Бидний тухай
Багш ажилтан
Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials with thermal memory, wave propagation in viscoelastic media, and charge transport in spatially heterogeneous semiconductor devices. In this study, we investigate a class of time-fractional telegraph systems with spatially varying coefficients using Lie symmetry analysis and the Riemann–Liouville fractional derivative. We establish a complete Lie group classification for sufficiently differentiable coefficient functions and determine all functional forms that admit such symmetry extensions. The symmetry structure is shown to depend fundamentally on the relationship between the transport coefficient and the potential function, resulting in three distinct symmetry classes. For each case, optimal systems of one-dimensional Lie subalgebras are constructed, and the governing fractional partial differential equations are systematically reduced to fractional ordinary differential equations. Exact invariant solutions are obtained in closed form and expressed in terms of Mittag–Leffler functions, generalized Wright functions, and Fox H-functions. These analytical solutions provide valuable insights into fractional telegraph-type transport phenomena and serve as important benchmarks for validating numerical methods in industrial transport modeling and fractional evolution systems.
In this note, we revisit the classical question of which integers can be repre- sented as norms of algebraic integers in a given Euclidean quadratic field. We present a proof based on basic properties of finite groups.
This talk addresses the construction of Whittaker functions for the principal series representations of SU( 2, 2). We analyze the holonomic system of differential equations associated with higher-dimensional minimal K-types and derive explicit solutions for specific classes of these functions.
In this talk we focus on the eigenspaces of (τµ,Vµ) which are parametrized by the set G(µ) of the Gelfand-Tsetlin patterns. These patterns are triangular arrays of integers and one can choose a basis (up to scalar multiples) in Vµ parametrized by the set G(µ).
This talk discusses several new aspects of Kummer theory arising from twisted forms of the group of roots of unity and their relation to algebraic tori. Classical Kummer theory describes cyclic extensions through the exact sequence associated with the multiplicative group, but this approach requires the base field to contain the corresponding roots of unity. When this assumption fails, the structure becomes substantially more complicated. The main goal of this work is to study analogous constructions in the quadratic twisted setting and to obtain explicit descriptions of the corresponding Galois cohomology.
2020 онд хэвлэгдсэн "A generalized Combinatorial Nullstellensatz for multisets" нэртэй өгүүллээ тайлбарлана.
Энэхүү илтгэлд алдарт Ландау-Зигелийн тэгүүдийн таамаглал түүний ач холбогдол болон сүүлийн үед батлагдсан үр дүнгийн талаар тайлбарлана.
Рациональ тоон талбар дээрх төгсгөлөг бүлгийн дүрслэлийн хамгийн бага боломжит хэмжээс нь тухайн бүлгийн”essential dimension”-тэй ижил байх таамаглалыг энд авч үзэх болно.
We study a class of linear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of group invariant solutions of this class of systems.
In this talk we focus on the eigenspaces of (τµ,Vµ) which are parametrized by the set G(µ) of the Gelfand-Tsetlin patterns. These patterns are triangular arrays of integers and one can choose a basis (up to scalar multiples) in Vµ parametrized by the set G(µ).
Жорж Блүман, Сүкэюүки Күмейнар1987 онд utt = c2(x)uxx хувьсах коеффициенттэй долгионы тэгшитгэл болон харгалзах ut = c2(x)vx, vt = ux системийн бүлгэн ангилал болон зарим инвариант шийдүүдийг олсон. Бид нар долгионы тэгшитгэлийн харгалзах системийн хугацаагаар бутархай эрэмбийн уламжлалтай өргөтгөлийг судалж, бүлгэн хувиргалтаар инвариант байдаг зарим шийдийг аналитик хэлбэрээр өгсөн.
Суурь талбар нэгжийн примитив язгуурыг агуулсан үед цикл өргөтгөлүүд Куммер онолоор тайлбарлагддаг. Энэ илтгэлд суурь талбар примитив язгуурыг агуулаагүй то- хиолдлыг авч үзэх болно.
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 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 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 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.
On the representation of primes by quadratic norm forms
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.
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).
