are, therefore, to propose an IoK model of Islamic and conventional financial (CF) convergence with leverage to fintech and demonstrate the potential of the waqf sector for such convergence and its equivalent revival and reform along such methodological contours. This paper is a methodological contribution. However, library research, critical content analysis, and heterodox methods of concretization, synthesis, and transdisciplinary analytical reasoning substantiate the paper’s methodology. Islamic sources of knowledge, i.e., Qur’an, justify this study’s unorthodox methodology. A background depicts the CF problems and persistent issues that justify alternatives. It is followed by rationalizing IE development via IoK to converge IF and CF. The IoK model developed for IE development follows and is schematically demonstrated as novel findings of this paper to bridge the gap between IF and CF and leverage waqfs’ role and potential. Greater reference to waqf projects institutionalized implications for IF and integration with CF. Further, leveraging waqf and even fintech as an indicator of digitalization within the IoK model has implications for attaining the defined maqāṣid and developing IE genuinely. A conclusion summarizes and provides actionable recommendations linked with the IoK model’s objectives to reform extant IF and conventional practice based on sound Islamic philosophical foundations and maqāṣid-oriented envisioning of IE development.
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Pan, Hao, and Andrei Prokhorov. "Asymptotic Properties of Special Function Solutions of the Painlevé III Equation for Fixed Parameters." Studies in Applied Mathematics 154, no. 4 (2025). https://doi.org/10.1111/sapm.70051.
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ABSTRACTIn this paper, we compute the small and large asymptotics of the special function solutions of the Painlevé‐III equation in the complex plane. We use the representation in terms of Toeplitz determinants of Bessel functions obtained by Masuda. Toeplitz determinants are rewritten as multiple contour integrals using Andrèief's identity. The small and large asymptotics are obtained using elementary asymptotic methods applied to the multiple contour integral. The asymptotics is extended to the whole complex plane using analytic continuation formulas for Bessel functions. The claimed result has not appeared in the literature before. We note that the Toeplitz determinant representation is useful for numerical computations of corresponding solutions of the Painlevé‐III equation.
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"Hyperasymptotics for integrals with saddles." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 434, no. 1892 (1991): 657–75. http://dx.doi.org/10.1098/rspa.1991.0119.
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Integrals involving exp { – k f ( z )}, where | k | is a large parameter and the contour passes through a saddle of f ( z ), are approximated by refining the method of steepest descent to include exponentially small contributions from the other saddles, through which the contour does not pass. These contributions are responsible for the divergence of the asymptotic expansion generated by the method of steepest descent. The refinement is achieved by means of an exact ‘resurgence relation', expressing the original integral as its truncated saddle-point asymptotic expansion plus a remainder involving the integrals through certain ‘adjacent’ saddles, determined by a topological rule. Iteration of the resurgence relation, and choice of truncation near the least term of the original series, leads to a representation of the integral as a sum of contributions associated with ‘multiple scattering paths’ among the saddles. No resummation of divergent series is involved. Each path gives a ‘hyperseries’, depending on the terms in the asymptotic expansions for each saddle (these depend on the particular integral being studied and so are non-universal), and certain ‘hyperterminant’ functions defined by integrals (these are always the same and hence universal). Successive hyperseries get shorter, so the scheme naturally halts. For two saddles, the ultimate error is approximately ∊ 2.386 , where ∊ (proportional to exp (— A │ k │) where A is a positive constant), is the error in optimal truncation of the original series. As a numerical example, an integral with three saddles is computed hyperasymptotically.
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Pathan, M. A., and Hemant Kumar. "On A Logarithmic Mittag-Leffler Function, its Properties and Applications." Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, June 16, 2021. http://dx.doi.org/10.18257/raccefyn.1325.
Full textAbstract:
In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions.
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de Gier, Jan, William Mead, and Michael Wheeler. "Transition probability and total crossing events in the multi-species asymmetric exclusion process." Journal of Physics A: Mathematical and Theoretical, May 15, 2023. http://dx.doi.org/10.1088/1751-8121/acd5be.
Full textAbstract:
Abstract We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process ($r$-ASEP) with underlying $U_q(\widehat{\mathfrak{sl}}_{r+1})$ symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on $\mathbb{Z}$ in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general $r$-ASEP we employ a vertex model approach within which the probability of total crossing can be derived from partial symmetrization of an explicit high rank rainbow partition function. In the case of $r$-TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of $r$ determinants. For $2$-TASEP we additionally derive convenient formulas for cumulative total crossing probabilities using Bernoulli-step initial conditions for particles of type 2 and type 1 respectively.