If d is square-free or is a fundamental discriminant, then let χd = χD denote the Kronecker character for the quadratic field Q( √ d) whose fundamental discriminant is D. Throughout D shall denote a fundamental discriminant. The D-quadratic twist of F , denoted F ⊗ χD, is the newform corresponding to the twist of F by the character χD. In particular, if gcd(M,D) = 1, then (F ⊗ χD)(z) = ∑∞ n=1 χ...

We introduce a technique for extending the classical method of Linear Discriminant Analysis to data sets where the predictor variables are curves or functions. This procedure, which we call functional linear discriminant analysis (FLDA), is particularly useful when only fragments of the curves are observed. All the techniques associated with LDA can be extended for use with FLDA. In particular ...

We present a non-stationary signal classi cation algorithm based on a time-frequency representation and a multiple hypothesis test. The time-frequency representation is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test the multiple hypotheses. The multiple hypot...

Two unsupervised pattern recognition algorithms, k-means, and Gaussian mixture model (GMM) analyses have been applied to classify seismic events in the vicinity of Istanbul. Earthquakes, which are occurring at different seismicity rates and extensions of the Thrace-Eskisehir Fault Zone and the North Anatolian Fault (NAF), Turkey, are being contaminated by quarries operated around Istanbul. We h...

the objective of this study was to classify the shoosh aquifer to several zones with different water quality in khuzestan province, iran. in this regard, the performance of classification methods (discriminant function and cluster analysis) for the classification of groundwater based on the level of pollution with an emphasis on the problem of over-fitting in training data were considered. an o...

Five Balkan paprika varieties at physiological maturity were investigated by means of Raman spectroscopy in order to discriminate the differences which stemmed from their genetic variability since plants grown under same experimental conditions. The spectra obtained using 532 nm wavelength. In an effort find best classification power, several pre-processing methods applied: 1) baseline correcti...

In 1989, Shanks introduced the NUCOMP algorithm [10] for computing the reduced composite of two positive definite binary quadratic forms of discriminant ∆. Essentially by applying reduction before composing the two forms, the intermediate operands are reduced from size O(∆) to O(∆) in most cases and at worst to O(∆). Shanks made use of this to extend the capabilities of his hand-held calculator...

Classification procedures are common and useful in behavioral, educational, social, and managerial research. Supervised classification techniques such as discriminant function analysis assume training data are perfectly classified when estimating parameters or classifying. In contrast, unsupervised classification techniques such as finite mixture models (FMM) do not require, or even use if avai...