123,127 results
Search Results
2. Ext-groups in the Category of Strict Polynomial Functors
- Author
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Van Tuan Pham
- Subjects
Polynomial ,Pure mathematics ,Functor ,Mathematics::Category Theory ,General Mathematics ,010102 general mathematics ,FOS: Mathematics ,Algebraic Topology (math.AT) ,Mathematics - Algebraic Topology ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
The aim of this paper is to study, by using the mathematical tools developed by Chałupnik, Touzé, and Van der Kallen, the effect of the Frobenius twist on $\operatorname{Ext}$-group in the category of strict polynomial functors. As an application, we obtain explicit formulas of cohomology of the orthogonal groups and symplectic ones.
- Published
- 2023
3. Invariant complex structures on solvable¶real Lie groups
- Author
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Gabriela P. Ovando
- Subjects
Algebra ,Pure mathematics ,Adjoint representation of a Lie algebra ,Representation of a Lie group ,General Mathematics ,Simple Lie group ,Lie algebra ,Lie group ,Real form ,Lie theory ,Representation theory ,Mathematics - Abstract
In this paper, we classify the invariant complex structures on four-dimensional, solvable, simply-connected real Lie groups with commutator of dimension three. The resulting complex surfaces corresponding to these structures are also determined. The classification is based on the determination of certain complex subalgebras of the complexifications of the corresponding real Lie algebras.
- Published
- 2000
4. Positivity preservers forbidden to operate on diagonal blocks
- Author
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Prateek Kumar Vishwakarma
- Subjects
Power series ,Applied Mathematics ,General Mathematics ,Diagonal ,Monotonic function ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Combinatorics ,Mathematics - Classical Analysis and ODEs ,Converse ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,15B48, 26A21 (primary), 15A24, 15A39, 15A45, 30B10 (secondary) ,Schur product theorem ,Mathematics - Abstract
The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative coefficients) preserve positivity on matrices of all dimensions. A famous result of Schoenberg and of Rudin [Duke Math. J. 1942, 1959] shows the converse: there are no other such functions. Motivated by modern applications, Guillot and Rajaratnam [Trans. Amer. Math. Soc. 2015] classified the entrywise positivity preservers in all dimensions, which act only on the off-diagonal entries. These two results are at "opposite ends", and in both cases the preservers have to be absolutely monotonic. We complete the classification of positivity preservers that act entrywise except on specified "diagonal/principal blocks", in every case other than the two above. (In fact we achieve this in a more general framework.) This yields the first examples of dimension-free entrywise positivity preservers - with certain forbidden principal blocks - that are not absolutely monotonic., Minor edits in exposition, 19 pages. The paper now uses the style file of Trans. AMS (to appear)
- Published
- 2023
5. Mathematical Methods for an Accurate Navigation of the Robotic Telescopes
- Author
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Vadym Savanevych, Sergii Khlamov, Oleksandr Briukhovetskyi, Tetiana Trunova, and Iryna Tabakova
- Subjects
mathematics ,image processing ,sky identification ,astrometric reduction ,celestial coordinates ,robotic telescopes ,calibration ,navigation ,General Mathematics ,Computer Science (miscellaneous) ,Engineering (miscellaneous) - Abstract
Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios.
- Published
- 2023
6. Mixed 𝐴₂-𝐴_{∞} estimates of the non-homogeneous vector square function with matrix weights
- Author
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Sergei Treil
- Subjects
Matrix (mathematics) ,Applied Mathematics ,General Mathematics ,Non homogeneous ,Mathematical analysis ,Mathematics - Abstract
This paper extends the results from a work of Hytönen, Petermichl, and Volberg about sharp A 2 A_2 - A ∞ A_\infty estimates with matrix weights to the non-homogeneous situation.
- Published
- 2023
7. Assumption Lean Regression
- Author
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Linda Zhao, Edward I. George, Lawrence D. Brown, Andreas Buja, Arun Kumar Kuchibhotla, Weijie J. Su, and Richard A. Berk
- Subjects
Statistics and Probability ,Generalized linear model ,FOS: Computer and information sciences ,General Mathematics ,05 social sciences ,01 natural sciences ,050105 experimental psychology ,Regression ,Methodology (stat.ME) ,010104 statistics & probability ,Linear regression ,Econometrics ,0501 psychology and cognitive sciences ,Observational study ,0101 mathematics ,Statistics, Probability and Uncertainty ,Statistics - Methodology ,Mathematics - Abstract
It is well known that models used in conventional regression analysis are commonly misspecified. A standard response is little more than a shrug. Data analysts invoke Box's maxim that all models are wrong and then proceed as if the results are useful nevertheless. In this paper, we provide an alternative. Regression models are treated explicitly as approximations of a true response surface that can have a number of desirable statistical properties, including estimates that are asymptotically unbiased. Valid statistical inference follows. We generalize the formulation to include regression functionals, which broadens substantially the range of potential applications. An empirical application is provided to illustrate the paper's key concepts., Comment: Submitted for review, 21 pages, 2 figures
- Published
- 2018
- Full Text
- View/download PDF
8. A Generalization of Pisier Homogeneous Banach Algebra
- Author
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Safari Mukeru
- Subjects
Independent and identically distributed random variables ,Mathematics::Functional Analysis ,Sequence ,Pure mathematics ,Unit circle ,General Mathematics ,Wiener algebra ,Banach *-algebra ,Fourier series ,Random variable ,Probability measure ,Mathematics - Abstract
In 1979, Pisier proved remarkably that a sequence of independent and identically distributed standard Gaussian random variables determines, via random Fourier series, a homogeneous Banach algebra P strictly contained in C(T), the class of continuous functions on the unit circle T and strictly containing the classical Wiener algebra A(T), that is, A(T)⫋P⫋C(T). This improved some previous results obtained by Zafran in solving a long-standing problem raised by Katznelson. In this paper, we extend Pisier’s result by showing that any probability measure on the unit circle defines a homogeneous Banach algebra contained in C(T). Thus Pisier algebra is not an isolated object but rather an element in a large class of Pisier-type algebras. We consider the case of spectral measures of stationary sequences of Gaussian random variables and obtain a sufficient condition for the boundedness of the random Fourier series ∑ n∈Zfˆ(n)ξnexp(2πint) in the general setting of dependent random variables (ξn).
- Published
- 2023
9. Codimension 2 and 3 pluricanonical embeddings in projective spaces
- Author
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Marina Bertolini
- Subjects
Discrete mathematics ,Pure mathematics ,Chern class ,Line bundle ,Degree (graph theory) ,General Mathematics ,Dimension (graph theory) ,Hyperplane section ,Codimension ,Algebraic geometry ,Projective test ,Mathematics - Abstract
In this paper some non existence results are given for smooth varieties of dimension bigger then 1, embedded in projective spaces with low codimension, by the pluricanonical system |mK X |, withm≥2. The only meaningful cases of codimension 2 are surfaces in P4 and threefolds in P5, whose existence is excluded. When the codimension is 3, for surfaces in P5 is proven thatm=2, while for three-folds in P6 and fourfolds in P7 only two numerical possibilities for the degree are given.
- Published
- 1996
10. The Tarski numbers of groups
- Author
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Mark Sapir, Gili Golan, and Mikhail Ershov
- Subjects
Discrete mathematics ,Arbitrarily large ,Group action ,Group (mathematics) ,General Mathematics ,FOS: Mathematics ,CA-group ,Group Theory (math.GR) ,Mathematics - Group Theory ,Mathematics - Abstract
The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. In this paper we investigate how Tarski numbers may change under various group-theoretic operations. Using these estimates and known properties of Golod-Shafarevich groups, we show that the Tarski numbers of 2-generated non-amenable groups can be arbitrarily large. We also use the cost of group actions to show that there exist groups with Tarski numbers 5 and 6. These provide the first examples of non-amenable groups without free subgroups whose Tarski number has been computed precisely., 26 pages. v4: We have added the result about the existence of groups with Tarski number 5 which previously appeared in a separate paper of the second author arXiv:1406.2097. Section 5 has been rewritten. Minor changes in Appendix B. We also replaced left group actions by right group actions
- Published
- 2014
11. SATURATION FOR THE BUTTERFLY POSET
- Author
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Maria-Romina Ivan, Ivan, Maria [0000-0003-0817-3777], and Apollo - University of Cambridge Repository
- Subjects
General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Combinatorics ,05D05 ,010201 computation theory & mathematics ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Saturation (chemistry) ,Partially ordered set ,Mathematics - Abstract
Given a finite poset $\mathcal P$, we call a family $\mathcal F$ of subsets of $[n]$ $\mathcal P$-saturated if $\mathcal F$ does not contain an induced copy of $\mathcal P$, but adding any other set to $\mathcal F$ creates an induced copy of $\mathcal P$. The induced saturated number of $\mathcal P$, denoted by $\text{sat}^*(n,\mathcal P)$, is the size of the smallest $\mathcal P$-saturated family with ground set $[n]$. In this paper we are mainly interested in the four-point poset called the butterfly. Ferrara, Kay, Kramer, Martin, Reiniger, Smith and Sullivan showed that the saturation number for the butterfly lies between $\log_2{n}$ and $n^2$. We give a linear lower bound of $n+1$. We also prove some other results about the butterfly and the poset $\mathcal N$., Comment: 13 pages
- Published
- 2023
- Full Text
- View/download PDF
12. Review of the Exponential and Cayley Map on SE(3) as relevant for Lie Group Integration of the Generalized Poisson Equation and Flexible Multibody Systems
- Author
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Andreas Müller
- Subjects
FOS: Computer and information sciences ,Mathematics - Differential Geometry ,Pure mathematics ,Geometric integration ,General Mathematics ,General Engineering ,General Physics and Astronomy ,Lie group ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Computational Physics (physics.comp-ph) ,Rigid body ,Cayley map ,Exponential function ,Computer Science - Robotics ,Differential Geometry (math.DG) ,FOS: Mathematics ,Poisson's equation ,Robotics (cs.RO) ,Physics - Computational Physics ,Mathematical Physics ,Mathematics - Abstract
The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed-form relations along with the relevant proofs, including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized- α scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.
- Published
- 2023
13. Teaching and Learning of Mathematics through CLIL, CBI, or EMI—A Systematic Literature Review
- Author
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Raul Ruiz-Cecilia, Leopoldo Medina Sánchez, and Antonio-Manuel Rodríguez-García
- Subjects
CLIL ,General Mathematics ,CBI ,Computer Science (miscellaneous) ,Systematic review ,Foreign language learning ,EMI ,Engineering (miscellaneous) ,Mathematics - Abstract
This study provides a systematic literature review of research in the field of teaching and learning mathematics through Content and Language Integrated Learning (CLIL), Content-Based Instruction (CBI), and English Medium Instruction (EMI). The review aims to examine the most relevant literature with a focus on mathematics and CLIL, CBI, or EMI in Scopus and Web of Science per the Preferred Reporting Items for Systematic Reviews (PRISMA) guidelines. Based on 151 sources, 52 papers were selected according to predefined selection criteria. The papers were analysed and coded according to the following categories: (1) geographical productivity, (2) diachronic productivity growth, (3) main objectives, (4) methodology, and research design, (5) variables and measurement instruments, (6) context and sample details, and (7) main findings. The results reveal that most of the research analysed has been carried out in the Asian continent, followed by Europe. The analysis of diachronic productivity shows that the study of the application of CLIL, CBI, and EMI programs in the teaching-learning process of mathematics has notably increased in recent years, especially in the last triennium (2020–2022). Regarding the objectives of the selected corpus, the majority aimed at teaching practices and learning processes, and outcomes in mathematics and language proficiency in CLIL, CBI, and/or EMI classrooms. The corpus analysed fits within one or more of the following categories: empirical, qualitative, descriptive, correlational, and cross-sectional. The samples utilized in different studies differ significantly, both in terms of quantity –ranging from one person to 700– and in the educational level being studied, which would be primary, secondary, or tertiary education. The main variables studied in the corpus focus on mathematical competence, language proficiency, teaching practices, teacher training, science competence, and teachers’ perceptions. The most widely used instruments have been objective tests, such as questionnaires, together with standardized tests to measure some aspects related to mathematical competence and language proficiency. They are followed by an analysis of documents (academic records, teaching materials, official documents...), participant or non-participant observation, interviews, and video and audio recordings. In summary, in the scientific literature analysed, a positive or neutral view predominates on the effects of the CLIL, CBI, and EMI approaches on the learning of mathematics and the L2. This can be due to methodological issues fundamentally related to the methodology, research design, sample, and measurement instruments. Thus, we must highlight that some of the results from the selected papers must be interpreted with caution. Taking this factor into consideration, further comparative studies on a wider scale are required to examine thoroughly the effects of CLIL, CBI, and EMI on the teaching and learning of mathematics in an L2. Besides, it is important to study in greater depth the different levels of language acquisition since the research analysed shows that these have not been sufficiently addressed in the mathematical field of knowledge.
- Published
- 2023
14. A curvature-free 𝐿𝑜𝑔(2𝑘-1) theorem
- Author
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Florent Balacheff and Louis Merlin
- Subjects
Discrete mathematics ,Lemma (mathematics) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,16. Peace & justice ,Curvature ,Mathematics::Geometric Topology ,01 natural sciences ,Volume entropy ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
This paper presents a curvature-free version of the Log ( 2 k − 1 ) \text {Log}(2k-1) Theorem of Anderson, Canary, Culler, and Shalen [J. Differential Geometry 44 (1996), pp. 738–782]. It generalizes a result by Hou [J. Differential Geometry 57 (2001), no. 1, pp. 173–193] and its proof is rather straightforward once we know the work by Lim [Trans. Amer. Math. Soc. 360 (2008), no. 10, pp. 5089–5100] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions.
- Published
- 2023
15. Combinatorial Approach to Milnor Invariants of Welded Links
- Author
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Haruko A. Miyazawa, Akira Yasuhara, and Kodai Wada
- Subjects
Pure mathematics ,Overline ,Mathematics::Complex Variables ,General Mathematics ,High Energy Physics::Phenomenology ,Geometric Topology (math.GT) ,Mathematics::Geometric Topology ,Mathematics - Geometric Topology ,Mathematics::Algebraic Geometry ,Mathematics::K-Theory and Homology ,FOS: Mathematics ,Isotopy ,Link (knot theory) ,Mathematics - Abstract
For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\overline{\mu}$-invariants. Recently, Chrisman extended Milnor $\overline{\mu}$-invariants to welded links by a topological approach. The aim of this paper is to show that Milnor $\overline{\mu}$-invariants can be extended to welded links by a combinatorial approach. The proof contains an alternative proof for the invariance of the original $\overline{\mu}$-invariants of classical links., Comment: 25 pages; v2: the title changed, Section 1 rewritten, remarks and references added; to appear in Michigan Mathematical Journal
- Published
- 2023
16. A Continuous Process for Validation, Verification, and Accreditation of Simulation Models
- Author
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Pau Fonseca i Casas, Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa, and Universitat Politècnica de Catalunya. IMP - Information Modeling and Processing
- Subjects
validation ,assumptions ,General Mathematics ,Verification ,Matemàtiques i estadística [Àrees temàtiques de la UPC] ,simulation ,accreditation ,Accreditation ,Validation ,Computer Science (miscellaneous) ,Assumptions ,verification ,Matemàtica ,00 General::00A General and miscellaneous specific topics [Classificació AMS] ,Engineering (miscellaneous) ,Mathematics ,Simulation - Abstract
A simulation model, and more generically, a model, is founded on its assumptions. Assurance of the model’s correctness and correct use is needed to achieve accreditation. Often the exercise of working with a specific code misunderstands the overall process, focusing the resources on the model coding and forgetting the needed resources to ensure the validation of every step of the model definition and coding. The goal of this work is to present a methodology to help in the definition and use of the assumptions in the modeling process. To do so, we present a process to conduct a simulation project, an assumptions taxonomy, and a method that simplifies working with those assumptions. We propose to extend the traditional Validation, Verification, and Accreditation processes to a process composed of eight Validation, Verification, and Accreditation phases that cover the overall life cycle of a model. Although this paper is focused on a simulation model, we can extend the proposed method to a more general modeling approach.
- Published
- 2023
17. On the density of multivariate polynomials with varying weights
- Author
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András Kroó and József Szabados
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,Multivariate polynomials ,Mathematics - Abstract
In this paper we consider multivariate approximation by weighted polynomials of the form w γ n ( x ) p n ( x ) w^{\gamma _n}(\mathbf {x})p_n(\mathbf {x}) , where p n p_n is a multivariate polynomial of degree at most n n , w w is a given nonnegative weight with nonempty zero set, and γ n ↑ ∞ \gamma _n\uparrow \infty . We study the question if every continuous function vanishing on the zero set of w w is a uniform limit of weighted polynomials w γ n ( x ) p n ( x ) w^{\gamma _n}(\mathbf {x})p_n(\mathbf {x}) . It turns out that for various classes of weights in order for this approximation property to hold it is necessary and sufficient that γ n = o ( n ) . \gamma _n=o(n).
- Published
- 2023
18. The Symmetric Minimal Surface Equation
- Author
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K. Fouladgar and Leon Simon
- Subjects
Minimal surface ,Mathematics - Analysis of PDEs ,General Mathematics ,Mathematical analysis ,35A30 ,FOS: Mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
For positive functions $u\in C^{2}(\Omega) $, where $\Omega$ is an open subset of $\mathbb{R}^{n}$, the Symmetric Minimal Surface Equation (SME), is $\sum_{i=1}^{n}D_{i}\bigl(\frac{D_{i}u}{\sqrt{1+|Du|^{2}}}\bigr)=\frac{m-1}{u\sqrt{1+|Du|^{2}}}$. Geometrically, the SME expresses the fact that the ``symmetric graph'' $SG(u)$, defined by $SG(u)=\bigl\{(x,\xi)\in \Omega\times\mathbb{R}^{m}:|\xi|=u(x)\bigr\}$, is a minimal (i.e.\ zero mean curvature) hypersurface in $\Omega\times\mathbb{R}^{m}$. A function $u\in C^{1}(\Omega)$ is said to be a singular solution if $u^{-1}\{0\}\neq \emptyset$, and if $u=\lim_{j\to\infty}u_{j}$, uniformly on each compact subset of $\Omega$, where each $u_{j}$ is a positive $C^{2}(\Omega)$ solution of the SME. The present paper develops are theory of singular solutions of the SME, including existence, H\"older and Lipschitz estimates for bounded solutions, and a compactness and regularity theory. We also prove that the singular set $u^{-1}{\{0\}}$ is codimension at most 2.
- Published
- 2023
19. On the trace embedding and its applications to evolution equations
- Author
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Antonio Agresti, Nick Lindemulder, and Mark Veraar
- Subjects
integral equations ,General Mathematics ,Probability (math.PR) ,Primary: 46E35, Secondary: 35B65, 35K90, 45N05, 46E40, 47D06, 60H15 ,traces ,weighted function spaces ,Triebel–Lizorkin spaces ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Mathematics - Analysis of PDEs ,stochastic maximal regularity ,Besov spaces ,Sobolev spaces ,Bessel-potential spaces ,FOS: Mathematics ,ddc:510 ,anisotropic function spaces ,Mathematics ,Mathematics - Probability ,Analysis of PDEs (math.AP) - Abstract
In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equation, where uniform trace estimates on the half-line are shown., Comment: Some typos corrected. Accepted for publication in Mathematische Nachrichten
- Published
- 2023
20. Optimal Sizing of a Photovoltaic Pumping System Integrated with Water Storage Tank Considering Cost/Reliability Assessment Using Enhanced Artificial Rabbits Optimization: A Case Study
- Author
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Abdolhamid Mazloumi, Alireza Poolad, Mohammad Sadegh Mokhtari, Morteza Babaee Altman, Almoataz Y. Abdelaziz, and Mahmoud Elsisi
- Subjects
photovoltaic pumping system ,optimal sizing ,cost/reliability assessment ,probability of interrupted water ,enhanced artificial rabbits optimization ,General Mathematics ,Computer Science (miscellaneous) ,Engineering sciences. Technology ,Engineering (miscellaneous) ,Mathematics - Abstract
In this paper, optimal sizing of a photovoltaic (PV) pumping system with a water storage tank (WST) is developed to meet the water demand to minimize the life cycle cost (LCC) and satisfy the probability of interrupted water (pIW) constraint considering real region data. The component sizing, including the PV resources and the WST, is determined optimally based on LCC and pIW using a new meta-heuristic method named enhanced artificial rabbits optimization (EARO) via a nonlinear inertia weight reduction strategy to overcome the premature convergence of its conventional algorithm. The WST is sized optimally regarding the lack of irradiation and inaccessibility of the pumping system so that it is able to improve the water supply reliability. The LCC for water extraction heights of 5 and 10 m is obtained at 0.2955 M$ and 0.2993 M$, respectively, and the pIW in these two scenarios is calculated as zero, which means the complete and reliable supply of the water demand of the customers using the proposed methodology based on the EARO. Also, the results demonstrated the superior performance of EARO in comparison with artificial rabbits optimization (ARO) and particle swarm optimization (PSO); these methods have supplied customers’ water demands with higher costs and lower reliability than the proposed EARO method. Also, during the sensitivity analysis, the results showed that changes in the irradiance and height of the water extraction have a considerable effect on the cost and ability to meet customer demand.
- Published
- 2023
21. Analogues of Entropy in Bi-Free Probability Theory: Microstates
- Author
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Paul Skoufranis and Ian Charlesworth
- Subjects
Free entropy ,General Mathematics ,FISHERS INFORMATION MEASURE ,01 natural sciences ,Upper and lower bounds ,46L54, 46L53, 47B80, 94A17 ,Ministate ,0103 physical sciences ,Subadditivity ,FOS: Mathematics ,Entropy (information theory) ,Statistical physics ,0101 mathematics ,Operator Algebras (math.OA) ,Central limit theorem ,Mathematics ,Science & Technology ,Mathematics::Operator Algebras ,010102 general mathematics ,Mathematics - Operator Algebras ,16. Peace & justice ,Free probability ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Physical Sciences ,010307 mathematical physics ,Random matrix - Abstract
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are developed, such as the behaviour of the entropy when transformations on the left variables or on the right variables are performed. In addition, the microstate bi-free entropy is demonstrated to be additive over bi-free collections provided additional regularity assumptions are included and is computed for all bi-free central limit distributions. Moreover, an orbital version of bi-free entropy is examined which provides a tighter upper bound for the subadditivity of microstate bi-free entropy and provides an alternate characterization of bi-freeness in certain settings., Comment: (new version contains corrections, orbital bi-free entropy, and a new characterization of bi-freenness)
- Published
- 2023
22. Teaching and Learning Mathematics in Primary Education: The Role of ICT-A Systematic Review of the Literature
- Author
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Carmen Rodríguez-Jiménez, Juan-Carlos de la Cruz-Campos, María-Natalia Campos-Soto, and Magdalena Ramos-Navas-Parejo
- Subjects
mathematics ,ICT ,primary education ,teaching–learning ,General Mathematics ,Teaching-Learning ,Computer Science (miscellaneous) ,Engineering (miscellaneous) ,Primary Education ,Mathematics - Abstract
Nowadays, ICT play a fundamental role in education, as they are essential in all areas of knowledge at any educational stage. Specifically, in the area of mathematics, within the Primary Education stage, they are also very valid resources. This is demonstrated by the latest scientific studies. In recent times, the scientific literature has provided evidence of all this through different research studies. The aim of this paper is to analyze all those publications that deal with the teaching–learning processes of mathematics through ICT in primary education. The aim is to show the current state of the scientific literature and what elements and aspects to highlight are common to the documents analyzed. By means of the systematic literature review method, we analyzed 11 articles indexed in Scopus and the Web of Science, with the result that the use of ICT in this area is still scarce, as the volume of publications in this respect is very low. This could also indicate a prevalence of traditional methodologies associated with the teaching of mathematics that could hinder students’ acquisition of mathematical competence. However, those studies that show the use of ICT demonstrate that its use leads to an improvement in performance, motivation, and problem solving.
- Published
- 2023
- Full Text
- View/download PDF
23. A semismooth equation approach to the solution of nonlinear complementarity problems
- Author
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Francisco Facchinei, Tecla De Luca, and Christian Kanzow
- Subjects
Mathematical optimization ,General Mathematics ,Numerical analysis ,media_common.quotation_subject ,Extension (predicate logic) ,System of linear equations ,Rate of convergence ,Complementarity theory ,Nonlinear complementarity problem ,Simplicity ,Mixed complementarity problem ,Software ,Mathematics ,media_common - Abstract
In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions. Other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration. We include numerical tests which show the viability of the approach.
24. Homeomorphisms of universal dendrites
- Author
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Janusz J. Charatonik
- Subjects
Discrete mathematics ,Dense set ,Group (mathematics) ,General Mathematics ,Algebra over a field ,Action (physics) ,Mathematics - Abstract
Homeomorphisms of some special universal dendrites are considered in the paper. In particular, dendrites are characterized for which the action onX of the group of autohomeomorphisms ofX has exactlyn≥3 orbits, and for each orbitB ofX and for each areA ⊂X the intersectionA∪B is a dense subset ofA. Some of the results generalize earlier ones from the author’s paper [2].
- Published
- 1995
25. CSP dichotomy for special triads
- Author
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Libor Barto, Miklós Maróti, Todd Niven, and Marcin Kozik
- Subjects
Discrete mathematics ,Conjecture ,triad ,Applied Mathematics ,General Mathematics ,Digraph ,Directed graph ,Computer Science::Computational Complexity ,Combinatorics ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,graph coloring ,Homomorphism ,Graph coloring ,Tree (set theory) ,constraint satisfaction problem ,Time complexity ,Constraint satisfaction problem ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
For a fixed digraph G, the Constraint Satisfaction Problem with the template G, or CSP(G) for short, is the problem of deciding whether a given input digraph H admits a homomorphism to G. The dichotomy conjecture of Feder and Vardi states that CSP(G), for any choice of G, is solvable in polynomial time or NP-complete. This paper confirms the conjecture for a class of oriented trees called special triads. As a corollary we get the smallest known example of an oriented tree (with 33 vertices) defining an NP-complete CSP(G).
- Published
- 2023
- Full Text
- View/download PDF
26. SOME LATTICE-THEORETICAL PROPERTIES OF GROUPS AND SEMI-GROUPS
- Author
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M N Arshinov and L E Sadovskii
- Subjects
Combinatorics ,Mathematics::Group Theory ,Group (mathematics) ,Semigroup ,Discrete group ,General Mathematics ,Lattice (order) ,Structure (category theory) ,Topological group ,Algebraic number ,Mathematics ,Group object - Abstract
During the period following the publication of the survey [5] a number of new papers appeared in which connections between the structure of an algebraic system (a group, a semigroup or a topological group) and the lattice of its subsystems (subgroups, subsemigroups, closed subgroups) are studied.In a sense the present article is a continuation of [5], although its style differs somewhat in that it includes fragments of proofs of the most interesting facts.It also considers other lattices similar to the subgroup lattice of a discrete group. Accordingly it contains five sections studying the subgroup lattice of infinite groups (§ 1), the subsemigroup lattice of these groups (§ 2), the subsemigroup lattice of a semigroup (§ 3), the subgroup lattice in groups with various finiteness conditions (§ 4), and finally the lattice of closed subgroups of a topological group (§ 5). All the definitions necessary for an understanding of the new results are given here. Definitions of other concepts that are already known well-enough can be found in [5] or in Kurosh's book [4].The authors have tried to examine all the available relevant literature; this is listed at the end of the article. Titles cited in [5] are repeated here only when they are directly referred to in the text in connection with new results not mentioned in [5].
- Published
- 1972
27. Primitively generated Hall algebras
- Author
-
Jacob Greenstein and Arkady Berenstein
- Subjects
Large class ,Pure mathematics ,General Mathematics ,01 natural sciences ,Nichols algebra ,Mathematics::Category Theory ,Mathematics - Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Quantum Algebra (math.QA) ,Finitary ,Representation Theory (math.RT) ,0101 mathematics ,Quantum ,exact category ,Mathematics ,Conjecture ,PBW property ,010102 general mathematics ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,16. Peace & justice ,Pure Mathematics ,Hall algebra ,010307 mathematical physics ,Indecomposable module ,Mathematics - Representation Theory - Abstract
In the present paper we show that Hall algebras of finitary exact categories behave like quantum groups in the sense that they are generated by indecomposable objects. Moreover, for a large class of such categories, Hall algebras are generated by their primitive elements, with respect to the natural comultiplication, even for non-hereditary categories. Finally, we introduce certain primitively generated subalgebras of Hall algebras and conjecture an analogue of "Lie correspondence" for those finitary categories., Comment: 36 pages, AMSLaTeX+AMSRefs; introduced multiplicity for elements of Grothendieck monoid; they play the role of root multiplicities in Kac-Moody algebras due to a reformulation of Kac conjecture (see Theorem 1.9)
- Published
- 2016
28. On the scattering of a plane wave by a perturbed open periodic waveguide
- Author
-
Andreas Kirsch
- Subjects
periodic structure ,General Mathematics ,scattering problem ,General Engineering ,ddc:510 ,radiation condition ,Mathematics - Abstract
We consider the scattering of a plane wave by a locally perturbed periodic (with respect to x_1) medium. If there is no perturbation it is usually assumed that the scattered wave is quasi-periodic with the same parameter as the incident plane wave. As it is well known, one can show existence under this condition but not necessarily uniqueness. Uniqueness fails for certain incident directions (if the wavenumber is kept fixed), and it is not clear which additional condition has to be assumed in this case. In this paper we will analyze three concepts. For the Limiting Absorption Principle (LAP) we replace the refractive index n=n(x) by n(x)+iε in a layer of finite width and consider the limiting case when ε tends to zero. This will give an unsatisfactory condition. In a second approach we require continuity of the field with respect to the incident direction. This will give the same satisfactory condition as the third approach where we approximate the incident plane wave by an incident point source and let the location of the source tend to infinity.
- Published
- 2023
- Full Text
- View/download PDF
29. Fractal Geometrry in Muslim Cities: How Succession Law Shaped Morphology
- Author
-
Mustapha Ben-Hamouche
- Subjects
Property (philosophy) ,Visual Arts and Performing Arts ,business.industry ,General Mathematics ,Urban morphology ,Urban design ,Islam ,Ecological succession ,Fractal ,Sharia ,Law ,Architecture ,business ,Subdivision ,Mathematics - Abstract
Islamic succession law has deeply affected the urban fabric of Muslim cities. Properties were subdivided according to a refined and elaborate system of shares that were prescribed by jurists. Successive iterations of subdivision over the course of decades or even centuries gave a fractal character to the cities and thus becomes the main source of their complexity. Most property was subject to successive subdivisions until minimum but functional parts were arrived at. However, this fragmentation should not be understood in isolation from other mechanisms which sometimes resulted in a reunification of the fragments, and thus established a dynamic equilibrium in the urban fabric. The paper will present the mechanisms of subdivision according to laws of succession, and illustrate by hypothetical example their direct impact on the urban morphology, as a means of understanding the complexity of old Muslim cities.
- Published
- 2011
30. Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions
- Author
-
Claude Lefèvre
- Subjects
Statistics and Probability ,Polynomial ,Distribution (number theory) ,Generalized Appell polynomials ,General Mathematics ,Mathematical analysis ,Boundary (topology) ,Poisson distribution ,symbols.namesake ,Compound Poisson distribution ,Simple (abstract algebra) ,Compound Poisson process ,symbols ,Mathematics - Abstract
This paper provides a review of recent results, most of them published jointly with Ph. Picard, on the exact distribution of the first crossing of a Poisson or discrete compound Poisson process through a given nondecreasing boundary, of curved or linear shape. The key point consists in using an underlying polynomial structure to describe the distribution, the polynomials being of generalized Appell type for an upper boundary and of generalized Abel–Gontcharoff type for a lower boundary. That property allows us to obtain simple and efficient recursions for the numerical determination of the distribution.
- Published
- 2007
31. Some parseval-goldstein type identities with illustrative examples
- Author
-
KARATAŞ, HİLAL BAŞAK, ALBAYRAK, DURMUŞ, UÇAR, FARUK, and KARATAŞ H. B., ALBAYRAK D., UÇAR F.
- Subjects
Matematik ,Generalized Glasser transforms ,Generalized Laplace transforms ,General Mathematics ,Temel Bilimler (SCI) ,Mellin transforms ,Fourier sine transforms ,MATHEMATICS ,Parseval-Goldstein type theorems ,Genel Matematik ,Generalized Stieltjes transforms ,Fizik Bilimleri ,Natural Sciences (SCI) ,Physical Sciences ,Fourier cosine transforms - Abstract
In the present paper, the integral transform which will be called generalized Laplace transform is considered. Iteration of generalized Laplace transform and Fourier cosine transform and Fourier sine transform is generalized Glasser transform. Some identities involving these transforms and the Mellin transform and the generalized Stieltjes transform are given.
- Published
- 2023
32. Special Cubic Four-Folds, K3 Surfaces, and the Franchetta Property
- Author
-
Fu, L. and Laterveer, Robert
- Subjects
General Mathematics ,Mathematics - Abstract
O’Grady conjectured that the Chow group of 0-cycles of the generic fiber of the universal family over the moduli space of polarized K3 surfaces of genus $g$ is cyclic. This so-called generalized Franchetta conjecture has been solved only for low genera where there is a Mukai model (precisely, when $g\leq 10$ and $g=12, 13, 16, 18, 20$), by the work of Pavic–Shen–Yin. In this paper, as a non-commutative analogue, we study the Franchetta property for families of special cubic four-folds (in the sense of Hassett) and relate it to O’Grady’s conjecture for K3 surfaces. Most notably, by using special cubic four-folds of discriminant 26, we prove O’Grady’s generalized Franchetta conjecture for $g=14$, providing the first evidence beyond Mukai models.
- Published
- 2023
33. The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
- Author
-
Karsten Kruse
- Subjects
General Mathematics ,Holomorphic function ,Duality (optimization) ,Omega ,Cauchy-Riemann ,Combinatorics ,Mathematics - Analysis of PDEs ,Fréchet space ,Computer Science::Systems and Control ,FOS: Mathematics ,35A01, 35B30, 32W05, 46A63 (Primary), 46A32, 46E40 (Secondary) ,ddc:510 ,Mathematik [510] ,Mathematics ,Kernel (set theory) ,Applied Mathematics ,Operator (physics) ,Hausdorff space ,Parameter dependence ,Weight ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Solvability ,Vector-valued ,Smooth ,Complex plane ,Analysis of PDEs (math.AP) - Abstract
This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator $$\overline{\partial }$$ ∂ ¯ on spaces $${\mathcal {E}}{\mathcal {V}}(\varOmega ,E)$$ E V ( Ω , E ) of $${\mathcal {C}}^{\infty }$$ C ∞ -smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights $${\mathcal {V}}$$ V . Vector-valued means that these functions have values in a locally convex Hausdorff space E over $${\mathbb {C}}$$ C . We derive a counterpart of the Grothendieck-Köthe-Silva duality $${\mathcal {O}}({\mathbb {C}}\setminus K)/{\mathcal {O}}({\mathbb {C}})\cong {\mathscr {A}}(K)$$ O ( C \ K ) / O ( C ) ≅ A ( K ) with non-empty compact $$K\subset {\mathbb {R}}$$ K ⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of $$\overline{\partial }:{\mathcal {E}} {\mathcal {V}}(\varOmega ,E)\rightarrow {\mathcal {E}}{\mathcal {V}} (\varOmega ,E)$$ ∂ ¯ : E V ( Ω , E ) → E V ( Ω , E ) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on $${\mathcal {E}}{\mathcal {V}}(\varOmega ,{\mathbb {C}})$$ E V ( Ω , C ) .
- Published
- 2023
34. Multiplicative operations in BP∗BP
- Author
-
Douglas C. Ravenel
- Subjects
Monoid ,Pure mathematics ,Ring (mathematics) ,Endomorphism ,Mathematics::Category Theory ,General Mathematics ,Mathematics::Rings and Algebras ,Multiplicative function ,Algebra over a field ,Hopf algebra ,Space (mathematics) ,Mathematics - Abstract
where S is the Landweber-Novikov algebra. S has the added advantage of being a cocommutative Hopf algebra over Z. This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BP*BP, (i.e. those operations which induce ring endomorphisms on BP*X for any space X)9 which we will denote by Γ{BP), has a submonoid analogous to the monoid of multiplicative operations in S.
- Published
- 1975
35. Cobordism of theta curves in S3
- Author
-
Kouki Taniyama
- Subjects
Combinatorics ,General Mathematics ,Cobordism ,Connected sum ,Knot (mathematics) ,Mathematics - Abstract
In this paper we show that the cobordism classes of theta curves in S3 form a group under vertex connected sum. We investigate this group by means of knot cobordism and link cobordism.
- Published
- 1993
36. Extension of the Wittrick-Williams Algorithm for Free Vibration Analysis of Hybrid Dynamic Stiffness Models Connecting Line and Point Nodes
- Author
-
Xiang Liu, Shaoqi Qiu, Suchao Xie, and Jnan Ranjan Banerjee
- Subjects
dynamic stiffness method ,line nodes ,point nodes ,Lagrange multiplier ,modal analysis ,Wittrick-Williams algorithm ,TL ,General Mathematics ,TA ,QA1-939 ,Computer Science (miscellaneous) ,QA ,Engineering (miscellaneous) ,Mathematics - Abstract
This paper extends the Wittrick-Williams (W-W) algorithm for hybrid dynamic stiffness (DS) models connecting any combinations of line and point nodes. The principal novelties lie in the development of both the DS formulation and the solution technique in a sufficiently systematic and general manner. The parent structure is considered to be in the form of two dimensional DS elements with line nodes, which can be connected to rigid/spring point supports/connections, rod/beam point supports/connections, and point connections to substructures. This is achieved by proposing a direct constrain method in a strong form which makes the modeling process straightforward. For the solution technique, the W-W algorithm is extended for all of the above hybrid DS models. No matrix inversion is needed in the proposed extension, making the algorithm numerically stable, especially for complex built-up structures. A mathematical proof is provided for the extended W-W algorithm. The proposed DS formulation and the extended W-W algorithm are validated by the FE results computed by ANSYS. This work significantly extends the application scope of the DS formulation and the W-W algorithm in a methodical and reliable manner, providing a powerful eigenvalue analysis tool for beam-plate built-up structures.
- Published
- 2022
37. Propagation of singularities of Moreau envelopes and distance functions in a Hilbert space
- Author
-
Thomas Strömberg
- Subjects
Matematik ,General Mathematics ,Mathematics - Abstract
The Moreau envelopes of nonconvex functions on a real Hilbert space have points of nondifferentiability called singularities. For the first time in an infinite-dimensional space, the propagation of singularities along intrinsic characteristic curves $${\varvec{x}}(t)$$ x ( t ) is studied. The properties of the intrinsic characteristics are investigated in some detail. It is proved that singularities propagate along intrinsic characteristics not only locally but globally in t. Actually, this paper distinguishes between “singularities” and “strong singularities,” two concepts that agree for distance functions but disagree for Moreau envelopes, in general. Along intrinsic characteristics, propagating singularities instantaneously transform into strong singularities. Concerning the distance function to a closed nonempty set E, it is demonstrated that the singular set and $$\complement E$$ ∁ E are homotopy equivalent provided E satisfies a certain condition which is weaker than the boundedness of $$\complement E$$ ∁ E . The notion of intrinsic characteristics was introduced by Cannarsa and Cheng (Calc Var Part Differ Equ 56, 2017).
- Published
- 2022
38. ON POSITIVITY OF SEVERAL COMPONENTS OF SOLUTION VECTOR FOR SYSTEMS OF LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS
- Author
-
Ravi P. Agarwal and Alexander Domoshnitsky
- Subjects
Stochastic partial differential equation ,Examples of differential equations ,Pure mathematics ,Matrix differential equation ,Linear differential equation ,Computer Science::Information Retrieval ,General Mathematics ,Linear form ,Ordinary differential equation ,Mathematical analysis ,First-order partial differential equation ,System of linear equations ,Mathematics - Abstract
In the classical theorems about lower and upper vector functions for systems of linear differential equations very heavy restrictions on the signs of coefficients are assumed. These restrictions in many cases become necessary if we wish to compare all the components of a solution vector. The formulas of the integral representation of the general solution explain that these theorems claim actually the positivity of all elements of the Green's matrix. In this paper we define a principle of partial monotonicity (comparison of only several components of the solution vector), which assumes only the positivity of elements in a corresponding row of the Green's matrix. The main theorem of the paper claims the equivalence of positivity of all elements in the nth row of the Green's matrices of the initial and two other problems, non-oscillation of the nth component of the solution vector and a corresponding assertion about differential inequality of the de La Vallee Poussin type. Necessary and sufficient conditions of the partial monotonicity are obtained. It is demonstrated that our sufficient tests of positivity of the elements in the nth row of the Cauchy matrix are exact in corresponding cases. The main idea in our approach is a construction of an equation for the nth component of the solution vector. In this sense we can say that an analog of the classical Gauss method for solving systems of functional differential equations is proposed in the paper.
- Published
- 2009
39. Combinatorial matrices derived from generalized Motzkin paths
- Author
-
Lin Yang and Sheng-Liang Yang
- Subjects
Class (set theory) ,Generalization ,Applied Mathematics ,General Mathematics ,Numerical analysis ,Extension (predicate logic) ,Pascal's triangle ,Main diagonal ,Combinatorics ,Set (abstract data type) ,symbols.namesake ,Matrix (mathematics) ,symbols ,Mathematics - Abstract
In this paper, we consider the generalized Motzkin paths whose step set consists of $$E = (1, 0), N= (0,1), U = (1,1)$$ and $$D = (1,-1)$$ . In the general case, for the number of such paths running from (0, 0) to $$(k,n-2k)$$ , we define a number triangle, which turns out to be a common extension of Pascal triangle and Delannoy triangle. Under the restriction of above or below the x-axis, these paths can be seen as an unified generalization of the well-known Dyck paths, Motzkin paths, and Schroder paths. We also consider the counting of such paths above the main diagonal. In every condition, we treat with two classes of paths, which are restricted and unrestricted paths. For each class of paths, the corresponding counting array is a Riordan array. Numerous Combinatorial matrices such as the Catalan matrix, Motzkin matrix, and Schroder matrix are special cases of these Riordan arrays.
- Published
- 2021
40. Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy
- Author
-
Blondia, Chris
- Subjects
push-out strategy ,bursty input ,finite capacity queue ,server vacations ,Markov chain ,General Mathematics ,Computer Science (miscellaneous) ,Engineering (miscellaneous) ,Mathematics - Abstract
In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the Nth customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.
- Published
- 2022
41. The central sphere of an ALE space
- Author
-
Nigel Hitchin
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Algebraic geometry ,Fixed point ,Space (mathematics) ,01 natural sciences ,Induced metric ,Action (physics) ,Set (abstract data type) ,Mathematics - Algebraic Geometry ,53C26 ,Differential Geometry (math.DG) ,0103 physical sciences ,Metric (mathematics) ,Algebraic surface ,FOS: Mathematics ,Mathematics::Differential Geometry ,010307 mathematical physics ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfaces, in particular the lines on a cubic., Dedicated to the memory of Michael Atiyah
- Published
- 2022
42. Economies of Scope between Research and Teaching in European Universities
- Author
-
Andrea Bonaccorsi, Paola Belingheri, and Luca Secondi
- Subjects
Economies of scope ,Efficiency analysis ,European higher education ,Higher education ,Seemingly unrelated regressions ,seemingly unrelated regressions ,efficiency analysis ,General Mathematics ,higher education ,Computer Science (miscellaneous) ,QA1-939 ,economies of scope ,Engineering (miscellaneous) ,Mathematics - Abstract
The estimation of economies of scope between research and teaching has been the object of a large literature in economics of education and efficiency analysis, with parametric and non-parametric specifications. The paper contributes to the literature by building a pan-European dataset that integrates official statistics on higher education at country level with bibliometric indicators. The dataset allows a breakdown by scientific and educational field, accounting for the heterogeneity among disciplines. We applied a technique which has not been used for the efficiency estimation of economies of scope in higher education, namely seemingly unrelated regression (SUR) applied to separate input–output equations describing the production of education and research. We found confirmation for economies of scope in some fields and with some specifications, or no relation between the equations. In no case did we find diseconomies of scope between teaching and research.
- Published
- 2022
43. Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry
- Author
-
Enrique Jelvez, Nelson Morales, and Julian M. Ortiz
- Subjects
stochastic final pit ,geostatistics ,open-pit mining ,risk management ,Pareto-optimal front ,General Mathematics ,0211 other engineering and technologies ,02 engineering and technology ,010502 geochemistry & geophysics ,01 natural sciences ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,Mathematics ,021102 mining & metallurgy ,0105 earth and related environmental sciences - Abstract
In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit.
- Published
- 2022
44. Full Information H2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises
- Author
-
Hongji Ma and Yang Wang
- Subjects
gramian ,H2 control ,markov chain ,General Mathematics ,riccati equation ,Computer Science (miscellaneous) ,MathematicsofComputing_GENERAL ,QA1-939 ,Computer Science::Programming Languages ,borel set ,Engineering (miscellaneous) ,Mathematics - Abstract
This paper addresses an H2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.
- Published
- 2022
45. Evaluating Auction Mechanisms for the Preservation of Cost-Aware Digital Objects under Constrained Digital Preservation Budgets
- Author
-
Josep Lluís De la Rosa i Esteva and Andres El-Fakdi
- Subjects
Internet auctions ,digital preservation ,distributed architectures ,self-preserving digital objects ,General Mathematics ,Subhastes electròniques ,Computer Science (miscellaneous) ,QA1-939 ,Digital preservation ,Preservació digital ,Engineering (miscellaneous) ,Mathematics - Abstract
Digital preservation is a field of research focused on designing strategies for maintaining digital objects accessible for general use in the coming years. Out of the many approaches to digital preservation, the present research article is a continuation work of a previously published article containing a proposal for a novel object-centered paradigm to address the digital preservation problem where digital objects share part of the responsibility for self-preservation. In the new framework, the behavior of digital objects is modeled to find the best preservation strategy. The results presented in the current article add a new economic constraint to the object behavior. Now, differently from the previous paper, migrations, copies and updates are not free to use, but subject to budget limitations to ensure the economic sustainability of the whole preservation system, forcing the now-called cost-aware digital objects for efficient management of available budget. The presented approach compares two auction-based mechanisms, a multi-unit auction and a combinatorial auction, with a simple direct purchase strategy as possible efficient behaviors for budget management. TiM, a simulated environment for running distributed digital ecosystems, is used to perform the experiments. The simulated results map the relation between the studied purchase models with the sustained quality level of digital objects, as a measure of its accessibility, together with its budget management capabilities. About the results, the best performance corresponds to the combinatorial auction model. The results are a good approach to deal with the digital preservation problem from a sustainable point of view and open the door to future implementations with other purchase strategies This research was funded by the PRESERVA 2019 PROD 00024 and VoteVote DEMOC00001 of the AGAUR
- Published
- 2022
46. Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning
- Author
-
Kristjan Reba, Matej Guid, Kati Rozman, Dušanka Janežič, and Janez Konc
- Subjects
udc:54 ,MCQD ,General Mathematics ,kemija ,protein graphs ,strojno učenje ,machine learning ,matematika ,maximum clique ,Computer Science (miscellaneous) ,QA1-939 ,algoritmi ,ProBiS ,Engineering (miscellaneous) ,grafi ,Mathematics - Abstract
Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.
- Published
- 2022
47. Stability for Representations of Hecke Algebras of Type A
- Author
-
Kun Wang, Shanshan Qi, Haitao Ma, Zhujun Zheng, Wang, Kun [0000-0001-6664-0455], and Apollo - University of Cambridge Repository
- Subjects
Hecke algebra ,representations ,representation stable ,General Mathematics ,Mathematics::Quantum Algebra ,Mathematics::Number Theory ,Computer Science (miscellaneous) ,QA1-939 ,Mathematics::Representation Theory ,Engineering (miscellaneous) ,Mathematics - Abstract
In this paper, we introduce the concept of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence of the representations of Hecke algebras is representation stable.
- Published
- 2022
48. Incorporating ‘Mortgage-Loan’ Contracts into an Agricultural Supply Chain Model under Stochastic Output
- Author
-
Liurui Deng, Shuge Wang, Yixuan Wen, and Yuting Li
- Subjects
output uncertainty ,agricultural supply chain ,assets mortgage ,General Mathematics ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,risk sharing ,Mathematics - Abstract
This paper constructs an internal financing model in which the purchaser acts as the core leading enterprise to provide loans when the farmer has fixed assets as collateral. Numerical results show that the existence of fixed assets will increase the expected profit of the farmer, redistributing the risk and profit between the purchaser and the farmer. At the same time, the purchaser and the government are encouraged to provide more funds to the farmer with low value of its fixed assets, which will aid the overall return of the supply chain and the development of supply chain finance. In addition, under the framework of this model, the increase of agricultural production is beneficial to the farmer, not the purchaser. In the case of the same output level, we can alleviate this problem by selecting high-end agricultural products with high price elasticity of demand and high choking price so as to improve the profits of both purchaser and farmer.
- Published
- 2022
49. A Hybrid Novel Fuzzy MCDM Method for Comprehensive Performance Evaluation of Pumped Storage Power Station in China
- Author
-
Peipei You, Sijia Liu, and Sen Guo
- Subjects
pumped storage power station ,hybrid fuzzy MCDM ,comprehensive performance evaluation ,fuzzy best worst method ,fuzzy TOPSIS ,General Mathematics ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,Mathematics - Abstract
Considering the goals of carbon peaking and carbon neutrality, along with their related policies, pumped storage power stations are set to develop quickly in China. The comprehensive performance of pumped storage power stations must urgently be evaluated, which can help investors in decision making and provide a reference for policymakers. In this paper, a hybrid novel fuzzy multicriteria decision-making (MCDM) method combining the fuzzy best worst method (BWM) and fuzzy TOPSIS was proposed for the comprehensive performance evaluation of pumped storage power stations in China. The fuzzy BWM was utilized to determine the criteria weights describing the comprehensive performance of pumped storage power stations, while the fuzzy TOPSIS was used to rank the comprehensive performance of pumped storage power stations. The index system for the comprehensive performance evaluation of pumped storage power stations in China incorporated economic, social, and environmental aspects. The comprehensive performance of four pumped storage power stations in China was empirically evaluated using the proposed hybrid novel fuzzy MCDM method, and the results indicate that pumped storage power station PSPS2 exhibited the best comprehensive performance, followed by pumped storage power stations PSPS1 and PSPS4, whereas pumped storage power station PSPS3 had the worst comprehensive performance. A sensitivity analysis and comparative analysis were also conducted. The results indicate that the proposed hybrid novel fuzzy MCDM method, combining the fuzzy BWM and fuzzy TOPSIS for comprehensive performance evaluation of pumped storage power stations, is robust and effective.
- Published
- 2022
50. A Novel Maximum Mean Discrepancy-Based Semi-Supervised Learning Algorithm
- Author
-
Qihang Huang, Yulin He, and Zhexue Huang
- Subjects
semi-supervised learning ,maximum mean discrepancy ,distribution consistency ,self-training ,co-training ,General Mathematics ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,Mathematics - Abstract
To provide more external knowledge for training self-supervised learning (SSL) algorithms, this paper proposes a maximum mean discrepancy-based SSL (MMD-SSL) algorithm, which trains a well-performing classifier by iteratively refining the classifier using highly confident unlabeled samples. The MMD-SSL algorithm performs three main steps. First, a multilayer perceptron (MLP) is trained based on the labeled samples and is then used to assign labels to unlabeled samples. Second, the unlabeled samples are divided into multiple groups with the k-means clustering algorithm. Third, the maximum mean discrepancy (MMD) criterion is used to measure the distribution consistency between k-means-clustered samples and MLP-classified samples. The samples having a consistent distribution are labeled as highly confident samples and used to retrain the MLP. The MMD-SSL algorithm performs an iterative training until all unlabeled samples are consistently labeled. We conducted extensive experiments on 29 benchmark data sets to validate the rationality and effectiveness of the MMD-SSL algorithm. Experimental results show that the generalization capability of the MLP algorithm can gradually improve with the increase of labeled samples and the statistical analysis demonstrates that the MMD-SSL algorithm can provide better testing accuracy and kappa values than 10 other self-training and co-training SSL algorithms.
- Published
- 2022
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