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Roman theatres have always been the subject of research studies, from an architectural perspective and archaeology. The border lines between these and other disciplines is always difficult to be established since the interrelation of various expertise is required to achieve a complete knowledge of ancient buildings, especially when documentations and archaeological sources are limited. The present work deals with the acoustic analysis of the Roman theatre of Volterra, located in northern Italy, which has already been the subject of archaeological and architectural studies since its discovery in 1950. Acoustic measurements have been carried out in line with the standard requirements outlined in ISO 3382. After model calibration, the acoustic simulations have been carried out using four specific scenarios, highlighting the contribution that different construction elements can have on the acoustic response of this open-air theatre in comparison with the existing conditions. The results were evaluated assuming that light music (classical quartets, unamplified) and prose are the main functions of the space, as this case was in the past. The simulated results show that the values for the main acoustic parameters are better than the measured values, to be closer to the optimal ranges of the criteria borrowed from studies on enclosed spaces, since there are no criteria for Roman theatres. The good acoustic response of the Roman theatre of Volterra raises new doubts about the function of the vessels that were located under the steps of the cavea, as mentioned by Vitruvius. [ABSTRACT FROM AUTHOR]

Historiography traditionally tends to attribute the Roman civitas of Arminius made explicit by ancient sources to a personal benefit accrued, viritim, for his war exploits during his militancy in the Roman army as a cavalry commander. Without denying the possibility that such special merits were granted, even in the Augustan period, to individuals who distinguished themselves for their services to the Roman state, an attempt will be made here to show how certain elements, and in particular the existence of an interesting epigraph from Volterra, might push toward the hypothesis of a Roman citizenship acquired by the Cheruscan prince through the mechanism of adoption. [ABSTRACT FROM AUTHOR]

The emerging high-bandwidth services of 6G, such as high-definition video transmission and real-time interaction, have promoted the progress of the fiber optic access network industry, driving its development towards the next-generation PON with higher speed and larger system capacity. In response to the future requirements of 200 Gb/s/λ PON for both 20 km and 30 km downlink transmission scenarios, this paper proposes a Simplified Volterra Equalization (SVLE) scheme based on Nyquist PAM4 single-sideband modulation direct detection (SSBM-DD) scheme. In order to verify its advantages, the IQ-modulated Kramers–Kronig reception (KK) scheme is introduced for comparison. Simulation validation platforms for two schemes are conducted, and the performance comparison of the SVLE and KK schemes is carried out. In both, the impact of the carrier signal power ratio (CSPR) on receiver sensitivity, the influence of input optical power on power budget and receiver sensitivity, and the tolerance of receiver sensitivity to the linewidth of the DFB laser are investigated in the simulation. Finally, a comprehensive comparison of the two schemes is presented in terms of system performance, cost, and DSP complexity. In the 20 km downlink transmission scenario, the SVLE scheme outperforms the KK scheme by 4.9 dB in terms of power budget. The total number of multiplications of the SVLE scheme is 37, while that of the KK scheme is 4358. Therefore, the DSP complexity of the SVLE scheme is much lower than that of the KK scheme. The results of the comparison demonstrate that, in downlink transmission scenarios, the SVLE scheme is more suitable than the KK scheme as it exhibits a higher power budget, lower DSP complexity, and lower cost. Consequently, the proposed SVLE scheme could be a highly promising solution for future ultra-high-speed PON downlink transmission. [ABSTRACT FROM AUTHOR]

Visiting Italy in 1978 as part of his own Grand Tour, Lebbeus Woods was able to see some of the treasures of the Renaissance and the Baroque. The ensuing mix of reality and imagination prompted the Editors of this 2, Aleksandra Wagner and Neil Spiller, to consider the visual travelogue –Cityscapes – in a similar manner, combining speculation and truth. [ABSTRACT FROM AUTHOR]

The emerging high-bandwidth services of 6G, such as high-definition video transmission and real-time interaction, have promoted the progress of the fiber optic access network industry, driving its development towards the next-generation PON with higher speed and larger system capacity. In response to the future requirements of 200 Gb/s/λ PON for both 20 km and 30 km downlink transmission scenarios, this paper proposes a Simplified Volterra Equalization (SVLE) scheme based on Nyquist PAM4 single-sideband modulation direct detection (SSBM-DD) scheme. In order to verify its advantages, the IQ-modulated Kramers–Kronig reception (KK) scheme is introduced for comparison. Simulation validation platforms for two schemes are conducted, and the performance comparison of the SVLE and KK schemes is carried out. In both, the impact of the carrier signal power ratio (CSPR) on receiver sensitivity, the influence of input optical power on power budget and receiver sensitivity, and the tolerance of receiver sensitivity to the linewidth of the DFB laser are investigated in the simulation. Finally, a comprehensive comparison of the two schemes is presented in terms of system performance, cost, and DSP complexity. In the 20 km downlink transmission scenario, the SVLE scheme outperforms the KK scheme by 4.9 dB in terms of power budget. The total number of multiplications of the SVLE scheme is 37, while that of the KK scheme is 4358. Therefore, the DSP complexity of the SVLE scheme is much lower than that of the KK scheme. The results of the comparison demonstrate that, in downlink transmission scenarios, the SVLE scheme is more suitable than the KK scheme as it exhibits a higher power budget, lower DSP complexity, and lower cost. Consequently, the proposed SVLE scheme could be a highly promising solution for future ultra-high-speed PON downlink transmission.

This paper considers the collocation method for the numerical solution of the Volterra integro- differential equation using polynomial basis functions. The modeled equation was converted into a linear algebraic system of equations and matrix inversion was employed to solve the algebraic equation. We substitute the result of algebraic into the approximate solution to obtain the numerical result. Some numerical problems are solved to show the method's efficiency and consistency.

Featured Application: Authors are encouraged to provide a concise description of the specific application or a potential application of the work. This section is not mandatory. A novel simplifying Volterra structure algorithm is proposed for an intensity modulation direct detection (IM-DD) optical fiber short distance communication system using the decision feedback equalization algorithm (DFE). Based on this algorithm, the signal damage for the four-level pulse amplitude modulation signal (PAM-4) is compensated, which is caused by device bandwidth limitation and dispersion during transmission. Experiments have been carried out using a 25 GHz Electro-absorption Modulated Laser (EML), showing that PAM-4 signals can transmit over 10 km in standard single-mode fiber (SSMF). The 112 Gbps and 128 Gbps signals can reach the error rate threshold of KP4-FEC (BER = 2 × 10−4) and HD-FEC (BER = 3.8 × 10−3), respectively. The simplified principle and process of the proposed Volterra-based equalization algorithm are presented. Experimental results show that the algorithm complexity is greatly reduced by 75%, which provides effective theoretical support for the commercial application of this algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method for solving second kind nonlinear Volterra integral equations is presented. The method is based upon the extension of unknown function by single term Walsh series. Indeed, the interval [0, 1) is divided to m equal subinterval and in each interval, the unknown function is extended by the first term of Walsh series functions. By using a collocation method the coefficients of these extensions are computed and a block-pulse approximation of the unknown function is obtained. By the block-pulse approximation both continuous and pointwise approximations can be obtained. A convergence analysis for continuous approximations are investigated. The numerical examples confirm the ability and accuracy of the method. The method is computationally attractive and can be easily generalized for the systems of nonlinear Volterra equations. [ABSTRACT FROM AUTHOR]

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial and boundary conditions. Closed-form solutions are always desirable, not only because they are more efficient, but also because they can be valuable benchmarks for validating approximate and numerical procedures. This paper presents a direct operator method for solving, in closed form, a class of Volterra–Fredholm–Hammerstein-type integro-differential equations under nonlocal boundary conditions when the inverse operator of the associated Volterra integro-differential operator exists and can be found explicitly. A technique for constructing inverse operators of convolution-type Volterra integro-differential operators (VIDEs) under multipoint and integral conditions is provided. The proposed methods are suitable for integration into any computer algebra system. Several linear and nonlinear examples are solved to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper presents a numerical computation approach to the solution of Volterra Integro-Differential Equation with delay via legendary Polynomial method. Computational code was developed and implemented on a Mathematical Software (Matlab 2009b) to solve the problem. The accuracy, efficiency and effectiveness of the method of solution were ascertained by comparing the solution obtained with the exact solution in the literature and it showed that the present results were in agreement with both the exact and existing results.

We experimentally demonstrate the transmission of multiorder quadrature amplitude modulation (QAM) millimeter wave (MMW) orthogonal frequency division (OFDM) signal at 28 GHz radio frequency (RF). To overcome these unfavorable channel properties such as high path loss, propagation loss, rain fading, etc., 5G MMW phased array antenna has been used. Meanwhile, probabilistic shaping (PS) technology is applied to extend transmission distance, and Volterra nonlinearity compensation (VNC) technology is used to alleviate the system nonlinearity. Using 5G MMW phased array antennas and technologies of PS and VNC, 6.72 Gbit/s 1024-QAM OFDM signal at 28 GHz can be transmitted over 55-m wireless distance in our experiment, satisfying the normalized general mutual information (NGMI) threshold of 0.83 with 25% soft-decision forward-error-correction (SD-FEC) overhead. To the best of our knowledge, this is the first time to demonstrate the transmission of multiorder QAM OFDM signal at 28 GHz RF using 5G MMW phased array antenna. [ABSTRACT FROM AUTHOR]

A novel simplifying Volterra structure algorithm is proposed for an intensity modulation direct detection (IM-DD) optical fiber short distance communication system using the decision feedback equalization algorithm (DFE). Based on this algorithm, the signal damage for the four-level pulse amplitude modulation signal (PAM-4) is compensated, which is caused by device bandwidth limitation and dispersion during transmission. Experiments have been carried out using a 25 GHz Electro-absorption Modulated Laser (EML), showing that PAM-4 signals can transmit over 10 km in standard single-mode fiber (SSMF). The 112 Gbps and 128 Gbps signals can reach the error rate threshold of KP4-FEC (BER = 2 × 10−4) and HD-FEC (BER = 3.8 × 10−3), respectively. The simplified principle and process of the proposed Volterra-based equalization algorithm are presented. Experimental results show that the algorithm complexity is greatly reduced by 75%, which provides effective theoretical support for the commercial application of this algorithm.

• This paper proposes a new nonlinear system model for signal processing and develops its corresponding adaptive algorithm. • This paper also gives a variant version of the proposed algorithm to reduce its complexity. • The performance analysis is derived and verified by simulations. • The superior behavior is demonstrated by examples of NSAEC and nonlinear channel identification. In the field of nonlinear signal processing, Volterra filter is generally used as an effective tool. The utilization of the augmented model can make the filter maintain its merit in both circular and non-circular signals. From this point of view, this paper proposes a new online nonlinear system model called the augmented Volterra model. To combat impulsive noise, we introduce the complex correntropy to the Volterra filter, and propose the augmented Volterra recursive maximum complex correntropy criterion (A-VRMCCC) algorithm. Considering the computational cost of the augmented Volterra model, we propose the decomposable method to effectively reduce its computational load. Additionally, the performance of A-VRMCCC has also been studied. Finally, simulation results validate the correctness of the performance analysis, and show that the newly proposed algorithms have a competitive advantage over other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for nonlinear Hammerstein, Volterra–Hammerstein, and Volterra equations in the space of functions of bounded second variation in the sense of Shiba, (Λ p 2 B V [ a , b ]) . [ABSTRACT FROM AUTHOR]

In the novel Forse che sì forse che no (1910), Gabriele D'Annunzio provides an interesting contamination of suggestions from Dante's Inferno with ancient Etruscan art and, more generally, with the mystifying landscape of the Tuscan city of Volterra. In doing so, he productively combines his typical imaginative and synaesthetic style with scholarly and cultural trends of the time suggesting that a secret 'blood memory' might tie together Tuscan art of all times – from the Etruscans to Dante to the modern era. This essay explores D'Annunzio's rendering of the 'Etruscan Dante' by setting it in the wider context of the reception of Dante and of ancient Italian art with a particular focus on the synaesthetic contaminations between suggestions from the text and the visual and tactual features of ancient Etruscan art. [ABSTRACT FROM AUTHOR]

We studied in this work a class of nonlinear Volterra integral equations with delay and present a sufficient condition for the bounded solution also we give an illustrative example which support the main result of this paper.

In this paper we study some nonlinear integral equations and give conditions for the functions and kernel involved in such equations under which we assure the existence, uniqueness, and continuity of solutions in the space of functions of bounded K-variation in the sense of Korenblum, (KBV ([a,b])). [ABSTRACT FROM AUTHOR]

Using a global inversion theorem we investigate properties of the following operator

In this paper we use the fixed-point theorem of Latrach, Taoudi and Zeghal under some conditions to find a solution for Volterra_Hammerstein integral equation in the Banach space L^p ([0,m],R). We use this fixed point theorem with new assumptions.

Copyright of Reti Medievali is the property of Firenze University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations. [ABSTRACT FROM AUTHOR]

We successively apply the rational Haar wavelet to solve the nonlinear Volterra integro-differential equations and nonlinear Fredholm integro-differential equations. Using the Banach fixed point theorem for these equations, we prove the convergence. In this method, no numerical integration is used. Numerical results are presented to show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In order to provide convincing artifical touch sensations, humans should be presented with high quality haptic stimuli. In the vibrotactile domain, signals are usually displayed through mechanical actuators. Current high quality actuators exhibit a high dynamic range and have the ability to display a wide range of frequencies. However, fundamentally all actuators introduce distortions into the displayed signals. These distortions are usually nonlinear with additive noise components and they can be detrimental to some vibrotactile application scenarios that require high signal playback precision. To neutralize these distortions, we propose a signal-based equalization setup with adaptive filtering. Such a setup is very general and can be applied to any actuator in a straightforward manner. We introduce a novel adaptive filter based on Volterra and bilinear filter models that is nonlinear and more robust than previous approaches. In simulations and experiments, we show that our filter model is able to consistently outperform existing adaptive filter models and equalize vibrotactile actuators efficiently. [ABSTRACT FROM AUTHOR]

Durante sua longa vida científica, Vito Volterra dedicou uma grande quantidade de energia à causa de jovens matemáticos. Ele ajudou muitos deles a encontrar o seu caminho na pesquisa, fornecendo aconselhamento sobre seus trabalhos e também ajudando-os a entrar na comunidade acadêmica. No presente trabalho, estamos estudando o caso particularmente importante dos intercâmbios de estudantes entre a Itália e a França, em que Volterra desempenhou um papel fundamental. Nós nos concentramos sobre o que pode ser visto como a gênese de uma tradição fecunda, infelizmente brutalmente interrompida pelo advento da Grande Guerra.

We report 108 Gb/s Duo-Binary PAM-8 (DB-PAM-8) transmission using direct-detection aided by Volterra equalizer. The bit-error-rate (BER) performance of the DB-PAM-8 signal has been evaluated through error counting by varying the bit rate, received optical power, and reach. The experimental results suggest that up to 108, 102, and 84 Gb/s signals can be propagated in back-to-back (B2B), and over 10, and 20 km of standard single-mode fiber (SMF), respectively, below the low-density parity-check forward error correction (LDPC-FEC) threshold. Furthermore, we derive a probabilistic model of the BER for multilevel DB-PAM-M signaling that is verified using our measurements. The model of this important performance metric turned out to be accurate enough, especially at low BER values, where its use is more convenient. [ABSTRACT FROM AUTHOR]

The archaeological excavations carried out between 2010 and 2011 for the building of the new Lucca Hospital, in the Arancio area, have made it possible to recompose a sequence of transformations of the landscape and settlements, ranging from the Iron Age to the present day. The first occupation of the area is evidenced by a burial ground – with six repeatedly disturbed depositions – dated by the materials and the typology of the tombs to the second half of the eighth century BC (Villanovan II B-II C); the necropolis is therefore contemporary with the settlement of Chiarone di Capannori, which until then was the only evidence of the Villanovan era in the Auser Serchio plain. The analysis of the materials confirms the solidity of the relationships between these communities and that of the Volterra area, which in this period experienced an “explosion” of settlements that combine the exploitation of agricultural resources with the arrangement along the road network that leads from the sea to the Apennines and the lively communities of the Po Valley. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the existence of an almost periodic solution of discrete Volterra systems by means of fixed point theory. Using discrete variant of exponential dichotomy, we provide sufficient conditions for the existence of an almost periodic solution. Hence, we provide an alternative solution for the open problem proposed in the literature.

Tuscany is for Cassola, who was born and had long been living in Rome, a land of choice where he moved after his Twenties and set almost all his works. The paper explores, both from a biographical and a literary point of view, the writer’s attachment to places whose importance and inspirational value were such that he even thought of them as possible principles of thematic organization in cycles for his entire literary production, that is Cecina, Volterra, and the inland of Maremma. The literary transposition of these beloved places is informed by the astonishment he felt when he discovered them as an adolescent on holiday. The beauty of landscapes is described with the lyricism of his writing’s existential realism.

The Legendre-based ultraspherical spectral method for ordinary differential equations (Olver, S. & Townsend, A. (2013) A fast and well-conditioned spectral method. SIAM Rev. 55 , 462–489.) is combined with a formula for the convolution of two Legendre series (Hale, N. & Townsend, A. (2014a) An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput. , 36 , A1207–A1220.) to produce a new technique for solving linear Fredholm and Volterra integro-differential equations with convolution-type kernels. When the kernel and coefficient functions are sufficiently smooth, then the method is spectrally accurate and the resulting almost-banded linear systems can be solved with linear complexity. [ABSTRACT FROM AUTHOR]

We present a method for calculating the numerical approximation of the two-dimensional mixed Volterra Fredholm integral equations, using the properties of the rationalized Haar (RH) wavelets and the matrix operator. Attaining this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve the integral equation without using common mathematical methods. An upper bound and the convergence of the mentioned method have been proved, by using the Banach fixed point. Moreover, the rate of the convergence method is O(n(2q)n). Finally, several examples of different kinds of functions are presented and solved by this method. [ABSTRACT FROM AUTHOR]

In 1887 Volterra was in search of a general vision for analysis. His most famous work led him to the definition of functionals , or more precisely to develop a differential and integral calculus for "functions that depend on other functions" or "line functions." However, Volterra's efforts to define a general context for certain analytical problems would also lead him to extend the notions of derivation and integration to substitutions—matrices whose coefficients are functions—which have an important role in the study of differential linear equations. In a memoir entitled Sui fondamenti della teoria delle equazioni differenziali lineari Volterra establishes a differential and integral calculus for substitutions. This work, which allows one to think of linear differential equations through two operations on substitutions—derivation and integration, also makes it possible to analyse the progression strategy implemented by the Italian mathematician in his search for a generalized analysis from the beginning of his career. We are examining the selection and reorganization processes that have enabled Volterra to transpose a well-established theory for ordinary functions to a framework adapted to substitutions. We thus reveal a dynamic of progress towards generality, and explore the elements on which his thoughts are based. Far from being an anecdotal, this text, which does not solve any conjecture, allows us to see a coherence in Volterra's way of progressing, and clarifies his role in the search for an analysis which would gradually become the functional analysis of the 20th century. [ABSTRACT FROM AUTHOR]

The high-speed multimode optical interconnects based on vertical-cavity surface-emitting laser and multimode fiber (MMF) are severely constrained by band-limited devices, modulation nonlinearity, and laser induced noises such as relative intensity noise, mode partition noise, and fiber-induced noises such as chromatic dispersion and mode dispersion. The advanced digital signal processing technologies have been viewed as the inevitable tool to mitigate the physical limitations of electrical and optical components and the noise interactions during the transmission. In order to achieve multimode 100 Gbps/lane over 100-m transmission with the existing devices, a Volterra equalizer has been proven as a very effective equalization solution to deal with nonlinear impairments. However, the practical implementation of this nonlinear equalizer has been constrained by its tremendously high computation complexity. In this paper, we propose the threshold-based pruned retraining Volterra equalization (TRVE) to reduce the computation complexity, while maintaining the transmission performance. Multimode 100-Gbps/lane transmission over 100-m OM3 MMF has been experimentally demonstrated with up to 70.7% computation complexity reduction, while keeping the bit error rate under the 7% hard-decision forward error correction limit. In addition, the TRVE with $\ell _1$ -regularization is also proposed and experimentally verified to optimize the threshold selection. [ABSTRACT FROM AUTHOR]

This study attempts to estimate the volatility of the American options pricing model under jump-diffusion underlying asset model. Therefore, the problem is formulated then inverted, and afterward, direct finance problems are defined. It is demonstrated, then, that the price of this type of options satisfies a free boundary Partial Integral Differential Equation (PIDE). The inverse method for estimating the volatility and the American options price is also described in three phases: first, transformation of the direct problem to a non-linear initial and boundary value problem. Second, finding the solution by using the method of lines and the fourthorder Runge-Kutta method. Third, presenting a minimization function with Tikhonov regularization. [ABSTRACT FROM AUTHOR]