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How to Check If a Number Is Prime Using a Finite Definite Integral

Jesús Sánchez
<span title="">2019</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wdwqs5h7yrgzvdpgc3pvqnamia" style="color: black;">Journal of Applied Mathematics and Physics</a> </i> &nbsp;
In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown.  ...  Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.  ...  Dirac delta in 5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jamp.2019.72028">doi:10.4236/jamp.2019.72028</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mfj4agzzzvgkxjldf4cjzh46qe">fatcat:mfj4agzzzvgkxjldf4cjzh46qe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502123858/https://file.scirp.org/pdf/JAMP_2019022115273700.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/98/fc/98fca8d484933d90510b8b7ec64e47285cbce66e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jamp.2019.72028"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Construction of Dirac Delta Function from the Discrete Orthonormal Basis of the Function Space

Hari Prasad Lamichhane
<span title="2017-10-12">2017</span> <i title="Nepal Journals Online (JOL)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vak3b5mowfhahgksvr4l4r5aya" style="color: black;">Himalayan Physics</a> </i> &nbsp;
Such a simple basis set is suitable to study closure property of the basis and various properties of Dirac delta function in Physics graduate lab.  ...  <p>Orthonormal basis of the function space can be used to construct Dirac delta function.  ...  , etc. to study the properties of the generator of Dirac delta function in the lab.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3126/hj.v6i0.18360">doi:10.3126/hj.v6i0.18360</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/me6qfjsoqjhqflkfqmi7lh46ci">fatcat:me6qfjsoqjhqflkfqmi7lh46ci</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180518041002/https://www.nepjol.info/index.php/HP/article/download/18360/14943" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/49/23/492333456532e459c597c97cedb53052f2c98290.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3126/hj.v6i0.18360"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Immersed Boundary Method for Simulating Interfacial Problems

Wanho Lee, Seunggyu Lee
<span title="2020-11-06">2020</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ye33srllvnanjouxn4tmrfgjsq" style="color: black;">Mathematics</a> </i> &nbsp;
Standard numerical simulations are performed in order to show the effect of the parameters and discrete Dirac-delta functions.  ...  The interaction between two different coordinates is involved in a discrete Dirac-delta function. We describe the IB method and its numerical implementation.  ...  Discrete Delta Function The Dirac-delta function, δ(x), plays an important role in the interaction of fluids and boundaries in the IB method.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math8111982">doi:10.3390/math8111982</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jwzn7go22vaetahzewanzmchsq">fatcat:jwzn7go22vaetahzewanzmchsq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201107234948/https://res.mdpi.com/d_attachment/mathematics/mathematics-08-01982/article_deploy/mathematics-08-01982.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/55/be/55be73b5e1c6606318d7ba80fd134881c4f0c4f1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math8111982"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

A 1-bit Synchronization Algorithm for a Reduced Complexity Energy Detection UWB Receiver

Marco Crepaldi, Mario R. Casu, Mariagrazia Graziano, Maurizio Zamboni
<span title="">2007</span> <i title="IEEE"> 2007 IEEE International Conference on Ultra-Wideband </i> &nbsp;
The operation of the algorithm is explained in a simplified case in which the received pulse is a Dirac delta I.  ...  Mean-Absolute-Error for CM1, CM3 and Dirac Delta, with Te with Tw 30nis, tstep =5n1s, T8 lOOns 30ns, tstep =lOins, T8 60ns _ Dirac Delta Maximum detection~~~~~~~~~~~~~~~~~Dirac Delta Maximum Detection  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icuwb.2007.4381036">doi:10.1109/icuwb.2007.4381036</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n6jcx7onenastekqj2c4vlvfzy">fatcat:n6jcx7onenastekqj2c4vlvfzy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427201505/https://iris.polito.it/retrieve/handle/11583/1664718/49011/icuwb07_2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d5/5d/d55d2124867c19e3dc5034245215ac83a758e306.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icuwb.2007.4381036"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Ochotona Curzoniae Image Segmentation Based on Improved CV Model

Hai-yan CHEN, Yu-hui ZENG, Ying LIN
<span title="2017-09-19">2017</span> <i title="DEStech Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oepoggqi3bgnbds2j2j6zruxjy" style="color: black;">DEStech Transactions on Engineering and Technology Research</a> </i> &nbsp;
In addition, to suppress the effects of background interference by using rectangular dirac delta function, to reduce the calculation of initialization of the evolving level set function by using Quadtree  ...  Tests and comparisons show that the new model has a better effect for Ochotona curzoniae image segmentation in autumn and winter season.  ...  In this paper, regularized dirac delta function is replaced by rectangular dirac delta function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12783/dtetr/amma2017/13367">doi:10.12783/dtetr/amma2017/13367</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ze3omijoejfdneveh2tudelfwi">fatcat:ze3omijoejfdneveh2tudelfwi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720000737/http://dpi-proceedings.com/index.php/dtetr/article/download/13367/12889" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/72/ed/72eddc808e8ee89632d4bb98e5be8ff0560c9df7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12783/dtetr/amma2017/13367"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

Hong Zhang, Zhiwei Wu, Tian Lan, Yanyu Chen, Peichao Gao
<span title="2020-03-26">2020</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
In addition, it has been recently criticized to be thermodynamically irrelevant.  ...  logarithmic of the space and the Dirac delta distribution.  ...  the Dirac delta distribution into the distribution of the extended logarithmic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e22040381">doi:10.3390/e22040381</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/33286154">pmid:33286154</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n5neui5nynb5petzkxxthusbj4">fatcat:n5neui5nynb5petzkxxthusbj4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200402210250/https://res.mdpi.com/d_attachment/entropy/entropy-22-00381/article_deploy/entropy-22-00381-v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bc/4e/bc4ed1c87c072b2890c74d5b83d71fd2e05ec7e9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e22040381"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Analytical and numerical solution of heat generation and conduction equation in relaxation mode: Laplace transforms approach
English

M Lawal, K Jha Basant, O Akusu Patrick, R Mat Isa Ahmad, R Nasiru
<span title="2015-05-16">2015</span> <i title="Academic Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oik5gyrpgrf2nbtuhx4rmj3cbi" style="color: black;">International Journal of Physical Sciences</a> </i> &nbsp;
The properties of heat source terms in four different cases are incorporated in the model and investigated.  ...  In this article analytical solution of one-dimensional heat equation in relaxation mode of heat generation and conduction using Laplace transforms method is presented.  ...  The pulsed energy source shows quasi-steady state behavior as the Dirac delta tends to unity. ,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5897/ijps2015.4285">doi:10.5897/ijps2015.4285</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ymwzldxx5nd7xizlmdgqa4znm4">fatcat:ymwzldxx5nd7xizlmdgqa4znm4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150621062544/http://www.academicjournals.org:80/article/article1432658737_Lawal%20et%20al.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/15/df/15dfa3ae59df229ebc9457941e9a224f551668ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5897/ijps2015.4285"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Parametric Dirac Delta to Simplify the Solution of Linear and Nonlinear Problems with an Impulsive Forcing Function

Enrique J. Chicurel-Uziel, Francisco A. Godínez-Rojano
<span title="">2013</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wdwqs5h7yrgzvdpgc3pvqnamia" style="color: black;">Journal of Applied Mathematics and Physics</a> </i> &nbsp;
In contrast with this, the parametric representation of the Dirac delta presented here works both in linear and nonlinear problems.  ...  The Laplace transform is a very useful tool for the solution of problems involving an impulsive excitation, usually represented by the Dirac delta, but it does not work in nonlinear problems.  ...  Derivation of the Parametric Dirac Delta Consider the approximation of the unit step with a near vertical riser, H Ra , shown in Figure 3 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jamp.2013.17003">doi:10.4236/jamp.2013.17003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bjov7ywl6bhkveydesdfpbvb6y">fatcat:bjov7ywl6bhkveydesdfpbvb6y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140720173903/http://www.scirp.org/journal/PaperDownload.aspx?paperID=40816" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/29/4c/294cbfb2294a3bb14b198a8aa845d33369a30468.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jamp.2013.17003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 2769 of Mathematical Reviews Vol. , Issue 95e [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper we collect several very recent and important results for the Dirac delta and formu- late them within a two-dimensional domain.  ...  It is the belief of the author that the Dirac delta functional offers enormous impact in fostering advances within distribution theory together with its applications.  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_mathematical-reviews_1995-05_95e/page/2769" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_mathematical-reviews_1995-05_95e/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Fourier-Laguerre Transform, Convolution And Wavelets On The Ball

Boris Leistedt, Jason McEwen
<span title="2013-09-09">2013</span> <i title="Zenodo"> Zenodo </i> &nbsp;
Publication in the conference proceedings of SampTA, Bremen, Germany, 2013  ...  We define the Dirac delta on the radial line at position s by s (r) ⌘ r 2 R (r s), where R is the usual Dirac delta defined on the infinite line R.  ...  Band-limited Dirac delta functions plotted on the radial line at positions s = {0.2, 0.3, 0.4} (plotted in blue, green and red, respectively).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.54414">doi:10.5281/zenodo.54414</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3qp37vi6ojdurjguq5abagulhq">fatcat:3qp37vi6ojdurjguq5abagulhq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200307161701/https://zenodo.org/record/54414/files/p329-mcewen.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1a/08/1a08c104eece556817871211269cfbb638832555.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.54414"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>

Fourier-Laguerre transform, convolution and wavelets on the ball [article]

J. D. McEwen, B. Leistedt
<span title="2013-07-04">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function.  ...  We define the Dirac delta on the radial line at position s by δ s (r) ≡ r −2 δ R (r − s), where δ R is the usual Dirac delta defined on the infinite line R.  ...  In order to recover a real space representation of the radial translation operator we must first consider the Dirac delta function on the radial line.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1307.1307v1">arXiv:1307.1307v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/msc64qfhbff7jbyiatksbxjl4a">fatcat:msc64qfhbff7jbyiatksbxjl4a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825015811/https://arxiv.org/pdf/1307.1307v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e9/11/e91172cd193862677676b268d560b05d0edb3998.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1307.1307v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Verification of goal-oriented HP-adaptivity

M. Paszyński, L. Demkowicz, D. Pardo
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
All terms in (2.8) must be understood as regular distributions, except for the Dirac delta term, and all derivatives must be understood in the distributional sense.  ...  MATLAB.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2005.03.018">doi:10.1016/j.camwa.2005.03.018</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jbcag6mhynhwxc524ey7v3mqze">fatcat:jbcag6mhynhwxc524ey7v3mqze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003151518/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/cde/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg5ODEyMjEwNTAwMzg5NQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/31/51/3151aeabff3300deeafec758e5a0111794e255f5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2005.03.018"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

POCP: a package for polynomial optimal control problems [article]

Didier Henrion , Carlo Savorgnan
<span title="2008-09-26">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP.  ...  In this paper we describe the basic features of POCP and illustrate them with some numerical examples.  ...  The second is a matrix whose columns contain the value of the variables (one column for each Dirac delta).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0809.4623v1">arXiv:0809.4623v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/payd4ki5bfhizf4dqqtmwesgf4">fatcat:payd4ki5bfhizf4dqqtmwesgf4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0809.4623/0809.4623.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0809.4623v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A new matrix formulation of the Maxwell and Dirac equations

Richard P. Bocker, B. Roy Frieden
<span title="2018-12-10">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ifjemtdanzevfbtz3nv7p24qjm" style="color: black;">Heliyon</a> </i> &nbsp;
Presented in this paper is a new matrix formulation of both the classical electromagnetic Maxwell equations and the relativistic quantum mechanical Dirac equation.  ...  As it turns out, the Dirac spacetime matrix equation is equivalent to four new vector equations, which are similar in form to the four Maxwell vector equations.  ...  See Appendix 3 in Roman [11] for details. The Dirac matrices have the following properties: = −1 , + = 2 4 , = † . Again, the symbol is the Kronecker delta.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.heliyon.2018.e01033">doi:10.1016/j.heliyon.2018.e01033</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/30582050">pmid:30582050</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC6290133/">pmcid:PMC6290133</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qurqchf3azbvxmuhszy4lhlse4">fatcat:qurqchf3azbvxmuhszy4lhlse4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191118233433/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC6290133&amp;blobtype=pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/41/70/417006a3a353cd42f6a8672b3934f12fa3c878f6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.heliyon.2018.e01033"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6290133" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Dirac mixture trees for fast suboptimal multi-dimensional density approximation

Vesa Klumpp, Uwe D. Hanebeck
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bfskugbd5vcy5dfpe5pwzmho7e" style="color: black;">2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems</a> </i> &nbsp;
We consider the problem of approximating an arbitrary multi-dimensional probability density function by means of a Dirac mixture density.  ...  The resulting computational complexity is linear in the number of components and linear in the number of dimensions.  ...  The runtime measurements were taken in MATLAB calling a C# sub-routine that computes the Dirac approximation. D.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mfi.2008.4648009">doi:10.1109/mfi.2008.4648009</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/mfi/KlumppH08a.html">dblp:conf/mfi/KlumppH08a</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/slzhoty4azebbp7dvb5wxsqqdu">fatcat:slzhoty4azebbp7dvb5wxsqqdu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810083623/http://isas.uni-karlsruhe.de/Publikationen/MFI08_Klumpp-DiracTrees.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/02/f7/02f7203870f5a3cc0a2e4fee5eb4929335bf53e4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mfi.2008.4648009"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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