Indian Institutes of Science Education and Research

About: Indian Institutes of Science Education and Research is a based out in . It is known for research contribution in the topics: Gravitational wave & LIGO. The organization has 584 authors who have published 731 publications receiving 40599 citations. The organization is also known as: IISERs.

Infinite image partition regular matrices - Solution in C-sets

Abstract: A finite or infinite matrix A is image partition regular provided that whenever $${\mathbb {N}}$$ is finitely colored, there must be some $$\vec {x}$$ with entries from $${\mathbb {N}}$$ such that all entries of $$A \vec {x}$$ are in the same color class. Comparing to the finite case, infinite image partition regular matrices seem more harder to analyze. The concept of centrally image partition regular matrices were introduced to extend the results of finite image partition regular matrices to infinite one. In this paper, we shall introduce the notion of C-image partition regular matrices, an interesting subclass of centrally image partition regular matrices. Also we shall see that many of known centrally image partition regular matrices are C-image partition regular.

Heat Kernels, Bergman Kernels, and Cusp Forms

Abstract: In this article, we describe a geometric method to study cusp forms, which relies on heat kernel and Bergman kernel analysis. This new approach of applying techniques coming from analytic geometry is based on the micro-local analysis of the heat kernel and the Bergman kernel from [3] and [2], respectively, using which we derive sup-norm bounds for cusp forms of integral weight, half-integral weight, and real weight associated to a Fuchsian subgroup of first kind.

Irreducibility of integer-valued polynomials I

Abstract: Let $S \subset R$ be an arbitrary subset of a unique factorization domain $R$ and $\K$ be the field of fractions of $R$. The ring of integer-valued polynomials over $S$ is the set $\mathrm{Int}(S,R)= \{ f \in \mathbb{K}[x]: f(a) \in R\ \forall\ a \in S \}.$ This article is an effort to study the irreducibility of integer-valued polynomials over arbitrary subsets of a unique factorization domain. We give a method to construct special kinds of sequences, which we call $d$-sequences. We then use these sequences to obtain a criteria for the irreducibility of the polynomials in $\mathrm{Int}(S,R).$ In some special cases, we explicitly construct these sequences and use these sequences to check the irreducibility of some polynomials in $\mathrm{Int}(S,R).$ At the end, we suggest a generalization of our results to an arbitrary subset of a Dedekind domain.

Weighted estimates for maximal functions associated with finite type curves in R2

Abstract: In this paper we establish weighted estimates for the maximal function associated with the finite type curve in the plane R 2 . We follow an approach used by M. Lacey to obtain sparse bounds for the maximal function. Further, using a different approach we obtain a characterisation of power weights for the weighted L p boundedness of the maximal function. We also obtain analogous results for the lacunary maximal function associated with the finite type curve in the plane R 2 .

Study of $X(3872)$ and $X(3915)$ in $B\rightarrow(J/\Psi\omega)K$ at Belle

Abstract: We present a preliminary study of X(3872) and X(3915) in the \(B\rightarrow (J/\psi \omega )K\) decay at Belle. This study is based on MC simulated events on the Belle detector at the KEK asymmetric-energy \(e+e-\) collider.