Dicuil (9th century) on triangular and square numbers

Dicuil was a ninth-century Irish monk who taught at the Carolingian school of Louis the Pious. He wrote a Computus or astronomical treatise in Latin in about 814–16, which contains a chapter on triangular and square numbers. Dicuil describes two methods for calculating triangular numbers: the simple method of summing the natural numbers, and the more complex method of multiplication, equivalent to the formula n(n?+?1)/2. He also states that a square number is equal to twice a triangular number minus the generating number, equivalent to n²?=?2[n(n?+?1)/2] – n. The multiplication formula for triangular numbers was first explicitly described in about the third century AD by the Greek authors Diophantus and Iamblichus. It was also known as a solution to other mathematical problems as early as 300 BC. It reappeared in the West in the sixteenth century. Dicuil thus fills a gap in our medieval knowledge.     

Singularities of functions of one and several bicomplex variables

In this paper we study the singularities of holomorphic functions of bicomplex variables introduced by G. B. Price (An Introduction to Multicomplex Spaces and Functions, Dekker, New York, 1991). In particular, we use computational algebra techniques to show that even in the case of one bicomplex variable, there cannot be compact singularities. The same techniques allow us to prove a duality theorem for such functions.     

Sato’s Hyperfunctions and Boundary Values of Monogenic Functions

We describe the relationship between Sato’s hyperfunctions and other theories of boundary values. In particular we show how monogenic functions can be used to represent classical hyperfunctions.     

Use of Sea Fennel as a Natural Ingredient of Edible Films for Extending the Shelf Life of Fresh Fish Burgers

The growing interest from consumers toward healthy and nutritious products and their benefits for health has increased the consumption of whole and processed fish. One of the main problems of fish is the short shelf life, especially when it is processed as in the case of burgers. The use of edible coating is an interesting strategy to extend the quality and safety of the product, reducing the need for artificial preservatives. This study evaluated the use of chitosan-based edible film formulated with sea fennel plant and sea fennel extracts. The analyses showed than the use of edible film extended the shelf life of fish burgers regardless of the incorporation of sea fennel mainly associated to the gas barrier properties and selective permeability of the film applied to the fish surface. The incorporation of sea fennel in the films did not produce any antimicrobial enhancement, although sea fennel (mostly extract) produced a better pH and enhanced the antioxidant properties and lipid oxidation of fish burgers. However, sensory analyses showed than fish burgers coated with sea fennel film plant had better acceptability than those with sea fennel extracts, probably due to the better odour and colour of the whole plant during storage. The study showed that the use of sea fennel plant at 12.5% extended the shelf life of fish burgers using a safe and clean label strategy.     

An Evaluation of Entropy Measures for Microphone Identification

Research findings have shown that microphones can be uniquely identified by audio recordings since physical features of the microphone components leave repeatable and distinguishable traces on the audio stream. This property can be exploited in security applications to perform the identification of a mobile phone through the built-in microphone. The problem is to determine an accurate but also efficient representation of the physical characteristics, which is not known a priori. Usually there is a trade-off between the identification accuracy and the time requested to perform the classification. Various approaches have been used in literature to deal with it, ranging from the application of handcrafted statistical features to the recent application of deep learning techniques. This paper evaluates the application of different entropy measures (Shannon Entropy, Permutation Entropy, Dispersion Entropy, Approximate Entropy, Sample Entropy, and Fuzzy Entropy) and their suitability for microphone classification. The analysis is validated against an experimental dataset of built-in microphones of 34 mobile phones, stimulated by three different audio signals. The findings show that selected entropy measures can provide a very high identification accuracy in comparison to other statistical features and that they can be robust against the presence of noise. This paper performs an extensive analysis based on filter features selection methods to identify the most discriminating entropy measures and the related hyper-parameters (e.g., embedding dimension). Results on the trade-off between accuracy and classification time are also presented.     

Robust archetypoids for anomaly detection in big functional data

Advances in Data Analysis and Classification - Archetypoid analysis (ADA) has proven to be a successful unsupervised statistical technique to identify extreme observations in the periphery of the...     

Cross-Coupling Reaction of Alkenyl Sulfoximines and Alkenyl Aminosulfoxonium Salts with Organozincs by Dual Nickel Catalysis and Lewis Acid Promotion

In this article, the cross-coupling reaction (CCR) of exocyclic, axially chiral, and acyclic alkenyl (N-methyl)sulfoximines with alkyl- and arylzincs is described_. The CCR generally requires dual Ni catalysis and MgBr₂ promotion, which is effective in diethyl ether but not in THF. NMR spectroscopy revealed a complexation of alkenyl sulfoximines by MgBr₂ in diethyl ether, which suggests an acceleration of the oxidative addition through nucleofugal activation. The CCR of alkenyl sulfoximines generally proceeds in the presence of Ni(dppp)Cl₂ as a precatalyst and MgBr₂ with alkyl- and arylzincs with a high degree of stereoretention at the C and the S atom. CCR of axially chiral alkenyl sulfoximines with Ni(PPh₃)₂Cl₂ as a precatalyst and ZnPh₂ does not require salt promotion and is stereoretentive. The reaction with Zn(CH₂SiMe₃)₂, however, demands salt promotion and is not stereoretentive. CCR of axially chiral α-methylated alkenyl sulfoximines afforded persubstituted axially chiral alkenes with high selectivity. Alkenyl (N-triflyl)sulfoximines engage in a stereoretentive CCR with Grignard reagents and Ni(PPh₃)₂Cl₂. Ni-Catalyzed and MgBr₂-promoted CCR of E-configured acyclic alkenyl sulfoximines and aminosulfoxonium salts with ZnPh₂ and Zn(CH₂SiMe₃)₂ is stereoretentive with Ni(dppp)Cl₂ and Ni(PPh₃)₂Cl₂. CCRs of acyclic alkenyl sulfoximines and alkenyl aminosulfoxonium salts, carrying a methyl group at the α position, take a different course and give alkenyl sulfinamides under stereoretention at the S and C atom. CCR of acyclic, exocyclic, and axially chiral alkenyl sulfoximines has been successfully applied to the stereoselective synthesis of homoallylic alcohols, exocyclic alkenes, and axially chiral alkenes, respectively.     

Enantioselective Synthesis of 3-Heterosubstituted-2-amino-1-ols by Sequential Metal-Free Diene Aziridination/Kinetic Resolution

A general protocol for the enantioselective synthesis of 3-heterosubstituted-2-amino-1-ols was developed based on metal- free intramolecular regio- and stereoselective diene aziridination and regioselective opening. Kinetic resolution of the resulting (1′-NR¹R² and 1′-SR)-4-oxazolidinones was performed using ABCs organocatalysts, expanding the application of this methodology.