Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalue...

A classical result of Aleksandrov allows one to estimate the size of a convex function u at a point x in a bounded domain Ω in terms of the distance from x to the boundary of Ω if R Ω det Du dx < ∞. This estimate plays a prominent role in the existence and regularity theory of the Monge-Ampère equation. Jerison proved an extension of Aleksandrov’s result that provides a similar estimate, in som...

Abstract. Let A (ε) be an analytic square matrix and λ0 an eigenvalue of A (0) of multiplicity m ≥ 1. Then under the generic condition, ∂ ∂ε det (λI −A (ε)) |(ε,λ)=(0,λ0) 6= 0, we prove that the Jordan normal form of A (0) corresponding to the eigenvalue λ0 consists of a single m × m Jordan block, the perturbed eigenvalues near λ0 and their eigenvectors can be represented by a single convergent...

We begin by recalling standard facts concerning Hecke algebras and modular forms, for details of which the reader is referred to Chapter 3 of Shimura’s book [11]. By definition H (in Shimura’s notation, R(Γ, GL2(Q) )⊗Q) is the Q-algebra spanned by double cosets [ΓγΓ], for γ ∈ GL2(Q) with det γ > 0. Write as usual Mk(Γ) for the complex vector space of holomorphic modular forms of weight k ≥ 0, a...

Recently, vector-borne diseases have been resurging in endemic areas and expanding their geographic range into nonendemic areas. Such changes have refocused attention to the potential for major public health events, as naive populations are exposed to these pathogens. Personal topical repellents, recommended by the United States Centers for Disease Control and Prevention and World Health Organi...

on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...

For the use of topical insect repellents, DEET and picaridin, human health risk assessments were conducted for various population subgroups. Acute, subchronic, and chronic dermal exposures were examined. No-observed-effect-levels (NOELs) of 200, 300, and 100mg/kg body weight (BW) were used as endpoints for DEET for acute, subchronic, and chronic exposures, respectively. For picaridin, a NOEL of...

The simplest objects with non-commutative multiplication may be 2 × 2 matrices with real entries. Such matrices of determinant one form a closed set under multiplication (since det(AB) = detA · detB), the identity matrix is among them and any such matrix has an inverse (since detA 6= 0). In other words those matrices form a group, the SL2(R) group [8]— one of the two most important Lie groups i...

We shall begin by recalling some material from quadrics1.pdf, which gave the classification of hyperquadrics in R and C up to affine equivalence: CONGRUENCE OR ISOMETRY CLASSIFICATION PROBLEM. Given two affine hyperquadrics Σ1 and Σ2 in R , is there a congruence or isometry T from R to itself mapping Σ1 onto Σ2? There are two possible versions of the question. An arbitrary isometry T from R to ...

Applicat,ioli of niactiirie inductiori l,cx-tlrliques in corriplcx doltlailis promises to push the computational limits of nofiincrc~rnerila.1, search ilitensive induction methods. 1,earning t~ff;~ctiverlcss in complex domains requires the developrrlerlt of iricrorrierital, cost effective methods. However, discussion 01 ciinierisioris fi>r corriparirig I,he utilily of diffcrirrg increrr~e~~tal ...