Autumn 1396

IASBS Mathematics Colloquium

Spring 1396

1396-01-29
Speaker: Ali Ebadian (Payame Noor University)
Title: On the geometric function theory
Abstract: ---

1396-02-12
Speaker: Fahimeh Kolahdouz (Ferdowsi University of Mashhad)
Title:
عملکرد دانشجویان در فرایند اثبات‌ ریاضی چگونه است؟
Abstract:
زمانی که دانش‌آموزان برای تحصیل در دوره لیسانس از دبیرستان وارد دانشگاه می‌شوند، تغییرات زیادی در شرایط آموزش و یادگیری آنها رخ می‌دهد. اغلب مطالعات نشان می‌دهند که دانشجویان، ‌بویژه کسانی که تازه از دبیرستان وارد دانشگاه می‌شوند، در ارتباط با بسیاری از فرایندهای ریاضی به‌ویژه اثبات‌های ریاضی با مشکلات جدّی مواجه هستند (سلدن، 2011، باردله و مارتینو، 2012). در این سمینار می‌خواهیم بر اساس مطالعات و تحقیقات در آموزش ریاضی، پیرامون این مشکلات صحبت نماییم.

1396-02-19
Speaker: Ashkan Nikseresht (IASBS)
Title: Dual of codes over finite quotients of polynomial rings
Abstract: In this talk, first we briefly review the basics and importance of the theory of codes over finite rings; then, assuming that $A=F[x]/f(x)$ where F is a finite field and $f(x)$ is a monic polynomial in $F[x]$, we present a "good generating set" for a linear A-code and also one for its dual. We give efficient algorithms for finding these generating sets and mention some relations with the theory of Grobner bases. Finally, if time allows, we show how these results could be used to find some self-dual $A$-codes and answer the question "when $F$-dual of every $A$-code is again an $A$-code?"

1396-02-26
Speaker: Fazlollah Soleymani (IASBS)
Title: Pricing European and American options via Meshfree Schemes
Abstract: In this work, we apply the local Wendland radial basis function (RBF) for solving the time-dependent multi dimensional option pricing PDEs. Firstly, cross derivative terms of the PDE are removed with a change of spatial variables based in $LDL^T$ factorization of the diffusion matrix. Then, it is discussed that the valuation of a multi-asset option up to 4D can be computed accurately using a modified shape parameter algorithm. Several experiments from the market containing are worked.

1396-03-02
Speaker: Hadi Khatibzadeh (University of Zanjan)
Title: Firmly nonexpansive mappings and resolvents
Abstract: In this talk we start Baillon's nonlinear ergodic theorem and discuss the behavior of orbits of nonexpansive and firmly nonexpansive mappings. Then, we present some examples of firmly nonexpansive mappings which have applications in fixed point theory, convex optimization and monotone operator theory. These examples are often resolvents of nonexpansive mappings, convex functions and monotone operators. We also study the asymptotic behavior of resolvents and strong convergence results. Finally we will have a brief look at nonexpansive semigroups.

1396-03-02 (Special Talk)
Speaker: Reza Naserasr (Laboratoire de Recherche en Informatique (LRI), France)
Title: Mapping planar graphs to the projective cubes
Abstract: We consider a conjecture in extension of the four-color theorem which claims every planar graph of odd-girth $2k+1$ admits a homomorphism to the projective cube of dimension $2k$. In support of the conjecture we prove that any partial $3$-tree of odd-girth $2k+1$ maps to projective cube of dimension $2k$.

1396-03-09
Speaker: Mohammad Yaghoub Rahimi Ardabili (University of Tabriz)
Title:
نگاهی کوتاه بر نجوم کروی و کاربرد آن
Abstract:
برای درک نجوم کروی دانستن مقدمات مثلثات کروی ضروری است. لذا در قسمت نخست به تعریف مثلث کروی و روابط اساسی آن می‌پردازیم و با ارائه فرمول‌های دالامبر و نپر کاربرد مثلثات کروی را در جهت‌یابی و در حالت خاص در قبله‌یابی بیان می‌کنیم. قسمت دوم به موضوع اساسی نجوم کروی اختصاص دارد. بعد از ارائه تعاریف مختصات محل (ارتفاع و سمت)، میل و زاویه ساعتی یک ستاره، به مسئله طلوع و غروب و محاسبه طول روز و حرکت ظاهری خورشید می‌پردازیم. در خاتمه با ارائه تعریف شفق و فلق، محاسبه اوقات شرعی بیان می‌گردد.

1396-03-23
Speaker: Mohammad Farrokhi Derakhshandeh Ghouchan (IASBS)
Title: Numbers and their sums of digits (in different bases)
Abstract: Studying different numbers in a given base is an old and well-studied problem in the theory of numbers. We study the opposite situation of writing a number in different bases, and describe the asymptotic behavior of the number of the corresponding digit sums, which illustrates a nice relationship between variety of digit sums and primes.