scholarly journals On uniqueness of p-adic period morphisms, II

2020 ◽  
Vol 156 (9) ◽  
pp. 1915-1964
Author(s):  
Wiesława Nizioł

We prove equality of the various rational $p$-adic period morphisms for smooth, not necessarily proper, schemes. We start with showing that the $K$-theoretical uniqueness criterion we had found earlier for proper smooth schemes extends to proper finite simplicial schemes in the good reduction case and to cohomology with compact support in the semistable reduction case. It yields the equality of the period morphisms for cohomology with compact support defined using the syntomic, almost étale, and motivic constructions. We continue with showing that the $h$-cohomology period morphism agrees with the syntomic and almost étale period morphisms whenever the latter morphisms are defined (and up to a change of Hyodo–Kato cohomology). We do it by lifting the syntomic and almost étale period morphisms to the $h$-site of varieties over a field, where their equality with the $h$-cohomology period morphism can be checked directly using the Beilinson Poincaré lemma and the case of dimension $0$. This also shows that the syntomic and almost étale period morphisms have a natural extension to the Voevodsky triangulated category of motives and enjoy many useful properties (since so does the $h$-cohomology period morphism).

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):  
Philip Isett

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.


2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps


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.


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