Arbitrary Level Research Articles

RESOURCE ALLOCATION MODELS IN HIERARCHICAL MANAGEMENT SYSTEMS

The article proposes a mathematical model of the hierarchical system of volume-dynamic resource allocation. The model describes resource consumption processes in multi-layered systems and allows us to view the management of such systems from a single perspective, to reflect the interrelationship of decisions formed at different levels of the hierarchy. According to the proposed model, a production (or business) system is considered as a large dynamic resource allocation system that is characterized by the interaction of three components: processes, resources, and time (R, P, and T.). Each of these components is represented by many lower-level elements with a defined ratio of a partial order, which sets the structure of the corresponding systems. The article proposes the way of description and features of the system of resources, processes and time, rules of aggregation, and disaggregation taking into account the structure of R, P, and T systems. On the basis of the described models, a description of the production system at the lower level in the form of a binary function π0 , as well as procedures for the formation of appropriate descriptions for arbitrary levels of the hierarchy in the form of a set of tetra relations πi. An algorithm for the formation of the solution π0 , as well as procedures for its transformation to the model of an arbitrary level, is proposed. The use of formal methods to describe the procedures of resource allocation at different levels of the hierarchy allows building a single database, to develop a structured and compact system of requests for information in the formation of management decisions. In such a system, data for processing queries are represented by a tuple of three elements Kin (levels of input aggregation by process and time resources), the basic solution πб, a set of elements R, P, T of the corresponding level, a tuple Kout (three levels of output aggregation). Depending on the Kin and Kout, values, the system handles the πб base solution using either aggregation or dis-aggregation procedures, resulting in a final result. Keywords: management, resources, processes, model, resource allocation, aggregation, disaggregation, math-ematical programming, optimization.

Frequency analysis of light field sampling for texture information.

Light field sampling (LFS) theory can properly reduce minimum sampling rate while ensuring that novel views are not distorted for image-based rendering (IBR). The minimum sampling rate is determined by spectral support of light field. The spectral support of light field has studied the influence of the following factors: the minimum depth and the maximum depth, non-Lambertian reflections, whether the scene surfaces are flat, maximum frequency of painted signals. In this paper, we further perfect the light field spectrum analysis from the quantitative description of scene texture information based on the existing spectrum analysis theory. The quantification of texture information can be interactively refined via detected regional entropy. Thus, we can derive a spectral analytical function of light field with respect to texture information. The new function allows the spectral support of light field to be analyzed and estimated for different texture information associated with scene objects. In this way, we limit the spectral analysis problems of light field to those of a simpler signal. We show that this spectral analysis approach can be easily extended to arbitrary scene complexity levels, as we simplify the LFS of complex scenes to a plane. Additionally, the spectral support of light field broadens as the plane texture information becomes more complex. We present experimental results to demonstrate the performance of LFS with texture information, verify our theoretical analysis, and extend our conclusions on the optimal minimum sampling rate.

Visualizing Properties of a Quadratic Function Using Torricelli’s Fountain

In the same chapter of his book Opera Geometrica, Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level H and determined the height of the hole with maximal range. In studying the pattern, Torricelli used the mentioned law of initial velocities and Galileo’s law of free fall and projectile motion. The first Torricelli discovery is now well known in physics education under the name Torricelli’s law. But the pattern of jets from a container entered into physics literature along two ways, which we propose to name “da Vinci’s way” and “Torricelli’s way.” Along “da Vinci’s way” educators and textbook authors (Ref. 2 and textbooks and articles cited by Biser and Atkin) present incorrect drawings of jets in order to incorrectly “demonstrate” the correct Torricelli’s law. Along “Torricelli’s way” educators point out that the shape and range of a jet depend on the initial velocity as well as on the time of flight of a jet. Using algebra and calculus (instead of geometry, proportions, and narrative used by Torricelli and Galileo) the shape of trajectories, their envelope, range, and meeting of two jets at an arbitrary datum level are determined by quadratic function and quadratic equation. Their detailed mathematical analysis is presented in this paper.

A theory of loosening earth pressure above a shallow tunnel in unsaturated ground

SummaryA theory is proposed to evaluate the loosening earth pressure (vertical earth pressure after excavation) acting on a shallow tunnel in unsaturated ground with an arbitrary groundwater level. The theory is developed based on the limit equilibrium theory, combining soil–water characteristic curves, Mohr–Coulomb failure criteria, and effective stress for unsaturated soils. The proposed theory is applied to predict the vertical distribution of loosening earth pressure in unsaturated ground, which shows a significant difference from that in saturated ground. In unsaturated ground, suction contributes to the increase in effective loosening earth pressure and shear resistance. The remarkable effects of groundwater depth, soil type, and scale of overburden height and trapdoor width on loosening earth pressure are also revealed. Based on the soil–water characteristic curve, the degree of saturation decreases, which causes wet density to decrease and the total and effective loosening earth pressures to have contrary tendencies. Moreover, effective loosening earth pressures vary with soil type as the degree of saturation varies. The total loosening earth pressures are, however, very similar regardless of soil type, because wet density and shear resistance have similar tendencies. The proposed theory provides a valid model for loosening earth pressure in unsaturated ground that will be useful for shallow tunnel excavations.

Modularity of Galois traces of ray class invariants

After Zagier’s significant work (in: Bogomolov and Katzarkov (eds) Motives, polylogarithms and hodge theory, part I, International Press, Somerville, 2002) on traces of singular moduli, Bruinier and Funke (J Reine Angew Math 594:1–33, 2006) generalized his result to the traces of singular values of modular functions on modular curves of arbitrary genus. In class field theory, the extended ring class field is a generalization of the ray class field over an imaginary quadratic field. By using Shimura’s reciprocity law, we construct primitive generators of the extended ring class fields by using Siegel functions of arbitrary level $$N\ge 2$$ and identify their Galois traces with Fourier coefficients of weight 3/2 harmonic weak Maass forms. This would extend the results of Jeon et al. (Math Ann 353:37–63, 2012) and Jung et al. (Modularity of Galois traces of Weber’s resolvents, under revision).

Design and Control of a DC Collection System for Modular-Based Direct Electromechanical Drive Turbines in High Voltage Direct Current Transmission

In response to an increasing demand for offshore turbine-based technology installations, this paper proposes to design a DC collection system for multi-connected direct drive turbines. Using tidal stream farm as the testbed model, inverter design and turbine control features were modelled in compliance with high voltage ride-through capabilities that operate in isochronous mode suggested by IEEE1547-2018. The aim of the paper is twofold. Firstly, operation analyses in engaging a single-stage impedance source inverter as an AC-link busbar aggregator to pilot a parallel-connected electromechanical drive system. It uses a closed-loop voltage controller to secure voltage-active power (Volt/Watt) dynamics in correspondence with turbine’s arbitrary output voltage level. It also aspires to truncate active rectification stages at generation-side as opposed to a traditional back-to-back converter. Secondly, a proposition for a torque-controlled blade pitching system is modelled to render a close to maximum power point tracking using blade elevation and mechanical speed manipulations. The reserve active power generation aids with compensating an over-voltage crisis as a substitute for typical reactive power absorption. The proposed Testbed system was modelled in PSCAD, adopting industrial related specifications and real-time ocean current profiles for HVDC transmission operations. Analytical results have shown a positive performance index and transient responses at respective tidal steam turbine clusters that observe fault ride-through criterion despite assertive operating conditions.

An unstructured finite element model for incompressible two‐phase flow based on a monolithic conservative level set method

SummaryWe present a robust numerical method for solving incompressible, immiscible two‐phase flows. The method extends both a monolithic phase conservative level set method with embedded redistancing and a semi‐implicit high‐order projection scheme for variable‐density flows. The level set method can be initialized conveniently via a simple phase indicator field instead of a signed distance function (SDF). To process the indicator field into a SDF, we propose a new partial differential equation‐based redistancing method. We also improve the monolithic level set scheme to provide more accuracy and robustness in full two‐phase flow simulations. Specifically, we perform an extra step to ensure convergence to the signed distance level set function and simplify other aspects of the original scheme. Lastly, we introduce consistent artificial viscosity to stabilize the momentum equations in the context of the projection scheme. This stabilization is algebraic, has no tunable parameters and is suitable for unstructured meshes and arbitrary refinement levels. The overall methodology includes few numerical tuning parameters; however, for the wide range of problems that we solve, we identify only one parameter that strongly affects performance of the computational model and provide a value that provides accurate results across all the benchmarks presented. This methodology results in a robust, accurate, and efficient two‐phase flow model, which is mass‐ and volume‐conserving on unstructured meshes and has low user input requirements, making it attractive for real‐world applications.

Probability of Ship High-Runs from Phase-Space Data

A clustering scheme has been applied for capturing qualitatively different surge motion patterns in the phase space. The scheme enables the identification of "high-run" incidents as soon as such motions are triggered and while their phenomenology has not yet been well developed. A "high run" is a surf-riding-like behavior, appearing in irregular following seas. The concept of finite-time coherent sets is exploited for deriving estimates of the probability of high-runs. The method is verified by identifying independently the corresponding hyperbolic Lagrangian coherent structures; then, consistency is sought between the two approaches. An important feature of the method is that it does not rely on the use of some empirical criterion for the high-run threshold, such as one based on the exceedance of an arbitrary high-speed level. Despite its computational burden, the proposed scheme offers "objective" statistical information on a ship's high-run tendency that can be used for benchmarking simpler (approximative) probability calculation schemes. 1. Introduction Current efforts to assess a ship's tendency for abnormal behavior in extreme seas are still limited from our inadequate grasp of the full variety of nonlinear ship motion phenomena that could be realized in an irregular seaway. A classification of these motion patterns would provide a sound basis for developing probabilistic calculation methods of ship operability and safety in extreme seas. A few recent research efforts in our group have been related to this target. In one case, it was endeavored to distinguish ship high-runs from ordinary surging, by engaging the concept of instantaneous wave celerity (Spyrou et al. 2014). In another, the derivation of a practical metric for the probability of high-run was pursued (Belenky et al. 2016). Also, high-run and broaching-to statistics were produced through a direct approach based on assigning prescriptive exceedance thresholds (Spyrou et al. 2016b). Moreover, the theory of surf-riding was extended for bichromatic waves, revealing some rather unexpected types of motion (Spyrou et al. 2018). Even richer phenomena could be conjectured for a multifrequency environment.

Reprogrammable Spatiotemporally Modulated Graphene-Based Functional Metasurfaces

Digital Metasurfaces have recently offered tremendous opportunities in real-time manipulation of terahertz (THz) waves in programmable ways to reach special applications that cannot be achieved using conventional architectures. Unlike the previous demonstrations at this spectrum, which only exploit spatial modulation, in this paper, we propose a spatiotemporally modulated graphene-based digital metasurface (STGDM) to carry out different missions in both space and frequency domains. Applying proper time-variant Fermi level controlling signals turns a 2-bit phase-only meta-atom into a powerful sub-wavelength scatterer with the ability to modulate both phases and amplitudes with arbitrary high quantization levels at center or harmonic frequencies. Several illustrative examples have been presented to demonstrate the excellent capability of our STGDM to dynamically realize different THz scattering behaviors, including beam deflection, vortex beam generation, spatial power dividing, harmonic focusing, and airy beam generation with a single digital interface. The employed space-time coding strategy reveals an additional knob for lifting some fundamental limitations of the previous graphene-based metasurfaces to achieve functionalities requiring both phase and amplitude modulations. Meanwhile, by facilitating the structural design to obtain high quantization levels, the proposed STGDM may be a reliable component in highly-efficient THz imaging and information systems.

On the Performance of Digital Back Propagation in Spatial Multiplexing Systems

Nonlinear performance in spatial multiplexing systems is strongly determined by the interplay between differential mode delay, linear mode coupling, and Kerr nonlinearity. In this article we review and extend the analysis of different solution methods for the linear coupling operator in the coupled nonlinear Schrodinger equation for spatial multiplexed propagation. Numerical solution methods are compared for different operational regimes as determined by differential mode delay and linear mode coupling. Finally, we review and extend the study of digital methods to mitigate the Kerr nonlinearity for arbitrary levels of random linear mode coupling. For the first time, it is shown that in spatial multiplexing systems transmission performance can be improved by reducing the number of back propagated channels for non-negligible levels of differential mode delay.

Skewness and critical current behavior in a graphene Josephson junction

In this work, the DC Josephson effect is investigated for a superconductor-graphene-superconductor junction in both short- and long-junction regimes. The electric transport properties are calculated while taking into account the contribution of the discrete and continuous energy spectrum. In our approach, the phase dependence of the critical current is calculated at arbitrary temperature and doping level, which generalizes previous results. We show that critical current ${I}_{c}$ and skewness $S$ exhibit critical points as a function of graphene doping ${E}_{F}$, which can be explained by Klein resonances in graphene. We give a general characterization of $S$ vs ${I}_{c}$ curves while fixing temperature or doping level. When the temperature dependence of ${I}_{c}$ is analyzed, we find differences with respect to conventional Josephson junctions, given that there is a relevant doping effect. In the long-junction regime with ${E}_{F}$ far away from the Dirac point, the ${I}_{c}$ vs $T$ curve may exhibit an exponential decay law, which has been measured recently. We report the temperature dependence of $S$ in the whole range of temperature, and our approach allows us to account for skewness suppression in the vicinity of the Dirac point, which is in agreement with recent experiments. We mention some effects which can be attained in Josephson junctions with well-defined edges and for transparency values below unity of the graphene-superconductor interfaces.

General formulae of designing novel photonic digital sensors with arbitrary levels of directional couplers for testing liquids

High sensitivity and rapid detecting photonic sensors are essential devices such as in medical diagnostics and biological test. Conventional biochemical sensors based on the directional couplers need other apparatus to measure the precise output power intensities. Conversely, a digital sensor is more efficiently utilized to determine the refractive index of the liquid sample. By simple mathematics induction, the formulae of designing a general photonic digital sensor, which comprises k (k ≥ 1) levels of the directional couplers composed of the ridge waveguides, are obtained in this paper. The performance of the sensor resembles an analog-to-digital converter and distinguishes 2k liquid samples. As long as k is large enough, the sensor can lower the quantization error and precisely determine the refractive index of the liquid sample. To demonstrate the validity of our formulae and design rules, we present the beam propagation method simulation results in this paper.

On the Separability of Parallel MISO Broadcast Channels Under Partial CSIT: A Degrees of Freedom Region Perspective

We study the K-user, M-subchannel parallel multiple-input-single-output (MISO) broadcast channel (BC) under arbitrary levels of partial channel state information at the transmitter (CSIT). We show that the parallel subchannels constituting this setting are separable from a degrees-of-freedom (DoF) region perspective if and only if the partial CSIT pattern is totally ordered. This total order condition corresponds to users abiding by the same order, with respect to their CSIT quality levels, in each of the parallel subchannels. For instance, let α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> and α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> be the CSIT quality parameters for users k and j over subchannel l. Under total order, having α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> ≥ α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> implies that α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[m]</sup> ≥ α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[m]</sup> holds for every subchannel m. In this case, the entire DoF region is achievable using simple separate coding, where a single-subchannel-type transmission scheme is employed in each subchannel. To show this separability result, we first derive an outer bound for the DoF region by extending the aligned image sets approach of Davoodi and Jafar to the considered setting. We then show that this outer bound coincides with the inner bound achieved through separate coding, given by the Minkowski sum of M single-subchannel DoF regions, under the total order condition, hence settling the if part of the main theorem. To prove the only if part of the theorem, we identify a set of DoF tuples achievable through joint coding across subchannels, yet not achievable through separate coding whenever the total order condition is violated. Moreover, we also highlight the implications of our main result on the design of CSIT feedback schemes for multi-carrier multi-antenna wireless networks.

Smoothness and monotonicity of the excursion set density of planar Gaussian fields

Nazarov and Sodin have shown that the number of connected components of the nodal set of a planar Gaussian field in a ball of radius $R$, normalised by area, converges to a constant as $R\to \infty $. This has been generalised to excursion/level sets at arbitrary levels, implying the existence of functionals $c_{ES}(\ell )$ and $c_{LS}(\ell )$ that encode the density of excursion/level set components at the level $\ell $. We prove that these functionals are continuously differentiable for a wide class of fields. This follows from a more general result, which derives differentiability of the functionals from the decay of the probability of `four-arm events' for the field conditioned to have a saddle point at the origin. For some fields, including the important special cases of the Random Plane Wave and the Bargmann-Fock field, we also derive stochastic monotonicity of the conditioned field, which allows us to deduce regions on which $c_{ES}(\ell )$ and $c_{LS}(\ell )$ are monotone.

Seismic performance of double skin semi-base-isolated structures

Base isolation technology is a popular and powerful isolation technology. This technique can greatly reduce the seismic response of the structure, so as to reduce the damage to the structure. Base isolation method decouples the superstructure from the base by installing a flexible layer under each column to reduce dynamic response in the earthquake and elongate the time period of structures due to its inherent flexibility. However, the long time period causes large displacement. In addition, base isolation devices are highly vulnerable due to uplift forces produced by lateral force resisting systems (LFRS). In this study, an adjustable structure with a new configuration, namely double skin semi-base-isolated (SBI) structure is presented to solve the above problems. The LFRS is omitted in the proposed SBI structure and the time period and displacement are reduced compared to the conventional base-isolated structure. The forcedeformation behavior of an isolator is modeled as bi-linear hysteretic behavior which can be effectively used to model all isolation system in practice. This study investigates the seismic performance of 10-story double skin SBI reinforced concrete (RC) structure under far-fault earthquake ground motion by numerical method. Results demonstrate that the SBI system is significantly adjustable with the use of RC coupling beams between the inner core and outer frames. By increasing or reducing the number of connected floors in the SBI system, dynamic behaviors of the SBI system can be changed. The adjusted structure can be created by adding and removing RC coupling beams at every arbitrary floor level.

Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term

This paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term $u_{t}-\triangle{u}-\triangle{u}_{t}+\int_{0}^{t}g(t-\tau)\triangle{u}(\tau)d\tau = |{u}|^{p}{u}$ in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite time blow-up results for the solutions with initial data at non-positive energy level as well as arbitrary positive energy level, and give some upper bounds for the blow-up time $T^{*}$ depending on the sign and size of initial energy $E(0)$. In addition, a lower bound for the life span $T^{*}$ is derived by means of a differential inequality technique if blow-up does occur.

Mock modular forms whose shadows are Eisenstein series of integral weight

The purpose of this article is to give a simple and explicit construction of mock modular forms whose shadows are Eisenstein series of arbitrary integral weight, level, and character. As application, we construct forms whose shadows are Hecke's Eisenstein series of weight one associated to imaginary quadratic fields, recovering some results by Kudla, Rapoport and Yang (1999), and Schofer (2009), and forms whose shadows equal $\Theta^{2k}(z)$ for $k\in \{1,2,3,4\}$, where $\Theta(z)$ denotes Jacobi's theta function.

Equivalent Space Vector Output of Diode Clamped Multilevel Inverters Through Modulation Wave Decomposition Under Carrier-Based PWM Strategy

The carrier-based PWM method (CBPWM) and the space vector PWM method (SVPWM) are two main modulation methods for diode clamped multilevel converters, and there is a certain relationship between these two modulation strategies. For general 8 segments SVPWM modulation sequence in the multilevel inverter, the inherent relationship between these two modulation methods have been researched, but the relationship between CBPWM and SVPWM in an arbitrary level sequence has not been obtained. To solve this problem, an in-depth study of the relationship between the multilevel SVPWM method and the CBPWM method has been made in this paper. By decomposing the modulation wave, and the SVPWM can be achieved by multi-modulation waves CBPWM. And the relationship between SVPWM and CBPWM in N level with an arbitrary number of segments sequence are obtained. Thus, through simple multi-modulation waves CBPWM strategy, less THD in the spectrum and higher DC voltage utilization switching sequences of multilevel inverters can be obtained. The simulation and experimental results illustrate that the relationship between CBPWM and SVPMM is correct.

A Closed-Form Transient Joule Heating Model for an Interconnect in an Integrated Circuit

Front and back ends of line (FEOL and BEOL) self-heating and mutual heating are important barriers to a sustained increase in processor speed and density. In this context, the severity of transient Joule heating in scaled interconnects under a variety of operating conditions (e.g., frequency and duty cycle) is not fully understood. Here we introduce the closed-form analytical transient Joule heating model to calculate the time-dependent temperature rise of an interconnect ( $\Delta {T}_{\textsf {Int}}({t})$ ) located at an arbitrary metal level within an integrated circuit (IC). The model is validated by high-fidelity finite element method simulations and specially designed test structures. Remarkably, the model predicts ${I}_{\textsf {Max}}$ (the interconnect-specific current for a certain degree of $\Delta {T}_{\textsf {Int}}$ ) within 20%–25% for an arbitrary duty cycle. Therefore, our model can be used to accurately predict temperature-accelerated interconnect reliability issues of a modern IC.

Mapping Atomic Motions with Electrons: Toward the Quantum Limit to Imaging Chemistry

Recent advances in ultrafast electron and X-ray diffraction have pushed imaging of structural dynamics into the femtosecond time domain, that is, the fundamental time scale of atomic motion. New physics can be reached beyond the scope of traditional diffraction or reciprocal space imaging. By exploiting the high time resolution, it has been possible to directly observe the collapse of nearly innumerable possible nuclear motions to a few key reaction modes that direct chemistry. It is this reduction in dimensionality in the transition state region that makes chemistry a transferable concept, with the same class of reactions being applicable to synthetic strategies to nearly arbitrary levels of complexity. The ability to image the underlying key reaction modes has been achieved with resolution to relative changes in atomic positions to better than 0.01 Å, that is, comparable to thermal motions. We have effectively reached the fundamental space-time limit with respect to the reaction energetics and imaging the acting forces. In the process of ensemble measured structural changes, we have missed the quantum aspects of chemistry. This perspective reviews the current state of the art in imaging chemistry in action and poses the challenge to access quantum information on the dynamics. There is the possibility with the present ultrabright electron and X-ray sources, at least in principle, to do tomographic reconstruction of quantum states in the form of a Wigner function and density matrix for the vibrational, rotational, and electronic degrees of freedom. Accessing this quantum information constitutes the ultimate demand on the spatial and temporal resolution of reciprocal space imaging of chemistry. Given the much shorter wavelength and corresponding intrinsically higher spatial resolution of current electron sources over X-rays, this Perspective will focus on electrons to provide an overview of the challenge on both the theory and the experimental fronts to extract the quantum aspects of molecular dynamics.