expression of specific water resource areas in the arts 554 S. Kato and J. Ahern

INTRODUCTION. In a classical article, Hess and Kato [HK] study the problem

Here, τ(G) is roughly the volume of G(AK)/G(K) with respect to Haar measures on G(Kv) for all places v, where we have to use L-functions to make the product measure converge, and also have to restrict to measuring some “compact part” of G(Kv), by taking the kernel of all |χ|v, χ : G→ Gm. Now, let’s formulate a version of this for abelian varieties. For simplicity, assume that E is an elliptic c...

The so called Wilkinson’s Schur complement trick plays a prominent role in the theory of eigenvalue estimates for finite matrices. We apply this technique to the problem of obtaining Ritz value spectral estimates for a positive definite self-adjoint operator in a Hilbert space. New estimates have a form of a Temple–Kato like inequality and are particularly suited to a situation in which we are ...

Let A and B be non-negative self-adjoint operators in a separable Hilbert space such that its form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary times in the L-norm, that is, one has

We prove a localized non blow-up theorem of the Beale–Kato–Majda type for solution 3D incompressible Euler equations.

The Tamagawa number conjecture of Bloch and Kato describes the behavior at integers of the L-function associated to a motive over Q. Let f be a newform of weight k ≥ 2, level N with coefficients in a number field K. Let M be the motive associated to f and let A be the adjoint motive of M . Let λ be a finite prime of K. We verify the λ-part of the Bloch-Kato conjecture for L(A, 0) and L(A, 1) wh...

INTRODUCTION This study analyzed the performance of the Kato Katz technique in detecting intestinal schistosomiasis in the State of Pará. METHODS Of three stool samples provided by each of 380 participants, a total of 16 Kato Katz slides were examined to define the reference value (RV) of positives for comparisons. RESULTS The RV revealed 37 (9.7%) infected participants in contrast to 10 (2...

Let κ ≥ 6 be an even integer, M an odd square-free integer, and f ∈ S2κ−2(Γ0(M)) a newform. We prove that under some reasonable assumptions that half of the λ-part of the Bloch-Kato conjecture for the near central critical value L(κ, f) is true. We do this by bounding the l-valuation of the order of the appropriate Bloch-Kato Selmer group below by the l-valuation of algebraic part of L(κ, f). W...

The implementation of an automated data entry and report generation system using an optical scanner and commercially available image processing program is described. This method could be easily adapted for use in other fields of medical research where the compilation of a large amount of repetitive data is involved, such as the filling in of questionnaires. Using an optical scanner for data ent...