Mixing Operation Research Articles

On the solvability of a cantilever-type boundary value problem by using the mixed monotone operator

In the present paper, by using the mixed monotone operator method we prove the existence and uniqueness of positive solution to the following cantilever-type boundary value problem u(4)(t)=f(t,u(t),u(αt))+g(t,u(t)),0<t<1,α∈(0,1),u(0)=u′(0)=u′′(1)=u′′′(1)=0.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\displaystyle \\left\\{ \\begin{array}{l} u^{(4)}(t)=f(t,u(t),u(\\alpha t))+g(t,u(t)),\\quad 0<t<1, \\quad \\alpha \\in (0,1),\\\\ u(0)=u'(0)=u''(1)=u'''(1)=0. \\end{array}\\right. \\end{aligned}$$\\end{document}Moreover, in order to illustrate the results we present an example.

Disjoint hypercyclicity, Sidon sets and weakly mixing operators

AbstractWe prove that a finite set of natural numbers J satisfies that $J\cup \{0\}$ is not Sidon if and only if for any operator T, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that T is weakly mixing. As an application we show the existence of a non-weakly mixing operator T such that $T\oplus T^2\oplus\cdots \oplus T^n$ is hypercyclic for every n.

Information loss, mixing and emergent type III1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity.We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.In a theory of Generalized Free Fields (GFF), we show that if the two-point function clusters in time, all operators are mixing, and the algebra is a type III1 factor. For example, in \U0001d4a9 = 4 SYM, above the Hawking-Page phase transition, clustering of the single trace operators implies that the algebra is a type III1 factor, settling a recent conjecture of Leutheusser and Liu. We explicitly construct the C∗-algebra and von Neumann subalgebras of GFF associated with time bands and, more generally, open sets of the bulk spacetime using the HKLL reconstruction map.

不同形态水肥高效混合模式研究与试验

This paper proposes a fertilizer mixing device that combines pressure relief return and mechanical agitation to address the issues in the current water-fertilizer integration equipment related to limited fertilizer mixing methods and inconvenient irrigation pressure regulation. The device employs different mixing modes for various fertilizer forms and uses pressure relief return to adjust irrigation pressure, thereby enhancing the efficiency of water-fertilizer mixing and optimizing energy consumption. The experimental results indicate that the reflux mode is suitable for liquid-type fertilizers which are fast dissolving and easy to diffuse, and its EC value is stable at about 6.60 mS/cm, which is close to the calibrated value of 6.80 mS/cm. The stirring paddle mode compensates for the reflux mode's weak mixing effect, making it suitable for solid powder-type fertilizers' mixing operation. The EC value remains stable at approximately 8.60 mS/cm when calibrated at 8.70 mS/cm. The “stirring paddle + two-way reflux” mode demonstrates the most robust mixing effect and is suitable for mixing solid granular fertilizers. When calibrated at 8.20 mS/cm, it stabilizes at approximately the calibration value after 105 s. This research provides technical support and a theoretical basis to accomplish efficient, energy-saving, and rational application of water-fertilizer integration across diverse fertilizer forms.

New results on the existence and uniqueness of positive almost periodic solution for the generalized Mackey–Glass hematopoietic model

This paper is concerned with the solution of the generalized hematopoietic model with multiple variable delays and multiple exponents. By using the fixed point theorem for mixed monotone operators, we prove that the generalized Mackey–Glass hematopoietic model has a unique positive almost periodic solution, and derive various new existence and uniqueness results under weaker conditions. Then, an iterative sequence is established and shown to converge to the unique solution under various conditions. Finally, four examples are given to illustrate the application of our theoretical results.

A trust-based quantum probabilistic linguistic multi-criteria group decision making model considering interference effect

In group decision-making (GDM), there exist cognitive and realistic uncertainties and humans exhibit hesitation and ambiguity. Using probabilistic linguistic term sets (PLTSs) can better adapt to the above challenges. However, the current PLTS-based methods rarely take the subjectivity and behavior of experts into account, especially the influence of trust relations and subjective beliefs. This paper combines the trust network and the quantum probability theory (QPT) in GDM, and proposes a new probabilistic linguistic multi-criteria group decision-making (MCGDM) model considering the trust relationships and the interference effects between experts. Firstly, probabilistic linguistic evaluations and trust information are collected. Then, the entropy-weight method based on PLTS is proposed to determine criterion weights. A new mixed multi-path trust transfer aggregation operator that integrates both the path length and the path quality is defined, to establish a complete trust network and measure the expert weight. Thirdly, because of the certain interference between experts, a quantum-like Bayesian network framework is built to aggregate the opinions of experts. During the process, the system is in a superposition state, and personal opinions are regarded as interfering wave functions, affecting the final results. Finally, an example of the prevention and control of COVID-19 in a city is used for verification and sensitivity and comparison analyses are provided to verify the effectiveness of the method.

Research on the Identification Method of Radionuclide Based on the Lightweight Model

Traditional CNN has problems with significant parameters and is difficult to deploy in a resource-constrained portable spectrometer for radionuclide identification. We propose a lightweight neural network model based on GhostNet to address these problems. First, the Ghost-CS module is built by adding the channel mixing operation in the Ghost module to enhance the information exchange between different channels; Secondly, using the ECA module reduces the noise information in the spectrum. The results showed that the algorithm maintains a high recognition accuracy while the number of model parameters is greatly reduced, making it easier to implement in portable spectrometers.

Efforts to Improve Student Activities and Results in Integrated Learning Using the Problem Based Model Learning at SDN 060924 District Sanding Field

This study aims to determine efforts to increase student activity and learning outcomes in learning multiplication with integers using the problem-based learning model at SDN 060924, Medan Amplas District. This research is a classroom action research. The model used in this study is the Spiral model from Kemmis &amp; Mc Taggart. This research was conducted in May 2023 at SDN 060924 Medan Amplas. In this study using a test instrument, namely multiple choice questions as many as 15 questions and non-tes, namely in the form of observation sheets, interviews, and documentation. There are several types of data collection techniques, namely tests, observations, and documentation. Based on the table about the development of student learning activities above, it shows an increase in student learning activities. In this case, the average increase in student learning activity in each aspect is 11,345% and all aspects of the activity reach the active criteria. Learning mathematics about integer material in cycles I, II and III that the application of problem based learning has in fact experienced an increase of 90% from the number of students who complete it in cycles I, II and III, the description of student learning activities regarding multiplication of integers increases greatly Good. It is known that the mastery of the mathematics learning results of class IV students on mixed arithmetic operations material reaches 90%, so that it meets the specified indicator of 70%. So in this case the researcher can be said to be successful and there is no need for further action in the next cycle. Observations from observers showed an increase in student activity in participating in learning.

Identifikasi Kesulitan Siswa SMPIQU Al-Bahjah Pusat dalam Menyelesaikan Soal Operasi Bilangan Bulat dan Pecahan

The purpose of this study was to find out the difficulties students experienced in solving integer and fraction operations in class VII students at SMIQu Al-Bahjah center. The type of research used is descriptive qualitative research and literature review with data collection techniques using diagnostic tests, interviews, and library data. Meanwhile, data analysis techniques are carried out through the stages of data collection, data reduction, data presentation, and drawing conclusions. The subjects of this study were 32 students of class VII SMPIQu Al-Bahjah Center who completed diagnostic test questions. The results showed that (1) students did not understand the concept of integer operations, especially negative integer operations and mixed integer operations; (2) students experience problems in reading word problems and converting them into mathematical models; and (3) difficulties with fraction operations in algebraic.

A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

AbstractGlobal air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the $\varepsilon$ -constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gökçen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

Empirical analysis and modeling of the allometric scaling of urban freight systems

Heavy trucks which undertake the majority of freight volume play an important role in urban freight systems. By analyzing heavy truck trip data, we find a superlinear scaling relationship for heavy truck trips and a sublinear scaling relationship for heavy truck numbers relative to urban population size. Although these allometric scaling relationships that widely appear in nature and social systems have been explained by many models, a simple model that can cover a wide range of scaling exponents in these systems is still lacking. Here, we develop a partially mixing city operation model by quantifying the mixability of the urban population to explain why the superlinear and sublinear scaling exponents are in the range of 1 and . This simple model not only helps us understand the mechanism of allometric scaling of urban freight systems, but also provides a new framework for other superlinear and sublinear scaling relationships in cities.

Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown functions and their fractional derivatives. Using the fixed point theorem for mixed monotone operators, we constructe iteration functions for arbitrary initial value and acquire the existence and uniqueness of extremal solutions. Moreover, a related example is given to illustrate our research results.

Implementation of Lesson Study in Teaching Mathematics in Region 3, Cluster XI South Palu

This research is a descriptive study with a qualitative approach, which aims to describe the application of Lesson Study in mathematics learning to teachers and students in Region 3 Cluster XI Palu Selatan. Lesson Study is effectively applied in learning mathematics. This can be proven from the results of interviews which explain that the application of lesson study in learning mathematics can be understood by most of the teachers who are members of the 3 Cluster XI area of South Palu. In addition, the results obtained in the activity plan are lesson plans, media used in learning, learning modules, and observation sheets. In the activities carried out there are three important activities, namely the activities of the teacher carrying out mathematics learning in mixed arithmetic operations, observers observing learning, and students in learning. In the listening activity, the model teacher starts the discussion by conveying his impressions, experiences, opinions about the implementation of the learning he has carried out.

DeMT: Deformable Mixer Transformer for Multi-Task Learning of Dense Prediction

Convolution neural networks (CNNs) and Transformers have their own advantages and both have been widely used for dense prediction in multi-task learning (MTL). Most of the current studies on MTL solely rely on CNN or Transformer. In this work, we present a novel MTL model by combining both merits of deformable CNN and query-based Transformer for multi-task learning of dense prediction. Our method, named DeMT, is based on a simple and effective encoder-decoder architecture (i.e., deformable mixer encoder and task-aware transformer decoder). First, the deformable mixer encoder contains two types of operators: the channel-aware mixing operator leveraged to allow communication among different channels (i.e., efficient channel location mixing), and the spatial-aware deformable operator with deformable convolution applied to efficiently sample more informative spatial locations (i.e., deformed features). Second, the task-aware transformer decoder consists of the task interaction block and task query block. The former is applied to capture task interaction features via self-attention. The latter leverages the deformed features and task-interacted features to generate the corresponding task-specific feature through a query-based Transformer for corresponding task predictions. Extensive experiments on two dense image prediction datasets, NYUD-v2 and PASCAL-Context, demonstrate that our model uses fewer GFLOPs and significantly outperforms current Transformer- and CNN-based competitive models on a variety of metrics. The code is available at https://github.com/yangyangxu0/DeMT.

Optimal operation of distribution networks and multiple community energy prosumers based on mixed game theory

Community energy systems are currently transitioning from conventional consumers to prosumers. Under this context, the coordinated management of multiple community energy prosumers (CEPs) is explored this study in accordance with the same distribution network. The aim of this study is to facilitate the coordination of unit operations, demand response, and peer-to-peer (P2P) energy trading among CEP coalitions based on the distribution network operator (DSO) by setting electricity prices. Thus, a mixed game-based optimal operation model of DSO and CEP alliances is developed, integrating Stackelberg and cooperative games. The upper layer aims at maximizing DSO revenue, whereas the lower layer minimizes the operation costs of CEP cooperative alliances while allocating benefits in accordance with the Nash-Harsanyi bargaining theory. The model is solved with a two-stage distributed algorithm that integrates the bisection method and the alternating direction method of multipliers (ADMM). Furthermore, cloud energy storage (CES) is introduced to optimize the economics of CEP. The effectiveness of the proposed method is verified through a case study, demonstrating the collaborative optimal scheduling of multiple CEPs and reasonable benefit distribution. Accordingly, this study is conducive to expediting the effective and economical management of CEPs under distribution networks.

Large Neighborhood Search for Electric Vehicle Fleet Scheduling

This work considers the problem of planning how a fleet of shared electric vehicles is charged and used for serving a set of reservations. While exact approaches can be used to efficiently solve small to medium-sized instances of this problem, heuristic approaches have been demonstrated to be superior in larger instances. The present work proposes a large neighborhood search approach for solving this problem, which employs a mixed integer linear programming-based repair operator. Three variants of the approach using different destroy operators are evaluated on large instances of the problem. The experimental results show that the proposed approach significantly outperforms earlier state-of-the-art methods on this benchmark set by obtaining solutions with up to 8.5% better objective values.

Design of the vector floating-point unit with high area efficiency

With the development of the information age, there is an increasing trend towards mixed precision and vector operations in floating point arithmetic. Traditional floating-point arithmetic is usually implemented using multiple modules to ensure the required speed. Still, this approach significantly increases area and reduces area efficiency, resulting in the wastage of hardware resources. This paper focuses on optimizing speed and area to improve the area’s efficiency. The proposed floating-point unit designed can perform half-precision, single-precision, and double-precision floating-point operations. Under the TSMC 7 nm process, its maximum operating frequency is increased by 5%–37%, the area is reduced by 33%–58%, and area efficiency is increased by 63%–144%.

Introduction to gravitational redshift of quantum photons propagating in curved spacetime

Gravitational redshift is discussed in the context of quantum photons propagating in curved spacetime. A brief introduction to modelling realistic photons is first presented and the effect of gravity on the spectrum computed for photons largely confined along the direction of propagation. It is then shown that redshift-induced transformations on photon operators with sharp momenta are not unitary, while a unitary transformation can be constructed for realistic photons with finite bandwidth. The unitary transformation obtained is then characterized as a multimode mixing operation, which is a generalized rotation of the Hilbert-space basis. Finally, applications of these results are discussed with focus on performance of quantum communication protocols, exploitation of the effects for quantum metrology and sensing, as well as potential for tests of fundamental science.

In-situ battery life prognostics amid mixed operation conditions using physics-driven machine learning

Accurately predicting in-situ battery life is critical to evaluate the system's reliability and residual value. The high complexity of battery aging evolution under variable conditions makes it a great challenge. We extract 6 physical features from voltage relaxation data to indicate battery performance fading, and then use data-driven techniques to predict battery life without considering any usage information. The model performance is validated against a dataset of 74 cells involving three battery types under mixed operation conditions. Experimental results show that battery lives are predicted accurately with the root-mean-squared-errors and mean absolute percentage errors being, respectively, generally less than 60 cycles and 10%. And the battery lives are classified quickly with the accuracies larger than 90%. This high prediction accuracy is maintained when only 6 sampling points taking 3–12 min are used. This work highlights the promise of using physics-driven machine learning to predict the behavior of complex systems under variable conditions.

A Choquard type equation involving mixed local and nonlocal operators

In the present work, we are concerned with an elliptic problem involving a mixed order diffusion operator with both local and nonlocal parts and a critical nonlinearity of Hartree type. We first investigate the corresponding Hardy-Littlewood-Sobolev inequality and establish the optimal constant. Using variational methods and a Pohožaev identity we then show existence and nonexistence results for the corresponding subcritical perturbation problem.