Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

On Li’s Coefficients for Some Classes of L-Functions

AMS Subj. Classification: 11M41, 11M26, 11S40

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

Verification of Procedural Programs via Building their Generalized Nets Models

Магдалина Василева Тодорова - В статията е описан подход за верификация на процедурни програми чрез изграждане на техни модели, дефинирани чрез обобщени мрежи. Подходът интегрира концепцията “design by contract” с подходи за верификация от тип доказателство на теореми и проверка на съгласуваност на модели. За целта разделно се верифицират функциите, които изграждат програмата относно спецификации според предназначението им. Изгражда се обобщен мрежов модел, специфициащ връзките между функциите във вид на коректни редици от извиквания. За главната функция на програмата се построява обобщен мрежов модел и се проверява дали той съответства на мрежовия модел на връзките между функциите на програмата. Всяка от функциите на програмата, която използва други функции се верифицира и относно спецификацията, зададена чрез мрежовия модел на връзките между функциите на програмата.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

The Legendre Formula in Clifford Analysis

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation

MSC 2010: 35J05, 33C10, 45D05

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

Seizure detection in subdural recordings using nonlinear decision functions

This dissertation proposed a new approach to seizure detection in intracranial EEG recordings using nonlinear decision functions. It implemented well-established features that were designed to deal with complex signals such as brain recordings, and proposed a 2-D domain of analysis. Since the features considered assume both the time and frequency domains, the analysis was carried out both temporally and as a function of different frequency ranges in order to ascertain those measures that were most suitable for seizure detection. In retrospect, this study established a generalized approach to seizure detection that works across several features and across patients. ^ Clinical experiments involved 8 patients with intractable seizures that were evaluated for potential surgical interventions. A total of 35 iEEG data files collected were used in a training phase to ascertain the reliability of the formulated features. The remaining 69 iEEG data files were then used in the testing phase. ^ The testing phase revealed that the correlation sum is the feature that performed best across all patients with a sensitivity of 92% and an accuracy of 99%. The second best feature was the gamma power with a sensitivity of 92% and an accuracy of 96%. In the frequency domain, all of the 5 other spectral bands considered, revealed mixed results in terms of low sensitivity in some frequency bands and low accuracy in other frequency bands, which is expected given that the dominant frequencies in iEEG are those of the gamma band. In the time domain, other features which included mobility, complexity, and activity, all performed very well with an average a sensitivity of 80.3% and an accuracy of 95%. ^ The computational requirement needed for these nonlinear decision functions to be generated in the training phase was extremely long. It was determined that when the duration dimension was rescaled, the results improved and the convergence rates of the nonlinear decision functions were reduced dramatically by more than a 100 fold. Through this rescaling, the sensitivity of the correlation sum improved to 100% and the sensitivity of the gamma power to 97%, which meant that there were even less false negatives and false positives detected. ^