Spectral asymptotics for the Schrödinger operator with a non-decaying potential

We study Schrödinger operators H ( h ) = − h 2 Δ + V ( x ) acting in L 2 ( R n ) for non-decaying potentials V. We give a full asymptotic expansion of the spectral shift function for a pair of such operators in the high energy limit. In particular for asymptotically homogeneous potentials W at infinity of degree zero, we also study the semiclassical asymptotics to give a Weyl formula of the spectral shift function above the threshold max W and Mourre estimates in the range of W except at its critical values.

Extended Graph of the Fuzzy Topographic Topological Mapping Model

Fuzzy topological topographic mapping (FTTM) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. The generated FTTMs can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the FTTM components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated FTTM pseudo degree zero with respect to n number of components and k number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture.

INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS

For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compact Riemann surface C and of the moduli space of G-Higgs bundles on C of degree zero. We derive several results concerning the P=W conjectures for these singular moduli spaces.

الاكتئاب وعلاقته بالتدين لدى طلبة الجامعة

اقتصر البحث على عينة مؤلفة من (400) طالب وطالبة من طلبة جامعتي القادسية والكوفة لكلا الجنسين (ذكور, وإناث)، والتخصص (العلمي, والإنساني) للعام الدراسي (2019-2020) وقد تم تطبيق المقاييس عليهم الكترونياً بسبب جائحة كورونا, ولتحقيق أهداف البحث الحالي تبنى الباحث مقياس بيك للاكتئاب من اعداد (Beck , 1984) تعريب الغريب (2000)، وبعد استخراج الخصائص السيكومترية للمقياس من صدق وثبات اصبح المقياس بصيغته النهائية يتكون (21) فقرة , امام كل فقرة اربعة بدائل يختار المفحوص البديل الذي ينطبق عليه ، تتراوح درجة البدائل من (صفر) الى (3) وفق للبديل الذي يقترب أو يبتعد عن قياس الاكتئاب ، لذا فإنَّ أعلى درجة يمكن أنَّ يحصل عليها المجيب في المقياس تكون (63) درجة وأدنى درجة (صفر) في حين يبلغ الوسط الفرضي للمقياس (31,5). واظهرت النتائج الاتي -ان عينة البحث يمتلكون الاكتئاب بمستوى ضعيف . تتمتع العينة بمستوى عالي من التدين، وان متوسط درجات أفراد العينة على مقياس التدين كان دال إحصائية.توجد علاقة بين الاكتئاب والتدين هي علاقة عكسية دالة احصائيا, وهذا يعني انه كلما كان مستوى الاكتئاب منخفضا لدى عينة البحث ارتفع مستوى التدين لديهم. Abstract: The research was limited to a sample of (400) male and female students from the Universities of Al-Qadisiyah and Kufa for both sexes (males and females), and specialization (scientific and humanitarian) for the academic year (2019-2020), and the standards were applied to them electronically due to the Corona pandemic, and to achieve Objectives of the current research The researcher adopted the Beck depression scale prepared by (Beck, 1984) Arabization of the stranger (2000), and after extracting the psychometric properties of the scale from validity and reliability, the scale became in its final form consisting of (21) items In front of each paragraph there are four alternatives, the examinee chooses the alternative that applies to him. The degree of the alternatives ranges from (zero) to (3) according to the alternative that approaches or moves away from measuring depression. Therefore, the highest score that the respondent can obtain on the scale is (63) degrees and the lowest. degree (zero), while the hypothetical mean of the scale is (31.5). The results showed the following .The research sample has depression at a weak level. The sample has a high level of religiosity, and the average scores of the sample members on the religiosity scale were statistically significant. There is a relationship between depression and religiosity is a statistically significant inverse relationship, which means that the lower the level of depression in the research sample, the higher their level of religiosity.

The degree zero of digital interfaces: a semiotics of audiovisual archives online

Interfaces have partially replaced editors. They now administer and have industrialized the processes of content circulation. Web platforms mediatize cultural memory and one example of this is that of online audiovisual archives which are a paradigmatic case involving interfaces mediating our image of the past. Therefore, their role as an enunciative framework is clearly worthy of thought and study. We will thus use a semiotic approach based on the starting hypothesis that digital interfaces shape our belief systems through a discursive framing of content to which they give access. By analyzing two case studies, we will argue that the transparency of interfaces appears to recall the notion of “mechanical objectivity” and thus refashion the reliability of the archives. However, a final counter-analysis of a document read in the framework of an on-site consultation invites us to reshape our considerations and enlarge the perspective from semiotic visual analysis to include the social processes linked to the publication of digital heritage.

Roland Barthes : pour une écologie de l'écriture

Roland Barthes: For an Ecology of Writing Abstract Even if the theoretical prestige of the notion of ecology is recent, an ecological writing has already been racticed, without receiving this name, by Roland Barthes. On several occasions, progressively after Writing Degree zero (1953), Roland Barthes envisaged writing as a multifaceted practice, the most suitable for overturning the only order worth to be revolutionized, the symbolic order. We will take a fresh look at Barthes' writing as a theoretical concept in the early 1950s, along a shift that takes the term first to the name of a technique. Finally, in the mid-1970s, writing comes to be defined by Barthes as a practice that ignores the dichotomy between matter or body and mind or idea, and which arrives, in a spiral return movement, at an inclusive conception that recovers both the concept and the practice. This is where writing meets, in Barthes' work, the act that Latour calls "greening" and which he defines above all as a new relationship between facts and values. In the light of the latest research in "Barthesian studies" we would like to show that the future of "theory", if it is ecology today, lies in the practice and ecological commitment of writing, as a mediator of meaning, a tool of "charitable fiction", at the confines of spirit and matter.

Aporia in Umayyad Art or the Degree Zero of the Visual Forms’ Meaning in Early Islam

This article re-examines the established findings about Umayyad art as a transitional production essentially anchored in the Western and Eastern Late Antique traditions that have inspired it. It argues instead that the Umayyads brought about an aesthetic revolution laying out the foundations of what has become known as “Islamic ornament,” a predominantly aniconic art form. An epistemological shift from art history to critical inquiry allows us to show that, beyond the adaptive borrowing of pre-existing forms, the Umayyads redefined the art’s condition of meaning based on an unprecedented attitude to images and visual discourse informed by Islamic ontotheology and logocentric metaphysics.