Бидний тухай
Багш ажилтан
Энэхүү илтгэлд 1948 онд батлагдсан Selberg-ийн анхны тооны теоремын элементар баталгааг тайлбарлана.
In this talk, we present a class of trinomials over the finite field 𝔽q of odd order q. We show that the class contains an irreducible trinomial and establish an irreducibility criterion, analogous to the well-known Serret's irreducibility criterion, for the class of trinomials.
In this talk we are concerned with Lagrange's resolvents arising from two-dimensional Kummer Sequences. Using resolvents, we construct cyclic polynomials and establish an irreducibility criterion, analogous to the well-known Vahlen-Capelli’s criterion. As an application, we present a class of irreducible trinomials over finite fields of odd order.
In this work we studied a generalized Fisher equation in cylindrical coordinate using Lie symmetry method. We have determined for what type of source function the generalized Fisher equation has Lie Symmetries other than time translation symmetry when the diffusion function is given by an exponential function. Also the reduced ordinary differential equations are obtained corresponding to Lie symmetries of the generalized Fisher equation.
In this article, we study the group analysis of time fractional generalized Fisher equations. The generalized equation includes nonlinear heat and wave equations with a source as particular cases. A complete group classification is obtained and we also constructed group invariant solutions corresponding to infinitesimal symmetries. Explicit solutions had been found for some cases.
In this presentation we will discuss results of recent work on two dimensional Kummer theory. In particular, a family of cyclic polynomials in the optimal number of parameters will be presented. Here the base field is assumed to be an index 2 subfield of a cyclotomic extension of an arbitrary field.
Нэгжийн n зэргийн язгуурыг агуулсан талбарын цикл өргөтгөлийг ангилах асуудал сонгодог Куммерийн олон гишүүнтээр бүрэн тайлбарлагддаг. Энэ илтгэлд нэгжийн n зэргийн язгуурыг агуулаагүй тодорхой талбаруудын хувьд Куммерийн теоремын аналоги оршин байдаг тухай үр дүнг тайлбарлана.
A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi in 1996. The investigated system of partial differential equations generalizes the Gauss-Aomoto-Gelfand system. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of 2 2 matrices of derivations with respect to certain variables. The Gauss- Aomoto-Gelfand hypergeometric system arises in numerous problems of algebraic geometry, partial differential equations, the theory of special functions and combinatorics. H. Sekiguchi generalized this construction by looking at determinants of ll matrices of derivations with respect to certain variables. In this poster we studied the dimension of global solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems.
In this talk we discuss a simple formula for the number of matching p-ary digits of certain terms of Lucas sequences for any odd prime p. Using this formula, we present a simple sufficient condition for the sequence (vp(a1^n +a2^n +· · ·+ak^n ))n≥0 to be unbounded, where a1, a2, . . . , ak (k ≥ 2) are given integers and vp is the p-adic valuation.
In this paper, we study algebraic properties of a family of certain polynomials arising from the functional equation for Dickson polynomials. We see that the roots and discriminants of those polynomials have very simple expressions, and each polynomial is cyclic. Further, we provide an irreducibility criterion analogous to the well-known criterion of Vahlen-Capelli. We finish the paper by showing that any cyclic extension of a certain field comes from a member of the family.
Хоорондох зай нь 2 байх анхны тоонуудыг ихэр анхны тоо гэдэг ба ихэр анхны тоонууд төгсгөлгүй олон байх уу? гэдэг асуудал нь тооны онолын хамгийн эртний алдартай асуудлуудын нэг юм. Энэхүү асуудал нь одоогоор шийдэгдээгүй байгаа боловч хоорондох зай нь 70 саяас ихгүй төгсгөлгүй олон анхны тоо оршино гэсэн гайхалтай үр дүнг Хятадын математикч Zhang 2013 онд баталжээ. Zhang-ийн үр дүнгийн дараа нь Terence Tao тэргүүтэй математикчид нийлэн polymath7 төс- лийг эхлүүлэн дараа дараагийн чухал үр дүнгүүдийг 2014-2015 онуудад баталсан. Тэдний үр дүн нь энэхүү илтгэлийн хүрээнд дээрх үр дүнгүү- дийг товч танилцуулна.
On the representation of primes by quadratic norm forms
Алгебрлаг бүлгийн салшгүй хэмжээсийн талаарх ойлголтыг тайлбарлаж, p^n эрэмбийн twisted Галуагийн үйлчлэлтэй μ_p^n бүлгийн хувьд нэгэн шийдэгдээгүй асуудлыг толилуулна. Уг асуудлын тооны онол дахь ач холбогдол, уг асуудлыг тодорхой нөхцөлтэйгөөр баталсан судалгааны үр дүнгээ танилцуулна.
The Combinatorial Nullstellensatz is one of the most powerful algebraic tools in combinatorics. The aim of this paper is to prove an extension of the Combinatorial Nullstellensatz for multisets due to Kós–Rónyai. Our generalization gives an improvement on the size of sets chosen in the statement of Combinatorial Nullstellensatz for some polynomials.
The Combinatorial Nullstellensatz is one of the most powerful algebraic tools in combinatorics. The aim of this paper is to prove an extension of the Combinatorial Nullstellensatz for multisets due to Kós–Rónyai. Our generalization gives an improvement on the size of sets chosen in the statement of Combinatorial Nullstellensatz for some polynomials.
We explicitly describe the (g,K)-module structures of the principal series representations of SU(2,2) associated with a maximal parabolic subgroup.
We give explicit formulas for certain Jacquet integrals on some standard principal series representations of the group SU(2, 2).
