scholarly journals Infinite Gammoids: Minors and Duality

10.37236/5107 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Seyed Hadi Afzali Borujeni ◽  
Hiu-Fai Law ◽  
Malte Müller

This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minor-closed. Also, we prove that finite-rank minors of gammoids are gammoids. Furthermore, the topological gammoids of Carmesin (2014) are proved to coincide, as matroids, with the finitary gammoids. A corollary is that topological gammoids are minor-closed.It is a well-known fact that the dual of any finite strict gammoid is a transversal matroid. The class of strict gammoids defined by digraphs not containing alternating combs, introduced in Afzali Borujeni et. al. (2015), contains examples which are not dual to any transversal matroid. However, we describe the duals of matroids in this class as a natural extension of  transversal matroids. While finite gammoids are closed under duality, we construct a strict gammoid that is not dual to any gammoid. 


Author(s):  
V. Castano ◽  
W. Krakow

In non-UHV microscope environments atomic surface structure has been observed for flat-on for various orientations of Au thin films and edge-on for columns of atoms in small particles. The problem of oxidation of surfaces has only recently been reported from the point of view of high resolution microscopy revealing surface reconstructions for the Ag2O system. A natural extension of these initial oxidation studies is to explore other materials areas which are technologically more significant such as that of Cu2O, which will now be described.



Author(s):  
G.D. Danilatos

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.





Author(s):  
حنان ساري ◽  
محمد أبو الليث الخيرآبادي

انتشرت لفظة الحداثة في عصرنا الحالي انتشاراً واسعاً، وأخذت مفهومات متعددة، ونحن لا نراها أكثر من أنها امتداد طبيعي للقلق الأوروبي.وسعى التيار الحداثي لتقديم مشاريع تعتمد كلية على مناهج وآليات غربية في دراستها وتعاملها مع القرآن الكريم والسنة، ولعل أهم الذين تقدموا بتلك المشاريع؛ محمد أركون، عبد المجيد الشرفي التونسي، محمد عابد الجابري، حسن حنفي، نصر حامد أبوزيد، الطيب التيزني السوري، محمد شحرور، جمال البنا وغيرهم، وطالبوا بإعادة قراءة القرآن الكريم على ضوء المناهج النقدية الغربية في عملية التقليد الأعمى، ومن ثم نقلوا التجربة الأوروبية بكل آثارها الفوضوية إلى ساحة الفكر الإسلامي. وإن مدعي تجديد الدين من هؤلاء، ليس لهم صلة بالدين أو علومه، بقدر ما تشبعت أفكارهم بمناهج علمانية، فالمراد من جهودهم ليس الدين، وإنما غرس الحداثة بدل الدين، فهي خطَّةٌ تقوم على التَّغيير من داخل البيت الإسلاميِّ من خلال العبث بالنُّصوص الشَّرعيَّة بتحريفها وتفريغها من محتواها الحقيقيِّ، ووضع المحتوى الذي يريدون؛ فهم يَطرحون أفكارَهم وآراءَهم على أنَّها رؤى إسلاميَّة ناشئة عن الاجتهاد في فهم الدِّين. وقد حَمَلَ هذا الاتجاهُ شعار (التَّحديث والعصرنة للإسلام)؛ فهم يريدون منَّا تركَ ما أَجْمَعَتْ عليه الأُمَّةُ من معاني القرآن والسُّنَّة، لفهم جديد مغاير لفهم السَّلَف الصَّالح يكون متناسبًا مع هذا العصر الذي نعيش فيه. الكلمات المفتاحيّة: الحداثة، أوهام، الحداثيون، قراءة معاصرة، العصرنة للإسلام. Abstract In modern times, the word Modernity has spread widely and has become widely understood, and we see it as a natural extension of European concern and confusion. The Modernist Movement strived to present the ideas that rely completely on Western methodologies and approaches in their study and dealing with Qur’an and Sunnah. The most important scholars that have presented these ideas are; Mohammad Arkoun, ‘Abd Al-Majid Sharafi al-Tunisi, Mohammed ‘Abed al-Jabri, Hassan Hanafi, Nasr Hamid Abu Zayd, Tayyeb Tizini, Muhammad Shahrour, Jamal Al-Banna, and others, they called for a re-reading and reinterpret the Qur’an in the light of Western critical approaches. Then, conveyed and brought the European experience and practice with all its chaotic effects to Islamic thought. The slogan of “Renewal of Religion” from these people has no relation to religion (Islam) or its sources, but instead saturated their ideas with secular methods. They tried to instill modernity rather than religion, and misinterpreted the Islamic sources by distorting it and evacuating it from the true context and setting it with their own understanding. They claim their ideas and opinions as the effort to understand religion and carried the slogan of “Modernization and Modernization of Islam”; they want us to leave the consensus of the Muslim scholars on religious issues (Ijmaa’ al-Ummah) especially relating to the meaning of the Qur’an and Sunnah and bring us to a new views and understanding on religious issues which are contradictory to the views of the past Muslim scholars (al-salaf al-soleh) to fulfill their opinions. Keywords: Modernity, Misunderstanding, Modernists, Contemporary Reading, Modernization of Islam.



Author(s):  
Daniel Canarutto

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.



2017 ◽  
Vol 26 (12) ◽  
pp. 1750081
Author(s):  
Sang Youl Lee

In this paper, we introduce a notion of virtual marked graphs and their equivalence and then define polynomial invariants for virtual marked graphs using invariants for virtual links. We also formulate a way how to define the ideal coset invariants for virtual surface-links using the polynomial invariants for virtual marked graphs. Examining this theory with the Kauffman bracket polynomial, we establish a natural extension of the Kauffman bracket polynomial to virtual marked graphs and found the ideal coset invariant for virtual surface-links using the extended Kauffman bracket polynomial.



Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.



2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Graham A. Niblo ◽  
Nick Wright ◽  
Jiawen Zhang

AbstractThis paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of $$\delta $$ δ -hyperbolicity.



2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ha-Bang Ban ◽  
Phuong Khanh Nguyen

AbstractThe Asymmetric Distance-Constrained Vehicle Routing Problem (ADVRP) is NP-hard as it is a natural extension of the NP-hard Vehicle Routing Problem. In ADVRP problem, each customer is visited exactly once by a vehicle; every tour starts and ends at a depot; and the traveled distance by each vehicle is not allowed to exceed a predetermined limit. We propose a hybrid metaheuristic algorithm combining the Randomized Variable Neighborhood Search (RVNS) and the Tabu Search (TS) to solve the problem. The combination of multiple neighborhoods and tabu mechanism is used for their capacity to escape local optima while exploring the solution space. Furthermore, the intensification and diversification phases are also included to deliver optimized and diversified solutions. Extensive numerical experiments and comparisons with all the state-of-the-art algorithms show that the proposed method is highly competitive in terms of solution quality and computation time, providing new best solutions for a number of instances.



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