Relevant bibliographies by topics / Dirac delta

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Dirac delta'

Author: Grafiati
Published: 3 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Dirac delta"

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Dhanuk, B. B., K. Pudasainee, H. P. Lamichhane, and R. P. Adhikari. "Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions." Journal of Nepal Physical Society 6, no. 2 (2020): 158–63. http://dx.doi.org/10.3126/jnphyssoc.v6i2.34872.

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One of revealing and widely used concepts in Physics and mathematics is the Dirac delta function. The Dirac delta function is a distribution on real lines which is zero everywhere except at a single point, where it is infinite. Dirac delta function has vital role in solving inhomogeneous differential equations. In addition, the Dirac delta functions can be used to explore harmonic information’s imbedded in the physical signals, various forms of Dirac delta function and can be constructed from the closure relation of orthonormal basis functions of functional space. Among many special functions, we have chosen the set of eigen functions of the Hamiltonian operator of harmonic oscillator and angular momentum operators for orthonormal basis. The closure relation of orthonormal functions used to construct the generator of Dirac delta function which is used to expand analytic functions log(x + 2),exp(-x2) and x within the valid region of arguments.
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Feng, Zaiyong, Linghua Ye, and Yi Zhang. "On the Fractional Derivative of Dirac Delta Function and Its Application." Advances in Mathematical Physics 2020 (October 14, 2020): 1–7. http://dx.doi.org/10.1155/2020/1842945.

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The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative of the Dirac delta function and its Laplace transform to explore the solution for fractional-order system. The paper presents the Riemann-Liouville and the Caputo fractional derivative of the Dirac delta function, and their analytic expression. The Laplace transform of the fractional derivative of the Dirac delta function is given later. The proposed fractional derivative of the Dirac delta function and its Laplace transform are effectively used to solve fractional-order integral equation and fractional-order system, the correctness of each solution is also verified.
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Ferrando, Juan Carlos. "A Dirac Delta Operator." Mathematics and Statistics 9, no. 2 (2021): 179–87. http://dx.doi.org/10.13189/ms.2021.090213.

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Bulnes, J. D., M. A. I. Travassos, and J. López-Bonilla. "On the non-separability of the Lanczos-Dirac Delta and a function presenting a property of this Delta." Journal de Ciencia e Ingeniería 16, no. 1 (2024): 1–4. http://dx.doi.org/10.46571/jci.2024.1.1.

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In this article, we show two independent proofs, which use of different properties of the Lanczos-Dirac Delta, of which, the Delta cannot be separable. Furthermore, the conditions that should be imposed on an ordinary function are identified so that it presents the translation property of the Lanczos-Dirac Delta.
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Andino, Fernando, Marlon Recarte, and Michael Spilsbury. "La Función Delta de Dirac." Revista de la Escuela de Física 2, no. 1 (2019): 55–61. http://dx.doi.org/10.5377/ref.v2i1.8292.

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La función de Dirac presenta propiedades verdaderamente útiles para modelar problemas de la física – matemática. Se presenta un resumen detallado de las principales características y propiedades de dicha ”función”, argumentándose la validez de las mismas.
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Ahmed, Zafar, Sachin Kumar, Mayank Sharma, and Vibhu Sharma. "Revisiting double Dirac delta potential." European Journal of Physics 37, no. 4 (2016): 045406. http://dx.doi.org/10.1088/0143-0807/37/4/045406.

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Schmeelk, John. "Two-dimensional dirac delta reconsidered." Foundations of Physics Letters 7, no. 4 (1994): 315–32. http://dx.doi.org/10.1007/bf02186682.

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Katz, Mikhail G., and David Tall. "A Cauchy-Dirac Delta Function." Foundations of Science 18, no. 1 (2012): 107–23. http://dx.doi.org/10.1007/s10699-012-9289-4.

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Khairi, Fathul, and Malahayati. "Penerapan Fungsi Green dari Persamaan Poisson pada Elektrostatika." Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education 1, no. 1 (2021): 56–79. http://dx.doi.org/10.14421/quadratic.2021.011-08.

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The Dirac delta function is a function that mathematically does not meet the criteria as a function, this is because the function has an infinite value at a point. However, in physics the Dirac Delta function is an important construction, one of which is in constructing the Green function. This research constructs the Green function by utilizing the Dirac Delta function and Green identity. Furthermore, the construction is directed at the Green function of the Poisson's equation which is equipped with the Dirichlet boundary condition. After the form of the Green function solution from the Poisson's equation is obtained, the Green function is determined by means of the expansion of the eigen functions in the Poisson's equation. These results are used to analyze the application of the Poisson equation in electrostatic.
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Murugan, A. R., C. Ganesa Moorthy, and C. T. Ramasamy. "A DEFINITION OF DIRAC DELTA FUNCTIONS." Advances in Mathematics: Scientific Journal 9, no. 3 (2020): 1205–12. http://dx.doi.org/10.37418/amsj.9.3.46.

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Dissertations / Theses on the topic "Dirac delta"

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Ghaderi, Hazhar. "Triangle Loop in Scalar Decay and Cutting Rules." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-212511.

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In this report we will calculate the amplitude for a scalar-to-scalars (φ3 <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> φ2φ2) decay which involves a triangle loop. We compute the real and imaginary part of the amplitude separately and will argue that this is much more straightforward and practical in this case rather than having to deal with or worry about branch cuts of logarithms. We will derive simple cutting rules closely related to the imaginary part of the amplitude. In doing this, we derive a formula that deals with expressions of the form δ[f(x,y)]δ[g(x,y)], containing two Dirac delta functions.
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GUSSON, M. F. "Potencial delta de Dirac em um cenário de comprimento mínimo." Universidade Federal do Espírito Santo, 2016. http://repositorio.ufes.br/handle/10/7361.

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Made available in DSpace on 2018-08-01T21:59:21Z (GMT). No. of bitstreams: 1 tese_10075_Dissertação Michael França Gusson.pdf: 344550 bytes, checksum: d7e7c3bf981fdbfb58991d5655c87141 (MD5) Previous issue date: 2016-07-08<br>Teorias que propõem a unificação da Relatividade Geral e da Mecânica Quântica, por exemplo a Gravitação Quântica e a Teoria de Cordas, apontam para a existência de um valor mínimo de comprimento observável. A existência deste implica em uma generalização do Princípio da Incerteza de Heisenberg, de modo a não admitir mais uma incerteza nula na posição, modificando assim a álgebra da Mecânica Quântica. Esta modificação na álgebra sugere uma reavaliação dos resultados obtidos nas situações usuais do contexto quântico. Neste trabalho é abordado o problema do potencial delta &#948;, sob um contexto de comprimento mínimo, e discutido as consequências e resultados relacionadas a esta generalização.
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Öhrn, Håkan, and Adam Lindell. "Discretization of the Dirac delta function for application in option pricing." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-297648.

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This paper compares two different approximations of the Dirac deltafunction used in a Fokker-Planck equation. Both methods deal with the singularity problem in the initial condition. The Dirac delta approximation, constructed in MATLAB with a method derived by Tornberg and Engquist, was compared to an already given method Aït-Sahalia. The methods were implemented as the initial condition in the Fokker-Planck equation, e.g approximating a probability density function. In most cases Aït-Sahalia and Tornberg-Engquist were interchangeable. During specific circumstances one method was significantly more accurate than the other. Increasing the amount of time/spatial steps enhanced the differences in error while having less time/spatial steps made the difference in error converge. The Aït-Sahalia method produces slightly more accurate results in more cases.
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Rocha, Luiz Roberto Baracho. "Resultados da mecanica quantica para um potencial com n funções Delta de Dirac." reponame:Repositório Institucional da UFPR, 1996. http://hdl.handle.net/1884/37220.

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Orientador: Bin Kang Cheng<br>Dissertação (mestrado) - Universidade Federal do Paraná<br>Resumo: Neste trabalho de tese estudamos inicialmente o formalismo quântico do potencial com n funções S de Dirac. Em seguida, obtemos os resultados quânticos resolvendo a equação de Schrödinger independente do tempo e usando o método de integral de caminhos. Estudamos dois casos particulares do potencial: (a) potencial não confinado com ri — 2 e (b) potencial confinado com n — 41. Pela solução da equação de Schrödinger independente do tempo podemos determinar completamente a função de onda e os autovalores da energia. Com a integral de caminho obtemos as funções de Green exatas. Para o potencial confinado com n = 4 temos também o traço da função de Green, da qual calculamos os níveis quânticos que estão em total acordo com os resultados obtidos da solução da equação de Schrödinger.<br>Abstract: In this thesis we first study the quantum formalism of the potential comprising of n Dirac S functions. We present the quantum results both by solving the time independent Schrödinger’s equation and by using the path integral method. We investigate two particular cases of the potential: (a) unbound potential with n = 2 and (b) bound potential with n = 42. From the Schrödinger equation we in fact determine completely the wave function and their energy levels. Applying the path integral method we obtain the exact Green functions and for the bound potential with n = 4 we also obtain the trace of the Green function, from which we evaluate the quantized energies which are in fully agreement with those obtained by solving the Schrödinger’s equation.
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Censi, Roberta. "Sulla nozione di distribuzione." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1390/.

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Urriola, Hector Jose Cabarcas. "Propriedades de continuação única para soluções de equações de Schrödinger com ponto de interação." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-20052016-141417/.

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Neste trabalho, estudamos propriedades de continuação única para as soluções da equação tipo Schrödinger com um ponto interação centrado em x=0, \\partial_tu=i(\\Delta_Z+V)u, onde V=V(x,t) é uma função de valor real e -\\Delta_Z é o operador escrito formalmente como \\[-\\Delta_Z=-\\frac\\frac{d^2}{dx^2}+Z\\delta_0,\\] sendo \\delta_0 a delta de Dirac centrada em zero e Z qualquer número real. Logo, usamos estes resultados para ver o possível fenômeno de concentração das soluções, que explodem, da equação de tipo Schrödinger não linear com um ponto de interação em x=0, \\[\\partial_tu=i(\\Delta_Zu+|u|^u),\\] com ho>5. Também, mostramos que para certas condições sobre o potencial dependente do tempo V, a equação linear em cima tem soluções não triviais.<br>In this work, we study unique continuation properties for solutions of the Schrödinger equations with an point interaction centered at $x=0$, \\begin\\label \\partial_tu=i(\\Delta_Z+V)u, \\end where $V=V(x,t)$ is real value function and $-\\Delta_Z$ is the operator formally written \\[-\\Delta_Z=-\\frac\\frac{d^2}{dx^2}+Z\\delta_0,\\] and $\\delta_0$ is Dirac\'s delta centered at zero and $Z$ is a real number. Next, we use these results in order to study the possible profile of the concentration of blow up solutions for the non linear Schrödinger equation with a point interaction at $x=0$, \\[\\partial_tu=i(\\Delta_Zu+|u|^u),\\] with $ho>5$. Besides, we show that the equation above has non trivial solutions for some conditions on the time dependent potencial $V$.
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Boaventura, Ana Paula Freitas Vilela. "Modelagem acústica de salas através da técnica de malhas de guias digitais de ondas." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/14746.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The modeling of reverberant environments using techniques based on geometry, such as Ray Tracing or behavior-based wave, such as Finite Elements are devoted respectively to large and small places . But the great difficulty arises in the simulation of medium enclosures, based on precision to the geometrical approach and the computational cost for the behavior-based wave. Therefore, the objective of this work is to obtain Impulse Response Room (Room Impulse Response - RIR ) in midsize through technical Digital Waveguide Mesh ( Digital Waveguide Mesh - DWG ) environments . During the simulations the excitation was made by a half-sine, representing an approximation of the Dirac Delta. To simulate the reverberant field, were explored different geometries of meshes. Applying the results obtained it was possible to predict numerically the acoustic behavior of a sample of the same audio playing through the auralization. Added to this, certain parameters of acoustic quality which are directly derived from the RIR could be calculated . Finally, a comparative study of the RIR obtained experimentally , theoretically and via DWG was performed . From the initial proposal of the work , we have reached a computational tool able to predict the acoustic behavior in two and three dimensional environments , a relatively low computational time and quality in their results . Therefore , it was possible to make a preliminary analysis of the acoustic quality of the room , including allowing the sound reproduced in the virtual room.<br>A modelagem de ambientes reverberantes por meio de técnicas baseadas na geometria, como o Ray Tracing ou na propagação de ondas acústica, como Elementos Finitos são consagrados respectivamente para recintos de grande e pequeno porte. Porém, a grande dificuldade reside na simulação dos recintos médios, em função da precisão, para a abordagem geométrica, e do custo computacional, para os baseados no comportamento da onda. Assim sendo, o objetivo deste trabalho consiste na obtenção da Resposta Impulsiva da Sala (Room Impulse Response RIR) em ambientes de médio porte por meio da técnica de Malhas de Guias Digitais de Ondas (Digital Waveguide Mesh DWG). Durante as simulações a excitação se deu por meio de um meio seno, representando uma aproximação do Delta de Dirac. Para simular o campo reverberante, foram exploradas diferentes geometrias de malhas. Aplicando os resultados obtidos numericamente foi possível prever o comportamento sonoro de uma amostra de áudio sendo reproduzida no mesmo, por meio da auralização. Somado a isso, certos parâmetros da qualidade acústica, que são diretamente derivados da RIR puderam ser calculados. Para finalizar, um estudo comparativo das RIR obtidas experimentalmente, teoricamente e via DWG foi realizado. A partir da proposta inicial do trabalho, chegou-se a uma ferramenta computacional capaz de prever o comportamento acústico em ambientes bi e tridimensionais, num tempo computacional, relativamente baixo e com qualidade em seus resultados. Por conseguinte, foi possível fazer uma análise prévia da qualidade acústica da sala, inclusive permitindo ouvir o som reproduzido no recinto virtual.<br>Doutor em Engenharia Mecânica
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Amato, Marco. "The Galerkin method for vibrational problem on stepped structures." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.

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Molti fenomeni fisici studiati in ingegneria sono modellati attraverso equazioni differenziali. In generale il problema ottenuto difficilmente trova soluzione analitica in forma chiusa. Ecco perché si è iniziato a cercare approcci numerici approssimati per risolvere le equazioni differenziali. Gli approcci più diffusi sono: il metodo degli elementi finiti, il metodo delle differenze finite e il metodo dei residui pesati. Quest'ultimo, in particolare, è una famiglia di metodi. Un membro di tale gruppo è l'argomento principale di questa tesi, ovvero il metodo Galerkin. Il metodo di Galerkin è stato proposto nel 1915. Molti articoli sono dedicati alla sua applicazione su strutture elastiche e in letteratura è anche possibile trovare diversi studi che riportano l'applicazione del metodo di Galerkin su strutture a gradini. In questi lavori la procedura di Galerkin viene applicata nella forma naïve. In questa tesi ci occupiamo del problema vibrazionale di strutture a gradini fornendo due versioni del metodo Galerkin. La prima, naïve, consiste nell'integrazione lungo ogni gradino, dove la rigidezza e la massa rimangono costanti. La seconda versione, denominata rigorous, consiste nel rappresentare la rigidezza e la massa come funzioni generalizzate. Questa implementazione utilizza la funzione di Heaviside, nonché il delta di Dirac e la sua derivata. Per verificare la solidità del metodo studiamo diversi elementi strutturali: bielle, travi e piastre in diverse condizioni di vincolo. Emerge che l’implementazione rigorous porta a termini aggiuntivi che non compaiono nell’implementazione naïve. Entrambe le versioni del metodo di Galerkin sono confrontate con la soluzione esatta. Il risultato ottenuto è che, contrariamente alla versione naïve, l'implementazione rigorous tende alla soluzione analitica. Questo lavoro dimostra che dobbiamo prestare attenzione quando implementiamo il metodo Galerkin per le strutture a gradini perché solo l’implementazione rigorous converge.
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Yamashita, Marcelo Takeshi. ""Sistemas fracamente ligados de três corpos: moléculas e núcleos exóticos leves"." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-04032005-105331/.

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Um potencial de dois corpos do tipo delta-Dirac foi utilizado para descrever sistemas fracamente ligados de três corpos. A trajetória completa dos estados Efimov em função da energia ligação de dois corpos foi calculada para o caso de três bosons idênticos: se o subsistema de dois corpos é ligado, conforme a razão entre a energia de ligação de dois e três corpos aumenta, o estado excitado desaparece e um estado virtual correspondente aparece quando a energia do estado fundamental atinge o limiar dado por 6.9hbar^2/(ma^2) (a - comprimento de espalhamento, m - massa do bóson). Quando o subsistema de dois corpos é virtual, o aumento da razão entre as energias faz com que o estado excitado se transforme em uma ressonância quando a energia do estado fundamental é 1.1hbar^2/(ma^2). Neste último caso as condições para a formação de moléculas triatômicas no interior de condensados é favorecida, pois a competição com dímeros fracamente ligados está ausente. A energia de ligação de trímeros com momento angular total nulo em condensados atômicos foi estimada através da correlação desta com o coeficiente de recombinação e com a energia do dímero, ambos conhecidos experimentalmente em alguns casos. Os tamanhos de moléculas fracamente ligadas (^4He_2$-X; Xequiv^4He, ^6Li, ^7Li e ^{23}Na) e de núcleos exóticos leves (^6He, ^{11}Li, ^{14}Be e ^{20}C) também foram calculados juntamente com um estudo sistemático do comportamento dos raios quadráticos médios conforme a interação dos subsistemas de dois corpos é variada. Neste último caso a classificação de um sistema de três corpos (tipo AAB) foi completada denominando de Samba a configuração formada por dois subsistemas de dois corpos ligados e um virtual. As equações subtraídas para os estados ligados de quatro bosons também foram deduzidas.
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Zsitva, Norbert. "Aproximace LTI SISO systémů s dopravním zpožděním pomocí zobecněných Laguerrových funkcí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2018. http://www.nusl.cz/ntk/nusl-376971.

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This final thesis deals with the approximation of time delay in time invariant systems. First, the generalized Laguerre functions and their characteristics are presented. After this, the approximation of the Dirac delta function with the help of these functions is shown. Also, the choice of the free parameters is discussed and the results are evaluated with the help of energy. In the final part of the thesis, the approximations of systems with generalized and simple Laguerre functions are compared.
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Books on the topic "Dirac delta"

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Ghatak, A. K. Quantum mechanics: Theory and applications. Kluwer Academic Publishers, 2004.

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Zobel, Kennedy. Dirac Delta Function. Independently Published, 2020.

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Delta de Dirac, O. Livraria da Física, 2002.

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Horing, Norman J. Morgenstern. Graphene. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0012.

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Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quantizing magnetic field on the Green’s function of a Graphene sheet and on its energy spectrum are derived in detail: Also the magnetic-field Green’s function and energy spectrum of a Graphene sheet with a quantum dot (modelled by a 2D Dirac delta-function potential) are thoroughly examined. Furthermore, Chapter 12 similarly addresses the problem of a Graphene anti-dot lattice in a magnetic field, discussing the Green’s function for propagation along the lattice axis, with a formulation of the associated eigen-energy dispersion relation. Finally, magnetic Landau quantization effects on the statistical thermodynamics of Graphene, including its Free Energy and magnetic moment, are also treated in Chapter 12 and are seen to exhibit magnetic oscillatory features.
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Mann, Peter. Noether’s Theorem for Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0028.

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This is a unique chapter that discusses classical path integrals in both configuration space and phase space. It examines both Lagrangian and Hamiltonian formulations before qualitatively discussing some interesting features of gauge fixing. This formulation is then linked to superspace and Grassmann variables for a fermionic field theory. The chapter then shows that the corresponding operatorial formulation is none other than the Koopman–von Neumann theory. In parallel to quantum theory, the classical propagator or the transition amplitude between two classical states is given exactly by the phase space partition function. The functional Dirac delta is discussed, and the chapter closes by briefly mentioning Faddeev–Popov ghosts, which were introduced earlier in the chapter.
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Bueno, Otávio, and Steven French. Applying Problematic Mathematics, Interpreting Successful Structures. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198815044.003.0007.

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In this chapter we consider whether, in applying mathematics in the ways described in previous chapters, there are grounds for taking the relevant mathematical entities to be indispensable. Our example here is Dirac’s introduction of the delta function into quantum mechanics and we point out, firstly, that Dirac himself was very clear about the function’s dispensability and, secondly, even if certain mathematical theories were indispensable, this wouldn’t justify a commitment to the existence of the associated entities. To illustrate this second point we use a further example, that of Dirac’s prediction of the existence of antimatter via the exploitation of surplus mathematical structure. We maintain here that commitment to the existence of the objects under consideration requires the satisfaction of certain criteria of existence and it is unclear whether mathematical entities meet these criteria.
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Ghatak, Ajoy, and S. Lokanathan. Quantum Mechanics: Theory and Applications (Fundamental Theories of Physics). Springer, 2004.

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Ghatak, Ajoy, and S. Lokanathan. Quantum Mechanics: Theory and Applications (Fundamental Theories of Physics, 137). Springer, 2004.

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Lokanathan, S., and Ajoy Kumar Ghatak. Quantum Mechanics: Theory and Applications. Kluwer Academic Publishers, 2004.

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Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).
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Book chapters on the topic "Dirac delta"

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Hassani, Sadri. "Dirac Delta Function." In Mathematical Methods. Springer New York, 2000. http://dx.doi.org/10.1007/978-0-387-21562-4_7.

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Weik, Martin H. "Dirac-delta function." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_5112.

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Cini, Michele. "La delta di Dirac." In UNITEXT. Springer Milan, 2006. http://dx.doi.org/10.1007/88-470-0425-x_3.

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Ghatak, Ajoy, and S. Lokanathan. "The Dirac Delta Function." In Quantum Mechanics: Theory and Applications. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2130-5_1.

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Kanwal, Ram P. "The Dirac Delta Function and Delta Sequences." In Generalized Functions. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8174-6_1.

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Kanwal, Ram P. "The Dirac Delta Function and Delta Sequences." In Generalized Functions Theory and Technique. Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4684-0035-9_1.

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Estrada, Ricardo, and Ram P. Kanwal. "Series of Dirac Delta Functions." In A Distributional Approach to Asymptotics. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-0-8176-8130-2_7.

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Estrada, Ricardo, and Ram P. Kanwal. "Series of Dirac Delta Functions." In Asymptotic Analysis. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4684-0029-8_6.

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Buttkus, Burkhard. "The Dirac Delta Function and its Fourier Transform." In Spectral Analysis and Filter Theory in Applied Geophysics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57016-2_4.

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Díaz Fernández, Álvaro. "Surface States in $$\delta $$-doped Topological Boundaries." In Reshaping of Dirac Cones in Topological Insulators and Graphene. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61555-0_5.

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Conference papers on the topic "Dirac delta"

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Cui, Zhenyu, Kailin Ding, Yanchu Liu, and Lingjiong Zhu. "A New Approach to Sensitivity Analysis Based on Dirac Delta Family Methods." In 2024 Winter Simulation Conference (WSC). IEEE, 2024. https://doi.org/10.1109/wsc63780.2024.10838623.

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Nieto-Chaupis, Huber. "Quantized Energies from Finite Chain of Dirac-Delta Impulses at MIMO Systems." In 2024 International Conference on Electrical, Computer and Energy Technologies (ICECET). IEEE, 2024. http://dx.doi.org/10.1109/icecet61485.2024.10698505.

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Wilcox, Bethany R., and Steven J. Pollock. "Student Difficulties with the Dirac Delta Function." In 2014 Physics Education Research Conference. American Association of Physics Teachers, 2015. http://dx.doi.org/10.1119/perc.2014.pr.064.

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ROSAS-ORTIZ, O. "ON THE DIRAC-INFELD-PLEBAŃSKI DELTA FUNCTION." In Proceedings of 2002 International Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772732_0031.

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Özc̣ağ, E. "Results on compositions involving Dirac-delta function." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’17. Author(s), 2017. http://dx.doi.org/10.1063/1.5007379.

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ASHOUR, H. S., A. I. ASS'AD, M. S. HAMADA, and M. M. SHABAT. "QUANTUM WAVEGUIDE TRANSPORT IN BINOMIALLY TAILORED DIRAC DELTA POTENTIAL." In Reviews and Short Notes to Nanomeeting-2005. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701947_0028.

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Correa, Javier, Martin Adams, and Claudio Perez. "A Dirac Delta mixture-based Random Finite Set filter." In 2015 International Conference on Control, Automation and Information Sciences (ICCAIS). IEEE, 2015. http://dx.doi.org/10.1109/iccais.2015.7338668.

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Huang, Xiang, Hongsheng Liu, Beiji Shi, et al. "A Universal PINNs Method for Solving Partial Differential Equations with a Point Source." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/533.

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In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs)method emerges to be a promising method for solving both forward and inverse PDE problems. PDEs with a point source that is expressed as a Dirac delta function in the governing equations are mathematical models of many physical processes. However, they cannot be solved directly by conventional PINNs method due to the singularity brought by the Dirac delta function. In this paper, we propose a universal solution to tackle this problem by proposing three novel techniques. Firstly the Dirac delta function is modeled as a continuous probability density function to eliminate the singularity at the point source; secondly a lower bound constrained uncertainty weighting algorithm is proposed to balance the physics-informed loss terms of point source area and the remaining areas; and thirdly a multi-scale deep neural network with periodic activation function is used to improve the accuracy and convergence speed. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning based methods with respect to the accuracy, the efficiency and the versatility.
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Degen, Christoph, Roy Streit, and Wolfgang Koch. "On the functional derivative with respect to the Dirac Delta." In 2015 Sensor Data Fusion: Trends, Solutions, Applications (SDF). IEEE, 2015. http://dx.doi.org/10.1109/sdf.2015.7347696.

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Nieto-Chaupis, Huber. "Computational Reconstruction of Dirac- Delta Function from Quantum Electrodynamics Rules." In 2022 IEEE 20th Biennial Conference on Electromagnetic Field Computation (CEFC). IEEE, 2022. http://dx.doi.org/10.1109/cefc55061.2022.9940888.

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Reports on the topic "Dirac delta"

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Fernández Gómez, Jorge. Hidrogenoaren eta harekin lotutako produktuen nazioarteko merkataritzaren garapenerako aurreikuspenak. Portuetan izan ditzakeen ondorioak. Edited by Patricia Canto. Universidad de Deusto, 2025. https://doi.org/10.18543/qktq7920.

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Lan honetan hidrogeno berriztagarriaren eta harekin lotutako produktuen nazioarteko merkataritzaren egungo garapen aurreikuspenak aztertzen dira, baita aurreikuspen horiek portuetan izan ditzaketen ondorioak ere. Horretarako, literatura akademikoaren eta ez-akademikoaren berrikuste ez-sistematiko bat egin dugu, arreta berezia jarriz energiaren arloko nazioarteko erakunde garrantzitsuenetan. Literaturaren azterketa horri esker, hidrogenoaren merkatu globala garatzeak dakartzan erronka garrantzitsuenak identifikatu ahal izan dira: (a) hidrogeno berriztagarriaren eskariarentzat eta eskaintzarentzat espero den bilakaera, epe ertainera eta luzera; (b) ekoizpen kostuak; (c) itsaso bidezko eta distantzia luzeko garraioaren bideragarritasun ekonomikoa; (d) erregulazio esparruaren garapena; (e) portuetako azpiegiturak garatzea; (f) garraioarekin lotutako ingurumen eraginak eta beste arrisku batzuk (osasunari, segurtasunari eta abarri dagokienez); eta (g) proiektuak finantzatzeko zailtasuna. Hidrogeno berriztagarriaren merkatu globalaren bilakaerak zalantzak sortzen baditu ere, energia bektore hori garrantzitsua izatea espero da eskualdeko industria hubetan, kontuan hartuta horietan nazioarteko merkataritza bolumena mugatua dela eta, oro har, kontinente bereko eskualdeez ari garela.
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Costanzi, Rogério Nagamine, Geraldo Sandoval Góes, and Felipe dos Santos Martins. Nota Técnica n. 25 (Dimac) : A Queda na contribuição previdenciária entre os jovens ocupados entre 2012 e 2023 no Brasil. Instituto de Pesquisa Econômica Aplicada (Ipea), 2024. https://doi.org/10.38116/ntdimac25-port.

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Com o intuito de analisar de forma mais profunda a evolução da contribuição previdenciária entre esses jovens, esta Nota Técnica está organizada, além desta introdução, em outras três seções: 1) Na segunda seção é feita uma análise da evolução da contribuição previdenciária entre os jovens ocupados de 20 a 29 anos, tentando, dentro do possível, avaliar aspectos que podem ter influenciado a referida evolução no período de 2012 a 2023 a partir dos microdados da PNAD Contínua; 2) Na terceira seção são realizados exercícios contrafactuais para obter estimativas de quais seriam as contribuições para a previdência dos jovens de 20 a 29 anos, em 2023, caso fossem mantidas as mesmas estruturas observadas em 2012 de: i) posição na ocupação; ii) grupamento de atividade econômica; iii) faixa de escolaridade; e iv) distribuição de rendimentos e 3) Na quarta parte são feitas as considerações finais.
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Fernández Gómez, Jorge, and Jaime Menéndez Sánchez. Euskal Autonomia Erkidegoko hidrogeno sistemaren garapena epe ertainera. Edited by Patricia Canto. Universidad de Deusto, 2023. http://dx.doi.org/10.18543/hhcr1526.

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Txosten honek Euskal Autonomia Erkidegoan hidrogenoa garraiatzeko azpiegituren sistemak epe ertainean izan dezakeen bilakaera du aztergai. Zehazki, lanak hiru helburu ditu: (1) epe ertainera (10-15 urteko epean) azpiegiturak garatzeko jokalekuen ezaugarriak definitzea; (2) EAEko hidrogeno sistemaren garapenean eragina duten funtsezko faktoreak identifikatzea eta epe ertaineko jokalekuak zehazteko orduan izan dezaketen eragina aztertzea; (3) Euskal Autonomia Erkidegorako ondorio estrategikoak ateratzea. Hidrogenoaren ekoizpen eta garraio sistemari dagozkion jokalekuak askotarikoak dira: guztiz deszentralizatutako egoera batetik hasi (tokiko ekoizpen azpiegiturak dituena, kontsumo instalazioetan edo industria hubetan) eta gaur egungo gas saretik abiatuta, guztiz zentralizatutako sistema batera arte joan daitezke. Txostenaren ondorio nagusia da Euskal Autonomia Erkidegoaren ikuspuntutik epe laburrerako estrategia onena dela industria hubetan (Bilboko Portuaren inguruan) hidrogenoa azkar hedatzen laguntzea eta gainerako erabakiak hartzeko pixka bat itxarotea, sektorea datozen urteetan nola garatzen den ikusteko eta, horren arabera, epe luzeagoko azpiegiturak osatzen hasteko.
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