General Operator Research Articles

Special Military Operation as a Strategic Technology for Choosing the Future of Russia and the World

The chronicle of the situation development, which actually came very close to a global military catastrophe, only outwardly looks like a random kaleidoscope of events. Behind the chaos of events, are becoming more evident extremely strict strategic schemes for operating with global power factors in various spheres of activit y: political, military, economic, etc. The article outlines the systemic elements of an approach that considers military conflict in general and Special military operation in particular as a militarized form of struggle for power — an instrument of global economic regulation of economic activit y. This approach makes it possible to focus the key components of Russia’s necessary strategy in the context of a new round of struggle between imperialist predators for the format of systemic and structural redivision of the world that they need.

Weyl asymptotics for fractional-order Dirichlet realizations in nonsmooth cases

Let $P$ be a symmetric $2a$-order classical strongly elliptic pseudodifferential operator with \emph{even} symbol $p(x,\xi)$ on $\mathbb{R}^n $ ($0<a<1$), for example a perturbation of $(-\Delta )^a$. Let $\Omega \subset \mathbb{R}^n$ be bounded, and let $P_D$ be the Dirichlet realization in $L_2(\Omega)$ defined under the exterior condition $u=0$ in $\mathbb{R}^n\setminus\Omega$. When $p(x,\xi)$ and $\Omega$ are $C^\infty $, it is known that the eigenvalues $\lambda_j$ (ordered in a nondecreasing sequence for $j\to \infty$) satisfy a Weyl asymptotic formula \begin{equation*} \lambda _j(P_{D})=C(P,\Omega )j^{2a/n}+o(j^{2a/n}) \text {for $j\to \infty $}, \end{equation*} with $C(P,\Omega)$ determined from the principal symbol of $P$. We now show that this result is valid for more general operators with a possibly nonsmooth $x$-dependence, over Lipschitz domains, and that it extends to $\tilde P=P+P'+P”$, where $P'$ is an operator of order $<\min\{2a, a+\frac 12\}$ with certain mapping properties, and $P”$ is bounded in $L_2(\Omega )$ (e.g. $P”=V(x)\in L_\infty(\Omega)$). Also the regularity of eigenfunctions of $P_D$ is discussed.

Concentration-compactness type principle for systems with critical terms in [formula omitted

In this paper, we obtain some important variants of the Lions and Chabrowski Concentration-compactness principle, for nonlinear systems in the context of fractional Sobolev spaces with variable exponents. As an application of the results, we show the existence and asymptotic behaviour of nontrivial solutions for elliptic systems involving a new class of general nonlocal integrodifferential operators with variable exponents and critical growth conditions in RN.

Systematic review and meta-analysis of economic and healthcare resource utilization outcomes for robotic versus manual total knee arthroplasty

The introduction of robotics in orthopedic surgery has led to improved precision and standardization in total knee arthroplasty (TKA). Clinical benefits of robotic versus manual TKA have been well established; however, evidence for economic and healthcare resource utilization outcomes (HRU) is lacking. The primary objective of this study was to compare economic and HRU outcomes for robotic and manual TKA. The secondary objective was to explore comparative robotic and manual TKA pain and opioid consumption outcomes. Multi-database literature searches were performed to identify studies comparing robotic and manual TKA from 2016 to 2022 and meta-analyses were conducted. This review included 50 studies with meta-analyses conducted on 35. Compared with manual TKA, robotic TKA was associated with a: 14% reduction in hospital length of stay (P = 0.022); 74% greater likelihood to be discharged to home (P < 0.001); and 17% lower likelihood to experience a 90-day readmission (P = 0.043). Robotic TKA was associated with longer mean operating times (incision to closure definition: 9.27 min longer, P = 0.030; general operating time definition: 18.05 min longer, P = 0.006). No differences were observed for total procedure cost and 90-day emergency room visits. Most studies reported similar outcomes for robotic and manual TKA regarding pain and opioid use. Coupled with the clinical benefits of robotic TKA, the economic impact of using robotics may contribute to hospitals’ quality improvement and financial sustainability. Further research and more randomized controlled trials are needed to effectively quantify the benefits of robotic relative to manual TKA.

General-purpose data stream processing on heterogeneous architectures with WindFlow

Many emerging applications analyze data streams by running graphs of communicating tasks called operators. To develop and deploy such applications, Stream Processing Systems (SPSs) like Apache Storm and Flink have been made available to researchers and practitioners. They exhibit imperative or declarative programming interfaces to develop operators running arbitrary algorithms working on structured or unstructured data streams. In this context, the interest in leveraging hardware acceleration with GPUs has become more pronounced in high-throughput use cases. Unfortunately, GPU acceleration has been studied for relational operators working on structured streams only, while non-relational operators have often been overlooked. This paper presents WindFlow, a library supporting the seamless GPU offloading of general partitioned-stateful operators, extending the range of operators that benefit from hardware acceleration. Its design provides high throughput still exposing a high-level API to users compared with the raw utilization of GPUs in Apache Flink.

Spectral and steady-state properties of fermionic random quadratic Liouvillians

We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by MM random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, m=M/(2N_F)m=M/(2NF), we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for m=1/2m=1/2 and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below m=1/2m=1/2, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.

Majorization property for certain classes of analytic functions associated with general operator

In this study, we introduce two new classes $S_{k}[E, F;\mu; \gamma]$ and $T_{k}(\theta,\,\mu,\,\gamma)$ of analytic functions using the general integral operator. For these two classes, we study the majorization properties. Some applications of the results are discussed in the form of corollaries.

Schur complement dominant operator matrices

We propose a method for the spectral analysis of unbounded operator matrices in a general setting which fully abstains from standard perturbative arguments. Rather than requiring the matrix to act in a Hilbert space H, we extend its action to a suitable distributional triple D⊂H⊂D− and restrict it to its maximal domain in H. The crucial point in our approach is the choice of the spaces D and D− which are essentially determined by the Schur complement of the matrix. We show spectral equivalence between the resulting operator matrix in H and its Schur complement, which allows to pass from a suitable representation of the Schur complement (e.g. by generalised form methods) to a representation of the operator matrix. We thereby generalise classical spectral equivalence results imposing standard dominance patterns.The abstract results are applied to damped wave equations with possibly unbounded and/or singular damping, to Dirac operators with Coulomb-type potentials, as well as to generic second order matrix differential operators. By means of our methods, previous regularity assumptions can be weakened substantially.

Dynamic response of a dual-opposed free-piston Stirling generator

As a type of distributed power generation device, free-piston Stirling generator (FPSG) is characterised by compactness, high efficiency, and long life. This work devotes to exploring the dynamic response of a low-vibration dual-opposed FPSG by employing the newly-developed time-domain acoustic-electrical analogy (TDAEA) method. Transient evolutions of self-sustained oscillations are first exhibited, which contains the start-up and steady stages. An exploration on steady-state performance is then conducted, which shows the maximum thermal-to-electric efficiency of 46.6% with an electric power of 3.92 kW, implying its enormous potential in distributed power generation for low-vibration applications due to its dual-opposed configuration. Dynamic response with jump in external load and gradual variation in heating temperature are subsequently investigated in detail. The results indicate that an acute drop in electric resistance leads to an oscillation attenuation, particularly, a short circuit results in an emergency shutdown. With the heating temperature declining gradually, the oscillation attenuates and even stops. Based on these results, some general operating regulation principles for FPSGs are further concluded to avoid the cylinder striking as well as frequent start and stop. This study gives a deeper understanding on the dynamic characteristics of FPSGs, as well as broadens the usage of the TDAEA method.

Discrete Quantum Kinetic Equation

A semi-classical approach to the study of the evolution of bosonic or fermionic excitations is through the Nordheim—Boltzmann- or, Uehling—Uhlenbeck—equation, also known as the quantum Boltzmann equation. In some low ranges of temperatures—e.g., in the presence of a Bose condensate—also other types of collision operators may render in essential contributions. Therefore, extended— or, even other—collision operators are to be considered as well. This work concerns a discretized version—a system of partial differential equations—of such a quantum equation with an extended collision operator. Trend to equilibrium is studied for a planar stationary system, as well as the spatially homogeneous system. Some essential properties of the linearized operator are proven, implying that results for general half-space problems for the discrete Boltzmann equation can be applied. A more general collision operator is also introduced, and similar results are obtained also for this general equation.

A Heuristic Approach for Resolving Spatial Conflicts of Buildings in Urban Villages

Building displacement is a common operation to resolve the spatial conflicts between map features, and it has important theoretical value and practical application significance for multi-scale mapping. The prerequisite for a successful displacement operation is that there is extra space around the conflicting buildings into which they can be displaced. Otherwise, additional generalization operators need to be combined to resolve spatial conflicts. Based on this idea, this study proposes a new heuristic spatial conflict resolution framework that mainly resolves the spatial conflicts between buildings and other features in urban villages by combining three cartographic generalization operators: selection, displacement, and aggregation. This method first reduces the density of buildings in the block through selection operation, then resolves the spatial conflicts between buildings and other features through displacement operation, and finally, the aggregation operation is performed to eliminate any remaining conflicts and newly generated conflicts. Experiments were carried out using real urban village data, and visual inspection and quantitative analysis were used to evaluate the experimental results. The evaluation results show that the proposed framework can not only resolve spatial conflicts well, but also maintain the spatial distribution and area balance of the buildings in urban villages.

Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed Neural Networks (MINNs), a class of architectures specifically tailored to handle mesh based functional data, and thus of particular interest for reduced order modeling of parametrized Partial Differential Equations (PDEs). The driving idea behind MINNs is to embed hidden layers into discrete functional spaces of increasing complexity, obtained through a sequence of meshes defined over the underlying spatial domain. The approach leads to a natural pruning strategy which enables the design of sparse architectures that are able to learn general nonlinear operators. We assess this strategy through an extensive set of numerical experiments, ranging from nonlocal operators to nonlinear diffusion PDEs, where MINNs are compared against more traditional architectures, such as classical fully connected Deep Neural Networks, but also more recent ones, such as DeepONets and Fourier Neural Operators. Our results show that MINNs can handle functional data defined on general domains of any shape, while ensuring reduced training times, lower computational costs, and better generalization capabilities, thus making MINNs very well-suited for demanding applications such as Reduced Order Modeling and Uncertainty Quantification for PDEs.

The impact of COVID-19 on postoperative outcomes of emergency general surgery operations

The impact of COVID-19 on postoperative outcomes of emergency general surgery operations

Quantum remote control utilizing multiple degrees of freedom

We present protocols for remote implementation of general operators between two nodes, which are considered: the first where an arbitrary single-qubit operation acts on photon state in the polarization degree of freedom, and the second with photon state in the temporal degree of freedom. By employing simultaneous entanglement in two independent degrees of freedom, both protocols are fulfilled near deterministically in two steps. In the first step, the effective cross-Kerr interaction and X-quadrature measurements of the coherent states are main tools for achieving the goal. Together with the available existing optical elements and common single-photon detectors, the construction circuit of the second step is simple and feasible with current technologies. Our protocols are beneficial to long-distance quantum communication and quantum metrology.

On simultaneous similarity of families of commuting operators

Characterization of simultaneous similarity for commuting m m - tuples of operators is an open problem even in finite-dimensional spaces; known as “A wild problem in linear algebra”. In this paper we offer a criterion for simultaneous similarity of m m -tuples of k k -cyclic commuting operators on an arbitrary Banach space. Moreover, we obtain an additional equivalence condition in the case of finite dimensional Banach spaces, which extends the result found by Shekhtman [Math. Stat. 1 (2013), pp. 157–161] for pairs of cyclic commuting matrices. We also present two applications of our results, one in the case of general multiplication operators on Banach spaces of analytic function, and one for m m -tuples of commuting square matrices.

Trend of minimally invasive and open surgery experience of general surgery residents: Accreditation Council for Graduate Medical Education general surgery case log in Thailand.

Minimally invasive surgery (MIS) offers patients several benefits, such as smaller incisions, and fast recovery times. General surgery residents should be trained in both open and MIS. We aimed to examine the trends of minimally invasive and open procedures performed by general surgery residents in Thailand. A retrospective review of the Royal College of Surgeons of Thailand and Accreditation Council for Graduate Medical Education general surgery case logs from 2007 to 2018 was performed for common open and laparoscopic general surgery operations. The data were grouped by three time periods, which were 2007-2010, 2011-2014, and 2015-2018, and analyzed to explore changes in the operative trends. For Thai residents, the mean number of laparoscopic operations per person per year increased from 5.97 to 9.36 (56.78% increase) and open increased from 20.02 to 27.16 (35.67% increase). There was a significant increase in the average number of minimally invasive procedures performed among cholecystectomy (5.83, 6.57, 8.10; p < 0.001) and inguinal hernia repair (0.33, 0.35, 0.66; p < 0.001). Compared to general surgery residents in the United States, Thai residents had more experience with open appendectomy, but significantly less experience with all other operations/procedures. The number of open and minimally invasive procedures performed or assisted by Thai general surgery residents has slowly increased, but generally lags behind residents in the United States. The Thai education program must be updated to improve residents' technical skills in open and laparoscopic surgery to remain competitive with their global partners.

Recent Advances of Doped SnO2 as Electron Transport Layer for High-Performance Perovskite Solar Cells.

Perovskite solar cells (PSCs) have garnered considerable attention over the past decade owing to their low cost and proven high power conversion efficiency of over 25%. In the planar heterojunction PSC structure, tin oxide was utilized as a substitute material for the TiO2 electron transport layer (ETL) owing to its similar physical properties and high mobility, which is suitable for electron mining. Nevertheless, the defects and morphology significantly changed the performance of SnO2 according to the different deposition techniques, resulting in the poor performance of PSCs. In this review, we provide a comprehensive insight into the factors that specifically influence the ETL in PSC. The properties of the SnO2 materials are briefly introduced. In particular, the general operating principles, as well as the suitability level of doping in SnO2, are elucidated along with the details of the obtained results. Subsequently, the potential for doping is evaluated from the obtained results to achieve better results in PSCs. This review aims to provide a systematic and comprehensive understanding of the effects of different types of doping on the performance of ETL SnO2 and potentially instigate further development of PSCs with an extension to SnO2-based PSCs.

General fractional integrals and derivatives and their applications

In this survey paper, some recent results obtained for the general fractional integrals and derivatives and for the regularized general fractional derivatives are discussed. We start with a short historical survey of the general Fractional Calculus operators with the Sonin kernels and continue with a presentation of the recent developments regarding the general fractional derivatives and their applications. In particular, we introduce the first and the second fundamental theorems of Fractional Calculus for the general fractional derivatives of arbitrary order, for the regularized general fractional derivatives of arbitrary order, and for the sequential general fractional derivatives. As an application of these results, the generalized convolution Taylor formulas and the generalized convolution Taylor series with the coefficients and remainders in terms of the general fractional derivatives and the regularized general fractional derivatives are presented. Finally, we consider some Cauchy problems for the fractional differential equations with the general fractional derivatives.

A Dual-Inlet Pump with a Simple Valves System.

To ameliorate the deficient output flow performance of the piezoelectric pumps with cantilever valves, a dual-inlet pump with a simple valves system is proposed. On the basis of explaining the structure design of the prototype, the working principle of the prototype is explained, and the output flow is theoretically analyzed. Then, the manufacturing process of the prototype is introduced. The general operating frequency of the pump was obtained by combining the finite element analysis of the piezoelectric actuator under dry and wet modes with the mechanical vibration test, and a series of measured flow rates were compared and improved through valve stiffness optimization and pump chamber height adjustment in the subsequent control experiment. The proposed piezoelectric pump achieves a maximum flow rate of 33.18 mL/min at a 180 Vp-p voltage with the driving frequency of 100 Hz, which may bring new inspiration for the application of small intelligent pumps in the field of microfluidics.

Observer-Based Fault Estimation Applied to a Point Absorber Wave Energy Converter

The economic viability of wave energy conversion systems is one of the open points among the research community. To lower the energy cost, the devices in charge of extracting the wave power, called wave energy converters (WEC), are often controlled by means of optimal control (OC) strategies. Such OC systems, which have proven their effectiveness in wave energy applications, often rely on a mathematical model of the device (and, in some cases, on the wave excitation force) to optimize the control action provided to the system. Nevertheless, the marine environment results hostile for general device safe operations, potentially triggering a variety of faults in the WEC system. Such condition (for example, a sensor failure or additional friction inside a gearing) directly affects the system dynamics. If this deviation is not considered by the control algorithm, the energy production performance can degrade considerably, or the control action itself can cause a more serious fault. A possible solution is that of designing an algorithm capable of compensating for eventual faults in the system, while still respecting the initial design performance or, when not possible, preserving the main device functionalities. Such a control strategies belong to the family of Fault Tolerant Control (FTC) techniques, which can be divided into two macro-categories: Passive (PFTC) and active (AFTC) algorithms. While PFTC systems are designed offline and can account only for a predefined set of system faults, AFTC algorithms are more suitable to tackle significant system deviations from the nominal model. For this purpose, such algorithms may require some routine to detect, isolate and eventually estimate the specific fault. This task is accomplished by Fault Detection and Identification (FDI) routines. According to the AFTC algorithm, the FDI module must accomplish different tasks. Furthermore, the FDI module accuracy plays a crucial role in some AFTC strategies, since the poor estimation of a faulty signal can induce the controller to behave incorrectly. This paper presents an FDI algorithm applied to a point-absorber wave energy converter (WEC). The proposed structure consists of an observer-based strategy in charge of detecting, isolating, and tracking effectively faulty signals occurring in numerical simulations. The results demonstrate the proposed observer effectiveness for a predefined set of actuator and sensor faults, both in the case of independent, and simultaneous fault occurrence.