Recent zbMATH articles in MSC 44https://zbmath.org/atom/cc/442022-07-25T18:03:43.254055ZWerkzeugAdvanced engineering mathematics with MATLABhttps://zbmath.org/1487.000022022-07-25T18:03:43.254055Z"Duffy, Dean G."https://zbmath.org/authors/?q=ai:duffy.dean-gPublisher's description: In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books.
This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates.
To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace's equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus.
Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as \(z\)-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author.
MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book.
See the reviews of the 2nd and 3rd editions in [Zbl 1018.00003; Zbl 1210.00010]. For the 4th edition see [Zbl 1354.00004].Moment matrices, trace matrices, and the radical of idealshttps://zbmath.org/1487.130572022-07-25T18:03:43.254055Z"Janovitz-Freirech, Itnuit"https://zbmath.org/authors/?q=ai:janovitz-freirech.itnuit"Szántó, Agnes"https://zbmath.org/authors/?q=ai:szanto.agnes"Mourrain, Bernard"https://zbmath.org/authors/?q=ai:mourrain.bernard"Ronyai, Lajos"https://zbmath.org/authors/?q=ai:ronyai.lajosOrders of Nevanlinna matrices for strong moment problemshttps://zbmath.org/1487.300322022-07-25T18:03:43.254055Z"Njåstad, Olav"https://zbmath.org/authors/?q=ai:njastad.olav(no abstract)Generalized fractional integral formulas for the \(k\)-Bessel functionhttps://zbmath.org/1487.330032022-07-25T18:03:43.254055Z"Suthar, D. L."https://zbmath.org/authors/?q=ai:suthar.daya-l"Ayene, Mengesha"https://zbmath.org/authors/?q=ai:ayene.mengeshaSummary: The aim of this paper is to deal with two integral transforms involving the Appell function as their kernels. We prove some compositions formulas for generalized fractional integrals with \(k\)-Bessel function. The results are expressed in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some related assertion for Saigo, Riemann-Liouville type, and Erdélyi-Kober type fractional integral transforms.Fractional Fourier transform and stability of fractional differential equation on Lizorkin spacehttps://zbmath.org/1487.340452022-07-25T18:03:43.254055Z"Unyong, Bundit"https://zbmath.org/authors/?q=ai:unyong.bundit"Mohanapriya, Arusamy"https://zbmath.org/authors/?q=ai:mohanapriya.arusamy"Ganesh, Anumanthappa"https://zbmath.org/authors/?q=ai:ganesh.anumanthappa"Rajchakit, Grienggrai"https://zbmath.org/authors/?q=ai:rajchakit.grienggrai"Govindan, Vediyappan"https://zbmath.org/authors/?q=ai:govindan.vediyappan"Vadivel, R."https://zbmath.org/authors/?q=ai:vadivel.rajarathinam"Gunasekaran, Nallappan"https://zbmath.org/authors/?q=ai:gunasekaran.nallappan"Lim, Chee Peng"https://zbmath.org/authors/?q=ai:lim.chee-pengSummary: In the current study, we conduct an investigation into the Hyers-Ulam stability of linear fractional differential equation using the Riemann-Liouville derivatives based on fractional Fourier transform. In addition, some new results on stability conditions with respect to delay differential equation of fractional order are obtained. We establish the Hyers-Ulam-Rassias stability results as well as examine their existence and uniqueness of solutions pertaining to nonlinear problems. We provide examples that indicate the usefulness of the results presented.Computational modeling and theoretical analysis of nonlinear fractional order prey-predator systemhttps://zbmath.org/1487.340992022-07-25T18:03:43.254055Z"Ali, Amjad"https://zbmath.org/authors/?q=ai:ali.amjad.1"Shah, Kamal"https://zbmath.org/authors/?q=ai:shah.kamal"Alrabaiah, Hussam"https://zbmath.org/authors/?q=ai:alrabaiah.hussam"Shah, Zahir"https://zbmath.org/authors/?q=ai:shah.zahir"Ur Rahman, Ghaus"https://zbmath.org/authors/?q=ai:rahman.ghaus-ur"Islam, Saeed"https://zbmath.org/authors/?q=ai:islam.saeedRepresentation of solutions for linear fractional systems with pure delay and multiple delayshttps://zbmath.org/1487.341502022-07-25T18:03:43.254055Z"Elshenhab, Ahmed M."https://zbmath.org/authors/?q=ai:elshenhab.ahmed-m"Wang, Xing Tao"https://zbmath.org/authors/?q=ai:wang.xingtaoА nonhomogeneous system of linear fractional equations with pure delay and a nonhomogeneous system of multiple delays with linear parts are studied. Both cases of permutable and nonpermutable matrices are considered. The representations of their solutions are given. These representations are based on the application of delayed Mittag-Leffler matrix functions and Laplace transform
Reviewer: Snezhana Hristova (Plovdiv)A note on singular two-dimensional fractional coupled Burgers' equation and triple Laplace Adomian decomposition methodhttps://zbmath.org/1487.351592022-07-25T18:03:43.254055Z"Eltayeb, Hassan"https://zbmath.org/authors/?q=ai:eltayeb.hassan"Bachar, Imed"https://zbmath.org/authors/?q=ai:bachar.imedSummary: The present article focuses on how to find the exact solutions of the time-fractional regular and singular coupled Burgers' equations by applying a new method that is called triple Laplace and Adomian decomposition method. Furthermore, the proposed method is a strong tool for solving many problems. The accuracy of the method is considered through the use of some examples, and the results obtained are compared with those of the existing methods in the literature.Application of nonlinear time-fractional partial differential equations to image processing via hybrid Laplace transform methodhttps://zbmath.org/1487.354052022-07-25T18:03:43.254055Z"Jacobs, Byron A."https://zbmath.org/authors/?q=ai:jacobs.byron-a"Harley, C."https://zbmath.org/authors/?q=ai:harley.charis|harley.calvin-bSummary: This work considers a hybrid solution method for the time-fractional diffusion model with a cubic nonlinear source term in one and two dimensions. Both Dirichlet and Neumann boundary conditions are considered for each dimensional case. The hybrid method involves a Laplace transformation in the temporal domain which is numerically inverted, and Chebyshev collocation is employed in the spatial domain due to its increased accuracy over a standard finite-difference discretization. Due to the fractional-order derivative we are only able to compare the accuracy of this method with Mathematica's NDSolve in the case of integer derivatives; however, a detailed discussion of the merits and shortcomings of the proposed hybridization is presented. An application to image processing via a finite-difference discretization is included in order to substantiate the application of this method.Solution of fractional kinetic equations involving class of functions and Sumudu transformhttps://zbmath.org/1487.354152022-07-25T18:03:43.254055Z"Nisar, Kottakkaran Sooppy"https://zbmath.org/authors/?q=ai:sooppy-nisar.kottakkaran"Shaikh, Amjad"https://zbmath.org/authors/?q=ai:shaikh.amjad-salim"Rahman, Gauhar"https://zbmath.org/authors/?q=ai:rahman.gauhar"Kumar, Dinesh"https://zbmath.org/authors/?q=ai:kumar.dinesh|kumar.dinesh-kant(no abstract)Clifford-valued Stockwell transform and the associated uncertainty principleshttps://zbmath.org/1487.420202022-07-25T18:03:43.254055Z"Shah, Firdous A."https://zbmath.org/authors/?q=ai:shah.firdous-ahmad"Teali, Aajaz A."https://zbmath.org/authors/?q=ai:teali.aajaz-a"Bahri, Mawardi"https://zbmath.org/authors/?q=ai:bahri.mawardiSummary: In the framework of higher-dimensional time-frequency analysis, we propose a novel Clifford-valued Stockwell transform for an effective and directional representation of Clifford-valued functions. The proposed transform rectifies the windowed Fourier and wavelet transformations by employing an angular, scalable and localized window, which offers directional flexibility in the multi-scale signal analysis in Clifford domains. The basic properties of the proposed transform such as inner product relation, reconstruction formula, and the range theorem are investigated using the machinery of operator theory and Clifford Fourier transforms. Moreover, several extensions of the well-known Heisenberg-type inequalities are derived for the proposed transform in the Clifford Fourier domain. We culminate our investigation by deriving the directional uncertainty principles for the Clifford-valued Stockwell transform. To validate the acquired results, illustrative examples are given.Besov-type spaces for the \(\kappa\)-Hankel wavelet transform on the real linehttps://zbmath.org/1487.420862022-07-25T18:03:43.254055Z"Pathak, Ashish"https://zbmath.org/authors/?q=ai:pathak.ashish"Pandey, Shrish"https://zbmath.org/authors/?q=ai:pandey.shrish-kumarSummary: In this paper, we shall introduce functions spaces as subspaces of \(L^p_\kappa (\mathbb{R})\) that we call Besov-\(\kappa \)-Hankel spaces and extend the concept of \(\kappa\)-Hankel wavelet transform in \(L^p_\kappa (\mathbb{R})\) space. Subsequently we will characterize the Besov-\(\kappa\)-Hankel space by using \(\kappa\)-Hankel wavelet coefficients.Matrix valued conjugate convolution operators on matrix valued \(L^p\)-spaceshttps://zbmath.org/1487.430022022-07-25T18:03:43.254055Z"Ebadian, Ali"https://zbmath.org/authors/?q=ai:ebadian.ali"Jabbari, Ali"https://zbmath.org/authors/?q=ai:jabbari.aliLet \(G\) be a locally compact group with left Haar measure, and let \(M_n\) be the set of \(n \times n\) matrices endowed with the \(C^{\ast}\)-norm. Throughout this review \(p\) will denote a real number strictly greater than one. We shall write \(L^p(G, M_n)\) to indicate the space of \(p\)-integrable functions from \(G\) into \(M_n\). Let \(M(G, M_n)\) be the space of \(M_n\)-valued measures. In the paper under review the authors define a right conjugate convolution operator \(f \circledast \mu\) and a left conjugate convolution operator \(\mu \circledast_{\ell} f\), where \(\mu \in M(G, M_n)\) and \(f \in L^p(G, M_n)\). Several results concerning conjugate linear operators are given.
A bounded operator \(T: L^p(G, M_n) \rightarrow L^p(G,M_n)\) is called a matrix valued left \(p\)-convolution operator on \(G\) if \(T(_gf) = {_gT(f)}\) for all \(g \in G\) and \(f \in L^p(G, M_n)\). We shall say that \(T\) is a right \(p\)-convolution operator with entries in \(M_n\) if \(T(f_g) = T(f)_g\) for all \(g \in G\), \(f \in L^p(G, M_n)\). Let \(LCV_p(G, M_n)\) be the set of all matrix valued left \(p\)-convolution operators on \(G\) and let \(RCV_p(G, M_n)\) be the set of all matrix valued right \(p\)-convolution operators on \(G\). The space of matrix valued \(p\)-convolution operators is \(CV_p(G, M_n) = LCV_p(G, M_n) \cap RCV_p(G, M_n)\). This paper also relates matrix valued left and right \(p\)-convolution operators with conjugate convolution. An example of a result in this direction from this paper is:
Let \(G\) be a locally compact group and let \(T\) be a bounded linear operator on \(L^p(G, M_n)\). If \(T \in RCV_p(G, M_n)\) and \(T(g \circledast f) = T(g) \circledast f\) for all \(f \in L^1(G, M_n)\), \(g \in L^p(G, M_n)\), then \(T \in CV_p(G, M_n)\).
A similar result is also shown to be true for operators in \(LCV_p(G, M_n)\).
Reviewer: Michael J. Puls (New York)Inversion of higher dimensional Radon transforms of seismic-typehttps://zbmath.org/1487.440012022-07-25T18:03:43.254055Z"Chihara, Hiroyuki"https://zbmath.org/authors/?q=ai:chihara.hiroyukiSummary: We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of the independent variables, and are imposed some symmetry with respect to the axes. These transforms are higher dimensional version of generalization of the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.Streak artifacts from nonconvex metal objects in X-ray tomographyhttps://zbmath.org/1487.440022022-07-25T18:03:43.254055Z"Wang, Yiran"https://zbmath.org/authors/?q=ai:wang.yiran"Zou, Yuzhou"https://zbmath.org/authors/?q=ai:zou.yuzhouSummary: We study artifacts in the reconstruction of X-ray tomography due to nonlinear effects. For nonconvex metal objects, we analyze the new phenomena of streak artifacts from inflection points on the boundary of metal objects. We characterize the location and strength of all possible artifacts using notions of conormal distributions associated with the proper geometry.Discrete Lebedev's index transformshttps://zbmath.org/1487.440032022-07-25T18:03:43.254055Z"Yakubovich, Semyon"https://zbmath.org/authors/?q=ai:yakubovich.semyon-bThe author introduces discrete analogs of the Lebedev transforms with the product of the modified Bessel functions given by the Eqs.~(1.2), (1.3). The author investigates four transformations given by Eq.~(1.4) to Eq. (1.7) employing the theory of the discrete Kontorovich-Lebedev transform recently developed by the author [Ramanujan J. 55, No.~2, 517--538 (2021; Zbl 1476.44005)].
The author provides proofs for the inversion formulas for the expressions presented in Eq.~(1.4) and Eq.~(1.5) in Theorem~1 and Theorem~2, respectively. Finally, he gives the proofs of the inversion theorems (Theorem~3 and Theorem~4) for the discrete transforms presented in Eq.~(1.6) and Eq.~(1.7), respectively.
Reviewer: Shared Chander Pandey (Jaipur)Fractional operators associated with the \(\underline{p}\)-extended Mathieu series by using Laplace transformhttps://zbmath.org/1487.440042022-07-25T18:03:43.254055Z"Kahsay, Hafte Amsalu"https://zbmath.org/authors/?q=ai:kahsay.hafte-amsalu"Khan, Adnan"https://zbmath.org/authors/?q=ai:khan.adnan-a|khan.adnan-qadir"Khan, Sajjad"https://zbmath.org/authors/?q=ai:khan.sajjad-ahmad|khan.sajjad-ali"Wubneh, Kahsay Godifey"https://zbmath.org/authors/?q=ai:wubneh.kahsay-godifeySummary: In this paper, our leading objective is to relate the fractional integral operator known as \(P_\delta\)-transform with the \(\underline{p}\)-extended Mathieu series. We show that the \(P_\delta \)-transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the \(P_\delta\)-transform into a classical Laplace transform by changing the variable \((\ln[(\delta-1)s+1])/(\delta-1)\longrightarrow s\); then, we get the integral involving the Laplace transform.On a lemma arising in the solution of Waring's problemhttps://zbmath.org/1487.440052022-07-25T18:03:43.254055Z"Konyagin, S. V."https://zbmath.org/authors/?q=ai:konyagin.sergey-v"Protasov, V. Yu."https://zbmath.org/authors/?q=ai:protasov.vladimir-yuThe authors give a simple proof for the fact that the sequence
\[
c_n=\left\{\begin{array}{cl} \frac{(n)!}{(n/2)!} & \textrm{ if } n \textrm{ is even} \\
0 & \textrm{ else }\end{array}\right.
\]
is a truncated moment sequence, and has an atomic measure solution. The proof is non-constructive and uses mainly convex analysis, and especially Carathéodory's theorem.
The reasoning in this paper is close to \textit{C.~Bayer} and \textit{J.~Teichmann} [Proc. Am. Math. Soc. 134, No.~10, 3035--3040 (2006; Zbl 1093.41016)] where the question of representation of a truncated moment sequence with a finite known atomic measure is treated (Richter-Tchakaloff theorem).
Reviewer: Hamza El Azhar (El Jadida)Spectral analysis of integro-differential equations arising in thermal physicshttps://zbmath.org/1487.450132022-07-25T18:03:43.254055Z"Pankratova, E. V."https://zbmath.org/authors/?q=ai:pankratova.ekaterina-v|pankratova.evgeniya-vThis paper is devoted to the spectrum of an operator function arising in the study of the following abstract second-order integro-differential equation in a separable Hilbert space \(H\):
\[
\frac{d^2u(t)}{dt^2} + \int \limits ^t_0 Q(t - s)\frac{du(s)}{ds} ds + A^2u(t) - \int \limits ^t_0 K(t - s)A^2 2u(s) ds = f(t), \tag{1}
\]
with \(t \in \mathbb{R}_+\) and initial conditions \(u(+0) = \varphi_0\), \(u^{\prime}(+0) = \varphi_1\). Here, \(A \) is a linear operator on \( H\) and \(A: \operatorname{Dom}(A) \to H\) is a self-adjoint positive definite operator with compact inverse.
The author is mainly interested in the spectral analysis of the operator function resulting from applying the Laplace transform to the left-hand side of Equation~(1). In particular, the localization of the spectrum of this operator function is obtained. The asymptotics of the non-real part of the spectrum is constructed.
Reviewer: Anar Assanova (Almaty)Spectra of generalized Poisson integral operators on \(L^p(\mathbb{R}^+)\)https://zbmath.org/1487.470782022-07-25T18:03:43.254055Z"Miana, Pedro J."https://zbmath.org/authors/?q=ai:miana.pedro-j"Oliva-Maza, Jesús"https://zbmath.org/authors/?q=ai:oliva-maza.jesusLet \(f\in L^p([0, \infty))\) and \(K(\cdot,\cdot)\) be a measurable function which is homogeneous of degree \(-1\). It is well known by several techniques that the integral operator \[T_K:f\mapsto \int_0^{\infty}K(s,\cdot)f(s)\,ds \] is bounded on \(L^p([0, \infty))\) under suitable conditions on the kernel \(K(\cdot,\cdot)\), for all \(1<p<\infty\). When the kernel \(K(s,\cdot)\in L^1(\mathbb{R}_+)\), clearly the operator \(T_K\) is bounded in \(L^p(\mathbb{R}_+)\) and an upper bound can be explicit. In this article, the authors presents an upper bound for the operator \(T_K\) (called generalized Poisson operator) when the kernel \(K\) is given by \[K(s,t) = t^{\alpha\mu -\beta}\frac{s^{\beta-1}}{(s^{\alpha}+t^{\alpha})^{\mu}},\quad t\geq 0, \] for all \(\alpha,\beta,\mu>0\) such that \(0<\beta -1/p<\alpha\mu\) with \(1\leq p<\infty\). Also, the authors describe a subordination formula via the group of isometries \(T_{t,p}f(s):= e^{-t/p}f(e^{-t}s)\) on \(L^p\). By the previous result and the Fourier transform, they show that the spectrum \(\sigma(T)\) of the generalized Poisson kernel is given by \begin{align*} \sigma(T)=\left\{\frac{1}{\alpha}B(1/\alpha(\beta-1/p)+it,\mu - 1/\alpha(\beta-1/p)-it):t\in\mathbb{R} \right\}\cup \{0\} \end{align*} where \(B(\cdot,\cdot)\) denotes the beta function.
For the entire collection see [Zbl 1441.47001].
Reviewer: Marcelo Fernandes de Almeida (São Cristovão)Inverse tempered stable subordinators and related processes with Mellin transformhttps://zbmath.org/1487.600832022-07-25T18:03:43.254055Z"Gupta, Neha"https://zbmath.org/authors/?q=ai:gupta.neha"Kumar, Arun"https://zbmath.org/authors/?q=ai:kumar.arun-n|kumar.arun-mSummary: In this article, the infinite series form of the probability densities of tempered stable and inverse tempered stable subordinators are obtained using Mellin transform. Further, the densities of the products and quotients of stable and inverse stable subordinators are worked out. The asymptotic behaviors of these densities are obtained as \(x\to 0^+\). Similar results for tempered and inverse tempered stable subordinators are discussed. Our results provide alternative methods to find the densities of these subordinators and complement the results available in literature.Motion compensation strategies in tomographyhttps://zbmath.org/1487.651352022-07-25T18:03:43.254055Z"Hahn, Bernadette N."https://zbmath.org/authors/?q=ai:hahn.bernadette-nSummary: Imaging modalities have been developed and established as important and powerful tools to recover characteristics of the interior structure of a studied specimen from induced measurements. The reconstruction process constitutes a well-known application of the theory of inverse problems and is well understood if the investigated object is stationary.
However, in many medical and industrial applications, the studied quantity shows a time-dependency, for instance due to patient or organ motion. Most imaging modalities record the data sequentially, i.e. temporal changes of the object during the measuring process lead to inconsistent data sets. Therefore, standard reconstruction techniques which solve the underlying inverse problem in the static case lead to motion artefacts in the computed image and hence to a degraded image quality.
Consequently, suitable models and algorithms with a specific treatment of the dynamics have to be developed in order to solve such time-dependent imaging problems. This article provides a respective theoretical framework as well as numerical results from different imaging applications, including a study of 3D cone-beam CT.
For the entire collection see [Zbl 1471.65006].Microlocal properties of dynamic Fourier integral operatorshttps://zbmath.org/1487.651362022-07-25T18:03:43.254055Z"Hahn, Bernadette N."https://zbmath.org/authors/?q=ai:hahn.bernadette-n"Garrido, Melina-L. Kienle"https://zbmath.org/authors/?q=ai:kienle-garrido.melina-l"Quinto, Eric Todd"https://zbmath.org/authors/?q=ai:quinto.eric-toddSummary: Following from the previous chapter Motion compensation strategies in tomography, this article provides a complementary study on the overall information content in dynamic tomographic data using the framework of microlocal analysis and Fourier integral operators. Based on this study, we further analyze which characteristic features of the studied specimen can be reliably reconstructed from dynamic tomographic data and which additional artifacts have to be expected in a dynamic image reconstruction. Our theoretical results, in particular the affect of the dynamic behavior on the measured data and the reconstruction result, is then illustrated in detail at various numerical examples from dynamic photoacoustic tomography.
For the entire collection see [Zbl 1471.65006].Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delayshttps://zbmath.org/1487.652002022-07-25T18:03:43.254055Z"Moosavi Noori, Seyyedeh Roodabeh"https://zbmath.org/authors/?q=ai:moosavi-noori.seyyedeh-roodabeh"Taghizadeh, Nasir"https://zbmath.org/authors/?q=ai:taghizadeh.nasir(no abstract)Measuring higher-order photon correlations of faint quantum light: a short reviewhttps://zbmath.org/1487.811702022-07-25T18:03:43.254055Z"Laiho, K."https://zbmath.org/authors/?q=ai:laiho.kaisa"Dirmeier, T."https://zbmath.org/authors/?q=ai:dirmeier.t"Schmidt, M."https://zbmath.org/authors/?q=ai:schmidt.michael-g|schmidt.m-o|schmidt.marian|schmidt.mike|schmidt.martin.1|schmidt.maxie-d|schmidt.mikkel-n|schmidt.marius-alexander|schmidt.markus-r|schmidt.michael-p|schmidt.marie|schmidt.martin-ulrich|schmidt.mark|schmidt.martin|schmidt.matthias.1|schmidt.martin-a|schmidt.matthias|schmidt.melanie|schmidt.marius|schmidt.miroslaw|schmidt.marcus|schmidt.michael-j|schmidt.marc|schmidt.martin-b|schmidt.matthew-c|schmidt.michael-w|schmidt.malena|schmidt.m-r|schmidt.michael-a|schmidt.markus|schmidt.marcel.1|schmidt.miriam|schmidt.morgan-s|schmidt.marcel|schmidt.malgorzata|schmidt.marco.1|schmidt.martin.2|schmidt.margot|schmidt.maximilian|schmidt.markus-h|schmidt.michael-f-w"Reitzenstein, S."https://zbmath.org/authors/?q=ai:reitzenstein.s"Marquardt, C."https://zbmath.org/authors/?q=ai:marquardt.christophSummary: Normalized correlation functions provide expedient means for determining the photon-number properties of light. These higher-order moments, also called the normalized factorial moments of photon number, can be utilized both in the fast state classification and in-depth state characterization. Further, non-classicality criteria have been derived based on their properties. Luckily, the measurement of the normalized higher-order moments is often loss-independent making their observation with lossy optical setups and imperfect detectors experimentally appealing. The normalized higher-order moments can for example be extracted from the photon-number distribution measured with a true photon-number-resolving detector or accessed directly via manifold coincidence counting in the spirit of the Hanbury Brown and Twiss experiment. Alternatively, they can be inferred via homodyne detection. Here, we provide an overview of different kind of state classification and characterization tasks that take use of normalized \textit{higher-order} moments and consider different aspects in measuring them with free-traveling light.A guide to signals and systems in continuous timehttps://zbmath.org/1487.930032022-07-25T18:03:43.254055Z"Lafortune, Stéphane"https://zbmath.org/authors/?q=ai:lafortune.stephanePublisher's description: This textbook is a concise yet precise supplement to traditional books on Signals and Systems, focusing exclusively on the continuous-time case. Students can use this guide to review material, reinforce their understanding, and see how all the parts connect together in a uniform treatment focused on mathematical clarity. Readers learn the ``what'', ``why'' and ``how'' about the ubiquitous Fourier and Laplace transforms encountered in the study of linear time-invariant systems in engineering: what are these transforms, why do we need them, and how do we use them? Readers will come away with an understanding of the gradual progression from time-domain analysis to frequency-domain and s-domain techniques for continuous-time linear time-invariant systems. This book reflects the author's experience in teaching this material for over 25 years in sophomore- and junior-level required engineering courses and is ideal for undergraduate classes in electrical engineering.