Memory Effects

In this study, we aim to comprehensively investigate a drinking model connected to immigration in terms of Atangana-Baleanu derivative in Caputo type. To do this, we firstly extend the model describing drinking model by changing the derivative with time fractional derivative having Mittag-Leffler kernel. The existence and uniqueness of the drinking model solutions together with the stability analysis is shown by the help of Banach fixed point theorem. The special solution of the model is investigated using the Sumudu transformation and then, we present some numerical simulations for the different fractional orders to emphasize the effectiveness of the used derivative.

Increasing the flexibility in spectrum access is a key to enhanced efficiency in radio spectrum utilization. Noncontiguous carrier aggregation (CA) is one enabling technology towards more flexible spectrum access, but can also lead to serious implementation challenges in terms of transmitter linearity. Especially when a single power amplifier (PA) is deployed for all carriers, serious intermodulation components will rise which can easily limit the maximum transmit power. In this paper, a low-complexity digital predistortion (DPD) solution is developed to reduce the most critical spurious components at the PA output, opposed to more classical full bandwidth linearization. The developed concept and associated parameter learning and optimization are particularly tailored towards mobile devices, building on limited narrowband feedback receiver with reduced instrumentation complexity and reduced-rate DPD processing. The developed DPD solution can handle PAs with substantial memory effects, and is verified with extensive simulation examples in various non-contiguous carrier aggregation scenarios and practical PA models with memory.

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE's domain of definitionD, using only temperature information in a small subdomainE⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong l...

Logically predicted, three spatial and one temporal axes, closed into themselves, in common form the hyper-spherical 4D cosmos. The super-spherical 3D space is propagating along the circular t-axis, at the speed of light determined by the medium features. This is projected into 3D space as the sine pulsating cosmos and cyclic time. Hobble’s ratio of a distance and speed of the motion away depends on the two unknowns: the temporal radius and phase of development. The cosmic forces and energies are also mutually related.

This paper demonstrates how the linearity performance of a 10W GaN HEMT can be dramatically improved by actively engineering the baseband impedance environment around the device. An important refinement to existing active load-pull measurement capability is proposed that allows the precise and independent control of all significant baseband and RF components that result from the amplification of a complex 9carrier multi-sine modulation. The synthesis of constant, modulation frequency independent negative baseband impedances, resulting in specific baseband voltage waveforms has delivered a 24dB improvement in ACPR compared to the classical baseband short case, even when the device is operating with RF components terminated into a non-optimal 50 RF environment. This linearization concept is further investigated through the broadband emulation of a class-J impedance environment around a single device. Using this enhanced system and a two-tone modulated excitation, optimum baseband loads are identified that result in a 18.5dB and 24dB improvement in IM 3 and IM 5 inter-modulation products respectively, again relative to the case of a traditional IF short circuit. The significance of this last observation is that unlike the 50 case, the optimum class-J IM 3 and IM 5 baseband impedances disperse, becoming reactive and moving away from the real axis.

Amorphous SiO2-Nb2O5 nanolaminates and mixture films were grown by atomic layer deposition. The films were grown at 300 o C from Nb(OC2H5)5, Si2(NHC2H5)6, and O3 to thicknesses ranging from 13 to 130 nm. The niobium to silicon atomic ratio was varied in the range of 0.11-7.20. After optimizing the composition, resistive switching properties could be observed in the form of characteristic current-voltage behavior. Switching parameters in the conventional regime were well defined only in a SiO2:Nb2O5 mixture at certain, optimized, composition with Nb:Si atomic ratio of 0.13, whereas low-reading voltage measurements allowed recording memory effects in a wider composition range.

In this paper we show that ensembles of well-structured and unstructured proteins can be distinguished by borrowing concepts from non-equilibrium statistical mechanics. For this purpose, we represent proteins by two different polymer models and interpret the resulting polymer configurations as random walks of a diffusing particle in space. The first model is the trace of the Cα-atoms along the protein main chain and the second their projections onto the protein axis. The resulting trajectories are subsequently analyzed using the theory of the Generalized Langevin Equation. Velocities are replaced by displacements relating consecutive points on the discrete protein axes and equilibrium ensemble averages by averages over appropriate protein structure ensembles. The resulting displacement autocorrelation functions resemble those of velocity autocorrelation functions of simple liquids and display a minimum, which can be related to the lengths of secondary structure elements. This minimum is clearly more pronounced for well-structured proteins than for unstructured ones and the corresponding memory function displays a slower decay, indicating a stronger "folding memory".

Honestamente não sei nem por onde começar... Acredito que o mestrado foi mais uma incrível experiência do que simplesmente o trabalho aqui apresentado. Agradeço à minha orientadora Nadja, que afinal passou a ser mais uma amiga. Obrigada por todos os conselhos, críticas, apoio e por ter me proporcionado momentos de grande aprendizado na vida acadêmica. Agradeço a Fernando de Melo, meu colaborador com quem tive ótimas conversas e que me guiou durante todo esse trabalho. Um agradecimento especial aos meus pais, Nadja e Clemens, a quem eu dedico esse trabalho e tudo o que eu venha a produzir na minha jornada. Graças a todo esse mais sincero amor, estou aqui hoje finalizando mais uma etapa da minha vida. A Guilherme, obrigada por ter sido mais do que um companheiro, um grande amigo. Por me fazer rir até nos piores dias, por cuidar de mim, e me incentivar a ser a mulher que eu quero ser e a fazer o que me faz feliz. Agradeço a Lucas, meu irmão de outros pais, que tornou leve o fato de ser a única menina da turma, desde o primeiro período da graduação. Um grande amigo, seja pra me ajudar a fazer uma conta, a escolher uma roupa, a terminar uma cerveja ou um café. Ele é o cara certo pra isso. A Polly, a Bruna e a Aninha, obrigada pela ótima amizade, pelas risadas, pela imensa cumplicidade e por me fizeram lembrar de que nem tudo é só física e que sair pra dançar é muito necessário às vezes. A João e Bia pelos nossos encontros, que por mais esporádicos que sejam, nunca deixam de ser memoráveis e dançantes. A Yuri, a Toni e a Bento, que fazem eu me sentir como uma pedrinha preciosa na vida deles, mal sabem que eles que são na minha. Aos meus mentores computacionais, Írio e Pedro, obrigada pelos conselhos e por uma bela amizade regada à café e risadas. Agradeço aos professores que tanto contribuíram para a minha formação, em especial Fernando Parisio, Leonardo Cabral e Bruno Carneiro da Cunha. Obrigada por partilharem de seu conhecimento de maneira tão inspiradora, despertando meu interesse em assuntos que nunca antes tinha pensado em conhecer. À minha família pelo suporte, em especial ao meu Tio Neilson, que me acolheu há 6 anos atrás quando eu era apenas uma menina querendo cursar Física. Obrigada pelo apoio. Por fim, agradeço ao Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), pelo suporte financeiro, sem o qual não teria sido possível a realização deste e demais importantíssimos trabalhos que contribuem para a ciência brasileira. Agradeço também ao Programa de Pós-graduação do Departamento de Física da UFPE, que me possibilitou participar de eventos científicos imprescindíveis à minha formação.

Amorphous SiO2-Nb2O5 nanolaminates and mixture films were grown by atomic layer deposition. The films were grown at 300 o C from Nb(OC2H5)5, Si2(NHC2H5)6, and O3 to thicknesses ranging from 13 to 130 nm. The niobium to silicon atomic ratio was varied in the range of 0.11-7.20. After optimizing the composition, resistive switching properties could be observed in the form of characteristic current-voltage behavior. Switching parameters in the conventional regime were well defined only in a SiO2:Nb2O5 mixture at certain, optimized, composition with Nb:Si atomic ratio of 0.13, whereas low-reading voltage measurements allowed recording memory effects in a wider composition range.

The impact of baseband electrical memory effects on the dynamic transfer characteristics of microwave power transistors. In Workshop on Integrated Nonlinear Microwave and Millimeter-Wave Circuits 2010 (INMMIC) Gothenberg, Sweden (pp. 148-151). Institute of Electrical and Electronics Engineers (IEEE).

This paper presents a fully automated measurement system based around a Tektronix sampling oscilloscope. The system is capable of measuring calibrated time domain voltage and current waveforms at the device plane. A novel active load-pull loop is incorporated which has proved very useful for increasing the speed of multi-tone device characterization, moreover the architecture opens up the possibility of multi-tone load pull measurements, novel concepts are discussed which explain how the system can be used to perform non-linear device characterization in real time, the system also incorporates an intermediate frequency (IF) test set to measure the complete waveforms, which could be useful in characterization of memory effects. Triggering issues of sampling oscilloscopes are discussed in some detail along with a novel sampling approach which allows for more efficient measurement of multi-tone waveforms. Some interesting applications of the system are also introduced.

U radu je demonstrirana primena metode automatizovanog ponavljanja nezavisnih simulacionih eksperimenata sa prikupljanjem statistike slučajnih procesa, u dostizanju i kontroli tačnosti simulacionih rezultata u simulaciji sistema masovnog opsluživanja Monte Karlo. Metoda se zasniva na primeni osnovnih stavova i teorema matematičke statistike i teorije verovatnoće. Tačnost simulacionih rezultata dovedena je u direktnu vezu sa brojem ponavljanja simulacionih eksperimenata. Ključne reči: simulacije Monte Karlo, kontrola tačnosti, masovno opsluživanje. Uvod avremene ratove karakteriše visok nivo intenziteta naprezanja snaga, nelinearnost i asimetričnost dejstava, dinamičnost i relativna kratkotrajnost uz oduvek prisutnu složenost i neizvesnost. Potreba za proučavanjem kompleksne fizionomije savremenog ratovanja nameće niz zahteva istraživačima. Simulacione metode pokazale su se kao veoma pogodne u modelovanju složenih sistema i procesa u kojima postoje faktori stohastičke prirode. Međutim, simulacione metode imaju i jedan nedostatak; to je problem kontrole tačnosti simulacionih rezultata, što je posebno izraženo u simulaciji stohastičkih sistema i procesa. Preokupirani rešavanjem složenosti modela, istraživači često zanemaruju pitanje obezbeđenja tačnosti izlaznih simulaconih rezultata. Ipak, problem tačnosti simulacija prepoznat je u naučnim krugovima, što je rezultiralo nizom pokušaja njegovog rešavanja. Jedno od prvih otvorenih upozorenja svima koji se bave simulacijom ili koriste njene rezultate, uputio je Gaither B., 1990, glavni urednik časopisa ACM Performance Evaluation Review, u svom članku "Empty empiricism" 0, u kojem kaže: "...Nije mi poznata ni jedna druga inženjerska ili naučna oblast u kojoj je dopuštena tolika sloboda u tumačenju rezultata kao u simulaciji".

The Radio Frequency Power Amplifier is the major source of the nonlinear distortion which affect the signal modulated in the Radiocommunication transmission system. To analyse and treat the distortion caused to the amplified signal, this paper presents the parameters estimation of a behavioral model. Based on baseband signals, this model includes a polynomial function representing AM/AM and AM/PM characteristics in addition with MIMO continuous filter to describe the PA dynamics. Using the baseband input and output data, model parameters are obtained recursively by an iterative identification algorithm based on Output Error method. Initialization and excitation problems are resolved by an association of a new technique using initial values extraction with a multi-level binary sequence input exciting all PA dynamics. Finally, the proposed estimation method is tested and validated on experimental data.

Digital predistortion (DPD) using baseband signals is commonly used for power amplifier linearization. This paper is devoted to this subject and aims to reduce DPD complexity. In this study, we propose a structure that allows to decrease the number of DPD parameters by using multiple blocks, with each one of them dedicated to characterizing the non-linear behavior and/or memory effects. Such a structure is based on the feedback Wiener system, involving a FIR filter used as a feedback path to reproduce the PA inverse dynamics. A memory polynomial block (MP) is inserted as the final element to minimize the modeling errors. A relevant model identification method, based on an iterative algorithm, has been developed as well. The proposed architecture is used for the linearization of a commercial class-AB LDMOS RF PA by NXP Semiconductors, in wideband communication systems. Comparison of performance with the conventional generalized memory polynomial model (GMP) shows that the proposed model offers similar results, with its advantage consisting in the reduced number of parameters.

We examine a model for the propagation of heat through a one-dimensional object with an interior "flaw". The flaw is modeled as a nonlinear relationship between the flux and temperature jump at an interior point of the object. Under realistic hypotheses, the resulting nonlinear initial boundary value problem is shown to have a unique and suitably smooth solution.

The adhesion strength of magnetic films of intermetallic alloys on different substrates specifies their long‐term magnetic functionality, among other physicochemical characteristics of the films. Nanospheroids of Sm/FeTaN intermetallic alloys were grown from the Sm13.8 Fe82.2 Ta4.0 target by pulse laser deposition at 157 nm. The high‐temperature, liquefied nanodroplets were formed in the plume. They eventually solidified on the surface of a Ta substrate covered with a thin Ta/O layer in the form of biphasic nanospheroids, consisting of a crystalline nucleus surrounded by an amorphous mantle. Such nanostructures exhibit a ferromagnetic response because the oxidization of the inner crystalloid nucleus, which specifies the magnetic properties, is prevented by the amorphous spheroid mantle. The strength of adhesion of the nanodroplets on the Ta substrate was inversely proportional to the Sm/Fe concentration. The nanodroplets with high Sm/Fe concentration were bound on the Ta substrate...

This article proposes an alternative method, based on reflection measurements, to characterize intermodulation distortion (IMD) in MEMS switches. Because of the low intermodulation level generated in MEMS switches, its characterization is problematic, requiring high-power RF tones (high power amplifiers). Using the proposed reflection-based method, IMD can be characterized saving up to 6 dB power when compared with that power required in a traditional 2-tone intermodulation measurement setup in transmission.

The design, the abilities and a characteristic application of an in-house made interface for combining thermogravimetry (TG) with mass spectrometry (MS) are presented. The TG-MS interface consists mainly of three co-axial tubes. The position of the intermediate tube was determined after calculation of the temperature profile at the TG furnace exit tube. The inner tube position was determined taking into consideration its protection against condensation of heavy molecules and the time delay for the transfer of the evolved gases. This interface allows either continuous sampling and transferring of the evolved gases from the TG to the MS or repetitive introduction of short sampling pulses of TG evolved gases to MS. The interface is capable of coupling various commercial instruments. In the present work two configurations of this interface are demonstrated. Finally an example of application of this interface on forest fuel pyrolysis is presented.

Significance The Mpemba effect, wherein an initially hotter system relaxes faster when quenched to lower temperatures than an initially cooler system, has attracted much attention. Paradoxically, its very existence is a hot topic. Using massive numerical simulations, we show unambiguously that the Mpemba effect is present in the archetypical model system for complex behavior, spin glasses. We find that the Mpemba effect in spin glasses is due to the aging dynamics of the internal energy, as controlled by the nonequilibrium spin-glass coherence length. Interestingly, the effect is not present when the system remains all of the time in the paramagnetic phase. Therefore, the Mpemba effect suggests itself as an effective probe for a glass transition, potentially useful for other glass-forming systems.

This paper proposes a new class of multisine excitations that allows efficient characterization of nonlinear circuits. By offsetting the frequency of tones, one can distinguish between different intermodulation products in a multisine response. This property leads to many applications for nonlinear circuit characterization, such as in-band distortion measurements, memory effects characterization, and model performance assessment. Some applications are highlighted in this paper, focusing especially on the characterization of memory effects. The effectiveness of the approach is demonstrated with a series of measurement results.

A new behavioral model is proposed which can provide similar accuracy to the memory polynomial model (MPM) but is shown to have a more efficient architecture for digital hardware implementation. These features have been achieved by the proposed formulation, in which the nonlinear weights of the memory terms are a function of only the present input sample. The new approach is evaluated and compared with the conventional MPM using a Wideband Code Division Multiple Access (WCDMA) signal applied to two different amplifier circuits.

n the last decades, vector network analyzers (VNA) have been successful for the characterization and modeling of time-invariant RF devices exhibiting mildly nonlinear response using swept continuous wave (CW) excitations. As the demand on wireless communication has grown, new modulation schemes such as WiMAX and long-term evolution (LTE) have been introduced that require higher peak-to-average-power ratio (PAPR) in the time-domain and wider bandwidth in the frequency domain. These modulated signals have forced many components, especially power amplifiers, to operate in a harsher nonlinear regime. Modern power amplifiers must therefore handle modulated signals with higher PAPR while keeping high average power. To assist with the device modeling and the amplifier design process, improved measurement systems are required which characterize their nonlinear response under realistic operating conditions. Since the first work reported by Lott in 1989 [2], many large-signal VNAs (LSNAs) or nonlinear VNAs (NVNAs) have been developed to characterize, under calibrated conditions, nonlinear devices excited by CW or periodically modulated RF signals. The LSNA and NVNA measure the absolute amplitude and relative phase of the harmonics of voltage and current waves at the measurement reference planes. Among the various architectures, the most popular are the sampler-based LSNAs and the mixer-based NVNAs. The

Dijana Damljanovi}, dipl. in`. dr Slavica Risti}, dipl. in`. Vojnotehni~ki institut, Beograd Rezime: U radu su prikazani rezultati merenja aerodinami~kih sila i momenata, kao i vizualizacija strujanja u grani~nom sloju na krilima i krmilima modela laserski vo|ene bombe. Ispitivanje je izvr{eno u aerotunelu T-38. Analiziran je uticaj rastojanja vrha konusa tela, u odnosu na sekciju krmila, na aerodinami~ke karakteristike modela za dva Mahova broja M ∞ =0,8 i 0,9 i otklon krmila δ =15°. Normalne sile koje se javljaju na modelu i krmilu merene su unutra{njim aerovagama. Dobijeni rezultati merenja normalne sile na modelu i posebno na krmilu povezani su sa rezultatima vizualizacije strujanja metodom uljnih premaza. Prilo`ene fotografije vizualizacije strujanja ilustruju promene strujanja oko modela i potvr|uju rezultate aerodinami~kih merenja. Klju~ne re~i: aerotunel, laserski vo|ena bomba, aerodinami~ki koeficijenti, vizualizacija strujanja. EXPERIMENTAL INVESTIGATION OF AERODYNAMIC CHARACTERISTICS OF THE LASER GUIDED BOMB MODEL Summary: Aerodynamic test results and boundary layer flow visualization on the wings and fins of laser guided bomb model are presented in this article. Test was performed in the T-38 wind tunnel. Influence of fin position relative to conic top of the model on aerodynamic characteristics was analyzed. Analysis was performed on aerodynamic characteristics of the model for two Mach numbers M ∞ = 0,8 and 0,9 and fin deflection δ =15°. Normal forces present on the model and fin were measured by internal strain gauge balances. Obtained test results of normal force on the model and especially on the fin were associated with flow visualization results, which were performed by oil emulsion method. Presented images of flow visualization show changes of the flow around the model and confirm the results of the aerodynamic measurements.

An experimental study of nonlinear and memory effects at device and power-amplifier circuit level is presented in this paper. Effects produced by the device itself have been isolated from those caused by the introduction of particular biasing and matching networks in the power amplifier design. The influence of biasing and matching network topologies over nonlinear, short-and long-term memory behaviour of power amplifiers has been experimentally determined. The results of these measurements have been related with simulations of the impedance on the drain of the transistor for different prototypes. Finally, some guidelines for memoryless PA design can be extracted.

This paper considers the compensation of the envelope tracking (ET) amplifier. In particular, we propose a new predistortion architecture for the ET amplifier. In addition, we develop new algorithms for time misalignment compensation between the input signals of the ET amplifier and compare the methods to a previously presented method. Our results indicate that using the proposed architecture with optimal predistorter, we achieve over 40 dB better adjacent channel power than using a previously presented architecture. In addition, the time misalignment compensation methods give very accurate timing estimates. The time misalignment compensation with the predistortion reduces spectral regrowth due to the nonlinear ET amplifier and improves the power efficiency of the ET amplifier.

Les techniques multiporteuses de type OFDM sont aujourd'hui largement deployees dans tous les systemes de communication sans fils notamment dans les reseaux cellulaires (L TE), les reseaux de diffusion (DVB) ou encore les reseaux WiFi. Cependant, les modulations multiporteuses se caracterisent par une tres grande dynamique mesuree par le Peak to Average Power Ratio (PAPR), ce qui empeche d'alimenter l'amplificateur de puissance non lineaire (utilise avant l'emission des signaux) a son point optimal et ainsi conduit a diminuer son efficacite energetique. Des techniques de reduction du PAPR peuvent alors etre mises en oeuvre pour reduire le PAPR du signal et des techniques de predistorsion peuvent alors etre utilisees pour compenser les non-linearites de l'amplificateur de puissance. L'approche developpee dans le cadre de cette these a pour objectif d'etudier une solution intelligente pour les implementations futures pour controler la reduction du PAPR et l...

In this work we introduce a variant of the Yule-Simon model for preferential growth by incorporating a finite kernel to model the effects of bounded memory. We characterize the properties of the model combining analytical arguments with extensive numerical simulations. In particular, we analyze the lifetime and popularity distributions by mapping the model dynamics to corresponding Markov chains and branching processes, respectively. These distributions follow power-laws with well defined exponents that are within the range of the empirical data reported in ecologies. Interestingly, by varying the innovation rate, this simple out-of-equilibrium model exhibits many of the characteristics of a continuous phase transition and, around the critical point, it generates time series with power-law popularity, lifetime and inter-event time distributions, and non-trivial temporal correlations, such as a bursty dynamics in analogy with the activity of solar flares. Our results suggest that an appropriate balance between innovation and oblivion rates could provide an explanatory framework for many of the properties commonly observed in many complex systems.

Evolution problems in materials with memory are here considered. Thus, linear integro-differential equations with Volterra type kernel are investigated. Specifically, initial boundary value problems are studied; physical properties of the material under investigation are shown to induce the choice of a suitable function space, where solutions are looked for. Then, combination with the application of Fourier transforms, allows to prove existence and uniquenes of the solution. Indeed, the original evolution problem is related to an elliptic one: existence and uniqueness results are proved for the latter and, thus, for the original problem. Two different evolution initial boundary value problems with memory which arise, in turn, in the framework of linear heat conduction and of linear viscoelasticity are compared.

• Power-law acceleration in rates of long period earthquakes observed before large explosive eruption at Tungurahua volcano, Ecuador • Earthquake source characteristics indicate repeated quasi-periodic activation of single source driven by accelerated loading • New Bayesian gamma point process methodology applied to analyze dataset and provide probabilistic eruption forecasts

This paper proposes a comprehensive and systematic characterization methodology that is suitable for the forward and reverse behavior modeling of wireless transmitters (Txs) driven by wideband-modulated signals. This characterization approach can be implemented in adaptive radio systems since it does not require particular signal or training sequences. The importance of the nature of the driving signal and its average power on the behavior of radio-frequency Txs are experimentally investigated. Critical issues related to the proposed characterization approach are analytically studied. This includes a new delay-estimation method that achieves good accuracy with low computational complexity. In addition, the receiver linear calibration and its noise budget are investigated. To demonstrate the accuracy and robustness of the proposed method, a full characterization (including the memoryless nonlinearity and the memory effects) of a 100-W Tx driven by a multicarrier wideband code-division multiple-access signal is carried out, and its forward and reverse models are identified. Cascading the identified reverse model derived using the proposed methodology and the Tx prototype leads to excellent compensation of the static nonlinearities and the memory effects exhibited by the latter. Critical issues in implementing this approach are also discussed.

This letter proposes a novel metric to measure quantitatively the electrical memory effects in wideband power amplifiers (PAs) fed with modulated signals. With the proposed memory effect metrics, the intensity of the electrical memory effects for different PAs, under a variety of the excitation modulated signals, can be quantitatively defined. The examples given in this letter illustrate the effectiveness of this definition in measuring the electrical memory effects. Index Terms-Adjacent channel power ration (ACPR), memory effects, power amplifiers (PAs).

This work is reserved for the study of a special category of boundary value problems ( BVP s) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. This fractional model and its boundary value conditions (BVCs) involve different simple BVP s, in which the second BVC as a linear combination of two Caputo derivatives of the unknown function equals a nonzero constant. The Banach principle gives a unique solution for this Liouville–Caputo BVP . Further, the Krasnoselskii and Leray–Schauder criteria give the existence property regarding solutions of the mentioned problem. For each theorem, we provide an example based on the required hypotheses and derive numerical data in the framework of tables and figures to show the consistency of results from different points of view.

The concept of a minimal state was introduced in recent decades, based on earlier work by Noll. The property that a given quantity is a functional of the minimal state is of central interest in the present work. Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this result and recent work on constructing free energy functionals, it is shown that if the kernel of the rate of dissipation functional is given by sums of products, the associated free energy functional is a functional of the minimal state.

The impact of baseband electrical memory effects on the dynamic transfer characteristics of microwave power transistors. In Workshop on Integrated Nonlinear Microwave and Millimeter-Wave Circuits 2010 (INMMIC) Gothenberg, Sweden (pp. 148-151). Institute of Electrical and Electronics Engineers (IEEE).

Analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative are presented in this paper. For this analysis, three cases are considered, the classical, the damped and the damped with a source term defined by fractional wave equations. We show that these solutions are special cases of the time fractional equations with exponential law. Illustrative examples are presented.

In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation with time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS expressed in terms of a multivariate Mittag-Leffler function in the Fourier domain. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension n and of the fractional parameters α and β.

Bacterial pathogens are known for their wide range of strategies to specifically adapt to host environments and infection sites. An in-depth understanding of these adaptation mechanisms is crucial for the development of effective therapeutics and new prevention measures. In this study, we assessed the suitability of Fourier Transform Infrared (FTIR) spectroscopy for monitoring metabolic adaptations of the bacterial pathogen Listeria monocytogenes to specific host genotypes and for exploring the potential of FTIR spectroscopy to gain novel insights into the hostpathogen interaction. Three different mouse genotypes, showing different susceptibility to L. monocytogenes infections, were challenged with L. monocytogenes and re-isolated bacteria were subjected to FTIR spectroscopy. The bacteria from mice with different survival characteristics showed distinct IR spectral patterns, reflecting specific changes in the backbone conformation and the hydrogen-bonding pattern of the protein secondary structure in the bacterial cell. Coupling FTIR spectroscopy with chemometrics allowed us to link bacterial metabolic fingerprints with host infection susceptibility and to decipher longtime memory effects of the host on the bacteria. After prolonged cultivation of hostpassaged bacteria under standard laboratory conditions, the host's imprint on bacterial metabolism vanished, which suggests a revertible metabolic adaptation of bacteria to host environment and loss of host environment triggered memory effects over time. In summary, our work demonstrates the potential and power of FTIR spectroscopy to be used as a fast, simple and highly discriminatory tool to investigate the mechanism of bacterial host adaptation on a macromolar and metabolic level.

Increasing the flexibility in spectrum access is a key to enhanced efficiency in radio spectrum utilization. Noncontiguous carrier aggregation (CA) is one enabling technology towards more flexible spectrum access, but can also lead to serious implementation challenges in terms of transmitter linearity. Especially when a single power amplifier (PA) is deployed for all carriers, serious intermodulation components will rise which can easily limit the maximum transmit power. In this paper, a low-complexity digital predistortion (DPD) solution is developed to reduce the most critical spurious components at the PA output, opposed to more classical full bandwidth linearization. The developed concept and associated parameter learning and optimization are particularly tailored towards mobile devices, building on limited narrowband feedback receiver with reduced instrumentation complexity and reduced-rate DPD processing. The developed DPD solution can handle PAs with substantial memory effects, and is verified with extensive simulation examples in various non-contiguous carrier aggregation scenarios and practical PA models with memory.

In a two-dimensional space domain, we consider a reaction-diffusion equation whose diffusion term is a time convolution of the Laplace operator against a nonincreasing summable memory kernel k. This equation models several phenomena arising from many different areas. After rescaling k by a relaxation time ε > 0, we formulate a Cauchy-Dirichlet problem, which is rigorously translated into a similar problem for a semilinear hyperbolic integro-differential equation with nonlinear damping, for a particular choice of the initial data. Using the past history approach, we show that the hyperbolic equation generates a dynamical system which is dissipative provided that ε is small enough, namely, when the equation is sufficiently "close" to the standard reactiondiffusion equation formally obtained by replacing k with the Dirac mass at 0. Then, we provide an estimate of the difference between ε-trajectories and 0-trajectories, and we construct a family of regular exponential attractors which is robust with respect to the singular limit ε → 0. In particular, this yields the existence of a regular global attractor

We consider a conserved phase-field system of Caginalp type, characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient, respectively. The latter dependence is a law of Gurtin-Pipkin type, so that the equation ruling the temperature evolution is hyperbolic. Thus the model consists of a hyperbolic integrodifferential equation coupled with a fourth-order evolution equation for the phase-field. This model, endowed with suitable boundary conditions, has already been analyzed within the theory of dissipative dynamical systems, and the existence of an absorbing set has been obtained. Here we prove the existence of the universal attractor.

We consider a conserved phase-field system of Caginalp type, characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient, respectively. The model consists of a parabolic integrodifferential equation, coupled with a fourth-order evolution equation for the phase-field. This system, supplemented with suitable boundary conditions, can be interpreted as a dissipative dynamical system in a proper phase-space. In a previous joint work, the last two authors have proved the existence of a global attractor of finite fractal dimension. Here we show the existence of an exponential attractor, by means of the techniques we developed for nonconserved phase-field systems with memory.

Increasing the flexibility in spectrum access is a key to enhanced efficiency in radio spectrum utilization. Noncontiguous carrier aggregation (CA) is one enabling technology towards more flexible spectrum access, but can also lead to serious implementation challenges in terms of transmitter linearity. Especially when a single power amplifier (PA) is deployed for all carriers, serious intermodulation components will rise which can easily limit the maximum transmit power. In this paper, a low-complexity digital predistortion (DPD) solution is developed to reduce the most critical spurious components at the PA output, opposed to more classical full bandwidth linearization. The developed concept and associated parameter learning and optimization are particularly tailored towards mobile devices, building on limited narrowband feedback receiver with reduced instrumentation complexity and reduced-rate DPD processing. The developed DPD solution can handle PAs with substantial memory effects, and is verified with extensive simulation examples in various non-contiguous carrier aggregation scenarios and practical PA models with memory.

This paper is devoted to the extraction of the temporal component of the source term for the fractional diffusion-wave equation. The main features of the inverse problem are the presence of non-local damping term involving two parameter Mittag -Leffler type function and family of Samarski-Ionkin type boundary conditions. Estimates of infinite series of three parameter Mittag-Leffler type function and their convolution are established to prove the existence of the solution.

Memory effects play a critical role in complex immune systems. In this paper, the recent efficient and realistic Atangana-Baleanu fractional order derivative, with non-local and non-singular kernel, was employed in two mathematical models for immune systems having multiple immune effectors. For each model, we derive the conditions under which a unique set of exact solutions exists. Stability analysis of equilibrium points of the two systems is carried out where the effects of model's parameters and fractional derivatives are examined. Furthermore, a recent numerical scheme is utilized to solve each model numerically and to compare theoretical results with those of numerical experiments. Results depict that memory influences induce stabilization of immune systems such that the solution trajectories of the model always converge to either a single immune effector or a persistent immune effector/antigen equilibrium states.

We study the dynamics of a spin-1/2 particle interacting with a multi-spin environment, modelling the corresponding open system dynamics through a collision-based model. The environmental particles are prepared in individual thermal states, and we investigate the effects of a distribution of temperatures across the spin environment on the evolution of the system, particularly how thermalisation in the long-time limit is affected. We study the phenomenology of the heat exchange between system and environment and consider the information-to-energy conversion process, induced by the system-environment interaction and embodied by the Landauer principle. Furthermore, by considering an interacting-particles environment, we tune the dynamics of the system from an explicit Markovian evolution up to a strongly non-Markovian one, investigating the connections between non-Markovianity, the establishment of system-environment correlations, and the breakdown of the validity of Landauer principle.

We address memory effects in the dynamics of a two-level open quantum system interacting with a classical fluctuating field via dipole interaction. In particular, we study the backflow of information for a field with a Lorentzian spectrum, and reveal the existence of two working regimes, where memory effects are governed either by the energy gap of the two-level system, or by the interaction energy. Our results shows that non-Markovianity increases with time, at variance with the results obtained for dephasing and despite the dissipative nature of the interaction, thus suggesting that the corresponding memory effects might be observed in practical scenarios.

U radu se prikazuje metodologija koja je nastala kao rezultat potrebe da se matematički rigorozno opišu poja-ve i procesi kod prostorno heterogenog strujanja, tj. strujanja u sredinama koje ispunjavaju i tečna i čvrsta faza ili strujanja neposredno iznad elemanata rapavosti bilo da je reč o krupnom nanosu, životinjskim orga-nizmima na dnu ili vodenoj vegetaciji. Reč je o meto-dologiji dvostrukog osrednjavanja u kojoj se Navije-Stoksove jednačine sukcesivno osrednjavaju po vremenu i prostoru. Kroz istorijski pregled pokazuje se kako se došlo do ideje kombinovanja vremenskog osrednjavanja karakterističnog za turbulentne tokove i prostornog osrednjavanja, karakterističnog za tečenje kroz poroznu sredinu, a potom i do ideje da se metodologija primeni u hidraulici otvorenih tokova za modeliranje tečenja u koritima sa krupnim nanosom (šljunkom, oblucima i gromadama), koritima i kanalima sa potopljenom i nepotopljenom vegetacijom ili preko plavnih površina. Daju se definicije fiktivne i so...