Dirichlet Forms and Brownian Motion Penetrating Fractals

Can a Brownian motion penetrate the two-dimensional Sierpinski gasket? This question was studied in [8], and an affirmative answer was given. In this paper, the problem is studied with a different approach, using Dirichlet forms and function space theory. The results obtained are somewhat different from, and from certain aspects more general than, the results in [8].

     

Invariants of trace forms in odd characteristic and authentication codes

We complete A. Klapper's work on the invariant of a one-term trace form over a finite field of odd characteristic. We apply this to computing the probability of a successful impersonation attack on an authentication code proposed by C. Ding et al. (2005).     

A modularity criterion for Klein forms, with an application to modular forms of level 13

We find some modularity criterion for a product of Klein forms of the congruence subgroup Γ₁(N) (Theorem 2.6) and, as its application, construct a basis of the space of modular forms for Γ₁(13) of weight 2 (Example 3.4). In the process we face with an interesting property about the coefficients of certain theta function from a quadratic form and prove it conditionally by applying Hecke operators (Proposition 4.3).     

Three Spectrophotometric Methods for the Determination of Oxomemazine Hydrochloride in Bulk and in Pharmaceutical Formulations Using Bromocresol Green,Congo Red,and Methyl Orange

Abstract

Three simple, sensitive, and highly accurate spectrophotometric methods have been developed for the determination of oxomemazine hydrochloride (OXO‐HCl) in bulk and in pharmaceutical formulations. These methods are based on the formation of yellow ion‐pair complexes between the examined drug and bromocresol green (BCG), congo red (CR), and methyl orange (MO) as reagents in universal buffer solution of pH 3.0, 5.5, and 3.5, respectively. The formed complexes were extracted with chloroform and measured at 413, 495, and 484 nm, respectively for the three systems. The best conditions of the reaction were studied and optimized. Beer's law was obeyed in the concentration ranges 2.0–18.0, 2.0–14.0, and 2.0–16.0 µg ml^?1 with molar absorptivity of 4.1×10⁴, 1.1×10⁴, and 3.5×10⁴ mol^?1cm^?1, for the BCG, CR, and MO methods, respectively. Sandell's sensitivity, correlation coefficient, detection, and quantification limits are also calculated. The proposed methods have been applied successfully for the analysis of the drug in pure and in its dosage forms. No interference was observed from common pharmaceutical excipients and additives. Statistical comparison of the results with those obtained by HPLC method shows excellent agreement and indicates no significant difference in accuracy and precision.     

Fractional Nambu Mechanics

The fractional generalization of Nambu mechanics is constructed by using the differential forms and exterior derivatives of fractional orders. The generalized Pfaffian equations are obtained and one example is investigated in details. On leave of absence from Institute of Space Sciences, P.O. Box, MG-23, 76900, Magurele-Bucharest, Romania.     

Weierstrass points on X 0(p ℓ) and arithmetic properties of Fourier coefficients of cusp forms

Generally it is unknown, whether or not ∞ is a Weierstrass point on the modular curve X ₀(N) if N is squarefree. A classical result of Atkin and Ogg states that ∞ is not a Weierstrass point on X ₀(N), if N=pM with p prime, p ∤ M and the genus of X ₀(M) zero. We use results of Kohnen and Weissauer to show that there is a connection between this question and the p-adic valuation of cusp forms under the Atkin–Lehner involution. This gives, in a sense, a generalization of Ogg’s Theorem in some cases.      

Invariants of Directed Spaces

Directed spaces are the objects of study within directed algebraic topology. They are characterised by spaces of directed paths associated to a source and a target, both elements of an underlying topological space. The algebraic topology of these path spaces and their connections are studied from a categorical perspective. In particular, we study the preorder category associated to a directed space and various “quotient” categories arising from algebraic topological functors. Furthermore, we propose and study a new notion of directed homotopy equivalence between directed spaces.      

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.      

STRONG SUBORDINATION OF SYMMETRIC DIRICHLET FORMS

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On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.