Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (Xt : t ∈ V (T ))) such that G[Xt] has chromatic number at most k for each t ∈ V (T ). This seems to be a new concept, and this paper is a collection of observations on the topic. In particular we show that there are graphs with tree-chromatic number two and with arbitrarily large chromatic number; ...

This study evaluates the process conditions, (enzyme concentration (120-1200 U/g substrate), temperature (30-60 °C), and pH (3-9)) of enzymatic hydrolysis (EH) for sugar recovery from leftover croissants (LC) doughnut (LD), characterizing its residue hydrolysate. The highest yield recovered LC was 574.21 ± 0.74 mg/g (840 substrate, 49 °C 3) LD 460.53 (1176 47 3). fructose glucose were 14.47±0.7...

Mark Kac introduced a method for calculating the distribution of the integral Av= ∫ T 0 v(Xt) dt for a function v of a Markov process (Xt; t¿0) and a suitable random time T , which yields the Feynman–Kac formula for the moment-generating function of Av. We review Kac’s method, with emphasis on an aspect often overlooked. This is Kac’s formula for moments of Av, which may be stated as follows. F...

The level of linkage disequilibrium (LD) is a major factor to determine DNA polymorphism pattern of a population and to construct high-resolution maps useful in localizing and gene cloning of complicated traits. Here, we investigated LD level of three soybean populations with different genetic backgrounds and taxonomic status of G. gracilis by comparing the DNA polymorphism patterns of four hig...

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...

A mobile robot typically has access to a high dimensional stream of multi-modal sensor information. Modern mobile robots navigate uncertain environments using complex mixtures of camera, laser, and sonar sensor data. Manual calibration of these sensors is a tedious process that involves determining sensor behavior and geometry through model specification. To automate the construction of sensor ...

The i-local distinguishing number of G, denoted by LD i (G), was deened in 3]. Let T be a tree on n > 2 vertices with maximum degree bounded by some constant k. It is shown that LD 1 (T) = O(p n) and that for some trees this bound is tight. The result is extended to show that LD i (T) = O(n 1=(i+1)).

For a family of compact Riemann surfaces Xt of genus g > 1, parameterized by the Schottky space Sg, we define a natural basis of H(Xt, ω n Xt ) which varies holomorphically with t and generalizes the basis of normalized abelian differentials of the first kind for n = 1. We introduce a holomorphic function F (n) on Sg which generalizes the classical product ∏ ∞ m=1 (1 − q) for n = 1 and g = 1. W...

This overview article concerns the notion of fractional smoothness of random variables of the form g(XT ), where X = (Xt)t∈[0,T ] is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indic...

This overview article concerns the notion of fractional smoothness of random variables of the form g(XT ), where X = (Xt)t∈[0,T ] is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indic...