The detour pebbling number of a graph \(G\) is the least positive integer \(f^{*}(G)\) such that these pebbles are placed on vertices \(G\), we can move pebble to target vertex by sequence moves each taking two off and placing one an adjacent using path. In this paper, compute for commutative ring zero-divisor graphs, sum product zero divisor graphs.

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product R1 × R2 × · · · × Rn with respect to the diameters of the zero-divisor graphs of R1, R2, · · · , Rn−1 and Rn(n > 2).

A characterization of nef and good divisors is given: a divisor D on a smooth complex projective variety is nef and good if and only if the asymptotic multiplier ideals of sufficiently high multiples of e(D)·D are trivial, where e(D) denotes the exponent of the divisor D. Some results of the same kind are proved in the analytic setting.

We make an observation which enables one to deduce the existence of an algebraic stack of log maps for all generalized Deligne– Faltings log structures (in particular simple normal crossings divisor) from the simplest case with characteristic generated by N (essentially the smooth divisor case).

Some divisor class relations for genus 0 curves are proved and used to compute the Cartier divisor class of the virtual canonical bundle for genus 0 maps to a smooth target. Many results here first appeared in [6] and [5]; our proofs use a completely different method.

A determinação simultânea de ácido ascórbico (AA), ácido acetilsalicílico (ASP) e paracetamol (PAR) em misturas sintéticas e tabletes efervescentes foi realizada usando-se as técnicas de transformações de Haar e transformações de onda pequena tipo chapéu mexicano (HAAR-CWT e MEXH-CWT, respectivamente), juntamente com a técnica de divisor duplo. Os métodos de processamento de sinal são baseados ...

Given a divisor D on a tropical curve Γ, we show that reduced divisors define an integral affine map from the tropical curve to the complete linear system |D|. This is done by providing an explicit description of the behavior of reduced divisors under infinitesimal modifications of the base point. We consider the cases where the reduced-divisor map defines an embedding of the curve into the lin...

Almost 20 years ago, W. Narkiewicz posed the problem to give an arithmetical characterization of the ideal class group of an algebraic number field ([13, problem 32]). In the meantime there are various answers to this question if the ideal class group has a special form. (cf. [4], [5], [12] and the literature cited there). The general case was treated by J. Koczorowski [11], F. Halter-Koch [8],...

Proof: For a contradiction, assume there are finitely many, p1, . . . , pn. Construct N = Πi=1pi. Then for any i, pi does not divide N + 1, so N + 1 is not divisible by any prime. This is a contradiction, since all numbers ≥ 2 are divisible by some prime. (This can be easily proved by induction.) Definition 1.4. We say that two numbers, a, and b are congruent mod m, or a ≡ b mod m if m | b− a. ...